The variable in the equation 11 = –2z + 8 is z. Remembering the formula ax + b = c, what are the values of the constants in the equation?
A) a= -8, b = 8, c= 11
B) a= -2, b= 8, c= 11
C) a= -11, b= 8, c= 11
D) a= 8, b= -8, c= 11

Answers

Answer 1

Answer: The given equation is 11 = -2z + 8, which can be rearranged into the form of ax + b = c by moving the terms containing z to one side:

-2z + 8 = 11

-2z = 11 - 8

-2z = 3

z = -3/2

Comparing this with the standard form ax + b = c, we see that:

a = -2

b = 8

c = 11

Therefore, the correct answer is option B: a = -2, b = 8, c = 11.

Step-by-step explanation:


Related Questions

Please answer this easy math question!! 13 pts!!

Answers

Here in this image, we are given two acute angles forming a right angle. A right angle is equal to 90 degrees. To find the value of b, we will add the two acute angles and set it equal to the right angle, which is 90 degrees.

7b-8+6b+7=90
Combine like terms:
13b-1=90
Add 1 to both sides:
13b=91
Divide 13 to both sides:
b=7

Hope this helped!

Answer:

Step-by-step explanation:

The problem shows a 90° angle split by a ray, we know that both angles are equal to 90° because the whole is equal to the sum of its parts therefore adding 6b+7 and 7b-8 gives us 90° which is simplified as

13b°-1°= 90°

add 1  to both sides

13b°-1° + 1° = 90° +1°

13b° = 91°

divide by 13

13b°/13 = 91°/13

b= 7°

This is for college Algebra please help me ​

Answers

Step-by-step explanation:

h o g   =   6 ( x^2 + x - 2)   + 1

             = 6x^2 + 6x -12 + 1

             = 6x^2 + 6x -11              put in -7 for 'x'

                  6 (-7^2) + 6 (-7) - 11

               = 241

* * * edited * * *

Solve the equation. Round to the nearest tenth if necessary. 110=c^2​

Answers

Answer:

There are 2 answers:

-10.510.5

Step-by-step explanation:

110 = c²

√110 = √c²

±10.5 = c

Solve for c:

[tex]110=c^2[/tex]

Take the square root of 110

[tex]10.48\thickapprox10.5[/tex]

Answer:

[tex]\longrightarrow \boxed{\bold{c=10.5}}[/tex]

[tex]\text{so} \ \boxed{110=\bold{10.5^2}}[/tex]

Rectangle A has side lengths of
6
cm
6 cm6, start text, space, c, m, end text and
3.5
cm
3.5 cm3, point, 5, start text, space, c, m, end text. The side lengths of rectangle B are proportional to the side lengths of rectangle A.
What could be the side lengths of rectangle B?
Choose 2 answers:

Answers

The possible side lengths of rectangle B are 12 cm and 7 cm, or 9 cm and 5.25 cm, etc.

What are the side lengths of rectangle B?

The side length of rectangle B is calculated as follows;

Side length of rectangle A = 6 cm and 3.5 cm

If the two rectangles are proportional, the possible side lengths of rectangle B is calculated as follows;

Length of B = 2 x 6 cm = 12 cm

Width of B = 2  x 3.5 cm = 7 cm

or

Length of B = 1.5 x 6 cm = 9 cm

Width of B =1.5  x 3.5 cm = 5.25 cm

Thus, the side lengths of rectangle B will be increasing or decreasing at equal proportion.

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the mesures of two suplementary angles are (1/2x) and (x+30) betermine te value of x

Answers

Answer:

x = 100

Step-by-step Explanation:

Supplementary angles add up to 180 degrees, so we can set up the equation:

(1/2x) + (x + 30) = 180

To solve for x, we can start by simplifying the left side of the equation by combining the terms:

(1/2x) + x + 30 = 180

Multiplying both sides of the equation by 2 to eliminate the fraction:

1x + 2(x + 30) = 360

Simplifying the right side of the equation:

1x + 2x + 60 = 360

Combining like terms:

3x + 60 = 360

Subtracting 60 from both sides of the equation:

3x = 300

Dividing both sides of the equation by 3:

x = 100

Therefore, the value of x is 100.

Further explanation:

Supplementary angles are two angles whose sum is 180 degrees. Let's use this fact to form an equation with the given measures:

(1/2x) + (x+30) = 180

To solve for x, we need to isolate it on one side of the equation. Let's start by simplifying the left side:

1/2x + x + 30 = 180
3/2x + 30 = 180
3/2x = 150
x = 100

Therefore, the value of x is 100. To check this result, we can substitute x=100 into the original measures:

(1/2x) = 50
(x+30) = 130

And indeed, 50 and 130 are supplementary angles whose sum is 180.

Which equation is equivalent to the following 4(2x+1)-3(x-2)=20

Answers

Answer:

An equivalent equation would be 2x = 4.

Step-by-step explanation:

Expanding the brackets and simplifying, we get:

8x + 4 - 3x + 6 = 20

Combining like terms, we get:

5x + 10 = 20

Subtracting 10 from both sides, we get:

5x = 10

Dividing both sides by 5, we get:

x = 2

So an equivalent equation would be 2x = 4.

Answer:

The equivalent equation to 4(2x+1)-3(x-2)=20 is 5x+11=20

Step-by-step explanation:

One of the parking lot lights at a hospital has a motion detector on it, and the equation (x + 10)2 (y−8)2=16 describes the boundary within which motion can be sensed. What is the greatest distance, in feet, a person could be from the parking lot light and be detected? Responses a. 2 ft b. 4 ft c. 9 ft d. 256 ft

Answers

The greatest distance, in feet, a person could be from the parking lot light and be detected is 4 ft. So, correct option is B.

The equation (x + 10)^2 + (y−8)^2=16 describes a circle with center (-10,8) and radius 4. The distance from the center of a circle to any point on its circumference is equal to the radius. Therefore, the greatest distance a person could be from the parking lot light and still be detected is equal to the radius of the circle, which is 4 feet.

This means that any point on the circumference of the circle with a distance of 4 feet or less from the center (-10,8) would be within the range of the motion detector.

Option (a) 2 feet is too small and would fall inside the circle, meaning the person would not be detected. Option (c) 9 feet and option (d) 256 feet are too large and fall outside the circle, meaning the person would also not be detected.

Therefore, the correct answer is option (b) 4 feet.

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All of my faces are equal in
size.
All 6 of my faces are square.

Answers

Answer:

Cube

Step-by-step explanation:

A cube is a three-dimensional shape with six square faces that are all congruent to each other. Each face of a cube is perpendicular to the adjacent faces, and all of its edges are the same length.

Laura and Rich have been approved for a $325,000, 15-year mortgage with an APR of 5.3%. Using the mortgage and interest formulas, complete the two-month amortization table.

Answers

First, let's calculate the monthly interest rate (i), which is the APR divided by 12 months:

i = APR / 12 months

i = 5.3% / 12

i = 0.00442 or 0.442%

Next, let's calculate the number of months (n) for the mortgage, which is 15 years multiplied by 12 months:

n = 15 years x 12 months/year

n = 180 months

Now, let's calculate the monthly payment (PMT) using the following formula:

PMT = P * i / [tex](1 - (1 + i)^(-n)[/tex])

where P is the principal amount, i is the monthly interest rate, and n is the number of months.

PMT = $325,000 * 0.00442 / (1 - [tex](1 + 0.00442)^(-180)[/tex]

PMT = $2,613.67 (rounded to the nearest cent)

Now, let's create the amortization table for the first two months:

Month | Payment | Interest | Principal | Remaining Balance

1 | $2,613.67 | $1,431.25 | $1,182.42 | $323,817.58

2 | $2,613.67 | $1,428.60 | $1,185.07 | $322,632.51

For each month, the Payment column shows the fixed monthly payment, the Interest column shows the calculated interest based on the remaining balance multiplied by the monthly interest rate, the Principal column shows the portion of the payment that goes towards reducing the principal, and the Remaining Balance column shows the remaining balance after subtracting the principal payment from the previous remaining balance.

The amortization table will continue in this manner for the remaining months until the mortgage is paid off.

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The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

To complete the two-month amortization table, we need to calculate the monthly payment, as well as the principal and interest amounts for each payment.

The formula for calculating a fixed-rate mortgage payment is:

[tex]Payment = P * r * (1 + r)^n / [(1 + r)^n - 1][/tex]

Where:

P = Principal amount borrowed

r = Monthly interest rate

n = Total number of payments

First, let's calculate the monthly interest rate.

Since the APR is an annual rate, we need to divide it by 12 to get the monthly rate:

Monthly interest rate = 5.3% / 12 = 0.0044167

Next, we need to calculate the total number of payments.

Since this is a 15-year mortgage, and we're completing a two-month amortization table, the total number of payments is:

Total number of payments = 15 years * 12 months per year = 180

Number of payments for two months = 2

Now we can plug these values into the formula to calculate the monthly payment:

Payment = [tex]$325,000 * 0.0044167 * (1 + 0.0044167)^180 / [(1 + 0.0044167)^180 - 1][/tex]

= $2,549.67

So the monthly payment is $2,549.67

Now we can use this value to complete the two-month amortization table:

Payment Interest Principal Balance

Month 1 $1,426.25 $1,123.42 $323,876.58

Month 2 $1,420.47 $1,129.20 $322,747.38

To calculate the interest and principal amounts for each payment, we use the following formulas:

Interest = Balance * Monthly interest rate

Principal = Payment - Interest

Balance = Balance - Principal

We start with the initial balance of $325,000 and apply the formulas for each payment.

The interest and principal amounts for the first payment are:

Interest = $325,000 * 0.0044167 = $1,426.25

Principal = $2,549.67 - $1,426.25 = $1,123.42

Balance = $325,000 - $1,123.42 = $323,876.58

For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:

Interest = $323,876.58 * 0.0044167 = $1,420.47

Principal = $2,549.67 - $1,420.47 = $1,129.20

Balance = $323,876.58 - $1,129.20 = $322,747.38

And so on, for each subsequent payment.

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how many mpg? ............

Answers

The fuel efficiency of the vehicle with the greatest weight which is around 2375kg on this scatter-plot showing vehicle weights & fuel efficiency is 16 mpg.

What is a scatter-plot?

The relationships between two variables in a data set are represented by graphs or scatter plots.  It displays data points on a Cartesian system or a two-dimensional plane. The dependent variable is represented or plotted on the Y-axis, while the independent variable or attribute is plotted or represented on the X-axis. The scatter plot's objective is to show what happens to one variable when another variable is modified. A theory that the two variables are connected is tested using the scatter plot.

The scatter plot shows the vehicle weights & fuel efficiency.

Data represented on X-axis(independent variable) : weights of vehicle

Data represented on Y-axis(dependent variable) : fuel efficiency.

Lowest weight of vehicle=1125 kg(approx)

Greatest weight of the vehicle=2375 kg(approx)

Lowest fuel efficiencies of surveyed vehicles=16 mpg.

Greatest fuel efficiency of surveyed vehicles=30 mpg.

∴The fuel efficiency of the heaviest vehicle=16 mpg.

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PLEASE HELP!!! There are two buildings that you want to have in the amusement park, but the size hasn’t been determined yet. Although you don’t know the specific dimensions, you do know the relationships between the sides.

The first is the rectangular gift shop. You know that the length will be 20x+24 feet and the width will be 36x-20 feet.

Write the expression that represents the area of the gift shop, in terms of x.
Write the expression that represents the perimeter of the gift shop, in terms of x.
If the perimeter is going to be 176 feet, what are the dimensions of the building?

Answers

There are two buildings that you want to have in the amusement park.

a) The expression that represents the area of the gift shop, in terms of x, is

Area = length x width

Area = (20x + 24) (36x - 20)

Area = 720[tex]x^{2}[/tex] + 208x - 480

Therefore, the area of the gift shop is 720[tex]x^{2}[/tex]  + 208x - 480 square feet.

b) The expression that represents the perimeter of the gift shop, in terms of x, is

Perimeter = 2(length + width)

Perimeter = 2(20x + 24 + 36x - 20)

Perimeter = 2(56x + 4)

Perimeter = 112x + 8

Therefore, the perimeter of the gift shop is 112x + 8 feet.

c) If the perimeter is going to be 176 feet, we can set the expression for the perimeter equal to 176 and solve for x

112x + 8 = 176

Subtracting 8 from both sides

112x = 168

Dividing both sides by 112

x = 1.5

Now that we know x, we can substitute it into the expressions for the length and width of the gift shop

Length = 20x + 24 = 20(1.5) + 24 = 54 feet

Width = 36x - 20 = 36(1.5) - 20 = 34 feet

Therefore, the dimensions of the gift shop are 54 feet by 34 feet.

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find circle the middle of this equation

Answers

Answer: (-15, 20)

Step-by-step explanation:

we can see that the equation is the standard form of a circle:

(X-h)

^2 + (y-k)r^2

Where (h,k) is the center of the circle and r is the radius

H= -15

K= 20

R^2= 100

Which of the following factors does not influence the consumer when deciding to buy a product?
A. External factors
B. Marketing
C. Time period
D. Internal factors

Answers

The factor that does not influence the consumer when deciding to buy a product is Time period. The correct option is C

What is Time period ?

An identifiable length of time such as a day, week, month, or year is referred to as a time period. Given that it can affect consumer behavior market conditions and the efficacy of various plans and tactic time is a crucial factor in many facets of business and marketing.

Therefore, Note that time is not a factor that influences customer behavior when determining whether to purchase a product in the context of the initial query. The factor that does not influence the consumer when deciding to buy a product is Time period

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As a candle burns, it decreases in height by 2 inches every hour. If the candle is 12 inches tall when it is lit, how will the height change over time? If the candle burned for 2 hours, how many inches tall will it be?

Answers

Answer: If every hour the candle decreases in height by 2 inches, turn it into a chart! If you learned this already, figure out which variable is the constant and the decrease in height for each hour. Or you could just multiply the amount of hours by 2, there for 2x2=4 so that a 4 inch decrease. 12-4=8 and the candle will be 8 inches tall. Hope this helps :D

Step-by-step explanation:

PLEASEEE PLEASEEE HELP ITS THE LAST QUESTION HURRYYY

Answers

Answer: C Q

Step-by-step explanation:

You need to Use Q And C In algebra if thats what your going for. Hopefully this help's.

Find the amount of money Lee can afford to borrow using the banker's rule. Lee makes $24,700 annually. What is the amount that can be borrowed?

Answers

Answer: $31,920.

Step-by-step explanation:

The banker's rule is a method used by lenders to determine the maximum amount of money that a borrower can afford to repay. According to this rule, the maximum amount of money that Lee can afford to borrow is determined by multiplying his annual income by a factor of 0.28.

Using this rule, the amount that Lee can afford to borrow can be calculated as:

Maximum affordable monthly payment = 0.28 x monthly income

Maximum affordable monthly payment = 0.28 x (24700/12)

Maximum affordable monthly payment = 0.28 x 2058.33

Maximum affordable monthly payment = 576.66

Therefore, Lee can afford to make monthly payments of up to $576.66. To calculate the total amount he can borrow, we need to determine the total cost of the loan, including principal and interest.

Assuming a 5-year loan with an interest rate of 4%, the total cost of the loan can be calculated using an online loan calculator or spreadsheet software.

Plugging in the numbers, the total amount that Lee can borrow is approximately $31,920.

It's important to note that this calculation is based on the banker's rule and assumes that Lee has no other debt obligations. Actual loan approval and loan amounts may vary depending on other factors such as credit score, debt-to-income ratio, and other lender-specific requirements.

As a candle burns, it decreases in height by 2 inches every hour. If the candle is 12 inches tall when it is lit, how will the height change over time? If the candle burned for 2 hours, how many inches tall will it be?

Answers

The height of the candle change over time as a linear function

How will the height of the candle change over time?

The height of the candle decreases by 2 inches every hour, which means the height of the candle is a linear function of time.

We can write the equation for the height of the candle as:

h(t) = 12 - 2t

where h is the height of the candle in inches and t is the time in hours.

If the candle burned for 2 hours, we can plug in t=2 into the equation to find the height:

h(2) = 12 - 2(2) = 8

So the height of the candle after 2 hours of burning is 8 inches.

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expand and simplify (x+3)(x-3)(3x+2)

Answers

Answer: To expand the expression, we can use the distributive property of multiplication:

(x+3)(x-3)(3x+2)

= (x^2 - 9)(3x+2) // using (a+b)(a-b) = a^2 - b^2

= 3x(x^2) + 2(x^2) - 9(3x) - 18 // using FOIL

= 3x^3 + 2x^2 - 27x - 18

This is the expanded form of the expression.

To simplify further, we can factor out the greatest common factor of the terms:

= 3(x^3 - 9x) + 2(x^2 - 9)

= 3x(x^2 - 9) + 2(x^2 - 9)

= (3x+2)(x^2 - 9)

= (3x+2)(x-3)(x+3)

So, the simplified expression is (3x+2)(x-3)(x+3).

Answer:

3x³ + 2x² - 27x - 18.

Step-by-step explanation:

To expand (x+3)(x-3)(3x+2), we can use the distributive property and multiply each term in the first expression by each term in the second expression, and then multiply the result by each term in the third expression.

(x+3)(x-3)(3x+2)

= (x²-3x+3x-9)(3x+2) // Using (a+b)(a-b)
= a² - b²
= (x²-9)(3x+2)
= 3x(x²) + 2x² - 9(3x) - 9(2) // Using distributive property
= 3x³ + 2x² - 27x - 18 // Simplifying

Therefore, (x+3)(x-3)(3x+2) expands and simplifies to 3x³ + 2x² - 27x - 18.

Dr. Price uses a table to organize the types of sea life and the positions relative to sea level of each location. Complete each sentence. The difference between Location A and Location B is meters. The difference between Location B and Location C is meters. The difference between Location C and Location D is meters. After observing Location B, Dr. Price returns to Location A before descending to Location C. What is the total distance she travels? Dr. Price descends to Location D to observe shrimp. She then ascends and stops to observe sea life that is halfway between Location B and Location C. What is the total distance between Location D and where Dr. Price stopped to observe?

Answers

The total distance that Dr. Price travels during her observations is 2567.1 meters, and the distance between Location D and the point halfway between Locations B and C is 1,317.125 meters.

First, we can look at the distances between each location. The table tells us that the difference between Location A and Location B is 203.15 meters. The difference between Location B and Location C is 1686.55 meters, and the difference between Location C and Location D is 474.25 meters.

To calculate the total distance that Dr. Price travels, we need to add up the distances for each part of her journey. First, she travels from Location A to Location B, a distance of 203.15 meters. Then she returns to Location A, so she travels the same distance back, for a total of 406.3 meters. Next, she descends from Location A to Location C, a distance of 1686.55 meters. Finally, she descends further to Location D, a distance of 474.25 meters. Adding up these distances, we get a total distance of 2567.1 meters.

For the second part of the question, we need to find the distance between Location D and the point halfway between Locations B and C. To do this, we first need to find the depth at the midpoint between Locations B and C. We can do this by taking the average of the depths for Locations B and C, which gives us -1,941.875 meters.

Next, we can calculate the distance between Location D and the midpoint between B and C. This is simply the difference in depth between Location D (-3,259 meters) and the midpoint (-1,941.875 meters), which gives us a distance of 1,317.125 meters.

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Complete Question:

Dr. Price uses a table to organize the types of sea life and the positions relative to sea level of each location. Complete each sentence. The difference between Location A and Location B is meters. The difference between Location B and Location C is meters. The difference between Location C and Location D is meters. After observing Location B, Dr. Price returns to Location A before descending to Location C. What is the total distance she travels? Dr. Price descends to Location D to observe shrimp. She then ascends and stops to observe sea life that is halfway between Location B and Location C. What is the total distance between Location D and where Dr. Price stopped to observe?

Location                         Sea Life               Depth Relative to Sea Level (m)

A                                             Eels                                 -895.9

B                                              Eels                                 -1,098 3/20

C                                           Shrimp                            -2,784.75

D                                          Shrimp                                -3,259

A use case description documents (among other things) ____.
A. a description of alternative courses of action
B. post conditions
C. preconditions
D. assumptions

Answers

A use case description documents (among other things) A. a description of alternative courses of action, B. postconditions, and C. preconditions. These elements help provide a clear understanding of how a system should interact with its users and the expected outcomes.

A document can be defined as a form of information that might be useful to a user or set of users1. It can be either digital or nondigital1. Different methods are used to store digital and non-digital documents

There are different types of documents such as job descriptions2, and project descriptions. and technical descriptions5.

A use case description documents (among other things) A. a description of alternative courses of action, B. postconditions, and C.

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which expression is eqivalent to 5( x -3)?

Answers

Answer:

5x - 15

Step-by-step explanation:

5(x - 3) ← multiply each term in the parenthesis by the 5 outside

= 5x - 15

A farmer has 15 boxes of eggs. There are 6 eggs in each box. Write, as a ratio, the number of eggs in three boxes to the total number of eggs. Give your answer in the simplest form.

Answers

Answer:

15 boxes of eggs × 6 eggs/box =

90 total eggs

3 boxes of eggs × 6 eggs/box = 18 eggs

The ratio of the number of eggs in 3 boxes to the total number of eggs is 18/90 = 1/5.

Yes this is correct

If a line with slope 4 has one point of intersection with the quadratic function y =
x² + 2x − 8, what is the y-intercept of the line?
-
4
a. 10
b.
-10
c. 4
d. -8

Answers

The y-intercept of the given quadratic function y = x² + 2x − 8 is (A) -4.

What is the y-intercept?

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation meets the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.

These points satisfy x = 0 because of this.

When the line touches the y-axis, it forms a y-intercept.

Find the y when x = 0 to find these.

When the line touches the x-axis, the position for the y-intercept will look like (0,y).

So, have the given quadratic function:

y = x² + 2x − 8

Now, plot the given quadratic function on the graph:

(Refer to the graph attached below)

As we can see that the y-intercept is -4.

Therefore, the y-intercept of the given quadratic function y = x² + 2x − 8 is (A) -4.

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If a line with slope 4 has one point of intersection with the quadratic function y = x² + 2x − 8, what is the y-intercept of the line?

a. -4

b. 10

c.-10

d. 4

e. -8

In triangle HJK, the exterior angle at K is 139° and the exterior angle at J is 53°. Which is the shortest side of triangle HJK?

Answers

The exterior angle at K in triangle HJK is 139°, whereas the exterior angle at J is 53°. Shortest side is JK.

We know that the sum of exterior angles of a triangle is 360°. So,

Exterior angle at K + exterior angle at J + exterior angle at H = 360°

139 + 53 + exterior angle at H = 360

exterior angle at H + 192 = 360

exterior angle at H = 360 - 192

exterior angle at H = 168°

Now, we will calculate the interior angles of triangle HJK. We know that exterior and interior angles are supplementary and makes a sum of 180 degree.

Interior angle K + exterior angle K = 180

Interior angle K + 139 = 180

Interior angle K = 180 - 139 = 41°

Interior angle H + exterior angle H = 180

Interior angle H + 168 = 180

Interior angle H = 180 - 168 = 12°

Interior angle J + exterior angle J = 180

Interior angle J + 53 = 180

Interior angle J = 180 - 53 = 127°

A triangle's shortest side is always opposite the smallest angle. So, in this question the smallest angle is ∠H and the side opposite to it is KJ, hence KJ is the shortest side.

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Find the geometric mean of the two lo and 90

Answers

To find the geometric mean of two numbers, we multiply the two numbers and then take the square root of the product. In this case, the two numbers are lo and 90.

First, we multiply the two numbers:

lo x 90 = 810

Next, we take the square root of the product:

√810 ≈ 28.46

Therefore, the geometric mean of lo and 90 is approximately 28.46.

If I could get help it would be appreciated :)

Answers

To proof that ΔLMQ ≅ ΔNPQ; we use the given statement "∠L is congruent to ∠N"

What is the proof that ΔLMQ is congruent to ΔNPQ?

To complete the proof that ΔLMQ is congruent to ΔNPQ, we have to follow the following steps.

Congruent triangles are two triangles that have exactly the same size and shape. In other words, all corresponding sides and angles of the two triangles are equal.

There are several ways to show that two triangles are congruent, including:

Side-Side-Side (SSS) Congruence: If the three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.Side-Angle-Side (SAS) Congruence: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.Angle-Side-Angle (ASA) Congruence: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

We will apply ASA method to proof that ΔLMQ ≅ ΔNPQ;

∠L is congruent to ∠N

Length LM is congruent to length NP

Looking at the options, only one was stated. (∠L is congruent to ∠N).

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A contractor is building a set of stairs out of concrete. Each stair is the same length, width, and height.

A) Which solid figures can the stairs be broken into? What are the dimensions of each solid figure?
B) How much concrete will be needed to form the stairs?

Answers

Corresponding to the data, we can deduce that the stairs can be broken into a series of blockish prisms.

Which solid numbers can the stairs be broken into? What are the confines of each solid figure?

The stairs can be broken into a series of blockish prisms. The confines of each blockish prism would be the same range and height as the stairs, but the length of each blockish prism would be the depth of one step.

How important concrete will be demanded to form the stairs?

To determine the quantum of concrete demanded to form the stairs, you would need to calculate the total volume of all the blockish prisms that make up the stairs. This can be done by multiplying the length, range, and height of each blockish prism and also adding the volumes of all the blockish prisms together.

The formula for calculating the volume of a blockish prism is V = l x w x h, where V is the volume, l is the length, w is the range, and h is the height. So, for illustration, if each stair is 3 bases wide,1.5 bases high, and 1 bottom deep, and there are 10 stairs, also the total volume of concrete demanded would be

V = (3 x 1.5 x 1) x 10 = 45 cubic feet of concrete.

Note that this calculation assumes that there is no space between the stairs or the rectangular prisms making up the stairs. If there is any space between the stairs or the rectangular prisms, this would need to be accounted for in the calculation.

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Ann and ben translate from German into English..
A set of documents that would take Ann 10 days and Ben 12 days.
Ann starts to translate the documents.
How many more days will it take to complete the work.
You must show your working.

Answers

They will need an additional 18/11 days to finish the job.

What is Equation?

There are two sides to it—a left side and a right side—and an equals sign (=) divides them. The members of the equation are the expressions on either side of the equals sign.

From straightforward arithmetic equations like 2 + 2 = 4 to more intricate equations in algebra and calculus, equations can be used to represent a broad variety of mathematical connections.

By determining the values of the variables that make the equation true, equations are frequently employed to solve issues. This is usually accomplished by manipulating the equation with algebraic operations like addition, subtraction, multiplication, and division on both sides of the equation.

In a variety of disciplines, including physics, chemistry, and engineering, equations can also be used to simulate real-world occurrences. For instance, the equation [tex]d=1/2gt^2[/tex] can be used to represent the motion of an object falling, where d is the distance fallen, g is the acceleration caused by gravity, and t is the amount of time that has passed.

Assume that there are D total papers that need to be translated. Then, we can claim that Ann's daily translation rate is D/10 and that she can translate D documents in 10 days. Ben's daily translation pace is D/12 since he can translate D documents in 12 days.

While Ben is still waiting to start working, Ann begins translating the documents at her daily rate. The total amount of work that Ann has finished is (x/10)D after she has worked for x days. Now that Ben has joined them, they can finish the remaining (1 - x/10)D work jointly at a rate of (D/10 + D/12) papers per day. To find x, we can construct the following equation:

(x/10)D + [(1 - x/10)D]/[(D/10 + D/12)] = D

When we simplify the equation, we obtain:

x/10 + (12 - x)/15 = 1

When both sides are multiplied by the least common multiple of 10 and 15, or 30, we obtain:

3x + 2(12 - x) = 30

Solving for x, we get:

x = 6

So, before Ben starts working, Ann finishes (6/10)D = (3/5)D of the work, and the two of them together finish the remaining (2/5)D of the job at a combined rate of (D/10 + D/12) = (11/60)D per day. Therefore, the total number of days required to accomplish the work is:

(2/5)D / (11/60)D = 24/11 days

Ben and Ann will need to work an extra 24/11 - 6 = 18/11 days to finish the work because Ann has already put in 6 days of effort. As a result, they will need an additional 18/11 days to finish the job.

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. a fair coin is flipped 8 times and thesequence of heads and tails is noted. in howmany outcomes are therea. exactly 6 heads?b. at least 3 heads?c. at most 6 heads?d. at most 2 head

Answers

The total number of possible outcomes when flipping a coin 8 times is 2^8 = 256.

a. To get exactly 6 heads, we need to choose 6 out of the 8 flips to be heads, and the remaining 2 flips to be tails. The number of ways to choose 6 out of 8 is given by the binomial coefficient (8 choose 6) = 28. Therefore, there are 28 possible outcomes with exactly 6 heads.

b. To get at least 3 heads, we need to count the number of outcomes with 3, 4, 5, 6, 7, or 8 heads. Using the same logic as part (a), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at least 3 heads.

Number of outcomes with 3 heads: (8 choose 3) = 56

Number of outcomes with 4 heads: (8 choose 4) = 70

Number of outcomes with 5 heads: (8 choose 5) = 56

Number of outcomes with 6 heads: (8 choose 6) = 28

Number of outcomes with 7 heads: (8 choose 7) = 8

Number of outcomes with 8 heads: (8 choose 8) = 1

Total number of outcomes with at least 3 heads = 56 + 70 + 56 + 28 + 8 + 1 = 219.

c. To get at most 6 heads, we need to count the number of outcomes with 0, 1, 2, 3, 4, 5, or 6 heads. Using the same logic as part (b), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at most 6 heads.

Number of outcomes with 0 heads: (8 choose 0) = 1

Number of outcomes with 1 head: (8 choose 1) = 8

Number of outcomes with 2 heads: (8 choose 2) = 28

Number of outcomes with 3 heads: (8 choose 3) = 56

Number of outcomes with 4 heads: (8 choose 4) = 70

Number of outcomes with 5 heads: (8 choose 5) = 56

Number of outcomes with 6 heads: (8 choose 6) = 28

Total number of outcomes with at most 6 heads = 1 + 8 + 28 + 56 + 70 + 56 + 28 = 247.

d. To get at most 2 heads, we need to count the number of outcomes with 0, 1, or 2 heads. Using the same logic as parts (b) and (c), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at most 2 heads.

Number of outcomes with 0 heads: (8 choose 0) = 1

Number of outcomes with 1 head: (8 choose 1) = 8

Number of outcomes with 2 heads: (8 choose 2) = 28

Total number of outcomes with at most 2 heads = 1 + 8 + 28 = 37.

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Q1: Use simple exponential smoothing with a = 0.75 to forecast the water pumps sales for February through May. Assume that the forecast for January was for 25 units. [4 marks) Month January February March April Air-condition sales 28 72 98 126

Answers

Therefore, using simple exponential smoothing with a = 0.75, the forecast for water pump sales for February through May are:- February: 26.5 units,  March: 37.63 units, April: 72.66 units.

To use simple exponential smoothing with a = 0.75, we first need to calculate the forecast for January:
F1 = 25 (given)
Next, we calculate the forecast for February using the formula:
F2 = a * Y1 + (1 - a) * F1
F2 = 0.75 * 28 + 0.25 * 25
F2 = 26.5 (rounded to one decimal place)
We repeat this process for each month, using the previous month's forecast and the actual sales data for the current month. The results are as follows:
Month      Actual Sales    Forecast
-------------------------------------
January           28          25
February          72          26.5
March             98          37.63
April            126          72.66
- May: 101.17 units
Hi, I'd be happy to help you with your question. To use simple exponential smoothing with a smoothing constant α = 0.75 to forecast the water pump sales for February through May, given that the forecast for January was 25 units, follow these steps:
Step 1: Start with the given forecast for January, which is 25 units.
Step 2: Calculate the forecast for February using the formula:
Forecast_February = α * (Actual_January) + (1 - α) * Forecast_January
Step 3: Calculate the forecast for March using the formula:
Forecast_March = α * (Actual_February) + (1 - α) * Forecast_February
Step 4: Calculate the forecast for April using the formula:
Forecast_April = α * (Actual_March) + (1 - α) * Forecast_March
Step 5: Calculate the forecast for May using the formula:
Forecast_May = α * (Actual_April) + (1 - α) * Forecast_April
Please note that you have provided sales data for air-conditioning sales, but the question is about water pump sales. If you meant to ask about air-conditioning sales, you can use the given sales data to calculate the forecasts for February through May. If you need help with water pump sales, please provide the correct sales data for January through April, and I will gladly help you with the calculations.

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