Use compatible numbers to estimate the correct quotient.

Answer: y = 10(x) + 56

Step-by-step explanation:

y=10(4) + 56

y = 40 + 56

y = 96

Answer:

1a. y = 10 x + 16

1b. 16

2a. y = 600x + 1500

2b. $8700

Step-by-step explanation:

1a. A linear model represents a relationship between two variables as a straight line. In this case, we want to represent the relationship between the number of hours a canoe is rented for and the total cost of the rental, including the deposit.

We can create a linear model by using the equation y = mx + b, where y is the total cost, x is the number of hours the canoe is rented for, m is the slope of the line (the rate at which the cost changes per hour), and b is the y-intercept (the total cost when x is 0).

Since the total cost includes a non-refundable deposit, we need to add this to the y-intercept. The deposit is not dependent on the number of hours the canoe is rented for, so it is not represented in the slope.

Based on the information given, the total cost is $56 when the canoe is rented for 4 hours, and the rental fee is $10 per hour. We can use these values to solve for the y-intercept and the slope:

y = mx + b

56 = (10) (4) + b

56 = 40 + b

b = 56 - 40

b = 16

So the linear model representing the relationship between the number of hours a canoe is rented for and the total cost of the rental, including the deposit, is: y = 10 x + 16

1b. We know that the total cost is $56 when the canoe is rented for 4 hours, and the rental fee is $10 per hour. We can use these values to solve for the y-intercept, which represents the non-refundable deposit:

y = (10) (4) + b

56 = 40 + b

b = 56 - 40

b = 16

So the non-refundable deposit is $16. This means that the total cost of the rental, including the deposit and the hourly fee, is $56.

2a. We can create a linear model by using the equation y = mx + b, where y is the total cost, x is the number of solar heaters produced, m is the slope of the line (the rate at which the cost changes per heater), and b is the y-intercept (the total cost when x is 0).

Based on the information given, it costs $7500 to produce 10 solar heaters, and it costs $13,500 to produce 20 solar heaters. We can use these values to solve for the y-intercept and the slope:

y = mx + b

7500 = m(10) + b

13500 = m(20) + b

Subtracting the second equation from the first equation gives:

-6000 = m(10) - m(20)

6000 = m(20) - m(10)

6000 = m(20 - 10)

6000 = m(10)

m = 6000/10

m = 600

Substituting this value for m in either of the original equations and solving for b gives:

7500 = (600)(10) + b

7500 = 6000 + b

b = 7500 - 6000

b = 1500

So the linear model representing the relationship between the number of solar heaters produced and the total cost of production is:

y = (600) x + 1500

According to this model, the total cost of producing 15 solar heaters would be $10,500.

2b. To find the total cost of producing 12 solar heaters, we can use the linear model that represents the relationship between the number of solar heaters produced and the total cost of production:

y = (600) x + 1500

Where y is the total cost, x is the number of solar heaters produced, m is the slope of the line (the rate at which the cost changes per heater), and b is the y-intercept (the total cost when x is 0).

To predict the total cost of producing 12 solar heaters, we can substitute 12 for x in the equation:

y = (600) (12) + 1500

y = 7200 + 1500

y = 8700

According to this model, the total cost of producing 12 solar heaters would be $8700.

Answer:

see explanation

Step-by-step explanation:

if (x - h) is a factor of f(x) then f(h) = 0

(a)

if (x - 2) is a factor of f(x) then f(2) = 0

f(2) = 2³ - 7(2) + 6

     = 8 - 14 + 6

     =  - 6 + 6

    = 0

since f(2) = 0 then (x - 2) is a factor of f(x)

(b)

using synthetic division to factor f(x)

insert a zero in the x² position on the table

 2 | 1   0   - 7   6

      ↓  2     4   - 6

     -----------------------

       1  2    - 3    0

quotient is

x² + 2x - 3 = (x + 3)(x - 1)

Then

f(x) = (x - 2)(x + 3)(x - 1)

Answer:

ez 2/1

Step-by-step explanation:

Answer: for 35x+21 the answer is 7(5+3)

for the second one, the answer is 4x+2x+2

the 3rd one the answer is 5(6-3x)

for the fouth one the answer is 40x+50

for the fifth one the answer is 4x+4x+3

Step-by-step explanation:

Total amount he will pay is equal to 62.880 after giving discount of 35% and adding the sales tax of 7.5%.

Discount is the total price which is deducted from the original terms so as we have to pay less.

Discount is always given on the marked price of the article.

Marked price is the cost at which article is marked.

Chandler buy shoes of $89.99.

Total discount on shoes = 35%

Price after getting Discount = 58.4935

Sales Tax = 7.5 %

Price after sales tax = 58.4935 + 7.5% of 58.4935

= 62.880

So total amount he will pay is equal to 62.880.

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standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{-8}{2 +4} \implies \cfrac{ -8 }{ 6 } \implies - \cfrac{ 4 }{ 3 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- \cfrac{ 4 }{ 3 }}(x-\stackrel{x_1}{(-4)}) \implies y -5 = - \cfrac{ 4 }{ 3 } ( x +4) \\\\\\ \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-5)=3\left( - \cfrac{ 4 }{ 3 } ( x +4) \right)}\implies 3y-15=-4(x+4) \\\\\\ 3y-15=-4x-16\implies 3y=-4x-1\implies {\Large \begin{array}{llll} 4x+3y=-1 \end{array}}[/tex]

23 pounds of type A coffee were used and 92 pounds of type B coffee were used, using the concept of formula equation we get -

A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

Let assume that, x represent the number of pounds of type A coffee that were used in the blend.

and y represent the number of pounds of type B coffee that were used in the blend.

Type A coffee costs Lena $4.10 per pound, and type B coffee costs $5.35 per pound.

The total cost of the mixture is $586.50.

Now,

4.10x + 5.35y = 586.50 ............ (i)

This month's blend used four times as many pounds of type B coffee as type A.

so, y = 4x

Substituting y = 4x into equation (i), we get -

4.10x + 5.35 × 4x = 586.50

or, 4.10x + 21.4x = 586.50

or, 25.5x = 586.50

or, x =  586.50/25.5

or, x = 23

Next, y = 4x = 4 × 23

y = 92

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Answer:8a<8b

Step-by-step explanation:

8a<8b

Answer:

Step-by-step explanation:

The given is the number of years she drives for and how much she drives in a year.

We can use this to figure out how many miles she drives in 3, 4, and 6 years.

To do that, just multiply the number of years by the number of miles she drives in a year

[tex]\frac{9000}{1} =\frac{miles}{x years}[/tex]

[tex]9000 * x years = 1 * miles[/tex]

[tex]3 * 9000 = 27,000\\4 * 9000 = 36,000\\6 * 9000 = 54,000[/tex]

Put points at (3,27000) , (4,36000) , (6,54000)

Draw a straight line through them (not like mine)

In this case, the terminal point of theta/2 can be determined using the following steps:

Since cos(theta/2) < 0 and the cosine function has a range of [-1, 1], it follows that theta/2 must be in the second or third quadrant (90 degrees to 180 degrees or 180 degrees to 270 degrees).

To find the terminal point of theta/2, we can use the formula for converting from polar to Cartesian coordinates: x = rcos(theta) and y = rsin(theta), where (x,y) is the Cartesian coordinates of the terminal point, r is the radius, and theta is the angle in radians.

In this case, the radius is 1 (since the terminal point is on the unit circle) and the angle is theta/2. Substituting these values into the formulas above, we get:

x = 1 * cos(theta/2)

y = 1 * sin(theta/2)

To find the values of cos(theta/2) and sin(theta/2), we can use the identity cos(theta/2) = sqrt((1 + cos(theta))/2) and sin(theta/2) = sqrt((1 - cos(theta))/2).

Substituting the given value of cos(theta) (-1/9) and the identities above into the formulas for x and y, we get:

x = sqrt((1 + (-1/9))/2) = -sqrt(2)/3

y = sqrt((1 - (-1/9))/2) = sqrt(8)/3

Thus, the coordinates of the terminal point of theta/2 are (-sqrt(2)/3, sqrt(8)/3).

The terminal point (a₁, a₂) for theta/2 is (-2/3, √(5) / 3).

To find the terminal point (a₁, a₂) of theta/2, use the half-angle identity for cosine:

cos(theta/2) = ± √((1 + cos(theta)) / 2)

Given that cos(theta) = -1/9 and cos(theta/2) < 0, the negative sign should be used in the half-angle identity.

Calculate cos(theta/2):

cos(theta/2) = - √((1 + cos(theta)) / 2)

cos(theta/2) = - √((1 - 1/9) / 2)

cos(theta/2) = - √((8/9) / 2)

cos(theta/2) = - √(8/18)

cos(theta/2) = - √(4/9)

cos(theta/2) = - 2/3

Cos(theta/2) = -2/3. To find the terminal point (a₁, a₂), determine the values of a₁ and a₂.

Since cos(theta/2) is negative, a₁ is negative. To find the value of a₂, use the Pythagorean identity:

cos²(theta/2) + sin²(theta/2) = 1

Since cos(theta/2) = -2/3, calculate sin(theta/2):

sin²(theta/2) = 1 - cos²(theta/2)

sin²(theta/2) = 1 - (-2/3)²

sin²(theta/2) = 1 - 4/9

sin²(theta/2) = 5/9

sin(theta/2) = ± √(5/9)

sin(theta/2) = ± √(5) / 3

Since theta is in the second quadrant (cos(theta) = -1/9), sin(theta) is positive in the second quadrant. Therefore, sin(theta/2) = √(5) / 3.

Now, sin(theta/2) = √(5) / 3.

So, the terminal point (a₁, a₂) for theta/2 is (-2/3, √(5) / 3).

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Using the distributive property we get 5y.

What is distributive property?

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical characteristics that is utilised the most. Commutative and associative qualities are the other two important features.

This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.

Using the distributive property

18y - 13y = (18 - 13)y

(18-13) y

Subtract the numbers: 18-13=5

=5 y

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The factored expression of 1/5c + 4/5 is 1/5(c + 4)

From the question, we have the following parameters that can be used in our computation:

1/5c + 4/5

From the above expression, we have the following highlights

In the above terms, we can see that the denominator of the terms is 5

When this denominator is removed, we have

Expression = c + 4

This means that

GCF =1/5

So, the factored expression is 1/5(c + 4)

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Answer:

ok

Step-by-step explanation:

3x+1=4x-8= -6

x=-6

this is the x

I hope you have understand

Answer:

60 square inches

Step-by-step explanation:

The width of the second frame is 2 times the width of the first frame, or 2 * 5 inches = 10 inches.

The area of the second frame is its length multiplied by its width, or 6 inches * 10 inches = 60 square inches.

Answer:

the volume of the cone is approximately 28.26 cubic inches.

Step-by-step explanation:

To find the volume of a cone, you can use the formula:

V = (1/3) * π * r^2 * h

where V is the volume of the cone, r is the radius of the base of the cone, and h is the height of the cone.

Using the dimensions provided in the diagram, the radius of the base of the cone is 3 inches and the height of the cone is 8 inches. Plugging these values into the formula, we get:

V = (1/3) * π * 3^2 * 8

= (1/3) * 3.14 * 9 * 8

= 28.26 cubic inches

So, the volume of the cone is approximately 28.26 cubic inches.

The parallelogram's area is 130 yards square.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

base*height

base=13

height=10

13*10

= 130 yds

Hence, The parallelogram's area is 130 yards square.

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Answer:

Below

Step-by-step explanation:

y+3=5(x+4)      Expand R side, then subtract 3 from both sides of equation

y = 5x+ 17     Done .

Answer:

y = 5x+17

Step-by-step explanation:

To get this equation to slope intercept form, get the y variable by itself on one side of the equal sign.

y+3=5(x+4)

[Distribute the 5 to x and 4]

y+3 = 5x+20

[Subtract 3 from both sides]

y = 5x+17

[Done!]

The expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or (-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

An algebraic expression is a number, variable, or the combination of both and operational symbols.

To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.

(-3 1/4d + 3/5) - (2 7/8d + 7/10)

⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10

⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10

⇒ (-13/4 - 23/8)d + 6/10 - 7/10

⇒ (-26/8 - 23/8)d - 1/10

⇒ -49/8 d - 1/10

Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.

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Answer:

C

Step-by-step explanation:

its 19735 hope it helps

Answer: EASY

Step-by-step explanation:

Answer:

72891

Step-by-step explanation:

150,000 is the base number

In the first year it will be the same, so it'll only count 13 years

the equation is: 150,000(0.946)^x

how:

150,000(100%-5.4%)^x

150,000(94.6%)^x

150,000(0.946)^x

*it's 100%-5.4% because that's that's remaining each year if it's decreasing by 5.4%. you would convert the percentage into decimals because it's decreasing by a percentage, not a whole number

150000(0.946)^13

*13 is the number of years, so it's x

72891.356467

In linear equation,  { 2x + 3y = 7.20 ,   { 4x + 2y = 8.80 the price per pound for oranges.

 What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                  Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Product B performed worse in the study because 32% failed to get relief with this product, whereas only 28% failed to get relief with Product A.

Working through this, the percentage who failed to find relief from product A is (25 - 18) / 25 = 28%. Doing the same type of calculation for product B, we can determine the percentage who failed to find relief as (50 - 34) / 50 = 32%. The description statement asks for which offered less relief, which we can find using the less than operator:

28% < 32%

Product A offered relief to all but 28% of the people, while product B offered relief to all but 32% of the people. Given that fewer people failed to find relief on product 28%, we can argue that more people did find relief on product A.

Given that the tests are both on multiples of 25 people, we can also see the percentages by multiplying the numerators and denominators to bring both to a scale of 100:

7/25 * 4/4 = 28% of product A users failed to find relief.

16/50 * 2/2 = 32% of product B users failed to find relief.

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The balance when the account went into overdraft was -48.61

An overdraft occurs when something is withdrawn in excess of what is in a current account. For financial systems, this can be funds in a bank account.

Let x be the balance when the account went into overdraft

To get back to a positive balance he deposited money at a steady rate of $31.97 per week.

Amount deposited per week = $31.97

Amount deposited 3 weeks = $95.91

Now amount in account after 3 weeks =x+95.91

We are given that After 3 weeks, he had $95.91 in the account.

So, x+95.91=47.3

x= 47.3-95.91

x= -48.61

Hence The balance when the account went into overdraft was -48.61

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Answer:five thousand six hundred eight

A) During the interval (0, 2) of the domain the water balloon's height is increasing.

B) During the interval (2, 4) of the domain the water balloon's height is staying the same.

C) During the interval (8, 10) of the domain, the water balloon's height is decreasing the fastest.

D) The height of the balloon will be zero since the height of the balloon has remained the same from the 10th interval.

What is an interval?

In mathematics, an interval is quantified in terms of numbers. Every number between two specific integers is considered to be an interval. Between those two values, this range encompasses all real numbers. Real numbers can be of any type you can imagine.

All the numbers between a pair of provided numbers are considered an interval. It is crucial to indicate if the start and end numbers are included. The Number Line, Inequalities, and Interval Notation are the three primary methods for displaying intervals.

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That is a change in the hypotenuse's length of -2.6 inches per second.

What in math is a rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents

h = sqr(b^2 + a^2), b=30, a=40, b'=-5, a'=-7

h' = [(1/2)/sqr(b^2+a^2)](2bb' + 2aa') = sqr(30^2+40^2)(30(5)+40(-7)

= (150-280)/sqr2500 = (-130)/50 =-- -13/5 = -2.6 inches per second

2.6 inches are lost from the hypotenuse every second.

Check the response by observing what transpires in one second.

30 to 35 on the short leg

greater leg descends from 40 to 37

From 50 to 47.4 is the hypotenuse

In one second, 50-47.4 equals a 2.6 reduction. That is a change in the hypotenuse's length of -2.6 inches per second.

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The expected mean square can be generated in minitab as shown below :

What is expected mean square ?

Expected mean squares in statistics are the predicted values of certain statistics emerging in sums of squares partitions in the analysis of variance. They can be used to determine which statistic belongs in the denominator of an F-test that is being used to test the null hypothesis that a given effect is not there.

Not often, although in some circumstances, perhaps. The average squared departure of observed data values from the sample or population mean is known as variation. The average squared difference between actual and anticipated values is known as MSE (mean squared error).

Te expected mean squares for a balanced three-stage nested design assuming that A is fixed and that B and C are random.

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Answer:2.

2/5 times 5 is 10/5 or 2

Step-by-step explanation:

Answer:

42

Step-by-step explanation: