find the area of the triangle shown below

Answer: B

Step-by-step explanation: You can subtract 21 from 245 11 times but some will remain

y = 3(x-1)^2 - 8

y = 3(x^2 - 2x + 1) - 8 [Using the identity (a-b)^2 = a^2 - 2ab + b^2]

y = 3x^2 - 6x + 3 - 8 [Distributing the 3]

y = 3x^2 - 6x - 5 [Simplifying]

*IG:whis.sama_ent

Answer:

y=3x^(2)-6x-5

[tex]y=3x^2 -6x-5[/tex]

hope this helps ;)

Answer:

Step-by-step explanation:

Answer:

-20

Step-by-step explanation:

We can set up an equations with the conditions we are given. Let's use x for the missing number.

2(x-4)=3(x+4)

2x-8=3x+12

-20=xWe can set up an equations with the conditions we are given. Let's use x for the missing number.

2(x-4)=3(x+4)

2x-8=3x+12

-20=x

Answer:

9/13

Step-by-step explanation:

P(odd or less than 5) = number of odd cards + number of cards less than 5 / total number of cards

P(odd or less than 5) = (20 + 16) / 52

P(odd or less than 5) = 36 / 52

P(odd or less than 5) = 9 / 13

Therefore, the probability of picking an odd card or a card less than 5.

Answer is 9/13

Answer: 35% of thinner will be in total after the five litres is added so 85%-25% is 60% Therefore ur answer is 60%

Step-by-step explanation:

How many construction sites has each of the current Mohawk Skywalkers worked on in their lifetime? is a statistical question about the Mohawk Skywalkers. Option A.

A statistical question is a question that can be answered by collecting and analyzing data. It involves variability and asks about the distribution of a population, rather than just a single value or specific instance.

Option A is a statistical question because it asks about the variability of the number of construction sites each of the current Mohawk Skywalkers worked on in their lifetime.

Option B is also a statistical question as it asks about the distribution of New York City skyscrapers built with the help of Mohawk Skywalkers.

Option C is not a statistical question because it asks for a specific value, the number of generations of the Martin family who have worked as Mohawk Skywalkers, which does not involve variability or a population.

Option D is not a statistical question as it asks for a specific value, the number of Mohawk Skywalkers who helped build the Empire State Building, which does not involve variability or a population.

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The surface area of the cylinder is approximately 3015.93square inches when rounded to the nearest hundredth.

To find the surface area of a cylinder, we need to add the areas of the top and bottom circles, and the area of the lateral surface, which is the curved part of the cylinder.

The formula for the surface area of a cylinder is:

S.A. = 2πr² + 2πrh

where r is the radius of the cylinder, h is the height, and π is approximately equal to 3.14.

Given that the diameter is 32 inches, we can find the radius by dividing by 2:

r = d/2 = 32/2 = 16 inches

Now we can substitute the values into the formula and simplify:

S.A. = 2πr² + 2πrh

S.A. = 2π(16)² + 2π(16)(14)

S.A. = 2π(256) + 2π(224)

S.A. = 512π + 448π

S.A. = 960π

To approximate the answer to the nearest hundredth, we can use the value of π rounded to two decimal places (3.14):

S.A. ≈ 960(3.14)

S.A. ≈ 3015.93 square inches

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The surface area of the cylinder figure is derived to be equal to 3014.40 square inches rounded to the nearest hundredth.

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πr² + 2πrh

Where r is the radius of the base of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14159.

From the figure we have that:

r = 16 in

h = 14 in

surface area = 2 × 3.14 × 16 in × 16 in + 2 × 3.14 × 16 in × 14 in

surface area = 1607.68 in² + 1406.72 in²

surface area = 3014.40 in²

Therefore, the surface area of the cylinder figure is derived to be equal to 3014.40 square inches rounded to the nearest hundredth.

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The number of subsets that the set has are 128 subsets.

First, let's remove the duplicates from the set A. The distinct elements in set A are:

A = {a, r, i, t, m, e, c}

Now, we can find the number of subsets. For each element in the set, we have two choices: either it is included in the subset, or it is not. Therefore, there are 2^n subsets for a set with n distinct elements.

In our case, n = 7, so there are 2^7 = 128 subsets for the given set A.

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The journal entry to record the sale of the equipment would be:Cash $105,800,Loss on Sale of Equipment $35,650,Equipment $212,000

Accumulated Depreciation $66,000

How to solve the question?

a. To calculate the book value of the equipment at December 31 of the fifth year, we need to determine the accumulated depreciation for the first five years. The annual depreciation expense is calculated as follows:

Depreciation Expense = (Cost - Residual Value) / Useful Life

Depreciation Expense = ($212,000 - $14,000) / 15

Depreciation Expense = $13,200 per year

The accumulated depreciation for five years is therefore:

Accumulated Depreciation = Depreciation Expense x Number of Years

Accumulated Depreciation = $13,200 x 5

Accumulated Depreciation = $66,000

The book value of the equipment at December 31 of the fifth year is calculated as follows:

Book Value = Cost - Accumulated Depreciation

Book Value = $212,000 - $66,000

Book Value = $146,000

b.

To record depreciation for the three months until the sale date, we need to calculate the depreciation expense for the sixth year. The annual depreciation expense remains the same at $13,200, but since the equipment was sold on April 1, we need to prorate the depreciation for the first three months of the year.

Depreciation Expense for the Sixth Year = Depreciation Expense x (Months Remaining / 12)

Depreciation Expense for the Sixth Year = $13,200 x (9 / 12)

Depreciation Expense for the Sixth Year = $9,900

The journal entry to record depreciation for the three months until the sale date would be:

Depreciation Expense $9,900

Accumulated Depreciation $9,900

To record the sale of the equipment, we need to compare the sale price to the book value of the equipment at the time of the sale.

The book value of the equipment at the time of the sale is calculated as follows:

Book Value = Cost - Accumulated Depreciation

Book Value = $212,000 - ($13,200 x 5.25)

Book Value = $141,450

Since the sale price of $105,800 is less than the book value of $141,450, we need to record a loss on the sale of the equipment. The journal entry to record the sale of the equipment would be:

Cash $105,800

Loss on Sale of Equipment $35,650

Equipment $212,000

Accumulated Depreciation $66,000

The cash received from the sale is debited, and the difference between the sale price and the book value is recorded as a loss on the sale of the equipment. The equipment and its accumulated depreciation are removed from the books.

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Answer:

7.D

8.A

Step-by-step explanation:

For the function f(x) = √x+2+5:

(D) D= {x|x≥2}, R= {y|y≥5}

The domain is restricted to x values greater than or equal to 2 because the function contains the square root of x+2, which cannot be negative. The range starts at y = 5 because the lowest possible output of the function is √2+2+5 = 5.

(A) f(x)+∞o as x→ +∞o; f(x) +∞ as x――∞

As x approaches positive infinity, the output of the function approaches infinity as well. As x approaches negative infinity, the function is undefined since it involves taking the square root of negative numbers. However, the limit of the function as x approaches negative infinity from the right is positive infinity.

Answer:5,4

Step-by-step explanation:

The ice rink is 14.42 units away from the origin and other solutions are added below

First, we have the library at (7,8), which is 7 units to the right of the origin and 8 units up from the origin.

Next, we have the market at (3,6), which is 4 units to the left of the library (7-4=3) and 2 units down from the library (8-2=6).

Then, we have the bank at (3,8), which has the same x-coordinate as the market (3) and a y-coordinate of 8.

We have the school at (10,8), which has the same y-coordinate as the bank (8) and an x-coordinate of 10.

The pool is located at (7,3), which is 5 units down from the school (8-5=3) and 3 units to the left from the school (10-3=7).

Finally, the park is located at (7,1), which has the same x-coordinate as the pool (7) and a y-coordinate of 1.

The completed table is:

Point Ordered Pair (x, y)

Library (7,8)

Market (3,6)

Bank (3,8)

School (10,8)

Pool (7,3)

Park (7,1)

Bao's new location can be found by moving 5 blocks down from his current location of (3,13) and then 2 blocks right.

This gives us the new coordinates of (5,8) for Boo.

The new location is 5 units right and 8 units up of the origin

To get to the baseball diamond, he traveled 3 blocks to the right from his starting point (3 - 3 = 0) and 8 blocks down (15 - 8 = 7), which gives us the new coordinates of (3, 15) for the baseball diamond.

Bao's starting point was (0, 7).

Bao's starting point can be found by moving 5 blocks to the left from his current location of (14, 13) and then 10 blocks down.

This gives us the new coordinates of (9,3) for Bao's starting point.

The distance between the ice rink and the origin can be found using the distance formula:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, we have:

d = √((12 - 0)^2 + (8 - 0)^2) = √(144 + 64) = √(208) ≈ 14.42

So the ice rink is approximately 14.42 units away from the origin.

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If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.

A mathematical concept known as a vector has both a magnitude and a direction. Physical quantities like force, velocity, and acceleration are represented by it. In the physical sciences, engineering, and computer graphics, vectors are frequently employed. They can also be used to represent abstract concepts like magnitude, directions, and other things.

Here in the question,

(0, 0) is the beginning position. There should be an arrow above each vector name listed below.

Ink a line beginning at (3, -1). A vector has an origin of (0,0) and a destination of (3, -1).

Put a line through points (2,2). The vector B has a start point of (0, 0) and an end point of (2, 2).

These two vectors add up to: a + b = (3-1) + (2,2) = (5,1) when combined.

Whatever order they are in, b + a = (2,2) + (3, -1) = (5,1) regardless.

Either way, the same conclusion is reached.

The terminal point of A + B is at (5, 1).

If the vector is drawn from (0,0) to (5, -1), the outcome vector is drawn.

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there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.

How to solve the question?

The number of ways to draw 7 cards from a standard deck of 52 cards can be calculated using the combination formula, which is:

C(52, 7) = 52! / (7! * (52-7)!)

where "!" represents the factorial function.

To simplify this expression, we can use the property that n! / k! = n * (n-1) * (n-2) * ... * (n-k+1) for positive integers n and k such that k ≤ n.

Using this property, we can rewrite the above expression as:

C(52, 7) = (52 * 51 * 50 * 49 * 48 * 47 * 46) / (7 * 6 * 5 * 4 * 3 * 2 * 1)

Simplifying this expression, we get:

C(52, 7) = 133,784,560

Therefore, there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.

To understand why this is the case, we can think of each draw as a separate event with no replacement. The first card can be drawn in 52 ways, the second card can be drawn in 51 ways (since one card has already been drawn), the third card can be drawn in 50 ways (since two cards have already been drawn), and so on. Therefore, the total number of ways to draw 7 cards is the product of the number of ways to draw each individual card, which is 52 * 51 * 50 * 49 * 48 * 47 * 46. However, since the order in which the cards are drawn does not matter, we need to divide by the number of ways to arrange 7 cards, which is 7 * 6 * 5 * 4 * 3 * 2 * 1 (i.e., 7 factorial). This gives us the final answer of 133,784,560.

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Tje number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.

To find out how many items there are in 1 part of the ratio, we need to add together the two parts of the ratio. In this case, 8+27 = 35.

To proportion the items according to the ratio, we need to divide the total number of items (1225) by the number of parts in the ratio (35).

This gives us:

1 part of the ratio = 1225 / 35 = 35

To find out how many items there are in each part of the ratio, we need to multiply this value by the corresponding part of the ratio.

For the part that corresponds to 8, we have:

8 parts of the ratio = 8 x 35 = 280 items

For the part that corresponds to 27, we have:

27 parts of the ratio = 27 x 35 = 945 items

Therefore, the number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.

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The new mixture contains 34% peanuts.

Using a weighted average approach.

Let x be the percentage of peanuts in the new mixture. Then we can set up the following equation:

(0.16)(4) + (0.40)(12) = x(4 + 12)

simplifying the equation, we get:

0.64 + 4.8 = 16x

5.44 = 16x

x = 0.34 or 34%

Therefore, the new mixture contains 34% peanuts.

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The equivalent expressions is solved to give the quantity four ninths end quantity to the power of x. Option C

An algebraic expression can be described as an expression that is made up of terms, factors, coefficient, variables and constants.

These expressions are also composed of mathematical operations.

Also note that index forms are mathematical forms used to represent numbers too large or too small.

From the information given, we have that;

(2/3)²⁽ˣ⁾

expand the bracket, we get;

(2/3)²ˣ

Find the square of both the numerator and denominator, we get;

(4/9)ˣ

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As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.

An ordered set of number with a pattern or rule regulating their values is referred to as a sequence in mathematics. A word is used to characterize each number in a sequence. There are many various kinds of sequences, but a few of the most popular ones are as follows: A common differential, or constant number, is added to the respective period to produce an arithmetic series, each term of which is obtained. One arithmetic series with a following differences of three is 1, 4, 7, 10, 13, etc.

given

Given an arithmetic series with a first term (a1) and a common difference (d), the formula for the nth term (an) is as follows:

[tex]a = a1 + (n - 1) * d[/tex]

In this instance, the common difference (d) is 15, and the first term (a1) is 7. When these values are added to the formula, we obtain:

[tex]a = 7 + (n - 1) * 15[/tex]

As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.

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The distance traveled by the wheel when it turns 20 times is 150.7964 feet.

What is circumference?

The circumference of a wheel can be calculated as:

Circumference = 2 x π x radius

where π (pi) is a mathematical constant approximately equal to 3.14159.

The distance traveled by a wheel when it turns is equal to the circumference of the wheel multiplied by the number of times it turns.

Given that the radius of the wheel is 1.2 feet, the circumference of the wheel is:

Circumference = 2 x π x radius

Circumference = 2 x 3.14159 x 1.2

Circumference = 7.53982 feet (rounded to 5 decimal places)

Therefore, each time the wheel turns, it travels a distance of 7.53982 feet. To find the distance traveled when the wheel turns 20 times, we can multiply the distance traveled each time by the number of times the wheel turns:

Distance traveled = Circumference x Number of turns

Distance traveled = 7.53982 feet x 20

Distance traveled = 150.7964 feet (rounded to 4 decimal places)

Therefore, the distance traveled by the wheel when it turns 20 times is 150.7964 feet.

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Answer:

1600

Step-by-step explanation:

The answer you tried is equivalent.

1. The value of Angle STR is 19°

2. The value of arc ST is 134°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

Part of circle theorem states that: The angle in the same segment are equal.

1. Therefore the value of angle STR is calculated as;

= 180- ( 90+71)

= 180- 161

= 19°

2. The value of arc ST is calculated as;

Since arc SR = QR = 46°

representing the value of arc ST by x

therefore,

46+46+x+x = 360

92 +2x = 360

2x = 360-92

2x = 268

divide both sides by 2

x = 268/2

x = 134°

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A quadratic model for the data is y = -0.0076x² + 0.6915x + 14.711.

The fuel economy at 80 mph is 21.39.

In this scenario, the speed (x) would be plotted on the x-axis of the scatter plot while the fuel economy (y) would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the relationship between the speed (x) and fuel economy (y), a quadratic model for the line of best fit is given by:

y = -0.0076x² + 0.6915x + 14.711

When the speed (x) = 80 mph, the fuel economy (y) is given by;

y = -0.0076(80)² + 0.6915(80) + 14.711

y = 21.39

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The area the grass seed needs to cover is 7,425 square meters.

To find the total area of the lawn excluding the pool, we first need to calculate the area of the pool. Using the formula for the area of a rectangle, we multiply the length and width of the pool together to get:

= 7.5 m x 3.25 m

= 24.375 square meters

Next, we can find the total area of the lawn by subtracting the area of the pool from the total area of the rectangle formed by the lawn:

= 50 m x 150 m

= 7,500 square meters

So, the area the grass seed needs to cover is:

= 7,500 square meters - 24.375 square meters

= 7,425 square meters.

Full question" Marcos wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 7 1/2 m by 3 1/4 m. Find the area the grass seed needs to cover. The dimensions of the lawn are 50 m x 150 m.

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The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.

A this double shape's perimeter is the space encircling its outside edge. It is the length of the object's sides. As an illustration, the perimeter of a rectangle is equivalent to the total of its four sides' lengths.

given

Assume that the rectangular field has a width of "x" yards.

The problem states that the field's length is three times its breadth, or three times yards.

The lengths of all the sides make up the rectangle's perimeter, therefore we can write:

[tex]Perimeter = 2 (length + width).[/tex]

In place of the values we hold:

[tex]400 = 2(3x + x)\\400 = 2(4x) (4x)\\400 = 8x\\x = 50[/tex]

The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.

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Answer:

4 cannot be written as a logarithm with a base of 4. A logarithm is an exponent that tells us how many times we need to multiply a base by itself to get a certain number. For example, log2(8) = 3 because 2^3 = 8. We can write this as an equation: logb(x) = y means b^y = x.

-4 cannot be written as a logarithm with a base of 4 because there is no exponent that can make 4 equal to -4. In other words, there is no y such that 4^y = -4. This is because any positive number raised to any power will always be positive. Therefore, log4(-4) is undefined or does not exist.

Therefore, -4 cannot be written as a logarithm with a base of 4.

Step-by-step explanation:

The measure of arc angle QT is determined as 142 ⁰.

The measure of m∠STR is determined as 23⁰.

The measure of angle subtended by the arc QT is calculated by applying the following formula.

Based on the angle of intersecting chord theorem, we will have the following equation.

The measure of  m∠STR is calculated as;

m∠STR = ¹/₂( arc SR )

m∠STR = ¹/₂ x 46⁰

m∠STR = 23⁰

The measure of arc QT is calculated as;

m∠QST = ¹/₂( arc QT )

arc QT = 2 (m∠QST)

arc QT = 2 x 71⁰

arc QT = 142⁰

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The x-intercept represents:

"The number of hours the taxi was driven before running out of fuel"

In standard notation, the variable x is the independent variable in the horizontal axis, here we can see that in the horizontal axis we are measuring the time (in hours) that the taxi was driving.

Then the x-intercept (the time when y = 0) is the number of hours until the fuel is down to zero, then the correct option is B i guess, but it should be worded as:

"The number of hours the taxi was driven before running out of fuel"

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We are given the system of equations:

y = 3x

y = 6x + 3

We can use substitution to solve this system. Since both equations are equal to y, we can set them equal to each other:

3x = 6x + 3

Subtracting 3x from both sides, we get:

0 = 3x + 3

Subtracting 3 from both sides, we get:

-3 = 3x

Dividing both sides by 3, we get:

x = -1

Now that we know x, we can use either equation to find y. Let's use the first equation:

y = 3x = 3(-1) = -3

Therefore, the solution to the system of equations is (-1, -3).

To check our solution, we can substitute these values back into both equations:

y = 3x gives us -3 = 3(-1), which is true

y = 6x + 3 gives us -3 = 6(-1) + 3, which is also true

Therefore, our solution is correct.

We can also plug in the other given points to check that they do not satisfy both equations, which means they are not solutions to the system.

If the width of a rectangle with perimeter P is 6 units, its length would be equal to L = P/2 - 6.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following;

P = 2(L + 6)

P = 2L + 12

P - 12 = 2L

L = (P - 12)/2

L = P/2 - 6.

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