Find XZ and the area of △WXY.

The length of the missing base is approximately 6.67 cm.

By applying the formula for the area of a trapezoid, we will be able to solve for the missing base.

Recall that the formula for the area of a trapezoid is:

A = [tex]\frac{1}{2} * h * (b_{1} + b_{2})[/tex]

where

A = area

h = height

b₁ and b₂ are the lengths of the parallel bases.

From the question, we are given:

A = 64 m²

h = 12 cm

b₁ = 4 cm.

Plug these values into the formula above to solve the missing base

64 = [tex]\frac{1}{2} * 12 * (4+ b_{2})[/tex]

Multiplying both sides by 2:

128 = 12(4 + b₂)

Simplifying:

128 = 48 + 12b₂

80 = 12b₂

b₂ = 80/12 = 20/3

b₂ = 6.67

Therefore, the length of the missing base is approximately 6.67 cm.

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Answer:0

Step-by-step explanation: -

-7 x -7 = 49

11 x 77 = 77

-7 + 7 = 0

49 + 77 + 28 = 154

154 ÷ 0 = 0

The amount in the account at the end of the year is $4998.

Percentage decrease is the measure of the reduction in the value of a quantity over time, expressed as a percentage of its original value. It is calculated by taking the difference between the original value and the new value, dividing it by the original value, and then multiplying the result by 100.

We know that;

Percentage decrease = 26.5%

Then the decrease in dollars = 26.5/100 * 6800

= $1802

The amount at the end of the year = $6800 - $1802

= $4998

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The surface area of the cylinder is 1851.97 square meters

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

Radius, r = 13.1 meters

Height, h = 9.4 meters

Using the above as a guide, we have the following:

Surface area = 2πr(r + h)

Substitute the known values in the above equation, so, we have the following representation

Surface area = 2π * 13.1 * (13.1 + 9.4)

Evaluate

Surface area = 1851.97

Hence, the surface area is 1851.97 square meters

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a. Apples:  Lily needs 10 cups of apples for her fruit bowl.

b. Watermelons: Lily needs 13-3/4 cups of watermelons for her fruit bowl.

c. Grapes: The amount of grapes that Lily has is not given

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

To make her fruit bowl, Lily needs 2½ times the amount of each fruit she currently has.

a. Apples:

2½ × 4 cups = 10 cups

Therefore, Lily needs 10 cups of apples for her fruit bowl.

b. Watermelons:

2½ × 5-½ cups = (2 × 5 + 1/2) × 5/2 cups = 13-3/4 cups

Therefore, Lily needs 13-3/4 cups of watermelons for her fruit bowl.

c. Grapes:

The amount of grapes that Lily has is not given, so we cannot calculate how much she needs for her fruit bowl.

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The elements of the sets  A ∩ (B ∪ C) is  {b, c, i}.

A universal set (U) is a set which has elements of all the related sets, without any repetition of elements.

Therefore,

U = {a, b, ….. i, j}

A = {b, c, i, j}

B = {a, c, g, i}

C = {a, b, d, i}

Therefore, let's find the elements A ∩ (B ∪ C).

Hence,

(B ∪ C) = {a, b, c, d, i, g}

A =  {b, c, i, j}

Finally,

A ∩ (B ∪ C). = {b, c, i}

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that L looking shape is a right angle, which is 90 degrees. and the question is saying that the part they cut off is 56 degrees. to find x you will need to subtract 90 from 56 to get 34.

The answer is 34 :)

Answer: 52-9 = 43 units

Step-by-step explanation:

Using the Intersecting secants theorem, the length of JK in the given diagram is 17

From the question, we are to determine the length of JK in the given diagram.

The diagram shows a circle with intersecting secants.

From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".

Then,

We can write that

JK × KL = NM × ML

From the given diagram,

KL = 14

NM = 14

ML = 17

Substituting the values

JK × 14 = 14 × 17

JK = (14 × 17) / 14

JK = 17

Hence, the length of JK is 17

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An expression for the height of the cuboid is 3p - 245q/49 meters.

In Mathematics and Geometry, the volume of a cuboid with a square base can be calculated by using this following formula:

Volume of a cuboid = L² × H

Where:

By substituting the given parameters into the formula for the volume of a cuboid cuboid with a square base, we have the following;

(147p - 245q) = 7² × H

(147p - 245q) = 49 × H

Height, H = (147p - 245q)/49

Height, H = 3p - 245q/49 meters.

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This is not true for all functions. To prove this, an example is given below. Let f(x) = x and g(x) = x².

A function is a relation that associates each element of a set, called the domain, to exactly one element of another set, called the range. It is a type of correspondence between two sets, where each element of one set is associated with exactly one element of another set.

The first derivative of f(x) is f ' (x) = 1 and the first derivative of g(x) is g ' (x) = 2x.

Therefore, ( f ⋅ g )' = ( x ⋅ x2 )'

= 1 ⋅ 2x + x ⋅ 2

= 2x + 2 ≠ 1 ⋅ 2x + 2x

= 4x

= f ' ⋅ g '

This example proves that the statement (f⋅g)' = f'⋅g' is incorrect. It is important to note that this does not mean that the statement is not true for all functions. It simply means that for the particular example given, the statement is not correct.

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From the calculations, only question 2 shows that f(x) is the inverse of function g(x) as the rest shows the parent functions are not inverse of g(x)

In the given question, we are to determine if the parent function f(x) is an inverse to g(x).

1. f(x) = 2x - 9

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

Let's switch the variables: y = 2x - 9 to x= 2y - 9.

We can proceed to solve the equation as;

x =2y - 9 for y.

y= x + 9 / 2

Therefore, f(x) is not an inverse of g(x)

2. f(x) = x - 3 / 4

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

Let's switch the variables:

y = x / 4 - 3/4 to x = y / 4 - 3/4

we can solve the equation for y to give us;

y = 4x + 3

This shows that f(x) is inverse of g(x)

4. f(x) = 7x^3/2 - 4

To find the inverse function, swap x and y and solve the resulting equation for x

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables:

y = 7x^3/2 - 4 will become x = 7y^3/2 - 4

Solving for y;

y = [(∛7(x + 4))^2/3] / 7

This shows f(x) is not the inverse of g(x)

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Answer:

2.362

Step-by-step explanation:

Use calculator: 2.361727836

Round: 2.362

Answer:

13.75 cm³

Step-by-step explanation:

In order to find the area of a rectangular prism you only need to multiply the width height and length together:

2.75 * 1.25 = 3.4375

3.4375 * 4 = 13.75

Hope this helps!

Answer:

a) x > -7

Step-by-step explanation:

an open circle (blank) means the greater than or less than symbols (< or >) and a close circle (filled in) means ≤ or ≥. the lining to your right looks more bold than the lining to your left so it's an; open circle, on -7, with the lining bold to your left.

in conclusion, x (the open circle) > -7

The bar model that represents the number of cousins that Sawyer has, given the cousins Hazel has is the fourth bar model.

The letter " c " is meant to represent the number of cousins that Sawyer has, in relation to those that Hazel has. This means that bar models A and C are out because they represent the cousins as B.

The question shows that Hazel has twice the number of cousins that Sawyer has. This means that if Sawyer's cousins are represented as " c " then Hazel would be 2 c. This is shown in the last bar model so this is the correct bar model.

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First part is:

Hazel has 8 cousins. Hazel has 2 times as many cousins as Sawyer.

How many cousins does Sawyer have?

Answer:

Option A

Concept Applied:

(g-f)(x) = g(x)-f(x)

Step-by-step explanation:

Substitute and solve

The length of the square is 1.75 inches, while the king's height is 2.25 inches.

Define length.

The length of an object or the extent of a one-dimensional object along its longest dimension is measured physically. It is a basic idea in physics and geometry and is frequently expressed in terms of meters (m), centimetres (cm), feet (ft), or inches (in).

According to the information provided, the square length to king's height ratio is 3.5 to 4.5 inches. Let's use this ratio to determine the square's length when the king is 2.25 inches tall.

We may make a proportion to get the square's length:

(square length) / (king's height) = 3.5/4.5

king's height = 2.25

Let's substitute the given values:

(square length) / 2.25 = 3.5/4.5

To solve for the length of the square, we can cross-multiply:

(square length) = (2.25) x (3.5/4.5)

(square length) = 1.75

Therefore, the length of the square is 1.75 inches, while the king's height is 2.25 inches.

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Answer: (0, 3)

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Answer:

Let the cost of one apple pie be A and the cost of one blackberry pie be B.

From the first statement, we can write the equation:

SA + 4B = 8140 ----(1)

From the second statement, we can write the equation:

4*B = 152

Solving for B:

B = 38

Substituting B in equation (1) and solving for A:

SA + 438 = 8140

S*A = 8008

A = 8008/S

We do not have enough information to find the value of S or A individually, but we can find the relationship between them:

A/B = (8008/S)/38 = 211/S

Therefore, the cost of one apple pie is 211 times the cost of one blackberry pie.

The ratio of spots to eyes can be described as follows;

There are 6 spots for every 2 eyes.

There are 3 spots for every 1 eye.

In Mathematics and Geometry, a ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

Based on the information provided above, we have the following ratio parameters:

The total number of spots = 6 spots.

The total number of eyes = 2 eyes.

Ratio = 6/2 = 3 spots.

In this context, we can reasonably infer and logically deduce that there are 6 spots for every two (2) eyes and three (3) spots for every one (1) eye.

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Complete Question:

Use the following image to complete the sentences describing the ratio of spots to eyes.

There are 6 spots for every ____ eyes.

There are _____ spots for every 1 eye.

Answer:

The perimeter of the entire frame is equal to the sum of the perimeters of the mat and the picture. The expression for the perimeter of the mat is (2m + 10) + (2m + 8) = 4m + 18, and the expression for the perimeter of the picture is 2(8) + 2(10) = 36. Therefore, the expression for the perimeter of the entire frame is (4m + 18) + 36 = 4m + 54.

The probability of the sample mean being less than 25.3 is given as follows:

0.9713 = 97.13%.

The sample mean would not be considered unusual, as it has a probability that is greater than 5%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 25, \sigma = 1.3, n = 68, s = \frac{1.3}{\sqrt{68}} = 0.1576[/tex]

The probability of a score less than 25.3 is the p-value of Z when X = 25.3, hence:

Z = (25.3 - 25)/0.1576

Z = 1.9

Z = 1.9 has a p-value of 0.9713.

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The annual depreciation expense for this car is $1,833.33.

Simply deduct the vehicle's current fair market value from the purchase price, less any applicable sales tax or fees, to determine how much value has been lost.

We must determine the total depreciation throughout the vehicle's useful life and divide it by the number of years to determine the annual depreciation expense:

Total depreciation = purchase price - resale value

= $28,500 - $17,500

= $11,000

Annual depreciation expense = total depreciation / useful life = $11,000 / 6 = $1,833.33 (rounded to the nearest hundredth)

Therefore, the annual depreciation expense for this car is $1,833.33.

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A graph of the line with slope 3 passing through the point (5, 3) is shown in the image attached below.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (5, 3) and a slope of 3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = 3(x - 5)  

y = 3x - 15 + 3

y = 3x - 12

In conclusion, we would use an online graphing calculator to plot the equation y = 3x - 12 as shown in the graph attached below.

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Answer:

The roots of the quadratic equation x² + 4x + 7 = 0 can be found using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 1, b = 4, and c = 7. Substituting these values into the formula, we get:

x = (-4 ± √(4² - 4(1)(7))) / 2(1)

x = (-4 ± √(16 - 28)) / 2

x = (-4 ± √(-12)) / 2

x = (-4 ± 2i√3) / 2

x = -2 ± i√3

Therefore, the roots of the equation x² + 4x + 7 = 0 are: A) 2 + i√3 or 2 - i√3.

So, the correct answer is A