Use the diagram to find the measures of the lengths of the
sides. The perimeter of the trapezoid on the right is 67
inches.

The measure of angle FBE in the figure is 40 degrees

The triangles represent the given parameter

This means that we make use of the triangles (the big and the small triangles) in our computation

Also, from the question, we have the following known parameters

CD = DA

AE = EB

FDE = 40 degrees

The congruent side equations CD = DA and AE = EB imply that the following side lengths are congruent

So, we have the following equations

DE = FB

DF = EB

This also means that DFBE is a parallelogram

The opposite angles of a parallelogram are congruent

So, we have

angle FBE = angle FDE

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

angle FBE = 40 degrees

Hence, the angle is 40 degrees

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answer: 77

Step-by-step explanation:

7×11=77

sorry if I'm wrong

Answer:

fijatebie nl aperguntaa

Step-by-step explanation:

The coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

Translation on the coordinate plane is sliding a point or figure in any direction without any changes in size or shape.

During translation, the coordinates of the vertices of a figure or point change, and they slide left or right, up, or down without changing size or shape.

Given the question above, we need to find the coordinates of the vertices for the image of the pre image that are translated 4 units right.

So,

\(\rightarrow\sf \boxed{\boxed{-5+4=1=\bold{(-1,2)}}}\)

\(\rightarrow\sf \boxed{\boxed{1+4=5=\bold{(5,3)}}}\)

\(\rightarrow\sf \boxed{\boxed{-3+4=1=\bold{(1,0)}}}\)

Thus, the coordinates of the vertices for the image of the pre image is translated 4 units right are: ’(-1, 2), B’(5, 3), and C’(1, 0).

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Given:-

\( \: \)

Solution:-

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

━━━━━━━━━━━━━━━━━━━━━━━━

Hope it helps! :)

Answer:

Step-by-step explanation:

The segment sum theorem tells you the whole is the sum of the parts. That can be used to write an equation for y.

  RS +ST = RT

  (5y +5) +(4y +8) = 67

Simplifying, we get ...

  9y +13 = 67

  9y = 54 . . . . . . . . subtract 13

  y = 6 . . . . . . . . . divide by 9

RS = 5y +5 = 5·6 +5 = 35

ST = 4y +8 = 4·6 +8 = 32

The values of interest are ...

The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

We have to given that,

Functions are defined as,

⇒ s (x) = 2x²

⇒ f (x) = 3x

Now, We can find the value of (s - f) (- 7) is,

⇒ (s - f) (- 7)

⇒ s (- 7) - f (- 7)

⇒ 2 (- 7)² - (3 × - 7)

⇒ 2×49 + 21

⇒ 98 + 21

⇒ 119

Therefore, The value of expression (s - f) (- 7) would be,

⇒ (s - f) (- 7)  = 119

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An equation for the linear function is f(x) = x - 3.

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

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At data point (-2, -5), a linear function in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - (-5) = (-1 - (-5))/(4 - (-2))(x - (-2))

y + 5 = (1 + 5)/(4 + 2)(x + 2)

y + 5 = 6/6(x + 2)

y = x + 2 - 5

f(x) = y = x - 3

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Answer in Picture :)

Answer: 2048

Step-by-step explanation: 1. Write the exponential growth model.

The population of the town doubles every year, so the growth factor is 2. The initial population is 112, so the equation is: P(t) = 112(2)^t where P(t) is the population in year t and t is the number of years since 2014.

2. Estimate the population of the town in 2023. To estimate the population of the town in 2023, we can set t=9, since 2023 is 9 years after 2014. Plugging this into the equation, we get: P(9) = 112(2)^9 = 2048

Therefore, the estimated population of the town in 2023 is 2048.

$0.09 will he have left after buying the greatest number of sunglasses and beach balls.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Model Inequality:  4x + 2.5x ≥  45.

Now, solving for inequality

4x + 2.5x ≥  45.

(4 + 2.5)x ≥ 45

6.5x ≥ 45

x ≥ 45/ 6.5

x≥ 6.92

x≥ 7 (approx)

So, the max price for sunglasses and beach balls = 4(6.92)+ 2.5(6.92)

                                                                                   = $44.91

Thus, the left money is = 45- 44.91 = $ 0.09

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The inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  

w + l ≥ 17.

What is inequality?

In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.

Given:

Mackenzie is working two summer jobs, washing cars and landscaping. She must work at least 17 hours altogether between both jobs in a given week.

Total number of hours is w + l and it should be at least 17 hours, (equal to 17 or greater).

We can set inequality as:

w + l ≥ 17

Hence, the inequality that would represent the possible values for the number of hours washing cars, w, and the number of hours landscaping, is  w + l ≥ 17.

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Answer:

1/2 on each cake

Step-by-step explanation:

Answer:

1\2

Step-by-step explanation:

The surface area of the rectangular prism is 396 square inches

He will need 504 tlles

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

7 in by 12 in by 6 in

The surface area of the rectangular prism is calculated as

Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)

Evaluate

Area = 396

Hence, the area is 396 square inches

The number of tiles is 7 * 12 * 6 = 504

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Question

wants to tile the surface of a rectangular storage case that is 7 inches​ long, 12 inches​ wide, and 6 inches tall. If he uses all green​ tiles, how many tiles will he​ need?

Answer:

Step-by-step explanation:

d=80 ft

r=80/2=40 ft

volume of cylinder=π r²h,where h is height or depth of cylinder.

π×40²×h=825,000

πh=825,000/40²=4125/8

h=4125/(8π)≈164.1285≈164.13 ft

The depth of water in the reservoir is approximately 21.92 feet.

To find the depth of water in the reservoir, we can use the formula for the volume of a cylinder:

Volume = π * r^2 * h

Where:

Volume is the total volume of water in the reservoir (in gallons),

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

r is the radius of the reservoir (half of the diameter), and

h is the depth of water in the reservoir (in feet).

Given:

Diameter = 80 feet

Volume = 825,000 gallons

We first need to calculate the radius (r) of the reservoir:

Radius (r) = Diameter / 2 = 80 feet / 2 = 40 feet

Now, we can convert the volume from gallons to cubic feet because we need the measurements to b²e in consistent units:

1 gallon ≈ 0.13368 cubic feet

Volume (in cubic feet) = 825,000 gallons * 0.13368 cubic feet/gallon ≈ 110,127 cubic feet

Now, we can find the depth (h) using the formula:

110,127 cubic feet = π * (40 feet)² * h

Solving for h:

h = 110,127 cubic feet / (π * 40 feet)² ≈ 110,127 cubic feet / 5026.5482 square feet ≈ 21.92 feet

Therefore, the depth of water in the reservoir is approximately 21.92 feet.

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The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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The transformations of f(x) are (a) a horizontal shrink by a factor of 1/4,

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

f(x) = x²

g(x) = (4x)²

Mathematically, these equations can be represented as

g(x) = f(4x)

The above equations implies that, we have the transformation to be:

The 4x implies that the function f(x) is horizontally shrunk by a factor of 1/4

Hence, the transformed function is (a)

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It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.

To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9

In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:

1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108

Unfortunately, the sum obtained from this expression is 108, not 100 as required.

It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.

Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.

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The histogram appears to roughly estimate a normal distribution. The frequencies normally increase to a maximum and then​ decrease, and the histogram is symmetric.

The Graph of Normal Distribution is bell-shaped. Here the value of y is less for the lower value of x and then the value of y is increased for a larger value of x, but after some time value of y again getting decreases as the value of x increases.

For the Histogram to appear to be a normal distribution, the graph of the histogram must have the same nature. Thus, option B is only the correct option.

The histogram is made up of many columns and bars that are vertical with no gaps between bars with different labels of numeric data of different heights showing the size of the group of different labels.

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The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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Step-by-step explanation:

Fraction = 280% / 100%

= 280/100 = 14/5 or 2 4/5.

Answer:

2⅘

Step-by-step explanation:

200% = 2

80% = ⅘

2+⅘ = 2⅘

I hope this helps you :)

Answer:

3.78541 liters (sorry I'm horrible at rounding)

The quotient when 480 is divided by -60 is 8.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

The numbers given are 480 and -60.

Both are in opposite signs, that is one negative and other positive.

So the quotient will be negative.

Now divide 480 by 60.

Since both of the numbers contain 0 at the end, cancel it.

Then it becomes 48 divided by 6.

48 / 6 = 8

Hence the quotient is 8.

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We know that

• Pure acid is added to a 5% acid solution.

• To obtain 95 liters of 28% solution.

Based on the given information, we can define the following formula

Where 0.05 is 5% and 0.28 is 28%.

Solving for x, we have

Now, to find the liters of 100% pure acid, we use the following equation.

The half-life of the particular compound is approximately 9.4 days. (Correct choice: B)

The statement indicates the decay function of a particular compound, which is an exponential function of the form:

y = a · exp(- λ · t)

Where:

The half-life of the particular compound is determined by the following expression:

t = ㏑ 2 / λ

Where t is the half-life.

If we know that λ = 0.0736, then the half-life of the particular compound is:

t = ㏑ 2 / 0.0736

t = 9.4 days

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The measure of the angle m∠ZYX of the trapezoid is equal to 139°

A trapezoid is a quadrilateral with two parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs. The adjacent angles of the trapezium are supplementary, so their sum is equal to 180°.

3x + 19 + x + 1 = 180°

4x + 20 = 180°

4x = 180 - 20 {collect like terms}

4x = 160

x = 160/4 {divide through by 4}

x = 40

m∠ZYX = 3(40) + 19 = 139°.

WXYZ is a trapezoid. Equation used to solve for x is (3x + 19) + (x + 1) = 180° because the angles m∠XYZ and m∠WXY are adjacent angles.

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The t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.

How are the degrees of freedom determined?

Hence, the t distribution is a family of similar probability distributions, with each individual distribution depending on a parameter known as the degrees of freedom.

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we know that

The formula to calculate the distance between two points is equal to

Find out the coordinates of point Q and point L

Looking at the graph

Q is (5,3) and L is (8,5)

substitute the given values in the formula