If x = 7 units, y = 2 units, and h = 9 units, find the area of the trapezoid shown above using decomposition.
A.
81 square units
B.
99 square units
C.
63 square units
D.
72 square units

Answer and Step-by-step explanation:

The first step in solving for x is to square both sides.

8x = 4 + 2x

Now, subtract 2x from both sides.

6x = 4

Now, divide each side by 6.

x = [tex]\frac{4}{6} = \frac{2}{3}[/tex]

x = [tex]\frac{2}3}[/tex] is the answer.

#teamtrees #PAW (Plant And Water)

Answer:

The area of the shaded region is:

Step-by-step explanation:

First, we're gonna find the area of the whole rectangle and next we can subtract the area of the triangles in the corners, we use the next formula:

And we replace the measurements in the picture (32 ft and 16 ft):

Now, we must calculate the area of a triangle, this can be made by this formula:

We can replace the values we have in the picture (4 ft and 6 ft), then:

As you can see in the picture, we have to subtract two triangles with the same measurements, by this reason, we multiply the area of the triangle by two and we'll obtain the area we must subtract:

At last, we take the area of the whole rectangle and subtract the area of the triangles:

The area of the shaded region is 488 ft^2.

Answer:

the center of the data set is 7 so probably 7

7 is the best representation of the center of given data set.

The correct answer is an option (C).

"It is the average of the given numbers."

"I is the middle value of a sorted list of numbers."

For given question,

We have been given a dot plot of the number of letters in each students first name.

From the given dot plot,

We have data as 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 11

From above data,

the total number of students in the class are n = 30

We write 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 9, 10, 10, 11, 11, 11 as 3, (4 × 2), (5 × 4), (6 × 7), (7 × 7), (8 × 3), 9, (10 × 2), (11 × 3)

So, the mean of the above data would be,

[tex]\Rightarrow \bar{X}=\frac{3+ (4\times 2)+(5\times 4)+(6\times 7)+(7\times 7)+(8\times 3)+9+(10\times 2)+(11\times 3)}{30}\\\\\Rightarrow \bar{X}=\frac{208}{30}\\\\\Rightarrow \bar{X}=6.93\\\\\Rightarrow \bar{X}\approx 7[/tex]

From above data we can observe that there are two numbers in middle of the data 6 and 7.

So, the median would be,

[tex]\Rightarrow M=\frac{6+7}{2}\\\\\Rightarrow M=6.5\\\\\Rightarrow M\approx 7[/tex]

Therefore, 7 is the best representation of the center of given data set.

The correct answer is an option (C).

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Step-by-step explanation:

....djdjbeoehehoeebdnskeje

Answer:

C. 360°

Step-by-step explanation:

I calculated it logically

Answer:

Answer is C) 360°

Step-by-step explanation:

Answer:

Circumference is 18.84956

Area: 28.27433

Step-by-step explanation:

(Circumference) C=2πr=2·π·3≈ 18.84956

(Area) A=πr2=π·32≈ 28.27433

Answer:

C

Step-by-step explanation:

Answer:

120.08

Step-by-step explanation:

15.8 x 7.6

-> 120.08 [tex]m^2\\[/tex]

Answer:

um sorry if I'm wrong....C?

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

2 3/8=19/8=2.375

Answer:

C - 100

Step-by-step explanation:

9514 1404 393

Answer:

  C.  100°

Step-by-step explanation:

Consecutive (same-side) exterior angles are supplementary.

  ∠1 = 180° -∠7 = 180° -80°

  ∠1 = 100°

Answer:

40

Step-by-step explanation:

if 20% were Caesar and 20 divided by 5 is 4, then every four salads sold is five percent.

Answer: C

Step-by-step explanation:

5 × 3.5 = 17.5 > 16 .

Answer:

8

Step-by-step explanation:

ok so this is just the first one but i think you use a variable for what you are trying to find out, and well call this x and then u subtract the variable from the product of the rate and the amount, and once you have it, you multiply it but its own conjugate so then u use the binomial that you get to create a function, and you can graph it if you want, and u can use the apothem (the formula involves cos, so you might need a calculator) of the polygon created on your graph to find the domain, which you will then get the 4th root of, which is your answer. anyway, i believe this is what it is, but i may be wrong. hope this helps!

Answer:

This depends on how many cars or trucks there are, but there could be 8 trucks when there is 10 cars, or 20 trucks when there is 25 cars.

Answer:

y = 2(x - 2)² + 3      vertex form

y = 2x² - 8x + 11     standard form

Step-by-step explanation:

Vertex form

y = a(x - h)² + k

(h, k) = (2, 3)

y = a(x - 2)² + 3

To find "a" plug in the y-intercept (0, 11)

11 = a(-2)² + 3

11 = 4a + 3

Subtract 3 from both sides

8 = 4a

a = 2

y = 2(x - 2)² + 3

Expand

y = 2(x² - 4x + 4) + 3

y = 2x² - 8x + 11

Answer:

Cost of each eagle stamp = $0.25

Cost of each racoon stamp = $0.4

Step-by-step explanation:

Given:

Cost of 8 eagle stamp and 2 racoon stamp = $2.80

Cost of 3 eagle stamp and 4 racoon stamp = $2.35

Find:

Cost of each stamp

Computation:

Assume;

Cost of each eagle stamp = e

Cost of each racoon stamp = r

So,

8e + 2r = 2.80........... Eq 1

3e + 4r = 2.35 ........... Eq 2

Eq 1 x 2

16e + 4r = 5.6 .........Eq3

Eq 3 - Eq 2

13e = 3.25

e = 0.25

Cost of each eagle stamp = $0.25

8e + 2r = 2.80

8(0.25) + 2r = 2.80

2 + 2r = 2.80

r = 0.4

Cost of each racoon stamp = $0.4

Answer:

whats the number of the class.

what's my height

how many students from each school in this city loves football

what is the height of each student inmy class

how many servings of fruit did I eat each day thus month

Answer:

sin∅=3/4

Step-by-step explanation:

sin²x+cos²x=1

sin²x+(√7/4)²=1

sin²x+7/16=1

sin²x=9/16

sinx=3/4

Therefore, sin∅=3/4

Answer:

pretty sure the answer is electrons  so D

Step-by-step explanation:

Electrons are particles that surround the nucleus of an atom like a cloud

Answer:

No

Step-by-step explanation:

Two triangles are  similar if their corresponding angles are congruent and the corresponding sides are in proportion  They  are the same shape, but not necessarily the same size

Triangle ABC  54 +68 +  58 = 180

Triangle EFG    68 +63 +49 = 180

In this case their corresponding angles are nor congruent

Answer:

D

Step-by-step explanation:

Find the slope by picking two ordered pairs in the table and using the slope formula( y2-y1/x2-x1) to get the slope. The smallest numbers are easiest to work with. (-1,1), (0,-2)

-2-1/0-(-1) = 3/0+1 = -3/1 = m=-3

Use one of the points you used and plug in the x and y values of the ordered pair into the equation with the slope to find your b( y-intercept). (0,-2)

-2= -3(0) +b

-2= 0+b

b=-2

The final equation will only have your slope and b( y-intercept). That should be your answer. Hope this helps!

Final Equation: y=-3x-2

Answer:

x=48

Step-by-step explanation:

You start with the values of 4 and 16. Figure out how many times 4 goes into 16, which is 4. (4*4=16)

Now, since 4 is multiplied by itself to reach the value of 16, 12 will also be multiplied by 4 to give you the value of x.

Answer:

Step-by-step explanation:

x-4/4=x/6+1

x-4 =4/6x+4

x-2/3x =8

1/3x =8

x=24

Answer: B

Step-by-step explanation: I hope I am good at math if not sorry

The combination of 8 large cabinets and 8 small cabinets maximizes the objective function, resulting in a value of 640. Option b is correct.

To maximize the objective function P = 50x + 30y, where x represents the number of large cabinets and y represents the number of small cabinets.

Need to determine the combination of x and y that results in the highest value for P.

For 0 large and 10 small:

P = 50(0) + 30(10)

= 0 + 300

= 300

For 8 large and 8 small:

P = 50(8) + 30(8)

= 400 + 240

= 640

For 4 large and 4 small:

P = 50(4) + 30(4)

= 200 + 120

= 320

For 4 large and 5 small:

P = 50(4) + 30(5)

= 200 + 150

= 350

Based on these calculations, 8 large cabinets and 8 small cabinets maximizes the objective function, resulting in a value of 640.

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Answer:

25 g

Step-by-step explanation:

0.1 kg can be written as 100 grams

& 75 g

while 1 kg is 1000 grams

so difference:-

(100- 75 ) grams

= 25 g

The difference between 0.1 kg and 75 g is 25 grams. To find the difference between 0.1 kg and 75g, you need to make sure both quantities have the same unit.

Since 1 kg is equal to 1000 g, you can convert 0.1 kg to grams:

0.1 kg = 0.1 * 1000 g = 100 g

Now, the two quantities are in the same unit:

0.1 kg - 75 g = 100 g - 75 g = 25 g

So, the difference between 0.1 kg and 75 g is 25 grams.

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