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Dmitry [639]
3 years ago
7

What is the area of this composite shape? Enter your answer in the box. _in²

Mathematics
1 answer:
LuckyWell [14K]3 years ago
3 0

The area of the composite figure is 40 in^2

Explanation:

From the given figure, we can see that the area of the composite figure = area of the rectangle + area of the triangle.

Area of the rectangle (A_1):

The formula is given by

A_1=length\times width

where length = 5 and width = 5

Substituting, we have,

A_1=7\times 5=35 in^{2}

Thus, the area of the rectangle = 35 i n^{2}

Area of the triangle (A_2):

The formula is given by

A_2=\frac{1}{2} bh

where b=5-3=2 i n

and h=12-7=5 \text { in }

Substituting, we have,

A_2=\frac{1}{2} (2)(5)\\A_2=5 in ^{2}

Thus, the area of the triangle = 5in ^{2}

Area of the composite figure = Area of the rectangle + area of the triangle

Area of the composite figure = 35 i n^{2}+5 i n^{2}=40 i n^{2}

Thus, the area of the composite figure is 40 in^2

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There are 20 students on the school's student council. A special homecoming dance committee is to be formed by randomly selectin
AysviL [449]

You can choose from 20 students for the first student, 19 for the second, 18 for the third, ..., 14 for the seventh student.

That gives you 20 * 19 * 18 * 17 * 16 * 15 * 14.

That number would allow you to write the students in different order. Since order here does not matter, any group with the same students in any order is the same group, you need to divide by the number of way you can order 7 items. Divide by 7 * 6 * 5 * 4 * 3 * 2 * 1

(20 * 19 * 18 * 17 * 16 * 15 * 14)/(7 * 6 * 5 * 4 * 3 * 2 * 1) = 77,520

Answer: 77,520

8 0
3 years ago
Read 2 more answers
Which of the following values are in the range of the function graphed below
expeople1 [14]

Answer:

Range of the given function = -4

Step-by-step explanation:

Range is the set of output values.

In a graph, the set of x-values of the function is know as domain and the set of y-values of the function is known as range.

In the graph red line represents the function.

From the given graph it is clear that the function is defined from x=-1 to x=4.

For each value of x the y-value is -4.

Hence, the range of the function is -4.

4 0
3 years ago
PLZ HELP !! Which of the points (s, t) is not one of the vertices of the shaded region of the
stira [4]

Answer:

A(0,10)

Step-by-step explanation:

Given the 4 inequalities:

s ≥ 12 - 0.5t (1)

s ≥ 10 -t (2)

s ≤ 20-t (3)

s ≥ 0

t ≥ 0

Let analyse all 4 possible answer:

  • A(0, 10)

Let substitute this point into (1) we have: 10 ≥ 12 -0.5*0 Wrong

We do not choose A

  • B (0, 20)

Let substitute this point into (1) we have: 20 ≥ 12 -0.5*0  True

Let substitute this point into (2) we have: 20 ≥ 10 - 0 True

Let substitute this point into (3) we have: 20 ≤ 20 - 0 True

We choose B as the vertex

  • C. (4, 16)

Let substitute this point into (1) we have: 16 ≥ 12 -0.5*4  True

Let substitute this point into (2) we have: 16 ≥ 10 - 4 True

Let substitute this point into (3) we have: 16 ≤ 20 - 4 True

We choose C as the vertex

  • D. (16,4)

Let substitute this point into (1) we have: 4 ≥ 12 -0.5*16 True

Let substitute this point into (2) we have: 4 ≥ 10 - 16 True

Let substitute this point into (3) we have: 4 ≤ 20 - 16 True

We choose B as the vertex

Hence, the point A(0,10)  is not one of the vertices of the shaded region of the  set of inequalities.

3 0
3 years ago
I need to know the answers
e-lub [12.9K]
Is that your test or homework
6 0
3 years ago
The two pyramids are similar. Find the volume of the smaller pyramid. Round your answer to the nearest hundredth.
mihalych1998 [28]

Answer:

A) 5.12mm³

Step-by-step explanation:

Step 1

Find the volume of the bigger pyramid

This is a triangular based pyramid.

The formula to use is given as Volume of Pyramid =

1/3 × Area of the triangle × Height

Area of the triangle = 1/2 × 3 mm × 4mm = 6mm²

Volume of the large pyramid = 1/3 × 6mm² × 5mm

= 10mm³

We are given the length of the small pyramid as 4mm

We would be using was is known as scale factor to find the volume of the small pyramid

The scale factor k = (Height of the small pyramid)³/ (Height of the Large pyramid)³

k = 4³/5³

k = Volume of small pyramid/ Volume of large pyramid

Volume of small pyramid = X

Volume of large pyramid = 10mm³

Hence,

4³/5³ = X/10

Cross Multiply

= 4³ × 10 = 5³ × X

X = (4³ × 10)/ 5³

X = 5.12mm³

5 0
3 years ago
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