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Ber [7]
3 years ago
11

1. Find the area of the composite figure to the nearest hundredth.

Mathematics
2 answers:
balandron [24]3 years ago
8 0

Answer:

  • 1. 745.31 mm²
  • 2. 426.96 km²

Step-by-step explanation:

#1

We can separate the figure into 3 parts and sum the areas.

<u>Semicircle with radius 12.5 mm:</u>

  • A = 1/2(πr²) = 1/2(3.14*12.5²) = 245.31 mm²

<u>Rectangle with sides 12.5 mm and its double size:</u>

  • A = 12.5*(2*12.5) = 312.5 mm²

<u>Triangle with height 12.5 mm and base 30 mm:</u>

  • A = 1/2*(55 - 2*12.5)*12.5 = 187.5 mm²

<u>Sum of the three:</u>

  • 245.31 + 312.5 + 187.5 = 745.31 mm²

#2

The shaded region is the difference of the areas of the triangle and the circle

<u>Triangle:</u>

  • A = 1/2*27*40 = 540 km²

<u>Circle:</u>

  • A = πr² = πd²/4 = 3.14*12²/4 = 113.04 km²

<u>Shaded region:</u>

  • 540  - 113.04 = 426.96 km²
Leto [7]3 years ago
6 0

Answer:

#1: 751.56 mm²

#2: 477 km²

Step-by-step explanation:

First I noted the semicircle on the left, which has a radius of 12.5 mm. The formula for finding the area of a semicircle is 1/2(πr²).

1/2(3.14 * (12.5)²)

<em>12.5 squared is 156.25.</em>

1/2(3.14 * 156.25)

<em>Multiply 3.14 by 156.25 to get 490.625.</em>

1/2(490.625)

<em>Divide 490.625 by 2 to get 245.3125.</em>

245.3125 mm² for the semicircle

Then, I split the rest of into a 12.5 by 25 rectangle and a 31 by 12.5 triangle.

(12.5 * 25) + 1/2(31 * 12.5)

<em>Multiply 12.5 by 25 to get 312.5.</em>

312.5 + 1/2(31 * 12.5)

<em>Multiply 31 by 12.5 to get 387.5.</em>

312.5 + 1/2(387.5)

<em>Multiply 1/2 by 387.5 to get 193.75</em>

312.5 + 193.75

<em>Add 312.5 and 193.75 to get 506.25.</em>

506.25 mm² for the rest of the figure.

Now add the two measures, and you have your answer for #1.

245.3125 + 506.25 = 751.5625 mm², which rounds to 751.56 mm².

The area of the composite figure is 751.56 mm².

Now for #2. First, find the area of the triangle.

1/2(40 * 27)

<em>Multiply 40 by 27 to get 1080.</em>

1/2(1080)

<em>Multiply 1/2 by 1080.</em>

590 km² for the triangle.

Now find the area of the circle.

3.14 * 6²

3.14 * 36

113.04 km² for the circle.

Now subtract the area of the circle from the area of the triangle.

590 - 113.04

476.96 km², which rounds to 477.0 km².

The area of the shaded region is 477 km².

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The algebraic equation which shows that the number of <em>x </em>people can go to the drive-in with one car for $19. 25 is,

5.50x+2.75=19.25

<h3>How to write algebraic equation?</h3>

Algebraic equation are the expression which consist the variables, coefficients of variables and constants.

The algebraic expression are used represent the general problem in the mathematical way to solve them.

Steps to write down the simple algebraic equation-

  • Identify all the factors of the expression.
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  • Use constant numbers for the fixed values.

The cost of going to a drive-in movie theater is $5.50 per person plus $2.75 per car. It has to create an algebraic equation that shows how many people can go to the drive-in with one car for $19. 25.

Suppose the total number of people in the car for drive-in movie theater is <em>x</em>. Thus, the cost of the<em> </em><em>x</em> person to watch the movie is,

C=5.50x

As the cost of one car is $2.75. Thus, the total cost of watching a movie by x person will be,

C=5.50x+2.75

Now, the total cost, drive-in with one car for $19. 25. This cost must be equal to the above expression for total cost. Therefore,

C=5.50x+2.75=19.25

Hence, the algebraic equation which shows that the number of <em>x </em>people can go to the drive-in with one car for $19. 25 is,

5.50x+2.75=19.25

Learn more about the algebraic expression here;

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If you go on desmos scientific calculator it makes it super easy

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Which values of P and Q result in an equation with no solutions?
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Try this solution/explanation:

<u>way 1</u>:

rule: for an equation where no roots P+Q=0. It means, Px-Qx=0, ⇔ x(P-Q)=0, ⇔ P=Q.

for answer 'D' P=Q=15.

<u>way 2</u>:

rule: if an equation of the line has a form y=kx+b, then y₁||y₂ if k₁=k₂. It means, for y₁=Px-45 || y₂=Qx+75, then P=Q. P=Q, if 'D' answer.

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Answer: (3, 18)

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