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horrorfan [7]
3 years ago
15

This figure is made up of a quadrilateral and a semicircle.

Mathematics
1 answer:
Arturiano [62]3 years ago
5 0

Answer:

The correct option is B. The area of the figure is 40.4 units².

Step-by-step explanation:

The line AB divides the figure in two parts one is a rectangle and another is semicircle.

The distance formula is

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

The length of AB is

AB=\sqrt{(2+3)^2+(4-2)^2}=\sqrt{25+4}=\sqrt{29}

The length of AD is

AD=\sqrt{(-1+3)^2+(-3-2)^2}=\sqrt{4+25}=\sqrt{29}

Since AB=AD, therefore ABCD is a square. The area of the of square is

A_1=a\times a=\sqrt{29}\times \sqrt{29} =29

The area of square is 29 units².

The area of a semicircle is

A_2=\frac{\pi}{2}r^2

Since AB is the diameter of the semicircle, therefore the radius of the semicircle is

r=\frac{d}{2}=\frac{\sqrt{29}}{2}

The area of the semicircle is

A_2=\frac{3.14}{2}(\frac{\sqrt{29}}{2})^2=40.3825

The area of the figure is

A=A_1+A_2=29+11.2825=40.3825\approx 40.4

Therefore the area of the figure is 40.4 units². Option B is correct.

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Two points located on are J(1,-4) and K(-2,8). What is the slope of ?
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Answer:

-4

Step-by-step explanation:

The slope is usually a function of the differences in y divided by the differences in x, and it can be described in the following equation,

Slope = \frac{y_{1} - y_{2} }{x{1} - x{2}}     (1)

We can select any of the two points to be our first point, let's say, J(1,-4) is point 1, so J (x1,y1). In other words, x_1 = 1 and y_1 = -4 and by the same way, for K(-2,8). Therefore, x_2 = -2 while y_2 = 8. By substituting these values in equation 1, we can deduce the following

slope = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - (-4)}{-2 - 1} = \frac{8 + 4}{-2 - 1} = \frac{12}{-3} = -4

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2 years ago
Sullivan’s boss has 5 eyes total. Three of his eyes are smaller than the other two. What percentage of his eyes are larger?
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Answer:

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Step-by-step explanation:

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2/5=x/100

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you'll get: 5x=200

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A restaurant wants to study how well it's salads sell. the circle graph shows the sales over the past few days. If 15 of the salads sold were caesar salads, how many total salads did the restaurant sell Caesar 30% Garden 58% Cobb 12%?

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3 years ago
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Round 3,989.23655 to the nearest thousandth
inysia [295]
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3 years ago
The average of your first 6 tests is 82. If your test average after your seventh test is an 80.5, what did you score on the seve
mart [117]
So average is  of the first 6 tests is 82   well that means 

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so now let do some cross multiplliying 

test1 + test2 + test3 + test 4 + test5 +test6 = 82*6

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(492 + test7 )/7 = 80.5

test7 = (80.5*7)-492 = 71.5 



7 0
3 years ago
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