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2 years ago

How much of the circle is shaded? Write your answer as a fraction in simplest form.

Mathematics

1 answer:

Stels [109]2 years ago

8 0

Answer:

8/21

Step-by-step explanation:

Add up the fraction that is not shaded

2/7 + 1/3

Get a common denominator of 21

2/7 *3/3 + 1/3 *7/7

6/21 + 7/21

13/21

The entire circle is 21/21

Subtract the unshaded from the entire circle to get the shaded

21/21 -13/21

8/21

You might be interested in

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

Arturiano [62]

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.

5 0

3 years ago

6. Describe a pattern shown in this sequence, and use the pattern to find the next two terms.

nlexa [21]

Answer:

The pattern is that each time, 8 is added. The next 2 numbers are 47, 55.

Step-by-step explanation:

7+8=15

15+8=23

23+8=31

31+8=39

39+8=47

47+8=55

7 0

2 years ago

F(x) = 2x + 5 then f(?) = 5 2 1 0 3

Romashka [77]

Answer: answer is 0

Step-by-step explanation:

F(0)=2(0)+5

F(0)=0+5

F(0)=5

8 0

2 years ago

Read 2 more answers

In one school, half of all students who like math like science as well. Also, in that school, a third of all students who like s

Nimfa-mama [501]

Answer:

2/3

Step-by-step explanation:

If we have 'x' students who like math and 'y' students that like science, we can formulate that:

Half of x likes math and science, and also one third of y likes math and science, so:

(1/2) * x = (1/3) * y

x / y = (1/3) / (1/2)

x / y = (1/3) * 2 = 2/3

So the ratio of the number of students who like math to the number of students who like science is 2/3

3 0

3 years ago

Read 2 more answers

Consider the two expressions 4b(b+1) and (2b+7)(2b-8). Compare their values if b=-3, b=-2, and if b=10. Is it true that for an v

frutty [35]

Answer:

FIRST EXPRESSION:

- If $b=-3$ , the value of $4b(b+1)$ is $24$

- If $b=-2$ , the value of $4b(b+1)$ is $8$

- If $b=10$ , the value of $4b(b+1)$ is $440$

SECOND EXPRESSION:

- If $b=-3$ , the value of $(2b+7)(2b-8))$ is $-14$

- If $b=-2$ , the value of $(2b+7)(2b-8))$ is $-36$

- If $b=10$ , the value of $(2b+7)(2b-8))$ is $324$

Yes, for any value of "b" the value of the first expression is greater than the value of the second expression.

Step-by-step explanation:

Substitute the given values of "b" into each expression and evaluate.

- For the first expression $4b(b+1)$ , you get:

If $b=-3$ → $4(-3)(-3+1)=24$

If $b=-2$ → $4(-2)(-2+1)=8$

If $b=10$ → $4(10)(10+1)=440$

- For the second expression $(2b+7)(2b-8))$ , you get:

If $b=-3$ → $(2(-3)+7)(2(-3)-8)=-14$

If $b=-2$ → $(2(-2)+7)(2(-2)-8)=-36$

If $b=10$ → $(2(10)+7)(2(10)-8)=324$

You can observe that for any value of "b" the value of the first expression is greater than the value of the second expression.

7 0

3 years ago