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Nezavi [6.7K]
2 years ago
7

the circumference of a circle is 11pi inches. what is the area, in square inches, of the circle? express in terms of pi.

Mathematics
2 answers:
zmey [24]2 years ago
8 0
Circumference = 2 * pi * r, where r is the radius
For this circle, the circumference is 11pi, so 11pi=2*pi*radius. Divide both sides by 2pi and you get r is = to 5.5 inches.

Area of a circle is pi*r^2. Since we just saw that r = 5.5 inches, the circle has an area of 5.5 inches * 5.5 inches * pi or 30.25 pi inches squared.
Tomtit [17]2 years ago
8 0

Answer:

30.25 pi

Step-by-step explanation:

The radius is 5.5 cm. So that's the answer.

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Two-thirds of a class are boys. If there are 12 boys, then<br> how many girls are in the class?
son4ous [18]

Step-by-step explanation:

so 2/3 OF the class are boys...

***REMEMBER IN MATHEMATICS, ^OF^ IS USED TO SAY MULTPLICATION***

so 2/3 OF class(x) are boys and there are 12 boys...

so 2/3 * x = 12

12 / (2/3) = x

to solve use the Keep, Change, Flip method

Keep 12, change / to multiplication, flip 2/3 to 3/2

it becomes 12 * 3/2 and to solve easier 12 is same thing as 12/1

12/1 * 3/2

Multiply across (numerator by numerator and denominator by denominator)

(12*3) / (1*2) = 36 / 2

Simplify

18

So the class has 18 students, and 2/3 of boys (12 of the students)

we can solve for how many girls are in the class

Depending on how your teacher wants to see the work:

either 18 - 12 = 6

or 1/3 * 18 which we rewrite as 1/3 * 18/1 = (1*18)/(3*1) which is 18/3... simplified it is  6

There are 6 girls in the class.

Hope this helps! :)

6 0
2 years ago
Fill in the missing work and justification for step 3 when solving 2(x + 1) = 10.
kirill115 [55]

Answer:

2(x + 1) = 10

x = 4

Step-by-step explanation:

Given:

2(x + 1) = 10

Solution:

Apply Distributive property

A*(B+C) = (A*B) + (A*C)

This means multiply 2 with x and 1

2*(x+1) = (2*x) + (2*1)

2x + 2 = 10      

Use Subtraction property of equality

A = B, then A - C = B - C

Subtracting 2 from both sides:

2x + 2 - 2 = 10 - 2

2x = 8                  Step 3

Use Division property of equality

It state that if you divide both sides of an equation by same nonzero number then the sides remain equal

Dividing both sides by 2

2x/2 = 8/2

x = 4

This means value of x is 4

Another method to solve this equation is:

2(x+1)=10  

Use Distributive property

A*(B+C) = (A*B) + (A*C)

2*(x+1) = (2*x) + (2*1)  

2*(x+1) = 2x + 2  

Use commutative property

A + (-B) = (-B) + A

2x + 2 + (-2) = 2x + (-2) + 2

2x + 2 + (-2) = 10 + (-2)

2x + 2 - 2 = 10-2  

2x = 8  

Using division property

AX = B  

AX / A = B / A

So

X = B/A

This becomes:

2x = 8

2x = 8.

Divide both sides by 2  

2x / 2 = 8 / 2  

x = 4

3 0
3 years ago
Given that 1ST GRAPH and 2N GRAPH, which theorem or postulate proves ΔPQR 3RD GRAPH ΔRST?
Monica [59]
HL congruence theorem is the answer.

Hope this helps :)
7 0
3 years ago
The sum of 3 consecutive even
aleksandrvk [35]

Answer:

The variable representation is x, x+2 and x+4 for this sequence.

Step-by-step explanation:

Given that:

The sum of 3 consecutive even numbers is 78.

Let,

The first even number is represented by x.

As the numbers are consecutive, thus,

First even number = x

Second even number = x+2

Third even number = x+4

Hence,

The variable representation is x, x+2 and x+4 for this sequence.

7 0
2 years ago
Which interval is the solution set to 0.35x - 4.8 &lt; 5.2 -0.9x?
8_murik_8 [283]

Answer:  (-\infty, 8)

Step-by-step explanation:

Given the following inequality:

0.35x - 4.8 < 5.2 -0.9x

You need to solve for "x" in order to find the solution.

The steps are:

1. Add 0.9x to both sides of the inequality:

0.35x - 4.8+0.9x < 5.2 -0.9x+0.9x\\\\1.25x-4.8

2. Add 4.8 to both sides:

1.25x-4.8+4.8

3. Divide both sides by 1.25:

\frac{1.25x}{1.25}

Notice that "x" is  less than 8. This indicates that 8 is not included in the solution and you must use parentheses.

The solution in Interval notation is:

(-\infty, 8)

8 0
3 years ago
Read 2 more answers
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