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3 years ago

What is the circumference os the circle shown below? (Round your answer to the nearest tenth.)

Mathematics

2 answers:

sdas [7]3 years ago

7 0

Answer:

Option C(66.0)

Step-by-step explanation:

C = 2πr

C=Circumference

π=3.14(pi)

r=radius

C=2x3.14x10.5

3.14x10.5=32.97

32.97x2=65.94

65.94 rounded to nearest tenth is 65.9, so basically 66.0.

likoan [24]3 years ago

4 0

Answer: C. 66.0

Step 1: Write an equation

To start off, we will need to write an equation. Before we solve, let’s write the formula for a circumference.

C= 2πr

Step 2: Substitute numbers

Now that we have the equation, we need to substitute the information shown in the shape. Let’s substitute r in the equation with 10.5. We will do this because this is the radius of the circle. We will not be using 14.8 since it does not go to the center of the circle. Let’s replace r now.

C= 2πr
C= 2π10.5

Step 3: Solve

Let’s solve for the circumference using the equation we have created. To make it easier, we will add a multiplication sign in between each number before we solve.

C= 2π10.5
C= 2 × π × 10.5
C≈ 65.97

The circumference is approximately 65.97. Since we are asked to round to the nearest tenth, the circumference will need to be rounded up. Let’s do this now.

C≈ 65.97
C≈ 66.0

This is your answer. Hope this helps! Comment below for more questions.

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3 years ago

Solve the system by substitution(show your work)

Gnesinka [82]

Answer:

x = 3 , y = 6 , z = -1

Step-by-step explanation using substitution:

Solve the following system:

{-x - y - z = -8

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

In the first equation, look to solve for x:

{-x - y - z = -8

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

Add y + z to both sides:

{-x = -8 + y + z

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

Multiply both sides by -1:

{x = 8 - y - z

-4 x + 4 y + 5 z = 7

2 x + 2 z = 4

Substitute x = 8 - y - z into the second and third equations:

{x = 8 - y - z

4 y - 4 (8 - y - z) + 5 z = 7

2 (8 - y - z) + 2 z = 4

4 y - 4 (8 - y - z) + 5 z = 4 y + (-32 + 4 y + 4 z) + 5 z = -32 + 8 y + 9 z:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

2 (8 - y - z) + 2 z = 4

2 (8 - y - z) + 2 z = (16 - 2 y - 2 z) + 2 z = 16 - 2 y:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

16 - 2 y = 4

In the third equation, look to solve for y:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

16 - 2 y = 4

Subtract 16 from both sides:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

-2 y = -12

Divide both sides by -2:

{x = 8 - y - z

-32 + 8 y + 9 z = 7

y = 6

Substitute y = 6 into the second equation:

{x = 8 - y - z

9 z + 16 = 7

y = 6

In the second equation, look to solve for z:

{x = 8 - y - z

9 z + 16 = 7

y = 6

Subtract 16 from both sides:

{x = 8 - y - z

9 z = -9

y = 6

Divide both sides by 9:

{x = 8 - y - z

z = -1

y = 6

Substitute z = -1 into the first equation:

{x = 9 - y

z = -1

y = 6

Substitute y = 6 into the first equation:

{x = 3

z = -1

y = 6

Collect results in alphabetical order:

Answer: {x = 3 , y = 6 , z = -1

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3 years ago

Use the graph of △ABC with midsegments DE, EF and DF. Show that EF is parallel to AC and that EF=1/2 AC

Vinvika [58]

According to the midsegment theorem, the midsegments are parallel to

and half the length of the opposite side.

The completed statement are as follows;

Because the slopes of $\overline{EF}$ and $\overline{AC}$ are both -4, $\overline{EF}$ ║ $\overline{AC}$

EF = $\underline{\sqrt{17}}$ and AC = $\underline{2 \cdot \sqrt{17} }$

Because $\underline{\sqrt{17} }$ = $\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17} }$ , $EF = \frac{1}{2} \cdot AC$

Reasons:

From the given graph of ΔABC, we have;

Coordinates of the points A, B, and C are; A(-5, 2), B(1, -2), and C(-3, -6)

The coordinates of the point D and E on $\mathbf{\overline{DE}}$ are; D(-4, -2), and E(-2, 0)

The coordinates of the point F is; F(-1, -4)

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\displaystyle Slope \ of \ line \ \overline{AC} = \mathbf{\frac{(-6) - 2}{-3 - (-5)} = \frac{-8}{2}} = -4$

$\displaystyle Slope \ of \ line \ \overline{EF} = \frac{0 - (-4)}{-2 - (-1)} = \frac{4}{-1} = -4$

$Length \ of \ segment,\ l = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}$

Length of EF = √((-1 - (-2))² + (-4 - 0)²) = √(17)

Length of AC = √((-3 - (-5))² + (-6 - 2)²) = √(4 × 17) = 2·√(17)

Therefore, we have;

Because the slope of $\mathbf{\overline {EF}}$ and $\mathbf{\overline {AC}}$ are both , -4, $\overline {EF}$ ║ $\overline {AC}$ . EF = $\underline{\sqrt{17}}$ , and AC

= $\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}$ ,. Because $\underline{\sqrt{17}}$ = $\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}$ , $EF =\mathbf{ \frac{1}{2} AC}$