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3 years ago

Use the area to find the radius. If you could include steps that’ll be very helpful :)

Mathematics

1 answer:

Marizza181 [45]3 years ago

5 0

Answer:

Radius = 13 m

Step-by-step explanation:

Formula for area of circle is given as:

$A = \pi {r}^{2} \\ \\ \therefore \: 169\pi \: = \pi {r}^{2} \\ \\ \therefore \: {r}^{2} = \frac{169\pi }{\pi} \\ \\ \therefore \: {r}^{2} = 169 \\ \\ \therefore \: {r} = \pm \sqrt{169} \\ \\\therefore \: r = \pm \: 13 \: m \\ \\ \because \: radius \: of \: a \: circle \: can \: not \: be \: a \: negative \: \\quantity \\ \\ \huge \red{ \boxed{\therefore \: r = 13 \: m }}$

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Put the following equation of a line into slope-intercept form, reducing all fractions.

Reil [10]

Answer:

y = (-1/5)x - 9

Step-by-step explanation:

15y = -3x - 135

Divide both sides by 15

y = (-1/5)x - 9

3 0

4 years ago

Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ

In-s [12.5K]

PART A

The equation of the parabola in vertex form is given by the formula,

$y - k = a {(x - h)}^{2}$

where

$(h,k)=(1,-2)$

is the vertex of the parabola.

We substitute these values to obtain,

$y + 2 = a {(x - 1)}^{2}$

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.

$6 + 2 = a {(3 - 1)}^{2}$

$8= a {(2)}^{2}$

$8=4a$

$a = 2$
Hence the equation of the parabola in vertex form is

$y + 2 = 2 {(x - 1)}^{2}$

PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

$y + 2 = 2{(x - 1)}^{2}$

This implies that

$y + 2 = 2(x - 1)(x - 1)$

We expand to obtain,

$y + 2 = 2( {x}^{2} - 2x + 1)$

This will give us,

$y + 2 = 2 {x}^{2} - 4x + 2$

$y = {x}^{2} - 4x$

This equation is now in the form,

$y = a {x}^{2} + bx + c$
where

$a=1,b=-4,c=0$

This is the standard form

7 0

3 years ago

What's the perimeter of (-9,8) (-9,16) and (-17,8)

TiliK225 [7]

Answer:

16 + sqrt(128)

Step-by-step explanation:

find the lengths of all 3 sides:

the side from (-9,8) to (-9,16) will be 16-8=8 (x stays constant)

The side from (-9,8) to (-17,8) is 8 (-9- (-17)=8)

The side from (-9,16) to (-17,8) will be found from the distance formula

d=sqrt((-17-9)^2 + (8-16)^2))

= sqrt(128)

So the perimeter will be these 3 numbers added together

P=sqrt(128) + 8 + 8

= 16 + sqrt(128)

which can simplify to:

= 16 + 4sqrt(8)

= 16 + 8sqrt(2) = 8+ sqrt(2)

4 0

3 years ago

What is the approximate value of x in the equation below? log Subscript 5 Baseline 15 = x + 3

Lilit [14]

12=x ! Just subtract 3 from both sides.

8 0

3 years ago

Solve for x if both sides are similar

kodGreya [7K]

Answer:

x = 12

Step-by-step explanation:

we can put this is a proportion: (new side 1) / (old side 1) = (new side 2) / (old side 2)

so in this case, 18 would be old side 1, x would be new side 1

12 would be old side 2, and 8 would be new side 2

plug these in: x/18 = 8/12

cross multiply 18 and 8: x = 144/12

now simplify: x = 12

4 0

3 years ago

Read 2 more answers