So you are given that 45 people in the age range of 18 to 29 who voted make up 10% of the total voters.

And you also know that 30% of the voters are in the age range of 30-49. And you need to find out how many people aged 30-49 voted.

So 10% of the total make up 45 people.
That means for 30% of the total number people, there would be 45 x 3 people, or 135 people. Because 10% x 3 = 30%

So, great job! :D

3 0

3 years ago

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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

The length of a rectangle is 5 m less than twice the width, and the area is 33 m. Find the dimensions of the rectangle.

MrMuchimi

Check the picture below

it can't be -3... since is width unit, so it has to be the other

and recall that length = 2w - 5

7 0

3 years ago

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