Ask question

Ask question

All categories

3 years ago

9

To make a punch Anna adds 8 ounces of apple juice for every 4 ounces of orange juice if she uses 32 ounces of apple juice which

proportion can she use to find the number of ounces of orange juice x she should add to make the punch

1 answer:

Veronika [31]3 years ago

8 0

Answer:

x= 16 ounces

Step-by-step explanation:

Apple juice: Orange Juice

8:4 = 2:1

For every 2 parts of Apple Juice, 1 part of Orange Juice is used.

So 32 ounces would be equivalent to 2 parts..

This means the proportion of Orange Juice needed would be 16 ounces.

You might be interested in

I need the answer to this problem

chubhunter [2.5K]

After making six monthly payments on her car loan, Thomas's savings account will be lower.

6 0

3 years ago

The quadratic equation 8x²+12x-14 has two real roots. What is the sum of the squares of these roots?

mars1129 [50]

Answer:

The real roots are

$x=\frac{(-3+\sqrt{37})}{4}$ and $x=\frac{(-3-\sqrt{37})}{4}$

The sum of the squares of these roots is $\frac{-3}{2}$

Step-by-step explanation:

The given quadratic equation is $8x^2+12x-14$ has two real roots.

To find the roots .

$8x^2+12x-14=0$

Dividing the above equation by 2

$\frac{1}{2}(8x^2+12x-14)=\frac{0}{2}$

$4x^2+6x-7=0$

For quadratic equation $ax^2+bx+c=0$ the solution is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Where a and b are coefficents of $x^2$ and x respectively, c is a constant.

For given quadratic equation

a=4, b=6, c=-7

$x=\frac{-6\pm\sqrt{6^2-4(4)(-7)}}{2(4)}$

$=\frac{-6\pm\sqrt{36+112}}{8}$

$=\frac{-6\pm\sqrt{148}}{8}$

$=\frac{-6\pm\sqrt{37\times 4}}{8}$

$=\frac{-6\pm\sqrt{37}\times\sqrt{4}}{8}$

$=\frac{-6\pm\sqrt{37}\times 2}{8}$

$=2\frac{(-3\pm\sqrt{37})}{8}$

$=\frac{-3\pm\sqrt{37}}{4}$

$x=\frac{(-3\pm\sqrt{37})}{4}$

The real roots are

$x=\frac{(-3+\sqrt{37})}{4}$ and $x=\frac{(-3-\sqrt{37})}{4}$

Now to find the sum of the squares of these roots

$\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3+\sqrt{37}-3-\sqrt{37}}{4}$

$=\frac{-6}{4}$

$=\frac{-3}{2}$

$\left[\frac{-3+\sqrt{37}}{4}+\frac{(-3-\sqrt{37})}{4}\right]^2=\frac{-3}{2}$

Therefore the sum of the squares of these roots is $\frac{-3}{2}$

3 0

3 years ago

Factor by using the GCF.

Lady_Fox [76]

Both terms have a 2x^4 in common. When this GCF is factored out you get 2x^4(x^2 - 6).

Answer is C

5 0

3 years ago

slega [8]

ARST was translated, then dilated, to create AZXY

3 0

2 years ago

What is the percentage of the shaded area

DanielleElmas [232]

Answer:

273%

Step-by-step explanation:

Step 1:

273/200 = 2.73

Step 2:

2.73 = 273%

Answer:

273%

Hope This Helps :)

3 0

4 years ago