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3 years ago

A recipe for fruit punch requires 1 1/2 quarts of orange juice to make 6 quarts of punch. How many

Mathematics

1 answer:

Bingel [31]3 years ago

6 0

Answer:

$\frac{1}{4}$ quarts of orange juice.

Step-by-step explanation:

Given:

Quarts of orange juice required for 6 quarts of punch = $1\frac{1}{2} =\frac{3}{2}$

∴ Quarts of orange juice required for 1 quart of punch = $\frac{\frac{3}{2}}{6}=\frac{3}{2}\times \frac{1}{6}=\frac{3}{12}=\frac{1}{4}$

Therefore, $\frac{1}{4}$ quarts of orange juice are required for one quart of punch.

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34. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.

skad [1K]

Answer:

The linear equation for the line which passes through the points given as (-1,4) and (5,2), is written in the point-slope form as $y=\frac{1}{3} x-\frac{13}{3}$ .

Step-by-step explanation:

A condition is given that a line passes through the points whose coordinates are (-1,4) and (5,2).

It is asked to find the linear equation which satisfies the given condition.

Step 1 of 3

Determine the slope of the line.

The points through which the line passes are given as (-1,4) and (5,2). Next, the formula for the slope is given as,

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substitute 2&4 for $y_{2}$ and $y_{1}$ respectively, and $5 \&-1$ for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows,

$m=\frac{2-4}{5-(-1)}$\\ $m=\frac{-2}{6}$\\ $m=-\frac{1}{3}$$

Step 2 of 3

Write the linear equation in point-slope form.

A linear equation in point slope form is given as,

$y-y_{1}=m\left(x-x_{1}\right)$

Substitute $-\frac{1}{3}$ for m,-1 for $x_{1}$ , and 4 for $y_{1}$ in the above equation and simplify using the distributive property as follows,

$y-4=-\frac{1}{3}(x-(-1))$\\ $y-4=-\frac{1}{3}(x+1)$\\ $y-4=-\frac{1}{3} x-\frac{1}{3}$$

Step 3 of 3

Simplify the equation further.

Add 4 on each side of the equation $y-4=\frac{1}{3} x-\frac{1}{3}$ , and simplify as follows,

$y-4+4=\frac{1}{3} x-\frac{1}{3}+4$\\ $y=\frac{1}{3} x-\frac{1+12}{3}$\\ $y=\frac{1}{3} x-\frac{13}{3}$$

This is the required linear equation.

5 0

2 years ago

What is the slope of the line that passes through the points (-1,1) and (1,-15)

Luda [366]

Answer:

$\boxed{\text{The slope is -8.}}$

Step-by-step explanation:

To find the slope of the line, you have to use a slope formula.

Slope formula:

$\Longrightarrow:\sf{\dfrac{y_2-y_1}{x_2-x_1} }$

⇒ y2=(-15)

⇒ y1=1

⇒ x2=1

⇒ x1=(-1)

Rewrite the whole problem down.

$\Longrightarrow: \sf{\dfrac{-15-1}{1-\left(-1\right)}=\dfrac{-16}{2}=\boxed{\sf{-8}}$

So, the slope is -8, which is our answer.

I hope this helps you! Let me know if my answer is wrong or not.

5 0

2 years ago

If a fraction is less than what do u know about its reciprocal?

Inga [223]

The reciprocal is the fraction flipped so I guess its less than if the fraction is less than

7 0

3 years ago

I’m not good at stuff like this but I would give my life if someone can help me please

Rudik [331]

Answer:

I want so much to help u, but I can't right now. I will come back tomorrow and answer it.

7 0

2 years ago

Which algebraic expression matches

Hatshy [7]

Answer:

A) $\frac{n}{4 - 8}$

Step-by-step explanation:

The quotient of a number four minus eight

n/ 4 - 8

If the question was "The quotient of a number and four", the answer would be n/4. But the question says "four minus eight", so the answer is $\frac{n}{4 - 8}$ .

Hope this helps!

3 0

3 years ago

Read 2 more answers