As the height of a dropped ball decreases, what happens to its potential energy?

Mrs. Carter's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to ma

Alla [95]

Answer:

2 cups of peanut butter

Step-by-step explanation:

Mrs. Carter's famous peanut butter cookies call for 1 cup of peanut butter for every 1/2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?

From the above question:

1/2 cup of oil = 1 cup of peanut butter

1 cup of oil = x

Cross Multiply

1/2x = 1 × 1

x = 1 ÷ 1/2

x = 1 × 2/1

x = 2 cups of peanut butter.

Therefore, for huge batch with 1 cup of oil, she should use 2 cups of peanut butter.

4 0

3 years ago

A 20-gallon salt-water solution contains 15% pure salt. How much pure water should be added to it to produce a 10% solution?

Elanso [62]

15% of 20 gal = 0.15 * 20 gal = 3 gal, so the solution contains 3 gal of salt.

If we add x gal of water to the solution, we end up with (20 + x) gal of solution. We want the new mixture to have a concentration of 10%, or

10% of (20 + x) gal = 0.1 * (20 + x) gal = 2 + 0.1x gal

of salt.

The amount of salt in the tank hasn't changed. Solve for x :

2 + 0.1x = 3

0.1x = 1

x = 10 gal

3 0

3 years ago

Reason abstractly. Are all horizontal lines parallel? Use slope explain how you know.

ohaa [14]

Answer:

All horizontal lines are NOT parallel.

Step-by-step explanation:

We learned that lines go on forever.

If one line is slightly slanted, and the other line is completely straight, these lines are not parallel, as they will meet at some point.

Hope this helped :)

6 0

3 years ago

Write an algebraic equation for this tape diagram. Then determine the value of x. You may use a calculator.

tresset_1 [31]

Answer:

3× + 16 = 22.75

3× = 22.75 - 16

3x = 6.75

3 3

x = 2.25

7 0

3 years ago

Simplify this please

Ugo [173]

Answer:

$\frac{12q^{\frac{7}{3}}}{p^{3}}$

Step-by-step explanation:

Here are some rules you need to simplify this expression:

Distribute exponents: When you raise an exponent to another exponent, you multiply the exponents together. This includes exponents that are fractions. $(a^{x})^{n} = a^{xn}$

Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). $a^{-x} = \frac{1}{a^{x}}$ , and to help with this question: $\frac{a^{-x}b}{1} = \frac{b}{a^{x}}$ .

Multiplying exponents with same base: When exponential numbers have the same base, you can combine them by adding their exponents together. $(a^{x})(a^{y}) = a^{x+y}$

Dividing exponents with same base: When exponential numbers have the same base, you can combine them by subtracting the exponents. $\frac{a^{x}}{a^{y}} = a^{x-y}$

Fractional exponents as a radical: When a number has an exponent that is a fraction, the numerator can remain the exponent, and the denominator becomes the index (example, index here ∛ is 3). $a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}$

$\frac{(8p^{-6} q^{3})^{2/3}}{(27p^{3}q)^{-1/3}}$ Distribute exponent

$=\frac{8^{(2/3)}p^{(-6*2/3)}q^{(3*2/3)}}{27^{(-1/3)}p^{(3*-1/3)}q^{(-1/3)}}$ Simplify each exponent by multiplying

$=\frac{8^{(2/3)}p^{(-4)}q^{(2)}}{27^{(-1/3)}p^{(-1)}q^{(-1/3)}}$ Negative exponent rule

$=\frac{8^{(2/3)}q^{(2)}27^{(1/3)}p^{(1)}q^{(1/3)}}{p^{(4)}}$ Combine the like terms in the numerator with the base "q"

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}$ Rearranged for you to see the like terms

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}$ Multiplying exponents with same base

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(7/3)}}{p^{(4)}}$ 2 + 1/3 = 7/3

$=\frac{\sqrt[3]{8^{2}}\sqrt[3]{27}p\sqrt[3]{q^{7}}}{p^{4}}$ Fractional exponents as radical form

$=\frac{(\sqrt[3]{64})(3)(p)(q^{\frac{7}{3}})}{p^{4}}$ Simplified cubes. Wrote brackets to lessen confusion. Notice the radical of a variable can't be simplified.