together Charlotte and vinny have 20 marbles. charlotte has 4 times as many as vinny. how many marbles does Charlotte have.

Answer:

make use of the properties of equality of of inverse functions and operations

Step-by-step explanation:

In algebra, each of the operations and functions we study has an inverse. As a rule, in any "solve for ..." situation, you want to "undo" the operations and functions performed on the variable of interest. You can use the Order of Operations to determine the order those operations are performed, then undo them in reverse order.

Trivial example:

Solve x + 3 = 5 for x. We observe that the variable x has had 3 added to it. We "undo" the addition of 3 by adding its opposite, -3. The properties of equality require that we add this value to both sides of the equation:

x +3 -3 = 5 -3

x = 2 . . . . . after simplification

__

Rearranging also involves combining terms, finding a common denominator, rationalizing denominators, and similar algebraic operations. These sorts of operations are performed on variables and expressions in virtually the same way they are performed on numbers.

Less trivial example:

Suppose we have the equation of a circle, and we want to rearrange it to find an expression for y.

(x -h)^2 +(y -k)^2 = r^2

We observe that y has k subtracted, the result is squared, and an x-term is added. Undoing these in reverse order means we first subtract the x-term, then take the square root, and finally add k.

(y -k)^2 = r^2 -(x -h)^2 . . . . . . we subtracted the x-term from both sides

y -k = √(r^2 -(x -h)^2) . . . . . . and took the square root. Notice we have retained only the positive square root, so the bottom half of the circle will go missing from our final equation.

y = k + √(r^2 -(x -h)^2) . . . . . finally, we added k

This is the formula for a circle rearranged to find y in terms of x. The value of y is that associated with the top half of the circle. If we want the bottom half, we must negate the square root:

y = k - √(r^2 -(x -h)^2) . . . . . . formula rearranged to give the bottom half

Note that the root function is used to "undo" the operation of raising to a power. As we said, each of the operations we study in algebra has its "undo". It is useful to pay attention to the inverse operation associated with any new operation or function you learn about. (trig functions, log functions, exponentiation come to mind)

3 0

3 years ago

What is the answer to this

NeX [460]

First equation answer:
(j= -7)
Second equation answer:
(j= 5)

4 0

3 years ago

Why is the sum of two rational numbers always rational? Select from the drop-down menus to correctly complete the proof.

baherus [9]

when adding you always get a rational number because you never go outside the bounds of reality XD

8 0

4 years ago

Read 2 more answers

Suppose that you work for a newly restructured automotive company with nearly 100,000 employees. You are in charge of purchasing

saul85 [17]

Answer:

The p-value of the test is 0.0764 > 0.05, which means that there is not enough evidence to reject the null hypothesis that the proportion is of at most 0.009, and thus we can conclude that the supplier has met the guarantee.

Step-by-step explanation:

Your overseas supplier of engines guarantees that no more than 0.9% of the new engines shipped to you will fail a simple electrical test.

At the null hypothesis, we test if the proportion is of at most 0.9% = 0.009, that is:

$H_0: p \leq 0.009$

At the alternative hypothesis, we test if the proportion is of more than 0.009, that is:

$H_1: p > 0.009$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.009 is tested at the null hypothesis:

This means that $\mu = 0.009, \sigma = \sqrt{0.009*0.991}$

50 of these engines, and you find that 1 is defective.

This means that $n = 50, X = \frac{1}{50} = 0.02$

Value of the test statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.02 - 0.009}{\frac{\sqrt{0.009*0.991}}{\sqrt{50}}}$

$z = 1.43$

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion above 0.02, which is 1 subtracted by the p-value of z = 1.43.

Looking at the z-table, z = 1.43 has a p-value of 0.9236.

1 - 0.9236 = 0.0764.

The p-value of the test is 0.0764 > 0.05, which means that there is not enough evidence to reject the null hypothesis that the proportion is of at most 0.009, and thus we can conclude that the supplier has met the guarantee.

8 0

3 years ago

Answer quick plzz...........................

Pachacha [2.7K]

Answer:

.

Step-by-step explanation:

6 0

3 years ago