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3 years ago

Which number, when substituted for x, makes the equation 4x+8=16 true?

Mathematics

1 answer:

romanna [79]3 years ago

5 0

Answer:

Step-by-step explanation:

Given: 4x+8=16

Subtract 8 from both sides: 4x=8

Divide both sides by 4: x=4

Answer: x=4

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when asked to factor the x^2 - 100, a student gives the answer (x -10) (x-10). what is wrong with this answer?

aalyn [17]

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2 years ago

PLEASE HELP! I WILL GIVE BRAINLIEST!!!! (no trolls) PLEASE SHOW WORK OR GIVE EXPLANATION!!!!!!

IgorLugansk [536]

explanation:

The fastest way to find the missing endpoint is to determine the distance from the known endpoint to the midpoint and then performing the same transformation on the midpoint. In this case, the x-coordinate moves from 4 to 2, or down by 2, so the new x-coordinate must be 2-2 = 0. The y-coordinate moves from 4 to -5, or down by 9, so the new y-coordinate must be -5-9 = -14.

An alternate solution would be to substitute (4,4) for (x1,y1) and (2,-5) for (x,y) into the midpoint formula:

x=(x1+x2)/2

y=(y1+y2)/2

Solving each equation for (x2,y2) yields the solution (0,-14).

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8 0

3 years ago

Read 2 more answers

Find an equation in slope intercept form of a line having slope 6 and y-intercept 2

xz_007 [3.2K]

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

We have the slope m = 6, and the y-intercept b = 2.

Substitute:

$y=6x+2$

4 0

3 years ago

Suppose that the functions q and r are defined as follows.

satela [25.4K]

Answer:

(r o g)(2) = 4

(q o r)(2) = 14

Step-by-step explanation:

Given

$g(x) = x^2 + 5$

$r(x) = \sqrt{x + 7}$

Solving (a): (r o q)(2)

In function:

(r o g)(x) = r(g(x))

So, first we calculate g(2)

$g(x) = x^2 + 5$

$g(2) = 2^2 + 5$

$g(2) = 4 + 5$

$g(2) = 9$

Next, we calculate r(g(2))

Substitute 9 for g(2)in r(g(2))

r(q(2)) = r(9)

This gives:

$r(x) = \sqrt{x + 7}$

$r(9) = \sqrt{9 +7{$

$r(9) = \sqrt{16}$ {

$r(9) = 4$

Hence:

(r o g)(2) = 4

Solving (b): (q o r)(2)

So, first we calculate r(2)

$r(x) = \sqrt{x + 7}$

$r(2) = \sqrt{2 + 7}$

$r(2) = \sqrt{9}$

$r(2) = 3$

Next, we calculate g(r(2))

Substitute 3 for r(2)in g(r(2))

g(r(2)) = g(3)

$g(x) = x^2 + 5$

$g(3) = 3^2 + 5$

$g(3) = 9 + 5$

$g(3) = 14$

Hence:

(q o r)(2) = 14

8 0

2 years ago

Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old. How large a sample size

julsineya [31]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

For this case we can use as estimator for the proportion $\hat p =0.5$ , since we don't have any other previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

8 0

3 years ago