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2 years ago

Question in image, it asks to show your work

Mathematics

1 answer:

maxonik [38]2 years ago

8 0

<u>Answer:</u>

• f(g(x)) = $\sqrt{x^{2} + 1}$ + 8

• g(f(x)) = 16 $\sqrt{x}$ + x + 65

<u>Step-by-step explanation:</u>

• f(g(x)) = f(x² + 1)

= $\sqrt{x^{2} + 1}$ + 8

• g(f(x)) = g( $\sqrt{x + 8}$ )

= $(\sqrt{x } + 8)^{2}$ + 1

= x + 16 $\sqrt{x}$ + 64 + 1

= 16 $\sqrt{x}$ + x + 65

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3. Which statements about the line that passes through (-2, 0) and (2, -4) are true?

diamong [38]

Answer:

B, C, and D.

Step-by-step explanation:

Let's go through each answer choice.

A: To find the slope of a line from two points, we use this formula: $(y_2-y_1)/(x_2-x_1)$ . Plugging in the values (-2,0) and (2, -4), we get:

$(-4-0)/(2+2)$

$-4/4$
$-1$

Because option A says the slope is 1, but we got -1, option A is false.

B: To find the y-intercept, we use this formula: $b = y_1 - m * x_1$

$b = 0 -(-1) * (-2)$

$b = 1 * (-2)$

$b = -2$

Since we know the value of b is the y-intercept, we could write the y-intercept as (0,-2). Therefore, option B is true.

C: The equation of a line (in slope-intercept form) is y = mx + b, where y - y-coordinate, m = slope, x = x-coordinate, and b = y-intercept. Since we already solved for the y-intercept and slope, let's plug in those values:

$y = mx +b$
$y = -x -2$

As you can see, the equation we got here matches the one in option C, meaning it's true.

D: We know that a point is written like this: (x, y). If the x-coordinate is not zero but the y-coordinate is, then it's the x-intercept. Since the question says that (-2,0) is one of the points the line passes through, and option D says that the x-intercept is (-2,0), it's true.

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2 years ago

Read 2 more answers

Use Law of Sine to A if B is 115 degrees, b is 18, and c is 12

hoa [83]

Answer:

mhmm

Step-by-step explanation:

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3 years ago

Sample Size for Proportion As a manufacturer of golf equipment, the Spalding Corporation wants to estimate the proportion of gol

Dima020 [189]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56$

And rounded up we have that n=2663

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

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

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:

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

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 $ME =\pm 0.025$ 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)

We can assume an estimated proportion of $\hat p =0.5$ since we don't have prior info provided. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56$

And rounded up we have that n=2663

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3 years ago

What is the area of the shaded region and what steps do I have to do to find it out

natima [27]

Answer:

Usually, we would subtract the area of a smaller inner shape from the area of a larger outer shape in order to find the area of the shaded region.

Step-by-step explanation:

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2 years ago

Step 2: Radii OK and NL are perpendicular to OM because of the radius-tangent theorem. By definition of perpendicular, angles KO

viva [34]

Answer:

<h2>AAA postulate.</h2>

Step-by-step explanation:

Givens

Angles KOM and LNM are congruent, because both are right.
Angle LNM is common to both triangles.

If two internal angles of two triangles are congruent, then the third angle is also congruent.

Therefore, the similarity is proven by AAA postulate, which states that if we have three corresponding angles congruent, then those triangles are similar.

Remember that similarity is about proportion between sides and congruence between angles.

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3 years ago