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3 years ago

Which of the following graphs represents the equation below? f(x) = x^2 + 4x

Mathematics

1 answer:

Sindrei [870]3 years ago

7 0

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$f(x)=x^{2}+4x$

This is a vertical parabola open upward

The vertex is a minimum

step 1

Find the x-intercepts

The x-intercepts are the values of x when the value of the function is equal to zero

For f(x)=0

$0=x^{2}+4x$

Factor x

$0=x(x+4)$

The x-intercepts are (0,0) and (-4,0)

step 2

Find the y-intercept

The y-intercept is the values of the function when the value of x is equal to zero

For x=0

$f(x)=(0)^{2}+4(0)=0$

The y-intercept is (0,0)

step 3

Find the vertex

Convert the equation into vertex form

$f(x)=x^{2}+4x$

Complete the square

$f(x)=(x^{2}+4x+4)-4$

Rewrite as perfect squares

$f(x)=(x+2)^{2}-4$

The vertex is the point (-2,-4)

therefore

using a graphing a graphing tool

The graph in the attached figure

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When 21 is subtracted from the square of a number, the result is 4 times the number. Find the positive solution.

wel

Let x = your number.

x^2 - 21 = 4x. Subtract 4x from both sides.

x^2 - 4x - 21 = 0. Factor.

(x - 7) (x + 3) = 0. Set each term to 0.

x + 3 = 0. Subtract 3 from both sides.

x = -3. This is the negative solution.

Set the other term equal to zero.

x - 7 = 0. Add 7 to each side.

x = 7. This is the positive solution.

7 0

3 years ago

Which quadrant of the coordinate plane has ordered pairs in the form of a positive number

Setler [38]

Answer:

Quadrant IV

Step-by-step explanation:

On the graph, the x-axis numbers are positive and the y-axis numbers are negative

8 0

2 years ago

Simplify 8x^4/x^3+7x^4 and Find the excluded values

Maksim231197 [3]

So first what we do is we need to get the excluded values. So to get them we have: 8x^4/x^3+7x^4.

Lets factor out the second part. x^3+7x^4 = (x^(3/4)+7x))^4

So then we get 8x^4/(x^(3/4)+7x)^4

8x^4/(x^(3/4)+7x)^4

8 0

2 years ago

A recent study asked U. S. Adults to name 10 historic events that occurred during their lifetime that have had the greatest impa

Nadusha1986 [10]

Using the z-distribution, as we are working with a proportion, it is found that the 99% confidence interval for the proportion of all U. S. Adults who would include the 9/11 attacks on their list of 10 historic events is (0.7458, 0.7942). It means that we are 99% sure that the true proportion for all U.S. adults is between these two bounds.

<h3>What is a confidence interval of proportions?</h3>

A confidence interval of proportions is given by:

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which:

$\pi$ is the sample proportion.

z is the critical value.

n is the sample size.

In this problem, the parameters are:

$z = 2.575, n = 2000, \pi = 0.77$

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 2.575\sqrt{\frac{0.77(0.23)}{2000}} = 0.7458$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 2.575\sqrt{\frac{0.77(0.23)}{2000}} = 0.7942$

The 99% confidence interval for the proportion of all U. S. Adults who would include the 9/11 attacks on their list of 10 historic events is (0.7458, 0.7942). It means that we are 99% sure that the true proportion for all U.S. adults is between these two bounds.

More can be learned about the z-distribution at brainly.com/question/25890103

7 0

2 years ago

What the answer plz help fast? If you get it right i will mark you brainless ❤️

romanna [79]

Answer:

You'll mark me brainless?! I shouldn't answer corectly then XD

The answer (keep in mind that i'm answering incorrectly) A, or B, or D, or E.

Do you see what I did there ;)

Step-by-step explanation:

May I have brainliest please :)

3 0

3 years ago

Read 2 more answers