All categories

3 years ago

What are the zeros of the quadratic function? y = x^2 - 2x - 15

Mathematics

1 answer:

Pie3 years ago

3 0

Answer:

$x=\frac{1+\sqrt{31}}{2},\:x=\frac{1-\sqrt{31}}{2}$

Step-by-step explanation:

$-> 0=2x^2-2x-15$

-zeros means the solution aka x intercept, meaning y=0

$x_{1,\:2}=\frac{-\left(-2\right)\pm \sqrt{\left(-2\right)^2-4\cdot \:2\left(-15\right)}}{2\cdot \:2}$

=> according to quadratic formula

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

where $ax^2+bx+c=0$

=> $x_{1,\:2}=\frac{-\left(-2\right)\pm \:2\sqrt{31}}{2\cdot \:2}$

simplify

$x_1=\frac{-\left(-2\right)+2\sqrt{31}}{2\cdot \:2},\:x_2=\frac{-\left(-2\right)-2\sqrt{31}}{2\cdot \:2}$

$x=\frac{1+\sqrt{31}}{2},\:x=\frac{1-\sqrt{31}}{2}$

Cannot simplify farther

You might be interested in

The exclamation point (!) on a billboard consists of a circle sector and circle. The radius of the sector is 9 ft, and the radiu

harina [27]

Answer:

24.0 square feet

Step-by-step explanation:

The area of the sector is given by ...

A = (1/2)r²θ . . . . . where θ is the angle in radians

The area of the circle is the same, with θ=2π, so is ...

A = πr²

In this problem, the area of the sector is ...

A = (1/2)(9 ft)²(24π/180) = 27π/5 ft² ≈ 16.9646 ft²

The area of the circle is ...

A = π(1.5 ft)² = 9π/4 ft² ≈ 7.0686 ft²

Then the total area of the exclamation point is ...

16.9646 +7.0686 ≈ 24.0 . . . ft²

The area is about 24.0 square feet.

8 0

3 years ago

Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 1818 cans of the

ohaa [14]

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 18 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.14 oz, and they appear to be from a normally distributed population.

If the workers want the filling process to work so that almost all cans have volumes between 12.02 oz and 12.66 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.16 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16 oz. Use a 0.01 significance level. Complete parts (a) through (d) below.

a. Identify the null and alternative hypotheses.

b. Compute the test statistic.

c. Find the p-value.

d. State the conclusion.

Answer:

Null hypotheses = H₀: σ = 0.16 oz

Alternate hypotheses = H₁: σ < 0.16 oz

Critical value = 6.408

Chi-square value = $\chi^2$ = 13.016

Reject H₀ Since $\chi^2$ > Critical value

Reject H₀ Since p-value ≤ α

We have significant evidence at given significance level that the population of volumes has a standard deviation of less than 0.16 oz.

Step-by-step explanation:

Set up hypotheses:

The null hypotheses is that the population of volumes has a standard deviation of 0.16 oz

Null hypotheses = H₀: σ = 0.16 oz

The claim to be tested is that the population of volumes has a standard deviation of less than 0.16 oz

Alternate hypotheses = H₁: σ < 0.16 oz

Determine type of test:

Since the alternate hypothesis states that the population of volumes has a standard deviation of less than 0.16 oz, therefore we will use a lower-tailed chi-square test.

Determine the Critical value:

Given level of significance = 0.01

Since it is a lower-tailed test, the areas given in the chi-square table are the areas to the right of the critical value. To get the areas on the left, subtract it from one, and then look it up

α = 1 - 0.01 = 0.99

degree of freedom = df = n - 1 = 18 - 1 = 17

The critical value from the chi-square table at α = 0.99 and df = 17 is found to be

Critical value = 6.408

Using an online “chi-square p-value calculator”

The left tail p-value for df = 17 and Critical value = 6.408 is found to be

p-value = 0.01

Set up decision rule:

Reject H₀ If > Critical value

We reject the Null hypothesis If the calculated chi-square value is more than the critical value.

Reject H₀ If p-value ≤ α

Compute the test statistic:

$\chi^2 = \frac{(n-1) s^2}{\sigma^2} }$

$\chi^2 = \frac{(18-1) 0.14^2}{0.16^2} }$

$\chi^2 = 13.016$

Conclusion:

We reject H₀

Since $\chi^2$ > Critical value

13.016 > 6.408

Also

p-value ≤ α

0.01 ≤ 0.01

We have significant evidence at given significance level that the population of volumes has a standard deviation of less than 0.16 oz.

5 0

3 years ago

I need some help with this<br><br>

dalvyx [7]

$\pink{\underline{{\boxed{\bf{QUESTION: }}}}}$

-6(x+4) = _____

$\pink{\underline{{\boxed{\bf{OPTIONS:}}}}}$

6x - 4❌
-6x + 4❌
-6x - 24✔️
6x + 24❌

$\pink{\underline{{\boxed{\bf{ ANSWER: }}}}}$

-6(x+4) = <u>-6x - 24</u>

<h3>Hope It's helped! :)</h3>

4 0

3 years ago

Please help me on this!

Kipish [7]

Answer:

<u>B. The amount of money she saves each week </u> is 100% the correct answer

Step-by-step explanation:

325 is the amount she had

125 is the amoun she adds every week to her savings

Have a nice day! :)

6 0

2 years ago

Read 2 more answers

Slips of paper are numbered 1 through 10. If one slip is drawn and replaced 40 times, how many times should the slip with number

Masja [62]

Hey there!

We have 10 pieces of paper. The probability of drawing a 10 is 1/10. Therefore, if we were to draw ten times, the ten should probably be drawn once. If we multiplied our number of drawings by four (10*4=40), our outcome of seeing our slip with the ten should also quadruple and become four times. (1*4=4)

I hope that this helps! Have an awesome day!

6 0

3 years ago