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3 years ago

What are the solutions to the system of equations? y=x2−5x−6 y=2x−6

Mathematics

2 answers:

Leya [2.2K]3 years ago

4 0

Answer:

I graphed both equations to find the solutions.

Step-by-step explanation:

When x is 0, y is -6. When x is 7, y is 8.

x = 0 and 7

allsm [11]3 years ago

4 0

Answer: The solutions are

(0, - 6)

(7, 8)

Step-by-step explanation:

The given system of equations is expressed as

y = x² - 5x - 6- - - - - - - - - - - - 1

y = 2x - 6- - - - - - - - - - - 2

We would apply the method of substitution by substituting equation 2 into equation 1. It becomes

x² - 5x - 6 = 2x - 6

x² - 5x - 2x - 6 + 6 = 0

x² - 7x = 0

x(x - 7) = 0

x = 0 or x - 7 = 0

x = 7 or x = 0

Substituting x = 0 into equation 2, it becomes

y = 2 × 0 - 6

y = - 6

Substituting x = 7 into equation 2, it becomes

y = 2 × 7 - 6

y = 14 - 6

y = 8

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Which equation represents the line through (-8, 10) and (3, 7) in point-slope form?

alina1380 [7]

-3/11

Step-by-step explanation:

7-10/3-(-8)

7-10/3+8

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3 years ago

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r

jolli1 [7]

Answer:

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

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".

$\bar X=28$ represent the sample mean

$\mu$ population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.064$