IS (1, 2) of a solution set of x+ y = 3 and 2 x + 7 y = 16 ?

H (t) = -t2 + t + 12 <br> Solve by using quadratic formula

Sedaia [141]

The quadratic formula is:

$x=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}$

and

$x=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}$

Let's identify our a, b, and c values:

a: -1

b: 1

c: 12

Plug in the values for a, b, and c into the equation. Let's do the first equation:

$x=\frac{-1+\sqrt{(1)^2-4(-1)(12)}}{2(-1)}$

Simplify everything in the radical:

$x=\frac{-1+\sqrt{49}}{-2}$

Simplify the radical:

$x=\frac{-1+7}{-2}$

Combine like terms:

$x=\frac{6}{-2}$

Simplify:

$x=-3$

This is one solution, now, let's solve for the other equation:

Since when simplified, everything is the same except the subtraction sign, we can skip the simplification again and change the sign to subtraction:

$x=\frac{-1-7}{-2}$

Combine like terms:

$x=\frac{-8}{-2}$

Simplify:

$x=4$

Your final answers are:

$x=-3$

$x=4$

8 0

3 years ago

Read 2 more answers

What dose 3+5-5-3=????

aleksandr82 [10.1K]

The answer is it equals 0

6 0

3 years ago

Read 2 more answers

What is the length of the unknown side?

777dan777 [17]

Answer:

Hi there!

The correct answer is: 20

Step-by-step explanation:

knowing this a right triangle you can solve this problem in two ways

Method One: Pythagorean Theorem

a^2 + b^2 = c^2 then plug in the values

(12)^2 + (16)^2 = c^2 this will come out to be 400 = c^2

square root both sides and you get c = 20

Method Two: Pythagorean Identities

if you ever learned the Pythagorean identity 3,4,5

this triangle is indeed a 3,4,5 triangle it's just that each side is multiplied by the factor 4

so in this case since you know the missing side should be 5 you just multiply 5 by 4 and you get 20

4 0

3 years ago

HELP PLS ILL MARK U BRAINLIEST

umka2103 [35]

Answer:

-3.4p + 3p + 4

Step-by-step explanation:

Solve the parenthesis with the minus sign in front of it. Basically, inverse all of the operations within the parenthesis.

The -3q will become a 3q and the -4 will become a 4.

So now with the positive 3q and 4, you will just add those to the -3.4p

Therefore, the answer is -3.4p + 3p + 4

Hope this helped! Please mark me as brainliest!

5 0

3 years ago

A survey organization has used the methods of our class to construct an approximate 95% confidence interval for the mean annual

lawyer [7]

Answer:

$\bar X = \frac{66000+70000}{2}= 68000$

We can estimate the margin of error with this formula:

$ME= \frac{Upper -Lower}{2}= \frac{70000-66000}{2}= 2000$

And the margin of error is given by:

$ME = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

And we can rewrite the margin of error like this:

$ME =z_{\alpha/2}*SE$

Where $SE= \frac{\sigma}{\sqrt{n}}$

For 95% of confidence the critical value is $z_{\alpha/2}= \pm 1.96$

The Standard error would be:

$SE= \frac{ME}{z_{\alpha/2}}= \frac{2000}{1.96}= 1020.408$

For 99% of confidence the critical value is $z_{\alpha/2}= \pm 2.58$

And the new margin of error would be:

$ME = 2.58* 1020.408 = 2632.653$

And then the interval would be given by:

$Lower = 68000- 2632.653 = 65367.347$

$Upper = 68000+ 2632.653 = 70632.653$

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

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

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

The 95% confidence interval is given by (66000 , 70000)

We can estimate the mean with this formula:

$\bar X = \frac{66000+70000}{2}= 68000$

We can estimate the margin of error with this formula:

$ME= \frac{Upper -Lower}{2}= \frac{70000-66000}{2}= 2000$

And the margin of error is given by:

$ME = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

And we can rewrite the margin of error like this:

$ME =z_{\alpha/2}*SE$

Where $SE= \frac{\sigma}{\sqrt{n}}$

For 95% of confidence the critical value is $z_{\alpha/2}= \pm 1.96$

The Standard error would be:

$SE= \frac{ME}{z_{\alpha/2}}= \frac{2000}{1.96}= 1020.408$

For 99% of confidence the critical value is $z_{\alpha/2}= \pm 2.58$

And the new margin of error would be:

$ME = 2.58* 1020.408 = 2632.653$

And then the interval would be given by:

$Lower = 68000- 2632.653 = 65367.347$

$Upper = 68000+ 2632.653 = 70632.653$

7 0

4 years ago

IS (1, 2) of a solution set of x+ y = 3 and 2 x + 7 y = 16 ?​

IS (1, 2) of a solution set of x+ y = 3 and 2 x + 7 y = 16 ?