Help me please will give Brainliest

How to solve using perfect square <br> x^2-4x-32=0

zmey [24]

$Perfect\ square:(a-b)^2=a^2-2ab+b^2\\\\x^2-4x-32=0\ \ \ \ |add\ 32\ to\ both\ sides\\\\x^2-4x=32\\\\x^2-2x\cdot2=32\ \ \ \ |add\ 2^2\ to\ both\ sides\\\\x^2-2x\cdot2+2^2=32+2^2\\\\(x-2)^2=32+4\\\\(x-2)^2=36\iff x-2=-\sqrt{36}\ or\ x-2=\sqrt{36}\\\\x-2=-6\ or\ x-2=6\ \ \ \ |add\ 2\ to\ both\ sides\\\\\boxed{x=-4\ or\ x=8}$

5 0

3 years ago

HELP

charle [14.2K]

Answer:

2

Step-by-step explanation:

So let's call the time she needs to catch up "x", and so Terry's rate would be x-6 since he left home 6 hours earlier. Then we multiply the rates to get 20x - 120 = 80x. The answer is -2, but we can just say 2.

Checking our answer, that means if it took Sally 2 hours, it took Terry 8 hours for he left home 6 hours earlier. So 8 times 20 = 160km traveled. 2 times 80 = 160km traveled. Same distance.

3 0

3 years ago

What is the solution of the system? Use the elimination method. {4x+2y=182x+3y=15 Enter your answer in the boxes.

Oxana [17]

$\left \{ {{4x+2y=18(1)} \atop {2x+3y=15(2)}} \right.$
Lets multiply equation (2) by -2 to get:
$-4x-6y=-30$

Now we can add equations (1) and (2) to eliminate x:
$\left \{ {{4x+2y=18}+ \atop {-4x-6y=-30}} \right.$
$-4y=-12$
$y= \frac{-12}{-4}$
$y=3$
Now that we know the value of y, we can replace it in equation (1) to get the value of x:
$4x+2(3)=18$
$4x+6=18$
$4x=12$
$x= \frac{12}{3}$
$x=3$

We can conclude that both x and y are equal to 3.

6 0

3 years ago

Read 2 more answers

A driver averaged 41 miles per hour and took 11 hours to travel between two cities. what is the distance between the two cities

krek1111 [17]

multiply speed by time

41 x 11 = 451 miles

4 0

3 years ago

The drag Prevnar is a vaccine meant to prevent meningitis. It is typically administered to infants between 12 and 15 months of a

Fed [463]

Answer:

The pvalue of the test is 0.0058 < 0.01, which means that there is significant evidence to conclude the proportion of infants who receive Prevnar and experience of a loss of appetite is different from 0.135.

Step-by-step explanation:

Test if the proportion of infants who receive Prevnar and experience of a loss of appetite is different from 0.135

This means that the null hypothesis is:

$H_{0}: p = 0.135$

And the alternate hypothesis is:

$H_{a}: p \neq 0.135$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

0.135 is tested at the null hypothesis:

This means that $\mu = 0.135, \sigma = \sqrt{0.135*0.865}$

Of the 710 infants,121 experienced a loss of appetite.

This means that $n = 710, X = \frac{121}{710} = 0.1704$

Value of the test-statistic:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.1704 - 0.135}{\frac{\sqrt{0.135*0.865}}{\sqrt{710}}}$

$z = 2.76$

Pvalue of the test and decision:

The pvalue of the test is the pobability that the population proportion differs from the tested proportion by at least 0.1704 - 0.135 = 0.0354, which is P(|z| > 2.76). This probability is 2 multiplied by the pvalue of z = -2.76.

Looking at the z-table, z = -2.76 has a pvalue of 0.0029

2*0.0029 = 0.0058

The pvalue of the test is 0.0058 < 0.01, which means that there is significant evidence to conclude the proportion of infants who receive Prevnar and experience of a loss of appetite is different from 0.135.

7 0

3 years ago