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3 years ago

What are the solutions to the equation x² = 169? Choose all answers that are correct

2 answers:

6 0

Since you are finding what number doubled equals 169 you have to find the square root of 169 which is 13 because 13 times 13 equals 169

Alexxx [7]3 years ago

4 0

$x^2 = 169 \ \ | -169 \\ \\x^2 - 169 =169-169\\ \\x^2-13^2=0\\ \\(x-13)(x+13)=0\\ \\x-13 = 0 \ \ or \ \ x+13 =0 \\ \\ x=13 \ \ or \ \ x= -13$

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What is the solution to the equation

Dafna11 [192]

$\sqrt{4t+5}=3-\sqrt{t+5}\\\\D:4t+5\geq0\ \wedge\ t+5\geq0\ \wedge\ \sqrt{t+5}\leq3\\\\t\geq-\dfrac{5}{4}\ \wedge\ t\geq-5\ \wedge\ t\leq6$

therefore
$D:x\in\left< -\dfrac{5}{4};\ 6\right>$

$\sqrt{4t+5}=3-\sqrt{t+5}\ \ \ |^2\\\\(\sqrt{4t+5})^2=(3-\sqrt{t+5})^2\ \ \ |use:(a-b)^2=a^2-2ab+b^2\\\\4t+5=3^2-2\cdot3\cdot\sqrt{t+5}+(\sqrt{t+5})^2\\\\4t+5=9-6\sqrt{t+5}+t+5\ \ \ \ |-t\\\\3t+5=14-6\sqrt{t+5}\ \ \ \ |-14\\\\3t-9=-6\sqrt{t+5}\ \ \ \ |change\ signs$
$9-3t=6\sqrt{t+5}\ \ \ \ |:3\\\\3-t=2\sqrt{t+5}\ \ \ \ |^2\\\\(3-t)^2=(2\sqrt{t+5})^2\\\\3^2-2\cdot3\cdot t+t^2=4(t+5)\\\\9-6t+t^2=4t+20\ \ \ |-4t-20\\\\t^2-10t-11=0\\\\t^2+t-11t-11=0\\\\t(t+1)-11(t+1)=0\\\\(t+1)(t-11)=0\iff t+1=0\ \vee\ t-11=0\\\\t=-1\in D\ \vee\ t=11\notin D$
Answer: t = -1.

7 0

3 years ago

Read 2 more answers

At East Middle School, there are 585858 left-handed students and 609609609 right-handed students. The numbers of left- and right

lisabon 2012 [21]

Answer: C. Left-handed: 48 Right-handed: 504

E. Left-handed: 30 Right-handed: 315

Step-by-step explanation:

Here is the completed question:

At East Middle School, there are 58 left-handed students and 609 right-handed students. The numbers of left- and right-handed students at West Junior High are proportional to the numbers at East Middle School. Which of the following could be the numbers of left-handed and right-handed students at West Junior High?

A. Left-handed: 42 Right-handed: 483

B. Left-handed: 28 Right-handed: 378

C. Left-handed: 48 Right-handed: 504

D. Left-handed: 56 Right-handed: 560

E. Left-handed: 30 Right-handed: 315

Since it's direct proportion, we have to calculate the constant of proportionality which will simply be:

= 609 / 58 = 10.5

A. Left-handed: 42 Right-handed: 483

Constant = 483/42 = 11.5

Incorrect

B. Left-handed: 28 Right-handed: 378

Constant = 378/28 = 13.5

Incorrect

C. Left-handed: 48 Right-handed: 504

Constant = 504/48 = 10.5

Correct

D. Left-handed: 56 Right-handed: 560

Constant = 560/56 = 10

Incorrect

E. Left-handed: 30 Right-handed: 315

Constant = 315/30 = 10.5

Correct

Therefore, the correct options are C and E.

3 0

2 years ago

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Which of the following statements it’s true?

guapka [62]

Answer:

Step-by-step explanation:

7 0

3 years ago

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The total cost to rent a row boat is $8 times the number of hours the boat is used. How long can you rent the boat for $176?

MrMuchimi

Answer:

22 hours

Step-by-step explanation:

8•x= 176

Divide both sides by 8 and you get-

Y=22

3 0

3 years ago

Read 2 more answers

Men are believed to have a slightly longer average length of short hospital stays than women; 5.2 days versus 4.5 days respectiv

Georgia [21]

Answer:

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of singificance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

Step-by-step explanation:

1) Data given and notation

$\bar X_{1}=5.2$ represent the mean for group men

$\bar X_{2}=4.5$ represent the mean for group women

Assuming these values for the remaining data:

$\sigma_{1}=1.2$ represent the population standard deviation for the sample men

$\sigma_{2}=1.5$ represent the population standard deviation for the sample women

$n_{1}=32$ sample size for the group men

$n_{2}=30$ sample size for the group women

z would represent the statistic (variable of interest)

$p_v$ represent the p value

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean for men it's higher than the mean for women, the system of hypothesis would be:

H0: $\mu_{1} \leq \mu_{2}$

H1: $\mu_{1} > \mu_{2}$

If we analyze the size for the samples both are higher than 30, and we know the population deviation's, so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

We have all in order to replace in formula (1) like this:

$z=\frac{5.2-4.5}{\sqrt{\frac{1.2^2}{32}+\frac{1.5^2}{30}}}=2.02$

4) Find the critical value

In order to find the critical value we need to take in count that we are conducting a right tailed test, so we are looking on the normal standard distribution a value that accumulats 0.01 of the area on the right and 0.99 of the area on the left. We can us excel or a table to find it, for example the code in Excel is:

"=NORM.INV(1-0.01,0,1)", and we got $z_{critical}=2.33$

5) Statistical decision

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of significance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

6 0

3 years ago