Use the GCF and the distributive property to find the expression that is

miss Akunina [59]

In the smallest of the three triangles (with sides $a,b,3$ ) we have

$a^2+3^2=b^2$

In the second-largest triangle (with sides $a,108$ ), the length of the missing side is $\sqrt{a^2+108^2}$ . Then in the largest triangle (with sides $b,111,\sqrt{a^2+108^2}$ ), we have

$b^2+\left(\sqrt{a^2+108^2}\right)^2=(108+3)^2=111^2$

$\implies b^2+a^2+108^2=111^2$

$\implies b^2+a^2=657$

Equivalently, we have

$(a^2+9)+a^2=657\implies 2a^2=648\implies a^2=324\implies a=18$

In turn, we find

$b^2=18^2+3^2=298\implies b=\sqrt{333}=3\sqrt{37}$

6 0

2 years ago

The owner of Limp Pines Resort wanted to know the average age of its clients. A random sample of 25 tourists is taken. It shows

erma4kov [3.2K]

Answer:

C. ± 2.326 years.

Step-by-step explanation:

We have the standard deviation for the sample. So we use the t-distribution to solve this question.

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.98}{2} = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.01 = 0.99$ , so $z = 2.326/tex]Now, find the width of the interval[tex]W = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

In this question:

$\sigma = 5, n = 25$

So

$W = z*\frac{\sigma}{\sqrt{n}}$

$W = 2.326*\frac{5}{\sqrt{25}}$

The correct answer is:

C. ± 2.326 years.

7 0

2 years ago

How long does it take him to make $375.25

frez [133]

Where’s the root to the question

4 0

1 year ago

5x+5y=-30 find the x and y intercept

Masja [62]

<em>The x and y intercept of 5x + 5y = -30 are (-6, 0) and (0, -6) respectively.</em>

<h2 /><h2>Explanation:</h2>

The Standard Form of the equation of a line is given by:

$Ax+By=C \\ \\ A,B,C \ Real \ Constants \ and \ A>0$

So:

$5x+5y=-30$

is written in Standard Form. The x and y intercepts are:

$x-intercept: \ (x,0) \\ \\ y-intercept: \ (0,y)$

So:

FOR X-INTERCEPT:

$Let's \ set: \\ y=0 \\ \\ 5x+5(0)=-30 \\ \\ Isolating \ x: \\ \\ 5x=-30 \\ \\ x=-\frac{30}{5} \\ \\ \boxed{x=-6}$

FOR Y-INTERCEPT:

$Let's \ set: \\ x=0 \\ \\ 5(0)+5y=-30 \\ \\ Isolating \ x: \\ \\ 5y=-30 \\ \\ y=-\frac{30}{5} \\ \\ \boxed{y=-6}$

Finally,<em> the x and y intercept of 5x + 5y = -30 are (-6, 0) and (0, -6) respectively.</em>

<h2>Learn more:</h2>

Parallel lines: brainly.com/question/12169569

#LearnWithBrainly

6 0

2 years ago

Which property justifies step 3 Given: 4(x - 6) + 12 = 20

kap26 [50]

Answer:

x=8

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4(x−6)+12=20

(4)(x)+(4)(−6)+12=20(Distribute)

4x+−24+12=20

(4x)+(−24+12)=20(Combine Like Terms)

4x+−12=20

4x−12=20

Step 2: Add 12 to both sides.

4x−12+12=20+12

4x=32

Step 3: Divide both sides by 4.

4x

4

=

32

4

7 0

2 years ago