5) Justin went cliff diving. He started out on a cliff that
was 8 feet above the water, and ended up 15 feet
below the surface of the water. How far away from his
starting point was he when he finished?

Number

Problem 1

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Explanation:

Add the equations straight down.

The x terms add to 5x+(-3x) = 2x

The y terms cancel out since 3y+(-3y) = 0y = 0

The right hand sides add to -7+3 = -3

After adding the equations you should get 2x = -4 which solves to x = -2

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Problem 2

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Explanation:

Since 5x = 0, this means x = 0 after dividing both sides by 5.

Use this to find y

y = -4x+4

y = -4(0)+4

y = 4

If you want the value of z, then

x = -3y+z+6

0 = -3(4)+z+6

0 = z-6

6 = z

z = 6

Answer:

l=6

b=30

Step-by-step explanation:

b=5l

perimeter= 72

2(l+b)= 72

l+b= 36

l+5l= 36

6l= 36

l= 6

b=5l= 6*6= 30

Answer:

B and C

Step-by-step explanation:

All others have higher factors than 4

Answer:

B,(4,8) &C,(8,12)

Step-by-step explanation:

A,(2,4)=2=2

4=2^2(GCF of 2&4 is 2)

B,(4,8)=4=2^2

8=2^3(GCF of 4&8 is 4)

C,(8,12)=8=2^3

12=2^2*3(GCF of 8&12 is 4)

D,(8,16)=8=2^3

16=2^4(GCF of 8&16 is 8)

E,(12,24)=12=2^2*3

24=2^3*3(GCF of 12&24 is 12).

i hope it helps you

Answer: 5) 2, -8, 32, _,_

I believe that it would be -64, then 128

Step-by-step explanation:

Bc its positive then negative and its being multiplied by -4 each time so when you mutiply a negative to a negative its a positive which is were the positives and negatives come from. :)

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Explanation:

f(x) is continuous when x >= 1. The only discontinuity for f(x) is when x = 0, but 0 is not part of this interval.

f(x) is positive for any valid x value in the domain since x^6 is always positive. In general, x^n is positive for all x when n is any even number.

f(x) is decreasing. You can see this through a table of values or through a graph. For anything in the form 1/(x^k), it will be a decreasing function because x^k gets larger, so 1/(x^k) gets smaller, when x goes to infinity.

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The conditions to use the integral test have been met. So we have to see if [tex]\displaystyle \int_1^{\infty}f(x)dx[/tex] converges or not.

Let's integrate and find out

[tex]\displaystyle \int \frac{1}{x^6} dx = \int x^{-6} dx\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{1+(-6)}x^{-6+1}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = \frac{1}{-5}x^{-5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5}*\frac{1}{x^5}+C\\\\\\ \displaystyle \int \frac{1}{x^6} dx = -\frac{1}{5x^5}+C\\\\[/tex]

So we have

[tex]\displaystyle g(x) = \int f(x) dx\\\\\\\displaystyle g(x) = \int \frac{1}{x^6} dx\\\\\\\displaystyle g(x) = -\frac{1}{5x^5}+C\\\\\\[/tex]

Meaning that,

[tex]\displaystyle \int_{a}^{b} f(x) dx = g(b)-g(a)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = \left(-\frac{1}{5b^5}+C\right)-\left(-\frac{1}{5a^5}+C\right)\\\\\\\displaystyle \int_{a}^{b} \frac{1}{x^6} dx = -\frac{1}{5b^5}+\frac{1}{5a^5}\\\\\\[/tex]

If we plug in a = 1 and apply the limit as b approaches positive infinity, then the expression [tex]-\frac{1}{5b^5}+\frac{1}{5a^5}[/tex] will turn into [tex]\frac{1}{5}[/tex]

Therefore,

[tex]\displaystyle \int_{1}^{\infty} \frac{1}{x^6} dx = \frac{1}{5}\\\\\\[/tex]

Because this integral converges, this means the series [tex]\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^6}[/tex] also converges as well by the integral test.

Answer:

for example you are given a percentage and numbers you cross multiply

Step-by-step explanation:

hope it helps cause I don't know how to explain the answer

Answer:

power of for example 4 to the power of 2. 2 means square

Answer:

50

Step-by-step explanation:

i asked alexa so yeaaa

Answer:

6

Step-by-step explanation:

4x + 3 = 1

4x =-2

x = -1/2 so 4x +8 =4(-1/2) +8=6

Answer:

9

Step-by-step explanation:

3x3=9

its nine bruhhhhhhhhhhhhh

Answer:

I wish I could help you but i have not learn yhat yet. so sorrry :( pleaser forgive jme....... please i beg u plase

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

Answer:

Geometry so easy

Step-by-step explanation:

You can do it..

Answer:

You must first put the equation into slope-intercept form (y = mx + b). To do this, subtract x from both sides to isolate y. Then, since y will be negative, divide each side by -1, resulting in y = x - 3. Since a 1 is understood to be in front of the x, the slope is 1

How to graph:

x-0 y- -3 or (0,-3)

x- 3 y-0 or (3,0)

If you graph these points you should get your graph

Answer:

16 cups of water

Answer:

[tex]Solution: f(x)\ge-5\\Interval:[-5,\infty)[/tex]

Step-by-step explanation:

Equation: [tex]\frac{1}{4} x^2-5 = y[/tex]

1). [tex]\frac{1}{4} x^2-5 = y[/tex] →[tex]\frac{x^2}{4}-5=y[/tex]

2). [tex]\frac{x^2}{4}-5=y[/tex] ∴ [tex]a=\frac{1}{4}, b=0, c=-5[/tex]

3). [tex]x_v=-\frac{b}{2a}[/tex]

         [tex]=-\frac{0}{2(\frac{1}{4})}[/tex]

         [tex]=0[/tex]

4). now plug [tex]x_v[/tex] into [tex]y_v[/tex]

[tex]y_v=\frac{0^2}{4}-5[/tex]

    [tex]=-5[/tex]

5). Minimum (0,-5) ∴ [tex]f(x)\ge-5[/tex]

$$$$$$$$$$$$$$$$$$$$$$$$$$

he can make 4 stacks, leaving 8 chairs as single chairs

Answer:

there are 8 girl students

Step-by-step explanation:

28-4= 24

28 divided by 3 is 8

8x2=16

16+4=20

20+8= 28

therefore... there are 8 girls in the class

Answer:

it is 82.53 round to 82.50 ithink

Answer:

18,28,38,48,58,68

Step-by-step explanation:

You are adding by 10 every time

Answer:

the third one im pretty sure

Step-by-step explanation:

Answer:

Step-by-step explanation:

A1 = 9 x 4 = 36

A1 = 4 x 3 = 12

Total = 36 + 12

        = 48 in²

Answer:

In math, prime numbers are whole numbers greater than 1, which have only two factors – 1 and the number itself. Prime numbers are divisible only by the number 1 or itself. For example, 2, 3, 5, 7, and 11 are the first few prime numbers.

Step-by-step explanation:

hope this helps :)

Answer:

b, controlled variables are constant and unchanged

A controlled variable is what is held constant. When doing an experiment, it is ideal to only focus on one variable at a time while keeping everything else in check. This way you can compare two items effectively.

In contrast, a manipulated variable is one that is intentionally changed to see how it affects the subject. For example, if you're testing various fertilizers, then the fertilizer brand would be the manipulated variable. The soil, moisture, amount of sunlight, and other environmental factors are kept the same (each subject gets the same about of each) making them to be controlled variables.

Answer:

13.

Step-by-step explanation:

[tex]42 = a + (a+1) + (a+2) = 3a + 3 = 3(a+1)[/tex]

Then, [tex]a+1 = 14[/tex], so [tex]a=13.[/tex]