Is x = 15 a solution to the equation 8x − 8 = 120

9514 1404 393

Answer:

  7.51 m

Step-by-step explanation:

The distance traveled to the first floor hit is 1 m. The next hit has a height that is 14% less, so is 100% -14% = 86% = 0.86 times this height. The travel up and down to/from that height is added to the total.

The distance traveled to the second floor hit is 1 m + 2×(0.86×1 m).

The distance traveled to the third floor hit is 1 m + 0.86×2 m + 0.86²×2 m.

Then the distance traveled to the n-th floor hit is ...

  -1 m + Sum(0.86^k × 2 m) for k = 0 to n-1

The sum can be found from the formula for the sum of a geometric series:

  Sn = a1×(r^n -1)/(r-1) . . . . . where a1 is the first term and r is the common ratio.

For r = 0.86, n = 6, and a1 = (2m), the total distance is ...

  vertical distance = -1 m + (2 m)(0.86^6 -1)/(0.86 -1)

  = -1 m + (2 m)(-0.5954)/(-0.14) ≈ 7.5062 m

The total distance traveled to the 6th floor hit is about 7.51 meters.

_____

Alternate solution

Another way to answer the question is to add up the distances for each bounce. Attached is a spreadsheet that does that.

Answer:

Simplifying

5(x + 9) = 5x + 45

Reorder the terms:

5(9 + x) = 5x + 45

(9 * 5 + x * 5) = 5x + 45

(45 + 5x) = 5x + 45

Reorder the terms:

45 + 5x = 45 + 5x

Add '-45' to each side of the equation.

45 + -45 + 5x = 45 + -45 + 5x

Combine like terms: 45 + -45 = 0

0 + 5x = 45 + -45 + 5x

5x = 45 + -45 + 5x

Combine like terms: 45 + -45 = 0

5x = 0 + 5x

5x = 5x

Add '-5x' to each side of the equation.

5x + -5x = 5x + -5x

Combine like terms: 5x + -5x = 0

0 = 5x + -5x

Combine like terms: 5x + -5x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions

Step-by-step explanation:

Answer:

[tex]S_{7}[/tex] = - 119973

Step-by-step explanation:

The sum to n terms of a geometric sequence is

[tex]S_{n}[/tex] = [tex]\frac{a(r^n-1)}{r-1}[/tex]

where a is the first term and r the common ratio

Here a = - 3 and r = 18 ÷ - 3 = - 6 , thus

 [tex]S_{7}[/tex]   = [tex]\frac{-3(-279936-1)}{-6-1}[/tex]

    = [tex]\frac{-3(-279937)}{-7}[/tex]

    = [tex]\frac{839811}{-7}[/tex]

     = - 119973

Answer:

B. 140

Step-by-step explanation:

With this chart, you must know the fundamentals of the angles. In this case, angle c and e are supposed to equal to 180. In the question, it gives us both the formulas for both angles. So adding them up to 180 will give us x

(x - 10) + (2x + 40)

with a trusty calculator, you will get

= 3x + 30

Now equal this equation to 180

3x + 30 = 180

3x = 180 - 30

3x = 150

Now divide 150 to 3

150 divided by 3 = 50

x = 50

Now just add the x to the angle c

2(50) + 40

=140

To further check if its correct, add the x to angle e

(50) - 10

=40

140 +40 = 180

So the answer would be 140

Answer:

4+11a+8b

Step-by-step explanation:

1) 4+3a+2b+6b+5a+3a

2) 3a+3a+5a=11a. 2b+6b=8b

Answer:2 is equal to 18/1 which is 36 divided by 2

Step-by-step explanation:

Answer:

1 is 20/1 or 20 miles per hour

2 is 18/1 or 18 push ups per min

3 is 15/1 or 15 dollars per hour

4 is 50/1 or 50 km per hour

Step-by-step explanation:

divide the numerators by the denominators

Answer:

1176

hope this will help you

Answer:

Step-by-step explanation:

2L168      

2L84

2L42

3L21

7L7

2x2x2x3x7=168

2L196

2L98

7L49

7L7

2x2x7x7=196

Answer: 3 2/4 & 9 13/15

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

5x+5+4x=4-3x+6

Combine like terms

9x+5 = 10-3x

Add 3x to each side

9x+3x +5 = 10-3x+3x

12x+5 = 10

Subtract 5 from each side

12x+5-5 = 10-5

12x = 5

Divide each side by 12

12x/12 = 5/12

x=5/12

Answer:

x= 56 x= 89

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

75 divided by 5

Answer:

15 problems

Step-by-step explanation:

To find how many problems were correct, find 1/5 of 75:

Divide 75 by 5:

75/5

= 15

So, Harry got 15 problems correct.

Answer:

1. b 2. d 3 a

Step-by-step explanation:

Subtracting from the group or a number of things is what subtracting signifies in math, and the calculation can be defined as follows:

Following are the solution to the given subtraction equations:

For question 1:

A) 4.3 - (-0.9) = 4.3+ 0.9= 5.2 that is true

B)  4.3 - 0.9 = 5.2 that is false because answer is 3.4

C) -4.3 - 0.9 = 5.2 that is false because answer is -5.2

D)  -4.3 - (-0.9) = -4.3 +0.9 = 5.2 that is false because answer is -3.4

For question 2:

[tex]\to \frac{3}{4} + (-\frac{1}{2})\\\\\to \frac{3}{4} -\frac{1}{2}\\\\\to \frac{3-2}{4}\\\\\to \frac{1}{4}\\\\[/tex]

Therefore, the answer is "Option C".

For question 3:

[tex]\to \frac{2}{3} - (-\frac{2}{3})\\\\\to \frac{2}{3} +\frac{2}{3}\\\\\to \frac{4}{3}\\\\[/tex]

Therefore, the answer is "Option B".

For question 4:

[tex]\to \frac{2}{5} + (-\frac{4}{5})\\\\\to \frac{2}{5} -\frac{4}{5}\\\\\to \frac{2-4}{5}\\\\\to \frac{-2}{5}\\\\[/tex]

Therefore, the answer is "Option B".

For question 5:

[tex]\to[/tex] 4 – (-6)

[tex]\to[/tex] 4 +6

[tex]\to[/tex] 10

Therefore, the answer is "Option D".

For question 6:

[tex]\to - \frac{2}{6} + (\frac{3}{2})\\\\\to - \frac{1}{3} + \frac{3}{2}\\\\\to \frac{2-9}{6}\\\\\to \frac{-7}{6}\\\\[/tex]

Therefore, the answer is "Option B".

For question 8:

[tex]\to \frac{3}{4} - (-\frac{1}{4})\\\\\to - \frac{3}{4} + \frac{1}{4}\\\\\to \frac{3+1}{4}\\\\\to \frac{4}{4} \\\\ \to 1[/tex]

Therefore, the answer is "Option D".

For question 9:

A) -3.4 + 5.7 = -9.1 that's is false because answer is 2.3

B) -3.4 + (-5.7) = -9.1 that's is true.

C) 3.4 + (-5.7) = -9.1 that's is false because answer is -2.3

D) 3.4 + 5.7 = -9.1  that's is false because answer is 9.1

Find out more about the subtraction here:

brainly.com/question/1927340

Answer:

B:rate

Step-by-step explanation:

the formula distance= rate × time

Answer:

B

Step-by-step explanation:

The formula for distance is rate × time.

Flow and work don't make sense. Also, work is force × distance.

However, you were given rate is equal to distance/time (r=d/t) and were asked to find what distance would be:

in that case, we'll isolate d onto one side

here's the equation

r=d/t

multiply by t on both sides

rt=d, or rate × time equals distance

either way it's B

Hope this helps!

Answer:

[tex]\frac{4+16a^3+23a^3}{a^2}[/tex]

Step-by-step explanation:

Given

[tex]1/a^2-3a+2 + 1/a^2-5a+6 + 2/a^2-8a+15[/tex]

Required

Simplify

[tex]1/a^2-3a+2 + 1/a^2-5a+6 + 2/a^2-8a+15[/tex]

Collect Like Terms

[tex]1/a^2 + 1/a^2 + 2/a^2-3a-5a-8a+2+6+15[/tex]

[tex]1/a^2 + 1/a^2 + 2/a^2-16a+23[/tex]

Add Fractions:

[tex]\frac{1+1+2}{a^2} + 16a + 23[/tex]

[tex]\frac{4}{a^2} + 16a + 23[/tex]

This can be further expressed as:

[tex]\frac{4+16a^3+23a^3}{a^2}[/tex]

Answer:

Lets show that:

Use formula:

Multiply LHS by 2sinx/2sinx:

Now, we can easily find that:

Coming back to the original equation, we get:

Answer:

8 percent loss

Step-by-step explanation:

The percentage loss is -8%.

Given that,

Based on the above information, the percentage loss should be

[tex]= \frac{\$4.60-\$5}{\$5}[/tex]

= -8%

Therefore we can conclude that the percentage loss should be -8%.

Learn more: brainly.com/question/2155156

Answer:

A. 13 + t = 17

Step-by-step explanation:

The top rectangle shows 13 and t, the 13 and t rectangle is the same size as the 17 rectangle so 13 + t = 17. It's not multiplication as there's no multiple's of 13 or t on the diagram.

Answer:

64 Nickels

Step-by-step explanation:

172 coins equal $14.00

It took time to figure this out, I just used a calculator to shimmy down the gap of possibilities, starting here;

100d = $10.00

72n = $3.60

I got closer here;

110d = $11.00

62n =$3.10

I subtracted 2 dimes and added 2 nickels from the previous to get the answer.

108d = $10.80

64n = $3.20

$10.80 + $3.20 = $14.00

Answer:

20

Step-by-step explanation:

20 may be answer for this may be

Answer:

1. 6x+10

2. 3x+[tex]\frac{1}{2}[/tex]/5

3. 2.5x-1.1

I'm not sure if I did it in the correct format. :(

Answer:

The team made x<53 points total.

Step-by-step explanation:

1/4+1/10 is 7/20 or 0.35 in decimal form. If they both together scored 21 points then you can add another 7/20 (21 points) and have 14/20 (42 points). You have 6/20 more left. If you can solve what 1/20 could be then you would find the answer. Does this helps?

Answer:

The total number of points scored is 60.

Step-by-step explanation:

We can multiply a number to both fractions to get them to share a common denominator so we can add them easily. 20 is a multiple of both 4 and 5, so let us multiply both denominators so that they each have a denominator of 20.

1/10 * 2 = 2/20

1/4 * 5 = 5/20

Now we can add those fractions together because we want to see the total amount of points the team scored.

2/20 + 5/20 = 7/20

If 7/20 is 21 points, we can find out how much points takes up 1/20 of the fraction. We do this by dividing 21 by 7.

21 / 7 = 3

So 1/20 = 3

Now we multiply 3 by 20, which is 60. So therefore the total amount of points scored by the team is 60. Brian scored 1/10 of 60, which is 6. So he scored 6 points. Joe scored 1/4 of 60, which is 15. So Joe scored 15 points. Hope this helps.

Answer:Phil Wickham - Great Things (Official Lyric Video) -

Step-by-step explanation:

Given:

The table shown the number of campers, x, at a local campsite and the total amount of money, y, in dollars, earned by the camp site.

To find:

The unit for the rate of change.

Solution:

We know that, rate of change is the change in y-values with respect to x-values, i.e.,

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

In the given problem, y is the total earnings in dollars and x is the number of campers. So, the rate of change represents the change is earnings with respect to number of campers.

Thus, the unit of rate of change is dollars per camper.

Therefore, the correct option is D.

Answer:

37.5%

60%

75% and .75

Step-by-step explanation: