х
у
-3
0
-2
-5
-1
-25
0
-60
1
-110
2
-60
3
-25
4
-5
5
0

Answer:

Step-by-step explanation:

Initial height of the ball = 8feet

If it bounces 60% of its previous height, its new height will be;

60% of 8

= 60/100 * 8

= 480/100

= 4.8 ft

If it bounces 60% of its current distance, new height will be expressed as;

60% of 4.8

= 0.6 * 4.8

= 2.88

The height of the ball will keep reducing and form a geometric progression of the form 8, 4.8, 2.88...

In order to get the total distance traveled by the ball, we need to calculate the sum to infinity of the sequence;

S∞ = a/1-r where;

a is the first term = 8

r is the common ratio

[tex]r = \frac{4.8}{8} = \frac{2.88}{4.8}\\r = 0.6[/tex]

Substitute into the formula;

S∞ = a/1-r

S∞ = 8/1-0.6

S∞ = 8/0.4

S∞ = 20feet

Hence the total distance traveled by the ball is 20feet

Answer:

The rate of change of the diver's elevation was 10 53/89 ft./min

Step-by-step explanation:

The given parameters are;

The initial elevation of the diver = 0 feet (Ocean surface level)

The depth to which the diver dove = -59 9/10 feet

The rate at which the diver descended = -18.4 feet/minute

The duration the diver spends at the elevation, t₁ = 12 minutes

The depth to which the diver ascended to = -18 9/10 feet

The total time the diver takes so far in the ocean, [tex]t_{(tot)}[/tex] = 19 1/8 minutes

Therefore, we have;

The time it takes the diver to descend to -59 9/10 feet t₂ = -59 9/10/(-18.4) = 3 47/184 minutes

The duration of the divers ascent = [tex]t_{(tot)}[/tex] - t₁ - t₂ = 19 1/8 - 12 - 3 47/184 = 3 20/23 minutes

The rate of change of the divers elevation in ascent = Distance of elevation/Time

The rate of elevation of the divers elevation in ascent = (-18 9/10 - (-59 9/10))/(3 20/23) = 41/(3 20/23) = 943/89 feet/minute = 10 53/89 feet/minute

The rate of change of the diver's elevation = 10 53/89 ft./min ≈ 10.6 ft./min.

Answer:

$1.20 per candy bar

Step-by-step explanation:

7.2 ÷ 6 = 1.2

Step-by-step explanation:

Given the expression for the position of a body moving along the s-axis expressed as;

[tex]s = t^3-27t^2+200t[/tex]

The acceleration of the body function will be gotten by finding the second derivative of the displacement function as shown;

[tex]\frac{ds}{dt} = 3t^2-2(27)t+200\\ \frac{ds}{dt} = 3t^2-54t+200\\\\\\a = \frac{d^2s}{dt^2} = 2(3)t-54\\a = \frac{d^2s}{dt^2} = 6t-54\\[/tex]

First we need to get the time taken when the velocity is zero.

[tex]Given \ v(t) = \frac{ds}{dt} = 3t^2-53t+200\\at \ v(t) = 0\\0 = 3t^2-54t+200\\[/tex]

factorize;

t = 54±√54²-4(3)(200)/2(3)

t = 54±√2916-2400/2(3)

t = 54±√516/6

t = 54±22.72/6

t = 54+22.72/6 and 54-22.72/6

t = 12.79s and t = 5.21s

Get the acceleration;

at t = 12.79

a = 6t-54

a = 6(12.79)-54

a = 76.74-54

a = 22.74m/s²

at t = 5.21

a = 6t-54

a = 6(5.21)-54

a = 31.26-54

a = -22.74m/s²

Hence the body's acceleration each time the velocity is zero are 22.74m/s² and -22.74m/s²

Answer:

(3+x)+24

Step-by-step explanation:

24+(3+x)

Since addition is communitive, you could take out the parenthesis.

24+3+x

Hope this helps. Have an AWESOME night!!! :)

Answer:

-10

Step-by-step explanation:

Answer:

Slope= − 1.500/2.000

= -0.750

x intercept= 102/3

= 34

y−intercept= 102/4

= 51/2

= 25.50000

Step-by-step explanation:

sorry if this is wrong, I tried!

Answer:

So you pretty much just solved your math by yourself :)

Step-by-step explanation:

Answer:

16 ft^2

Step-by-step explanation:

If it is a perfect square, all you have to do is find the square root of the area, which in this case, is 16.

Answer:A

Step-by-step explanation:

Answer: 3.5

Step-by-step explanation:

Answer:

36

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Answer:

Richard gets £240

Step-by-step explanation:

Let

Stephen's share = x

Richards share = 3x

Natasha's share = 2(3x)

Total money = £800

Total money = Stephen's share + Richards share + Natasha's share

800 = x + 3x + 2(3x)

800 = 4x + 6x

800 = 10x

Divide both sides by 10

x = 800 / 10

= 80

x = £80

Stephen's share = x = £80

Richards share = 3x

= 3(80)

= £240

Natasha's share = 2(3x)

= 2(240)

= £480

Richard gets £240

Answer:

2

Step-by-step explanation:

Answer:

Angle STR = 78°

Step-by-step explanation:

So, since line QS is a straight line, we know that it's 180°. We also know that angles QTR and STR both add up to 180°. That gives us an equation:

20x + 12 + 10x + 33 = 180

Combine like terms

30x + 45 = 180

Subtract 45 from both sides

30x = 135

Divide both sides by 30

x = 4.5

Now we know the value of x. We just need to plug it into angle STR's given value:

10(4.5) + 33 = angle STR

45 + 33 = angle STR

78° = angle STR

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

[tex]Division \: \: \: Property[/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

The correct answer is (( A )) .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer: 360 degrees

Step-by-step explanation: There are 4 sides in an angle. Substitute that value in for n and u have: (4-2) x180. After doing that, subtract inside the parenthesis and multiply your difference by 180. You should get 360 degrees. I hoped this helped.

Answer:

360!!!!!!!!!!!!!!!!!!!! ;)

Step-by-step explanation:

Answer:

linear decreasing

Step-by-step explanation:

cause it is a straight line and it's going down so it's decreasing.

Answer:

linear decreasing

Step-by-step explanation:

the answer that will appear before mine is right

This question is incomplete

Complete Question

An arts academy requires there to be 5 teachers for every 90 students and 3 tutors for every 30 students.

How many students does the academy have per​ teacher?Per​ tutor?

How many tutors does the academy need if it has 80 students

Answer:

a) 18 students per teacher

b) 10 students per tutor

c) 8 tutors

Step-by-step explanation:

a) How many students does the academy have per teacher?

5 teachers for every 90 students

Hence,

5 teachers = 90 students

1 teacher = x students

Cross Multiply

5 × x = 1 × 90

5x= 90

x = 90/5

x = 18 students

We have 18 students per teacher

b) How many students Per​ tutor?

3 tutors = 30 students.

1 tutor = x students

3 × x = 30 × 1

x = 30/3

x = 10 students

We have 10 students per tutor

c) How many tutors does the academy need if it has 80 students

3 tutors = 30 students.

30 students = 3 tutors

80 students = x tutors

Cross Multiply

30 × x = 80 × 3

x = 80 × 3/30

x = 8 tutors

The school needs 8 tutors for 80 students.

2.73

For each pound of walnuts, it costs $2.73.

All you have to do is divide 10.92 by 4.

Answer:

y=3x+8

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

14 x + 1

Step-by-step explanation:

You aren't dumb, your teacher can't teach!

First we must add the x values together:

8x - 7 + 6x + 8

8 + 6 = 14

14x -7 + 8

Now we add the constants (regular numbers):

14x -7 + 8

-7 + 8

14x +1

There we go!

8x -7 + 6x +8

is

14x +1

Answer:

You line up the letters

Answer:

y=13.50x

Explanation:

Answer:

Step-by-step explanation:

stop the cappppppppppp

Answer:

X=51

y=39

Step-by-step explanation:

x=90-39=51

y=90-51=39

Answer:

1,820 trout

Step-by-step explanation:

Set up a proportion where x is the number of trout in the lake:

[tex]\frac{7}{25}[/tex] = [tex]\frac{x}{6,500}[/tex]

Cross multiply and solve for x:

25x = 45,500

x = 1820

So, you could expect 1,820 trout to be in the lake.

Answer: 2.4 x 10^8

Step-by-step explanation:

Answer: 2.4x10^8

Step-by-step explanation:start from the end and move the decimal point all the time way up to the middle of 2 and 4 and u move 8 times to get there which is how we got the exponent 8

Answer:

D. 81

Step-by-step explanation:

This answer was confirmed by two people in the comments.

What I did to get this answer was subtract 162 by 81 so the math that I did was to make sure I got the same number as the answers.

[tex]162-81=81[/tex] ☑

[tex]162-72=90[/tex] ☒

[tex]162-162=0[/tex] ☒

[tex]162-324=-162[/tex] ☒

So, therefore the answer is [tex]81[/tex].

I hope this helped you. :)