A rubber ball is dropped from a height of 5 feet and bounces to 1/3 of its height after each fall. If it continues to bounce until it comes to rest, find the total distance in feet it travels.

Step-by-step explanation:

it is a linear function, if the change in y is constant in relation to the changes of x.

in other words, if the slope y change/x change is the same for every point.

when we look at the table, we see x changes constantly by +2.

and y changes constantly by -6.

so, the change rate/slope is constantly -6/2 = -3.

and therefore it is a linear function.

the equation looks like (the slope is always the factor of x)

y = -3x + b

b we get by using one of the x,y pairs like 1,4

4 = -3×1 + b = -3 + b

b = 7

so, the full equation is

y = -3x + 7

Step-by-step explanation:

Given the table of values, {(-3, 16), (-1, 10), (1, 4), (3, -2), (5, -8)}:

We must determine whether the given relation or data can be modeled by a linear equation.  It is necessary to analyze the pattern that exists between changes in y-values, along with the changes in x-values.

Subtracting the x-coordinates provides a constant difference of 2:

If you perform these same steps throught the remaining rows, then you'll get the same difference of 2.

We can perform the same steps for the y-coordinates. Subtracting the y-coordinates provides a constant difference of -6.

If you perform these same steps throught the remaining rows, then you'll get the same difference of -6.

Since the constant change in y = -6, and the constant change in x = 2, then we can calculate for the slope as: Δy/Δx = -6/2 = - 3.  Hence, the constant rate of change = -3.

As demonstrated throughout this post, we can infer that there is a linear pattern that exists between the x- and y-values.

Therefore, the data can be modeled by a linear equation because the rate of change is constant.

In order to establish the linear equation that represents y as a function of x, we can use the slope, m = -3, and one of the given ordered pairs, (1, 4), to solve for the value of the y-intercept, b. Substitute these values into the slope-intercept form, y = mx + b:

y = mx + b

4 = (-3)1 + b

4 = -3 + b

Add 3 to both sides to isolate b:

4 + 3 = -3 + 3 + b

7 = b

Therefore, the linear equation that represents the given data is: y = -3x + 7.

Answer:

Step-by-step explanation:

Given function:

The vertex is (2, 3)

We know the vertex form:

Substitute coordinates to get:

Compare with given to find out:

amys share would be 45:30 so amys is 45 and marys 30

Answer:

0.375

Step-by-step explanation: All you need to do is divide 3 and 8

Answer:

9261

Step-by-step explanation:

Substitute -3 for a and -12 for b in (a - 2b)^3:

(-3 - 2·-12)^3, or

(-3 + 24)^3, or

21^3 = 9261 (answer)

Answer:

#a

This is a cube. Let us find the surface area of the cube now

Surface are of a cube = 6 a²

                                     = 6 × 1.2 × 1.2

                                     = 6 × 1.44

                                     = 8.64 cm²

# b

This is a right trianglular prism.

First you have to find the area of the 2 triangles

Before that,

we have to find the height of the triangle using pythagoras theorem.

Let us solve,

[tex]5^{2} =4^{2} +h^{2} \\25=16+h^{2} \\9 =h^{2}\\\sqrt{9} =h\\3=h[/tex]

Now let us find the area of 2 triangles.

[tex]Area =2*\frac{1}{2} *4*3\\[/tex]

[tex]Area =12mm^{2}[/tex]

Now lets find the total area of 3 rectangles.

( 7 mm × 4 mm) + ( 7 mm × 5 mm) + ( 7 mm × 3 mm )

28 mm² + 35 mm² +21 mm²

= 84 mm²

And now lets find the total surface area of this solid.

12 mm² + 84 mm²

= 96 mm²

Hope this helps you.

Let me know if you have any other questions :-)

Step-by-step explanation:

y = (x - 4)/x = x/x - 4/x = 1 - 4/x

c = 1

r = -4

done ...

Answer:

reserved tickets = 6 and general admissions tickets = 15

Step-by-step explanation:

[tex]25r + 10g = 150[/tex]

Use two variables to make the equation r for reserved tickets and g for general admission. Reserved cost 25 so put that with r and general cost 10 so out that with g. Since he has 150 to spend the equation will equal 150.

Set r equal to 0 since he isn't buying reserved tickets and only general. Solve for g

[tex]25(0) + 10g = 150 \\ 10g = 150[/tex]

divide both sides by 10

[tex] \frac{10g}{10} = \frac{150}{10} \\ g = 15[/tex]

Now set g equal to zero since he isn't buying any general tickets. Solve for r.

[tex]25r + 10(0) = 150 \\ 25r = 150[/tex]

divide both sides by 25

[tex] \frac{25r}{25} = \frac{150}{25} \\ r = 6[/tex]

Answer:

12.7272

Step-by-step explanation:

subtract 10 on both sides

divide by 11 on both sides 11/11>140/11

Answer:

x=130

Step-by-step explanation:

11x+10>=150

11x>= 150-10

11x>=140

x>=140-11

x>=129

so, because "x" is bigger than 129,

so, x=130

Answer:

In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of an ordering ( or ranking ) - of the class of objects to which it belongs.

Answer:

27 is the answer

Step-by-step explanation:

36/.75=27

Answer:

d

Step-by-step explanation:

Answer:

I say true

Step-by-step explanation:

How to calculate discount and sale price:

Find the original price (for example $90 )

Get the discount percentage (for example 20% )

Calculate the savings: 20% of $90 = $18.

Subtract the savings from the original price to get the sale price: $90 - $18 = $72.

And You're all set!

Answer:

False

Step-by-step explanation:

Sale price = original price - rate of discount * original price

Rate of discount is a percent  so we need to multiply by the original price to get a a price so that all the units are the same.

Answer:

2x^2+5x-3

Step-by-step explanation:

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

1, 6, and -5

make it 0

Answer:

Step-by-step explanation:

If two lines are parallel, then there is no intersection and therefore no solutions.

Correct choice is D

Answer:

D. The system of equations does not have one solution because the lines will never intersect.

edg2021Unit Test

Step-by-step explanation:

There won't be any change in the total mass of the atoms involved in a chemical reaction. According to the law of conservation of mass; it states that mass can neither be created nor destroyed in a chemical reaction. So, when atoms participate in a chemical reaction they might displace with other reactants but the total mass will remain the same.

_______

RainbowSalt2222 ☔

Answer:  12

Step-by-step explanation:

A 45 degree angle in a right triangle means that the third angle is also 45 degrees (180 -(90+35)) = 45.  Two 45 degree angles in a right triangle means that the two sides will be equal.  So we can find the hypotenuse, x, by:

(6[tex]\sqrt{2}[/tex])² + (6[tex]\sqrt{2}[/tex])² = x²

(6[tex]\sqrt{2}[/tex])² = 36*2 or 72

72 + 72 = x²

x² = 144

x = 12

Answer:

I think -1(20+16)= -1(36)= -36

Answer:

Step-by-step explanation:

-20 - 16

=> -36.

Unfortunately, there is no option of -36. Please include -36 in one of the options.

Step-by-step explanation:

the slope is -3

that is the answer

Answer:

m = 3/-6

Step-by-step explanation:

Look at attached photo

Answer: 30

Step-by-step explanation:

Answer:

30 po brainliest answer po ty

Answer:

  x = 4

Step-by-step explanation:

After you simplify the left side by eliminating parentheses and collecting terms, you have a 2-step linear equation.

  -3(4x +3) +4(6x +1) = 43 . . . . . . given

  -12x -9 +24x +4 = 43 . . . . . eliminate parentheses

  12x-5 = 43 . . . . . . . . . . . collect terms (now a 2-step equation)

  12x = 48 . . . . . . . . . . step 1, add the opposite of the unwanted constant

  x = 4 . . . . . . . . . . . step 2, divide by the coefficient of x

The solution is x = 4.

__

Check

  -3(4·4 +3) +4(6·4 +1) = 43 . . . . substitute for x

  -3(16 +3) +4(24 +1) = 43

  -3(19) +4(25) = 43

  -57 +100 = 43 . . . . . true

If g(x)=x4−3x3−x, the value of x such that g′(x)=12 is x = 2.67

The given function is:

[tex]g(x)=x^4-3x^3-x[/tex]

The derivative of the function g(x) is calculated below

[tex]g'(x)=4x^3-9x^2[/tex]

The question indicates that g'(x) = 12

This means that we are going to equate the derivative of g(x) gotten above to 12

[tex]4x^3-9x^2=12[/tex]

Solving the cubic equation above

The only real valid value of x is 2.67

Therefore, the value of x such that g′(x)=12 is x = 2.67

Learn more here: https://brainly.com/question/25754111

Answer:

y=x+2

Step-by-step explanation:

since the slope is 1, we have y=x +b. now plug in the point (2,4) to get 4=2+b, b=2, so the graph is y=x+2

(3, -1)  Looking at the two equations I see that you have a+ y in equation one and − y in equation two. By adding the two equations together I will eliminate the y variable and then you can solve for x.

Answer:

x = 7°

Step-by-step explanation:

∠WST is an exterior angle of the triangle

The two interior angles (5x - 1) and (57) add up to WST ( 12x + 7) because they are the non-adjacent interior angles

Solve:

(5x - 1) + (57) = (12x + 7)

5x - 1 = 12x - 50

-1 = 7x - 50

49 = 7x

x = 7

-Chetan K

Answer:

38

Step-by-step explanation:

No. of yellow envelopes she has

= 6-2

= 4

No. of green envelopes she has

= 7×4

= 28

Total number of envelopes she has

= 6+4+28

= 38

Answer:

95 degrees

Step-by-step explanation:

The sum of all the angles need to come to 360 degrees. We already have 2 90 degree angles, together 180 degrees. Subtract from 360 to get 180, so we know the other two angles together need to equal 180. x + x + 10 = 180

Add common terms, then subtract 10: 2x = 170

Divide by 2: x = 85

So angle F is 85 + 10, or 95 degrees.