A ball is dropped from a height of 20 feet. Each time the ball bounces it returns to 7/9 of the height it fell from. Let an represent the maximum height of the ball on the nth bounce.

A) Find a formula that describes an. Express the common ratio as a fraction. Hint: Use an = a1r^n-1 and place r in parentheses!
an = _____________

B) What is the maximum height of the ball on the 6th bounce? Round your answer to three decimal places.
_______________ feet

The linear equations that represent the relationships in the question order are;

A linear equation is an equation of the form; y = m·x + c

The slope of the line is found as follows;

(-5 - (-21))/(-1 - (-5)) = 4

The equation is y - (-5) = 4·(x - (-1)) = 4·x + 4

y = 4·x + 4 - 5 = 4·x - 1

The y-intercept is (0, 4), the x-intercept is (4, 0)

The slope is therefore; (0 - 4)/(4 - 0) = -1

The equation is therefore; y - 0 = -1 × (x - 4) = -x + 4

The y-intercept is (0, -1), the x-intercept is (4, 0)

The slope is therefore; (0 - (-1))/(4 - 0) = 1/4

The equation is therefore; y - 0 = (1/4) × (x - 4) = x/4 - 4/4 =

The slope of the line is; [tex]\dfrac{-3\frac{3}{4} - \left(-\frac{3}{4}\right) }{4-1} = -1[/tex]

y - (-3/4) = -1 × (x - 1) = -x + 1

y = -x + 1 - (3/4) = -x + 1/4

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Answer: false

Step-by-step explanation:

if the expected grade was 100 but passing was 80 then she couldn't have passes with a 48

Answer:

find p (A or ),given that A and B are independent

Answer: It indicates that the quadratic has a repeated real number solution.

Step-by-step explanation:

The area of the trapezoid is equal to 7 square units.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the trapezoid in a two-dimensional plane is called the area of the trapezoid.

Given that the area of a trapezoid is given by the formula A = 1/2

h(b₁ + b₂). The given values are h = 2, b₁=3, and b₂=4.

The area of the trapezoid is calculated as,

Area = (1 / 2) x h(b₁ + b₂)

Area = (1 / 2 ) x 2 x ( 3 + 4 )

Area = 7

Area = 7 square units

Therefore, the area of the trapezoid is equal to 14 square units.

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This is 224's prime factorization. This is the method of repeated division, and the prime factorization of 224 is 2 2 2 2 7.

Image for number 2. Show that the prime factorization of 220 is the same when 220 is multiplied by 2 times 110 or 10 times 22. What numbers might possibly be in the next form when numbers? Give two or three responses.

Therefore, 22 51 111, where 2, 5, and 11, can be expressed as 220's prime factorization.

220 has three prime factors, which are 22; 51; and 111. Here, the pair does not contain the prime factor 5. Consequently, 220 is not a square perfectly.

Consequently, the first ten multiples of 220 are as follows: 220, 440, 660, 880, 1100, 1320, 1540, 1760, 1980, and 2200.

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Answer:

A

Step-by-step explanation:

Fill in X and Y for each of the equations until you find one that fits

The equation of the line y=2x+3 passes through the (1,4) point only.
The line gave y=2x+3.

In order to check whether the line passes through the points the following steps are:

A) (1,4)

Here x=1 , y=4.

We will put these values in the line y=2x+3.

4= 2(1)+3

4=4
As L.H.S=R.H.S, therefore this point (1,4) passes through the line.

B) (-1,4)

Here x=-1 , y=4.

We will put these values in the line y=2x+3.

4= 2(-1)+3

4= -2+3
4 [tex]\neq[/tex] 1
As L.H.S  [tex]\neq[/tex]R.H.S, therefore this point (1,4) does not pass through the line.

C) (2,3)

Here x=2 , y=3.

We will put these values in the line y=2x+3.

3= 2(2)+3

3= 4+3
3 [tex]\neq[/tex] 7
As L.H.S  [tex]\neq[/tex]R.H.S, therefore this point (2,3) does not pass through the line.

D) (3,2)

Here x=3 , y=2.

We will put these values in the line y=2x+3.

2= 2(3)+3

2= 6+3
2 [tex]\neq[/tex] 9
As L.H.S  [tex]\neq[/tex]R.H.S, therefore this point (3,2) does not pass through the line.

Only (1,4) point passes through the line.

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The reasons put into the correct order to justify solving the inequality:

-2(x + 6) < 3(x + 1) - Given

-2x - 12 < 3x + 3 - Distributive Property

-2x < 3x + 15 - Addition Property of Order

-5x < 15 - Subtraction Property of Order

x > 3 - Division Property of Order

Check how to solve:

-2(x + 6) < 3(x + 1)

Open the parenthesis

-2x - 12 < 3x + 3

Add 12 to both sides

-2x - 12 + 12 < 3x + 3 + 12

-2x < 3x + 15

Subtract 3x from both sides

-2x - 3x < 3x + 15 - 3x

- 5x < 15

divide both sides by -5

x > 3

Therefore, the solution to the given inequality -2(x + 6) < 3(x + 1) is x > 3.

The properties mentioned above are properties of inequalities and hold for all situations of inequalities as given.

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The common denominator of the complex fraction is (1/a - 1/b)/(1/a + 1/b) is a²b² which is option D.

The provided complex fraction is  (1/a - 1/b)/(1/a + 1/b).

Now, to find the common denominator,

Solving this complex fraction.

First multiplying each component of every bracket to every component of the other bracket,

= 1/a² + 1/ab - 1/ab - 1/b²

Now, simplifying the equation,

= 1/a² + 1/b²

= (a²+b²)/a²b²

The denominator is the lower part of the fraction.

Hence, the common denominator of the complex fraction is a²b².

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Complete question - What is the common denominator of 1/a + 1/b in the complex fraction (1/a - 1/b)/(1/a + 1/b)?

A)a2 b2

B)a – b

C)a + b

D)ab

Question 1

Since the x-coordinates are the same, the line is vertical. Therefore, the slope is undefined.

Question 2

Since the y-coordinates are the same, the line is horizontal. Therefore, the slope is zero.

Using the rate, the number of book Mason reads per month is 2 books.

Mason read 4 books in 2 months. Mason reads at a constant rate. The number of books he reads each month can be calculated as follows;

The number of books he reads is at a constant rate. The rate formula can be used to find the number of book Mason read each month.

rate = number of books read / number of month

Therefore,

number of books read = 4 books

number of month = 2 month

Hence,

rate  = 4 / 2

rate = 2 books per month

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Answer:

[tex]f(h(x)) = ( \sqrt{x} - 3)^{2} + 4[/tex]

[tex]f(h(x)) = (x - 9) + 4[/tex]

[tex]f(h(x)) = x - 5[/tex]

Step-by-step explanation:

h(x) became x for function of f(x)

Factor the expression using the GCF 24y+88x

24y+88x

GCF is 8:

8(3y + 11x)

You can occasionally start by isolating and replacing a variable that is squared in both equations if you're required to solve a system of equations without a starting linear equation.

If there isn't a linear equation to begin with, you can pick out and use a squared variable in both equations.

Start by dividing both sides of the supplied nonlinear equation by the variable's coefficient, for instance.

After you've done that and isolated a variable, carry on with the problem-solving by adding that variable to the other equation.

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Answer:

30 tadpoles

Step-by-step explanation:

the 3 part of the ratio relates to the number of swans, that is 18 , then

18 ÷ 3 = 6 ← value of 1 part of the ratio

Then

number of tadpoles = 5 × 6 = 30

The domain and range of this square root function are: D: [–4, ∞) and R: [0, ∞).

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function or relation is defined. This ultimately implies that, a domain is the set of all possible input values (x-values) for a function while a range is the set of all possible output values (y-values) of a function.

Based on the information provided, the function is represented as follows:

g(x) = √(x + 4)

Since a square root function doesn't exist for all negative values, the domain of this function is given by:

x + 4 ≥ 0

x ≥ -4

Domain = [-4, ∞]

Since we do not have a vertical translation, the range of this square root function is given by:

x ≥ 0

Range = [0, ∞]

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Answer:

[–4, ∞) and R: [0, ∞)

Step-by-step explanation:

I got it right on the test.

The graph of f(x)=|x| and m(x)=|x+1| is 1 unit left translation

From the question, we have the following function that can be used in our computation:

f(x) = |x|

m(x) = |x + 1|

First, we have the transformation to be:

From f(x) = |x| to m(x) = |x + 1|

This means the function is translated left by 1 unit

So, we can conclude that

The graph function is translated left by 1 unit

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Answer:

[tex]2 \sqrt[3]{3} [/tex]

Step-by-step explanation:

[tex]24 {}^{ \frac{1}{3} } [/tex]

[tex] \sqrt[3]{24} [/tex]

[tex] \sqrt[3]{8 \times 3} [/tex]

[tex] \sqrt[3]{8} \times \sqrt[3]{3} [/tex]

[tex] \sqrt[3]{2 {}^{3} } \times \sqrt[3]{3} [/tex]

[tex]2 \times \sqrt[3]{3} [/tex]

[tex]2 \sqrt[3]{3} [/tex]

Answer:

$23.55

Step-by-step explanation:

First we will need to determine the total amount of sales Ryan and Carlos made. To do that we will multiply the amount of products sold by the product cost.

$2.75 x 12 = $33

Now we need to deduct the cost of supplies they need to pay back from their profits.

$33- $9.45= $23.55

Now we are left with Ryan and Carlos' total profit, which is $23.55

Charmaine sends 34 message, Jose send 75 texts and Shen send 25 messages.

What is linear equation?

An equation is a mathematical statement, which has an equal sign (=) between the algebraic expression. Linear equations are the equations of degree 1. It is the equation for the straight line.

Let C be charmaine text, S be shen text, J be jose text.

C +J+ S=134

Shen send 9 messages fewer than charmine .

S = C -9

C = S+9

And Jose sent 3 times more then shen

J =3S

We get,

S+9+3S+S=134

5S +9 = 134

5S = 134 -9

5S = 125

S = 25

C = 25 +9

= 34

J= 75

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Answer:

Answer:

[tex]8\sqrt{11}[/tex]

Step-by-step explanation:

Given:

[tex]x+\dfrac{1}{x}=\sqrt{11}[/tex]

Sum of two squares

[tex]\boxed{a^2+b^2=(a+b)^2-2ab}[/tex]

[tex]\textsf{Let}\; a = x[/tex]

[tex]\textsf{Let}\; b = \dfrac{1}{x}[/tex]

Therefore:

[tex]\begin{aligned}x^2+\dfrac{1}{x^2}&=\left(x+\dfrac{1}{x}\right)^2-2x\left(\dfrac{1}{x}\right)\\\\&=\left(\sqrt{11}\right)^2-2\\\\&=11-2\\\\&=9\end{aligned}[/tex]

Sum of two cubes

[tex]\boxed{a^3+b^3=(a+b)(a^2-ab+b^2)}[/tex]

[tex]\textsf{Let}\; a = x[/tex]

[tex]\textsf{Let}\; b = \dfrac{1}{x}[/tex]

Therefore:

[tex]\begin{aligned}x^3+\dfrac{1}{x^3}&=\left(x+\dfrac{1}{x}\right)\left(x^2-x\left(\dfrac{1}{x}\right)+\left(\dfrac{1}{x}\right)^2\right)\\\\ &=\left(x+\dfrac{1}{x}\right)\left(x^2-1+\dfrac{1}{x^2}\right)\\\\&=\left(x+\dfrac{1}{x}\right)\left(x^2+\dfrac{1}{x^2}-1\right)\\\\&=\sqrt{11}\left(9-1\right)\\\\&=8\sqrt{11}\end{aligned}[/tex]

The heights of both trees at the time when they have an equal height are equal to 4 inches and 48 inches respectively.

In order to graphically solve the system of equations, we would first of all write a system of equations that models the situation. Additionally, we would assign variables to the height of Tree A t years after being planted and height of Tree B t years after being planted, and then translate the word problem into algebraic equation as follows:

Therefore, translating the word problem into algebraic equation, we have the following:

A = 32 + 4t

B = 16 + 8t

On a graph, we would plot the height of Tree A on the x-axis while height of Tree B would be plotted on the y-axis of the cartesian coordinate.

By critically observing the graph, the point of intersection which gives a solution to the system of equations include the following:

Height of Tree A, A = 4 inches.

Height of Tree B, B = 48 inches.

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The coordinates of the point after the two reflections are (0.3,-7/10).

A reflection is a mapping from an isometric hyperplane with a set of fixed points acting as the reflection's axis or plane from a Euclidean space to itself. A figure's reflection creates its mirror image of that figure in the plane or axis of the reflection.

Given that, the point (-0.3, 7/10) is reflected over the y-axis and then over the x-axis respectively.

The coordinates of the point after the reflection in the y-axis are:
(0.3, 7/10)

Now, the coordinates of the point after the reflection in the x-axis are:
(0.3, -7/10)

Hence, the coordinates of the point after the two reflections are (0.3,-7/10).

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The graph of the inequality is plotted using the below points.

Graph:

In math, graph show you information as a visual image or picture.

Given,

Here we need to find the graph of the given inequality.

To graph an inequality:

To graph the related boundary line. We have to replace the <, >, ≤ or ≥ sign in the inequality with = to find the equation of the boundary line.

Now, we have to identify at least one ordered pair on either side of the boundary line and substitute those (x, y) values into the inequality.

Then shade the region that contains the ordered pairs that make the inequality a true statement.

Here if points on the boundary line are solutions, then use a solid line for drawing the boundary line. This will happen for ≤ or ≥ inequalities.

Where as if points on the boundary line are not solutions, then use a dotted line for the boundary line. This will happen for < or > inequalities.

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Answer:

Separating the variables , using equality symbol , drawing boundary line in XY plane , shading the area are the four steps in graphing linear inequalities

Step-by-step explanation:

Mathematical expressions known as linear inequalities compare two expressions using the inequality symbol. The expression may be either a numerical or an algebraic expression, or it may be both.

Step 1: Always start by separating the variable y from the left side of the inequality.

Step 2: The equality symbol should be used in place of the inequality symbol

Step 3: Draw the boundary line from step 2 in the XY plane.

Step 4: The last step is to partially or completely shade the border line.

Separating the variables , using equality symbol , drawing boundary line in XY plane , shading the area are the four steps in graphing linear inequalities

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Answer:

43x+3x+17y

Step-by-step explanation:

because 43x+17y+3x=43x+17y+3x

The function has the end behavior f(x) → -∞  as , x → -∞ as f(x) → +∞ , x → +∞

Since,  The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.

The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.  And, if the function has  positive leading coefficient with odd degree then its end behavior is    f(x) → -∞  as , x → -∞ as f(x) → +∞ , x → +∞

Here, The given function has positive leading coefficient with odd degree.

Therefore,  by the definition of end behavior of a function,

The function has the end behavior f(x) → -∞  as , x → -∞ and, f(x) → +∞ , x → +∞

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The cost per message is $0.025.

What is cost?

A cost is the worth of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.

Raw materials, labour expenditures, and other production-related expenses are all considered direct costs. A product, division, or project can simply be linked to the cost. As an illustration, Ford Motor Company (F) produces vehicles and trucks. A automobile is built by a factory employee in eight hours.

Let, Jerry's messaging phone plan is, he paid $0.75 for every 30 messages he send.

So, the cost of each message is,

[tex]\frac{0.75}{30} = 0.025[/tex].

Hence, the per message is, $0.025.

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Answer: 4/3

Step-by-step explanation:

The reciprocal of a/b is b/a.