Rick was given 2 new gaming consoles for his birthday, one from each set of grandparents. He wants to return one of the consoles and use the store credit to buy new video games. He will receive $299 in store credit, and each video game costs $60. You can use a function to describe the amount of store credit he will have left after purchasing x video games. Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x. f(x)=

find the length of the x

a^2 + b^2 = c^2

12x^2 + b^2 = 13^2

144 + b^2 = 169

b^2 = 25

b = 25; x = 5

use the formula

a = (1/2)(24)(5)

a = (1/2)(120)

area = 60

Answer:

f(-2) = 46

f(-1) = 17

f(0) = 2

f(1) = 1

f(2) = 14

Step-by-step explanation:

F(-2) = 46

F(-1)= 17

F(0)= 2

F(1)= 1

F(2)= 14

Answer:

Standard form of the equation for the circle

(x + 3)² + (y + 5)² = 40

Step-by-step explanation:

The equation of a circle in standard form is
[tex]\boxed{(x - a)^2 + (y-b)^2= r^2}[/tex]

where (a, b) is the center of the circle and r is the radius

To find center of circle

The end points of the diameter are (-5, -11) and (-1, 1)

The center of the circle is midway between these two points

The x-coordinate of the midpoint = (-5 + -1)/2 = -6/2 = -3

The y-coordinate of the midpoint is (-11 + 1) /2 = -10/2 = -5

So the center of the circle is at (-3, -5)

To find the radius,

Calculate the distance from (-3, -5) to any of of the endpoints.

Let's take the endpoint (-1, 1) and find its distance from (-3, -5)

The distance between any two points (x₁, y₁) and (x₂, y₂) is calculated from the formula

[tex]d^2 = {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2[/tex]

Substituting
(x₁, y₁) = (-1, 1)
(x₂, y₂)  = (-3, -5)

and r for distance

we get

[tex]r^2 = {(-3 - (-1))^2 + (-5 - 1)^2[/tex]

[tex]r^2 = {(-2)^2 + (-6)^2}[/tex]

[tex]r^2 = {{4} + {36}}[/tex]

[tex]r^2 = {40}[/tex]

So the center (a, b) is (-3, -5) and r² =40

Plugging this into the circle equation:
(x - (-3))² + (y - (-5))² = 40

(x + 3)² + (y + 5)² = 40

Answer:

Step-by-step explanation:

Answer:

[tex]\mbox{\large \textsf{Timothy bought 14 books}}[/tex]

Step-by-step explanation:

Let's use first letters of names to represent the number of books bought by that person. This makes it easier to explain.

Therefore, the books bought by each of the three persons are T(imothy), L(aurence) and M(ike)

We will now convert each of the word description into math equations and solve

We are given that the ratio of the number of books bought by Laurence and Mike were 2: 7

We can write this as:
[tex]\dfrac{L}{M} = \dfrac{2}{7}\\\\[/tex]

Multiplying both sides by M:
[tex]L = \dfrac{2}{7}M\cdots\cdots(1)[/tex]  

Timothy and Laurence bought a total of 20 books can be represented as
[tex]T + L = 20\cdots\cdots(2)[/tex]

Timothy and Mike bought a total of 35 books can be represented as
[tex]T + M = 35\cdots\cdots(3)[/tex]

Eq (3) - Eq (2):

[tex]T + M - (T + L) = 35 - 20\\\\T + M - T - L = 15\\\\M - L = 15 \cdots\cdots (4)[/tex]

Substituting for [tex]\displaystyle L = \frac{2}{7}M[/tex]  from equation (1) into equation (4) we get

[tex]M - \dfrac{2}{7}M = 15\\\\\dfrac{5}{7}M = 15\\\\M = \dfrac{7}{5} \times 15\\\\M = 21\\\\[/tex]

Given [tex]\displaystyle M = 21[/tex] using equation (3), [tex]\displaystyle T + M = 35[/tex] we get

[tex]T + 21 = 35\\\\T = 35 - 21\\\\\textrm{or}\\\\T = 14[/tex](Answer)

If we wanted to find out how many books Laurence bought use Eq(1)
[tex]L = \dfrac{2}{7}M\\\\L = \dfrac{2}{7} \times 21\\\\L = 6\\\\[/tex]

Answer:you never asked for like in what minutes or hours?

Step-by-step explanation:

The car, traveling at a speed 5 mph faster than the truck, will take more than 4.6 hours to be more than 23 miles ahead.

This question pertains to relative speed. When the car is traveling at 55 mph and the truck at 50 mph, the car is effectively moving away from the truck at (55 mph - 50 mph) = 5 mph. To calculate the time it will take for the car to be more than 23 miles ahead, we can use the formula: Time = Distance/Speed. So the time it would take is Time = 23 miles / 5 mph = 4.6 hours. Therefore, it will take the car more than 4.6 hours to be more than 23 miles ahead.

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Answer: 44.20-10.68=33.52

He need 33.52$

Step-by-step explanation:

The possible equation of the parabola is y = (x - 5)^2 - 4

from the question, we have the following parameters that can be used in our computation:

Vertex = (5, -4)

The vertex form of a parabola is given by:

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape of the parabola.

We are given that the vertex of the parabola is (5,-4). Substituting these values into the vertex form, we get:

y = a(x - 5)^2 - 4

Let a = 1

So, we have

y = (x - 5)^2 - 4

Hnce, the possible equation is y = (x - 5)^2 - 4

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x^2 - 2x + 1 is the required quadratic equation using the completing the square

Given the quadratic expression below

x^2 - 2x

We need to determine the constant that will make the expression a perfect square.

The constant will be the half of the square of coefficient of 'x'

Coefficient of 'x' = -2

Half of the coefficient of 'x' = -2/2 = -1

Square of the coefficient = (-2/2)^2

Square of the coefficient = 1

Hence the complete quadratic expression using the completing the square is x^2 - 2x + 1

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An equation to show the sequence is -25n.

When all the terms of the geometric sequence are added, than that expression is known as geometric series.

The sum of terms of a geometric sequence;

Now, lets suppose its initial term is   , multiplication factor will be r

and let it has total n terms, then, its sum is given as:

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

(sum till nth term)

We are given that;

The first term of sequence=-25

D= -50-(-25)

=-25

Now,

an = a + (n-1)d

=-25+(n-1)-25

=-25-25n+25

=-25n

Therefore, the answer of the sequence will be -25n.

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Answer:

D

Step-by-step explanation:

It's the most random and produces no bias.

Answer:

D

Step-by-step explanation:

Answer:

46.21%

Step-by-step explanation:

The area of the table top is 1.3 x 1.3 = 1.69 m²

The area of the circular tablecloth is given by πr² where r is the radius of the table cloth

Give diameter of tablecloth is 2m, radius r = 2/2 = 1 m

Area of tablecloth = π · 1² = π

So the excess area of the tablecloth which overhangs

= π - 1.69 = 1.45 m²  (taking π = 3.14)

So the fraction of the tablecloth that overhangs
= Excess area of tablecloth ÷ total area of tablecloth
= 1.45 /π

= 0.4621

As a percentage this would be
0.4621 x 100

= 46.21%

Answer:

p = x(y)(z)

Step-by-step explanation:

product is multiplication.

multiplication has no specific order.

Answer:

9 trucks/hour

Step-by-step explanation:

If he loaded 9 trucks in one hour, his loading speed is 9 trucks per hour.

Answer:

4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.

Step-by-step explanation:

To find the weight of 4.4 cubic feet of water in pounds, we need to find the number of gallons it contains and then multiply it by the weight of one gallon of water.

1 cubic foot = 7.48 gallons

So, 4.4 cubic feet = 4.4 * 7.48 = 32.912 gallons

And the weight of 32.912 gallons of water in pounds is:

32.912 gallons * 8.33 pounds/gallon = 273.5016 pounds

To convert this weight to tons, we divide the weight in pounds by 2000:

273.5016 pounds / 2000 = 0.13676 tons

So, 4.4 cubic feet of water weighs approximately 273.5016 pounds or 0.13676 tons.

The vertices of the image of triangle ABC are A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4) and C''(x, y) = (- 4, 4).

Any triangle can be generated by three points that are not collinear, in this problem we need to determine the image of a triangle, which is the result of two rigid transformations: (i) Reflection over the y-axis, (ii) Dilation centered at the origin with a scale factor of 2, whose definitions are shown below:

Reflection over the y-axis:

(x, y) → (- x, y)

Dilation centered at the origin with a scale factor of 2:

(x, y) → (2 · x, 2 · y)

If we know that A(x, y) = (3, 4), B(x, y) = (4, 2), C(x, y) = (2, 2), then the image of the vertices are determined below:

Reflection over the y-axis

A'(x, y) = (- 3, 4), B'(x, y) = (- 4, 2), C'(x, y) = (- 2, 2)

Dilation centered at the origin with a scale factor of 2

A''(x, y) = (- 6, 8), B''(x, y) = (- 8, 4), C''(x, y) = (- 4, 4)

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Answer: the answer is 5/12

Answer:

16

Step-by-step explanation:

As the question states, we are counting downwards which means with every interval we are going back -1. Therefore, 17 - 1 = 16

well, in 2007 it was 12000, so initially that's what it was, and in 2019 it went to 23000, so that's 12 years later, and in 2040, that'll be 33 years later.

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 23000\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12\\ \end{cases} \\\\\\ 23000 = 12000(1 + \frac{r}{100})^{12}\implies \cfrac{23000}{12000} =\left(1+ \cfrac{r}{100} \right)^{12} \\\\\\ \cfrac{23}{12}=\left(\cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{\cfrac{23}{12}}=\cfrac{100+r}{100}[/tex]

[tex]100\sqrt[12]{\cfrac{23}{12}}=100+r\implies 100\sqrt[12]{\cfrac{23}{12}}-100=r\implies \boxed{5.57\approx r} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to 5.57\%\to \frac{5.57}{100}\dotfill &0.0557\\ t=years\dotfill &\stackrel{year~2040 }{33}\\ \end{cases} \\\\\\ A \approx 12000(1 + 0.0557)^{33} \implies \boxed{A \approx 71782}[/tex]

The reasons for (1) and (2) are added below

One reason why it might be reasonable to model the relationship between time and height of the candle with a linear function is that the rate of change of the candle's height appears to be constant over time.

One reason why it might NOT be reasonable to model this relationship with a linear function is that the candle's height cannot continue to decrease indefinitely.

This means that the candle's height is bounded and cannot continue to decrease linearly forever.

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The two integers are 5 and 10.

What do you mean by Integers?

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.

A number is positive if it is greater than zero, so it said to be positive integers

A number is negative if it is less than zero, so it said to be negative integers.

A number line is a visual representation of numbers on a straight line. This line is used for the comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.

Given:

Let x be the positive number

2x be the other positive number

Find the first integer

[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]

[tex]\frac{2x - x}{2x^2} = \frac{1}{10}[/tex]

[tex]\frac{x}{2x^2} = \frac{1}{10}[/tex]

[tex]\frac{1}{2x} = \frac{1}{10}[/tex]

2x = 10

x = 5

Therefore, the first positive integer is 5.

Find the other integer

2x = 2(5) = 10

Therefore, the other integer is 10.

To check:

[tex]\frac{1}{x} - \frac{1}{2x} = \frac{1}{10}[/tex]

[tex]\frac{1}{5} - \frac{1}{10} = \frac{1}{10}[/tex]

[tex]\frac{2}{10} - \frac{1}{10} = \frac{1}{10}[/tex]

[tex]\frac{1}{10} = \frac{1}{10}[/tex]

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Answer:

Step-by-step explanation:

The amount that should be invested in order to have $2,290 in 16 years is $929.11.

What is compound interest?

The interest on a deposit calculated using both the initial principle and the accrued interest from prior periods is known as compound interest. In other words, compound interest is interest that is earned on interest.

Here, we have

Given: Xin will invest in an account paying an interest rate of 5.8% compounded annually.

Amount to invest = Future value / (1 + r)ᵗ

Where:

r = interest rate

t = time

X = $2,290 / (1 + 0.058)¹⁶

X = 2,290 / 2.46474

X = $929.11

Hence, the amount that should be invested in order to have $2,290 in 16 years is $929.11.

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Answer: Let's follow the same steps as in the previous example:

Identify the constants and the variables.

The known constant here is 4. Shailyn read 4 fewer books than Oswaldo. Let's call the number of books Oswaldo read "o".

Identify the operations.

The phrase "four fewer" tells us we need to subtract.

Rewrite the phrase as an expression.

"Four fewer books than Oswaldo" is o - 4.

So, the expression that shows how many books Shailyn read last year is o - 4.

Step-by-step explanation:

The equations of the parabolas are y = x² - 6x - 7 and y = x² - 7

Parabola 1

Given that

The points (-1,0), (7, 0) and (3,-16)

The equation is represented as

y = ax² + bx + c

So, we have

a - b + c = 0

49a + 7b + c = 0

9a + 3b + c = -16

Make c the subject in a - b + c = 0

c = b - a

So, we have

49a + 7b + b - a = 0

9a + 3b + b - a = -16

48a + 8b = 0

8a + 4b = -16

Multiply 8a + 4b = -16 by 2

48a + 8b = 0

16a + 8b = -32

Subtract

32a = 32

So, we have

a = 1

Recall that 48a + 8b = 0

So, we have

48 + 8b = 0

This gives

8b = -48

Divide

b = -6

Also, we have

c = b - a

This gives

c = -6 - 1

c = -7

So, the equation is

y = x² - 6x - 7

Parabola 2

Given that

The points (-4,9), (-3, 2) and (0,-7) and (4,9)

The equation is represented as

y = ax² + bx + c

So, we have

16a - 4b + c = 9

9a - 3b + c = 2

c = -7

16a + 4b + c = 9

The equations become

16a - 4b = 16

9a - 3b = 9

16a + 4b = 16

Add (1) and (3)

32a = 32

So, we have

a = 1

Subtract (1) and (3)

-8b = 0

So, we have

b = 0

So, the equation is

y = x² - 7

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(a) The union set is AUB'={f, k, m, x, y}.

(b) The union set is A'UB'={q,k, x, y}.

The union of two sets is also a set. This set contains all the elements of both two sets.

The universal set is U= {f, k, m, q, x,y} and two subsets are A={f, k, m, y} and B = {f, m,q}.

(a)

B' is the complementary set of B. So, find the elements of B'=U-B.

B'= {f, k, m, q, x,y}-{f, m,q}

={k, x,y}

Now, find the union set AUB'.

AUB' ={f, k, m, y}U{k, x,y}

={f, k, m, x, y}

Therefore, the required answer is AUB'={f, k, m, x, y}.

(b)

Also, A' is the complementary set of A. So, find the elements of A'=A-B.

A'= {f, k, m, q, x,y}-{f, k,m, y}

={q,x}

Now, find the union set A'UB'.

A'UB' ={q,x}U{k, x,y}

={q,k, x, y}

Therefore, the required answer is A'UB'={q,k, x, y}.

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In the equation, the number 5,000 represents the initial value of the motorcycle. The value of the motorcycle is increasing at a rate of 3% per year.

Exponential functions are functions where the independent variable, x is in the exponent.

The given exponential equation is,

V = 5,000 (1.03)^t

Here V represents the value of the motorcycle in t years.

When t = 0,

V = 5000 (1.03)⁰ = 5000

So 5000 represents the initial value of the motorcycle.

V = 5,000 (1 + 0.03)^t

At t = 0, V = 5000

At t = 1, V = 5000 (1.03)¹ = 5150

At t = 2, V = 5000 (1.03)² = 5304.5

So the value of the motorcycle is increasing.

The rate is 0.03 or 3%.

Hence, 5,000 represents the initial value of the motorcycle and the value of the motorcycle is increasing at a rate of 3% per year.

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Equivalence means to be same, whether it be value, temperature, size, etc.

Let's make an equation to solve this problem. We first would need to take the total (12 pounds) and divide that total by the amount each slice must weigh (1.5 pounds) to get an equal number of slices.

To check our work, we can take number of slices (8), and multiply that by the weight of each slice (1.5 pounds) to get the original weight of the watermelon.

Now, we know for sure that Mr. Ramirez can make 8 watermelon slices each weighing 1.5 pounds if he has a 12-pound watermelon.

The function operation (f/g)(x) in the functions f(x) = √( x² - 1 ) and g(x) = √( x - 1 ) is √( x + 1).

A function is simply a relationship that maps one input to one output.

Given the functions in the question;

To evaluate (f/g), replace the function designators in f/g with the actual functions.

(f/g)(x) = f(x) / g(x)

(f/g)(x) = ( √( x² - 1 ) ) / ( √( x - 1 ) )

Now, rewrite 1 as 1²

(f/g)(x) = ( √( x² - 1² ) ) / ( √( x - 1 ) )

Factor using difference of square

(f/g)(x) = ( √( (x - 1)(x + 1 ) ) / ( √( x - 1 ) )

Combine into a single radical

(f/g)(x) = √( ( (x - 1)(x + 1) ) / ( x - 1 ) )

Now, cancel out the common factors (x-1)

(f/g)(x) = √(  (x + 1) / 1 )

(f/g)(x) = √( x + 1)

Therefore, the function operation (f/g)(x) is √( x + 1).

Option A) √( x + 1) is the correct answer.

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