A home’s value increases at an average rate of 5.5% each year. The current value is $120,000. What function can be used to find the value of the home after x years?

Shown below

To solve this problem, we need to analyze the leading coefficient and the roots of the polynomial function:

[tex]f(x)=x^3-6x^2+11x-6[/tex]

Recall that a polynomial function can be represented by:

[tex]f(x)=a_{n}(x)+ \ldots +a_{1}x+a_{0}[/tex]

So the leading coefficient is [tex]a_{n}[/tex]. In our problem, this coefficient is [tex]a_{n}=1[/tex]

Since [tex]n[/tex] is odd and the leading coefficient [tex]a_{n}>0[/tex], then the graph must falls to the left and rise to the right. Also, the roots are [tex]x_{1}=1 \ x_{2}=2 \ and \ x_{3}=3[/tex]. So the only graph that matches this is the fourth one as indicated below.

Answer:

w

Step-by-step explanation:

for Plato

Hello!

Answer:

[tex]\boxed{X>-5}\checkmark[/tex]

The answer should have negative sign.

Step-by-step explanation:

Distributive property: a(b+c)=ab+ac

First, expand.

-4(x+3)=-4x-12

-4x-12<-2-2x

Then add by 12 both sides of an equation.

-4x-12+12<-2-2x+12

Simplify.

-4x<-2x+10

You add by 2x both sides of an equation.

-4x+2x<-2x+10+2x

Simplify.

-2x<10

Multiply by -1 both sides of an equation with reverse inequality.

(-2x)(-1)>10(-1)

Simplify.

2x>-10

Then you divide by 2 both sides of an equation.

2x/2>-10/2

Finally, simplify and solve to find this answer.

-10/2=-5

[tex]\boxed{x>-5}[/tex], which is our correct answer.

Hope this helps you!

Have a nice day! :)

Thank you!

-Charlie

Answer:

A

Step-by-step explanation:

You only have to pay the $50 one time and then you add the $15 and multiply it by however many months you choose to do.

Answer: A

Step-by-step explanation: Hope this helps

Answer:

Option A: f(x) = 4 * 2^x

Step-by-step explanation:

4 because it is the y intercept.

2 because if you see point (1,8), yousee the 8 = 4 * a^1 where a = 2

If you need more explanation, please comment below.

Thank you!!

Answer:

A. [tex]f(x)=4\cdot (2)^x[/tex]

Step-by-step explanation:

We have been given graph of a function. We are asked to write the function formula from given graph.

We can see that our given function is an exponential function, so it will be in form [tex]y=a\cdot b^x[/tex], where,

a = Initial value or y-intercept,

b = Growth rate.

We can see that y-intercept is 4.

Now, we will solve for b using the point (1,8) as:

[tex]8=4\cdot b^1[/tex]

[tex]8=4\cdot b[/tex]

[tex]\frac{8}{4}=\frac{4\cdot b}{4}[/tex]

[tex]2=b[/tex]

Therefore, our required function would be [tex]f(x)=4\cdot (2)^x[/tex] and option A is the correct choice.

Answer:

(P + 2)(p+ 16)

Step-by-step explanation:

Factor p 2 + 18p + 32.

Consider the form  x² +bx +c. Find a pair of integers whose product is  c  and whose sum is b .

In this case, whose product is  32  and whose sum is  18 .

2,16 .

Write the factored form using these integers.

(P + 2)(p+ 16)

                                        CHECK

(P + 2)(p+ 16)

distribute

p(p+16) + 2(p+16)

simplify

p² + 16p + 2p + 32

combine 16p + 2p = 18p

p² + 18p + 32

Please mark as brainliest

Answer:

(p + 2)(p + 16)

That's your answer!!

Quantities that are proportional to 26/13 are any other fractions that can reduce to positive 2.

26/13 = 26 ÷ 13 = 2

10/5 = 10 ÷ 5 = 2

200/100 = 200 ÷ 100 = 2

Answer:

So any fraction equal to 2 will work.

Step-by-step explanation:

Don't know which but I could tell you some that are equivalent to or proportional to 26/13.

26/13 reduces to 2 so 2 is a quantity that is proportional to 26/13

So any fraction equal to 2 will work.

Answer:

what are the graphs?

Step-by-step explanation:

Answer:

(0,6)

Step-by-step explanation:

Answer:

The rate of change in Erinn's hourly wage per year is [tex]1.25\$\ hour/year[/tex]

Step-by-step explanation:

we have that

x ----> the time in years that she worked at a company

y ----> represent the hourly wage

[tex]-5x+4y=32[/tex] ----> linear equation that represent the situation

Solve for y

[tex]4y=5x+32[/tex]

[tex]y=(5/4)x+32/4[/tex]

[tex]y=1.25x+8[/tex]

The slope m of the linear equation is

[tex]m=1.25\$\ hour/year[/tex]

The rate of change in Erinn's hourly wage per year is equal to the slope of the linear equation

so

The rate of change in Erinn's hourly wage per year is [tex]1.25\$\ hour/year[/tex]

Answer:

-10x^2 + 40x

Step-by-step explanation:

f(x) = 2x - 8

g(x) = -5x

f(x)g(x)= (2x-8) (-5x)

            = -10x^2 + 40x

Answer:

х – 9 = +9

Step-by-step explanation:

The equation results from taking the square root of both sides of

(x- 9)² = 81 is x -9 = ±9.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have Equation,

(x- 9)² = 81

Now, simplifying for x we get

Take square root on both side

x-9 = √81

x -9 = ±9.

Then, the equation results from taking the square root of both sides is

x -9 = ±9.

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Answer:

[tex]\boxed{6760}[/tex]

Step-by-step explanation:

The formula for the first n terms of an arithmetic sequence is

Sₙ = n(a₁+ aₙ)/2

1. Find the number of terms

n = (124 - 45) + 1 = 79 + 1 = 80

2. Find the sum

 a₁ =   45

a₈₀ = 124

[tex]S_{80} = 80 \left(\dfrac{45 + 124 }{2}\right) = 80 \times 84.5= \boxed{\mathbf{6760}}[/tex]

Answer:

1/3

Step-by-step explanation:

Slope intercept form: y=mx+b

m=rise/run (slope)

b= y-intercept

b=1/3

Answer:

x + 3x + 5 = 101

Step-by-step explanation:

Consider your problem and think of an equation of each person. We know that Aylen has a certain amount of money, which will be x. Rich though has 5 more than 3 times Aylen.

Aylen: x amount of money

Rich: 5 more than 3 times the amount of money of Aylen.

5 more indicates addition, 3 times indicates multiplication

So then:

Rich: 5 + 3x     (where x is the amount of money of Aylen)

Now both of them have $101 together, in other words, if you add up their money they would have $101. So we add their equations:

x + 5 + 3x = 101

Because the operation is addition, we can switch their places and the result will not change so the answer would be:

x + 3x + 5 = 101

Answer: y=-2x+2/4

Step-by-step explanation:

Answer:

y + 4 =1/2 (x + 4)

Step-by-step explanation:

Your welcome uwu

The parenthesis tell you which equation to do first.

P arenthesis

E xponents

M ultiplication

D ivision

A ddition

S ubtraction

Answer:

x=0, y=4

x=2, y=5

x=4, y=6

x=6, y=7

x=8, y=8

x=10, y=9

For every x value goes up one, the y value goes up 2.

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

x=0, y=4

x=2, y=5

x=4, y=6

Step-by-step explanation:

Answer:

[tex]\sqrt{98}[/tex]

Step-by-step explanation:

Using the distance formula

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (3, - 5)

d = [tex]\sqrt{(3+4)^2+(-5-2)^2}[/tex]

  = [tex]\sqrt{7^2+(-7)^2}[/tex]

  = [tex]\sqrt{49+49}[/tex]

  = [tex]\sqrt{98}[/tex]

C= [tex]\sqrt{98}[/tex]

We could say that the square root or the square cancel each other out. They are a inverse of each other. If we have the number written with the index two ( squared) then taking the square root simply means that we leave out the two ( this only applies on the positive numbers ).

Using the distance formula

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (3, - 5)

[tex]d= \sqrt{(3+4)^{2} +(-5-2)^{2}} \\\\= \sqrt{7^{2} + (-7)^{2}} \\\\= \sqrt{49+49} \\\\=\sqrt{98}[/tex]

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For this case we must simplify the following expression:

[tex]\sqrt [5] {\frac {10x} {3x ^ 3}}[/tex]

We rewrite the expression as:

[tex]\sqrt [5] {\frac {10x} {x * 3x ^ 2}} =[/tex]

We eliminate common factors:

[tex]\sqrt [5] {\frac {10} {3x ^ 2}} =\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}}[/tex]

We multiply the numerator and denominator:

[tex](\sqrt [5] {3x ^ 2}) ^ 4:\\\frac {\sqrt [5] {10}} {\sqrt [5] {3x ^ 2}} * \frac {(\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 4} =[/tex]

\frac {\ sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {\sqrt [5] {3x ^ 2} * (\sqrt [5] {3x ^ 2} ) ^ 4} =

[tex]\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {(\sqrt [5] {3x ^ 2}) ^ 5} =\\\frac {\sqrt [5] {10} * (\sqrt [5] {3x ^ 2}) ^ 4} {3x ^ 2} =[/tex]

[tex]\frac {\sqrt [5] {10} * \sqrt [5] {(3x ^ 2) ^ 4}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 8}} {3x ^ 2} =\\\frac {\sqrt [5] {10} * \sqrt [5] {81x ^ 5 * x ^ 3}} {3x ^ 2} =[/tex]

[tex]\frac {\sqrt [5] {10} * x \sqrt [5] {81x ^ 3}} {3x ^ 2} =\\\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]

Answer:

[tex]\frac {x \sqrt [5] {810x ^ 3}} {3x ^ 2}[/tex]

[tex]\frac {\sqrt [5] {810x ^ 3}} {3x}[/tex]

Answer:

The simplified form is [tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Step-by-step explanation:

we need to simplify the value of x in given expression:

[tex]\sqrt[5]{\frac{10x}{3x^{3}}}[/tex]

Re- write the above as,

[tex]\sqrt[5]{\frac{10}{3x^{2}}}[/tex]

[tex]\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^{2}}}[/tex]

Multiply numerator and denominator by [tex](\sqrt[5]{3x^{2}})^{4}[/tex]

[tex]\frac{\sqrt[5]{{10}}}{\sqrt[5]{3x^{2}}} \times \frac{(\sqrt[5]{3x^{2}})^{4}}{(\sqrt[5]{3x^{2}})^{4}}[/tex]

[tex]\frac{\sqrt[5]{{10}}{\sqrt[5]{(3x^{2}}})^4}{{3x^{2}}}[/tex]

[tex]\frac{\sqrt[5]{{10}}{\sqrt[5]{81x^{8}}}}{{3x^{2}}}[/tex]

[tex]\frac{x \sqrt[5]{810 x^{3}}}{3x^{2}}[/tex]

[tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Hence, the simplified form is

[tex]\frac{\sqrt[5]{810 x^{3}}}{3x}[/tex]

Answer:

the answer is C. Hope this helps

Answer:

Step-by-step explanation:

Answer:

D. 9/4 ÷ 3/4

Step-by-step explanation:

In the question, the number line represents 9/4 divided into 3 equal units.

The size of each unit is 3/4 as shown.

Showing that 3/4 divides 9/4 into 3 divisions:

9/4 ÷ 3/4

= 9/4 x 4/3

= 9/3 x 4/4

= 9/3 x 1

= 3 x 1

= 3

Hence, the number line represents three divisions given by 9/4 ÷ 3/4.

Answer:

D

Step-by-step explanation:

g(x)=f(5x)

this means plugging in 5x for x in f(x):

g(x)=f(5x)=(5x)^2

which can be further simplified:

5^2x^2=25x^2

Since the coefficient of x being larger means a vertical stretch, the answer is D

example:

g(2)=f(5*2)=f(10)=f(10^2)=100

so for g(x), it has the coordinates (2,100), which is most definitely not C

The graph of g(x) = f(5x) is a parabola that is narrower than the graph of f(x) by a factor of 1/5, with the vertex remaining the same.

The graph of g(x) = f(5x) can be obtained by substituting 5x for x in the function f(x) = x^2. So, g(x) = f(5x) = (5x)^2 = 25x^2. This means that the graph of g(x) is a parabola that is narrower than the graph of f(x) by a factor of 1/5. The vertex of the parabola remains the same, but the x-values and the y-values are scaled.

Answer:

12 + r or r + 12

Step-by-step explanation:

Either way can be written as the expression 12 is more than r or x

Answer:

f(r) = r + 12

Step-by-step explanation:

An expression is an equation that usually involves x and y. When we are dealing with a unknown number we use a variable. some common variable is x and y, in this instance we will use r. Therefore we have to have r in our expression. however, we need a output therefore we use function of r. (f(r))

p.s. F(r) usually represents y.

futhermore, if you see more than you know you will use addition.

hope this helps!

Answer:

D. 105.5 square feet

Step-by-step explanation:

Given:

The  rug has a radius of 3 feet.

The floor dimensions are 18 feet by 20 feet.

Now we have to find the area of the rug using area of the circle formula and also we need to find the area of the floor which is in rectangle shape.

Area of a circle = [tex]\pi r^2[/tex]

r = 3 feet and the value of [tex]\pi = 3.14[/tex]

Now plug in the given values in the above formula, we get

Area of a rug = 3.14*3*3

Area of a each rug is  28.27 square feet.

Now let's find the area of the floor.

Area of the floor = length * width

Here length = 18 feet and width = 20

The area of the floor = 18*20

= 360 square feet

Now we have to find how many rugs needed to cover the floor without overlap.

Here the radius of the rug = 3 feet

The diameter of the rug = 2*radius = 2*3 = 6 feet

So one rug covers 6 feet by length and width.

Therefore, 18/6 = 3

The width is 20 feet

20/6 = 3, we have to take the whole number part only.

So Emily needs only 3*3 = 9 rugs.

The area of the 9 rugs = 9*28.27  = 254.43

To find the bare floor will be visible around the rugs, we need to subtract the area of the 9 rugs from the floor area

Bare floor = 360 - 254.43

Bare floor = 105.5 square feet.

Answer:

Point-slope equations:

y - 5 = 4/3 (x - 6)

or

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

Step-by-step explanation:

Given two coordinate points (6, 5) and (3, 1)

Slope = (5 - 1)/(6 - 3) = 4/3

Point-slope equations:

y - 5 = 4/3 (x - 6)

or

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

Two point-slope equations for the line passing through the points

(6, 5) and (3, 1) are,

Here, the line passes through the points (6,5) and (3,1).

Let,

[tex]$$(6,5)=\left(x_{1}, y_{1}\right)$$[/tex]

[tex]$(3,1)=\left(x_{2}, y_{2}\right)$[/tex]

Substitute

Slope(m) = [tex]\frac{1-5}{3-6}=\frac{-4}{-3}[/tex]

Slope(m) =[tex]\frac{4}{3}[/tex]

Point-slope equations of the line passing through [tex]$(6,5 \6})$[/tex] and [tex](3}, 1)$[/tex]

Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(6,5)$[/tex]into [tex]$y-b=m(x-a)$[/tex]

[tex]y-5=\frac{4}{3}(x-6)[/tex] (point-slope equation)

Substitute[tex]$m=4 / 3$[/tex], and [tex]$(a, b)=(3,1)$[/tex] into [tex]$y-b=m(x-a)$[/tex]

[tex]$y-1=\frac{4}{3}(x-3)$[/tex] (point-slope equation)

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Answer:

Here's what I get.

Step-by-step explanation:

The formula for rotation of a point (x,y) by an angle θ about the origin is  

x' = xcosθ  -  ysinθ

y' = ycosθ + xsinθ

If θ = 270°, sinθ = -1 and cosθ = 0, and the formula becomes

x' =    y

y' =  -x

A: (-3,4)  ⟶ (4,3)

B: (-1,2)   ⟶ (2,1)

C: (-2,0) ⟶ (0,2)  

The vertices of A'B'C' are (4,3), (2, 1), and (0, 2).

The Figure below shows the triangle before and after the rotation.

Answer:

30 minutes

Step-by-step explanation:

3 pipes takes 60 minutes, so one pipe must take 3*60 minutes as it would be 3 times slower. This equates to 180 minutes.

1 pipe takes 180 minutes so 6 pipes would take 1/6 of the time or 6 times faster.

The equation becomes 180/6

= 30 minutes.

Equation is; 3*60/6 = 30 minutes

This is inverse proportion.

The answer is 30 minutes

If it takes 3 pipes 60 minutes to water the field

The amount of time it will take one pipe can be calculated as follows

t= constant(k) × number of pipes

60= k/3

cross multiply

k = 60×3

= 180

Since it takes one pipe 180 minutes to water the field, then the amount of time it will take 6 pipes can be calculated as follows

= 180/6

=  30

Hence it will take 6 pipes 30 minutes to water the field

It is an inverse proportion because an increase in one quantity leads to a decrease in the other.

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Answer:

It was A.

Step-by-step explanation:

the rate of change of item I is greater than the rate of change of item II.

I just had it and answer B. was wrong

The rate of change of item I is greater than the rate of change of item II. (Option A)

Suppose that the considered linear equation is of the form [tex]y = mx + c[/tex]

Then, when we change x by 1 unit, then:

[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]

where [tex]\delta y[/tex] shows the change in y as x changes by 1 unit.

We found that this change is the value of 'm'.

It is called slope of the line this equation represents (each linear equation represents a line).

Finding rate of each item:

The rate is 3 units increment in y per unit increment in x. In short, the rate is 3 unit / unit increment in x

Since graph of a straight line is given, we can find its slope which would represent its rate.

Consider x = 0, for which y = 0 is given in graph.

Now change x by 1 unit, so x becomes x = 1

At x =1 , y = 2

So we see that as x changes by 1 unit, y goes from 0 to 2 (change of 2 units).

Hence, the rate is 2 units increment in y per unit increment in x. In short, the rate is 2 unit / unit increment in x

Thus, the rate of change of item I is greater than the rate of change of item II. (Option A)

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[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (t^9)^{-8}\implies t^{-8\cdot 9}\implies t^{-72}\implies \cfrac{1}{t^{72}}[/tex]

Answer:

The missing information is attached in the picture below.

The company made $292.5 dollars in profit.

Step-by-step explanation:

Using the information provided by the table, we can calculate how much money was spent

1. gravel

12 and a half cubic yards * $15  = $187.5

2. tar/sealant

$0.15 per square foot * (75*20 ft^2) = $225

3. labor

$10 per hour * 25 hours = $250

4. insurance

fixed $45

We add all the expenses together

$(187.5 + 225 + 250 + 45)  = $707.5

The profit will be equal to

$1000 - $707.5 = $292.5

Step-by-step explanation: