Marco runs 22 miles in four hours. What is his unit rate?

Answer:

[tex]P(x)=2x^3-2x^2-49x+48[/tex]

Step-by-step explanation:

Let the original polynomial be [tex]P(x)[/tex].

We know that when it is divided by [tex](x-5)[/tex], the quotient is [tex]2x^2+8x-9[/tex] and we get a remainder of 3.

Therefore, this means that:

[tex]\frac{P(x)}{x-5}=2x^2+8x-9+\frac{3}{x-5}[/tex]

Remember what it means when we have a remainder. Say we have 13 divided by 3. Our quotient will be 4 R1, or 4 1 over 3. We put the remainder over the divisor. This is the same thing for polynomials.

So, to find our original polynomial, multiply both sides by [tex](x-5)[/tex]:

[tex](x-5)\frac{P(x)}{x-5}=(x-5)(2x^2+8x-9+\frac{3}{x-5})[/tex]

The left side will cancel. Distribute the right:

[tex]P(x)=2x^2(x-5)+8x(x-5)-9(x-5)+\frac{3}{(x-5)}(x-5)[/tex]

Distribute:

[tex]P(x)=(2x^3-10x^2)+(8x^2-40x)+(-9x+45)+(3)[/tex]

Combine like terms:

[tex]P(x)=(2x^3)+(-10x^2+8x^2)+(-40x-9x)+(45+3)[/tex]

Evaluate:

[tex]P(x)=2x^3-2x^2-49x+48[/tex]

And we're done!

Answer:

x=3 x= -1

Step-by-step explanation:

(x-3)(x+1)

x-3=0. x+1=0

x=3 x= -1

Answer:

Number of adults that attended the show = 400

Number of children that attended the show = 359

Total people who attended the show = 759

Step-by-step explanation:

Total earned = 15,385

Adults = $25

Children = $15

Let

Adults = A

Children = C

The number of adults who attendee the show was 41 more than the number of children who attended the show

A = C + 41

25A + 15C = 15,385

Substitute

A = C + 41

25(C+41) + 15C = 15,385

25C + 1,025 + 15C = 15,385

40C + 1,025 = 15,385

40C = 15,385 - 1,025

40C = 14,360

Divide both sides by 40

C = 14,360 / 40

= 359

C = 359

Substitute C = 359 into

A = C + 41

A = 359 + 41

= 400

A = 400

Number of adults that attended the show = 400

Number of children that attended the show = 359

Total people who attended the show = 759

Answer:

Step-by-step explanation:

I have "and" but not "or"

"and" is when your talking about the decimal point for example:

1.2

one, and, two tenths

Answer:

[tex]\frac{y-b}{x}[/tex]=m

Step-by-step explanation:

y=mx+b

-b          -b

y-b=mx

[tex]\frac{y-b}{x}[/tex]     =  [tex]\frac{mx}{x}[/tex]

[tex]\frac{y-b}{x}[/tex]=m

Answer:

B) -510 per yr

Step-by-step explanation:

2005 = 14,550 CDs sold

2010 = 12,000 CDs sold

Difference in years = 2010 - 2005

= 5 years

Difference in CDs sold = 12,000 - 14,550

= - 4,550

Rate of change in the number of CDs sold = change in the number of CDs / change in years

= -4,550 / 5

= -510 per year

The correct answer is B) -510 per yr

Answer:

The cube is a 8x8x8

so a side length is 8

Answer:

3 full miles; anything less than 4 miles

Step-by-step explanation:

5 + 2.50x = 15

subtract 5 from both sides

2.50x = 10

divide both sides by 2.50

x = 4

4 miles is how long he can travel by spending all $15

Anything less will cost him less than $15

Answer:

4 miles

Step-by-step explanation:

well we have a budget of 15$. We use 5$ for the ride so we have 10$ left. 10/2.5 is 4.

Answer: Y= 1/-1x+4

Step-by-step explanation: Y equals 1 over negative 1 x plus 4

Answer: D

Step-by-step explanation: The > points to the right so the line goes that way and, in order to get rid of the fraction you multiply 5 * -4 = -20 so

Z > -20

Answer:

please add the image coz it's not clear

An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles, using this property we get, the value of k is: k = 10.

Here, we know that, an exterior angle is equal to the sum of the two opposite inside angles.

The picture shows an exterior angle of 115 degrees.

It's two opposite inside angles are the two equations.

This means:

(4k +5) + (6k+10) = 115

Combine like terms:

10k + 15 = 115

Subtract 15 from both sides:

10k = 100

Divide both sides by 10:

k = 100/10

k = 10

Hence,  The value of k is: k = 10.

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complete question:

attached

Answer:

9+6i

Step-by-step explanation:

3+6=9

5+1=6

Answe

Step-by-step explanation:

Answer:

haha

Step-by-step explanation:

doing this for points

Answer:

jackpot

Step-by-step explanation:

The fraction of the dishes were cooked by Rooms 102 and 104 is 4/5

Fraction of the dishes were cooked by Rooms 102 and 104 = 1/2 + 3/10

= (5+3) / 10

= 8 / 10

= 4 / 5

Therefore, the fraction of the dishes were cooked by Rooms 102 and 104 is 4/5 in the simplest form

Learn more about fraction:

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Answer:

Please see below :)

Step-by-step explanation:

4 cubed + 8 is the sum.

y is the variable.

9/y is the quotient.

Hope this helps!

Answer:

Please see below :)

Step-by-step explanation:

4 cubed + 8 is the sum.

y is the variable.

9/y is the quotient.

Hope this helps!

Answer:

x = 31

Step-by-step explanation:

Given that the triangles are congruent, then corresponding angles are congruent, then

∠ D = ∠ A

The sum of the 3 angles in a triangle = 180° , thus

∠ A = 180° - (61 + 57)° = 180° - 118° = 62°

Thus

2x = 62 ( divide both sides by 2 )

x = 31

Answer:

4(1/2) = 2

2-8 = -6

-6 is your answer

hope this helps!

For finding g(1/2) you need to substitute the value of x= 1/2

Thus , g(1/2):

[tex] = 4 \times \dfrac{1}{2} - 8[/tex]

[tex] = 2 - 8[/tex]

= [tex]\red{\bold{\large{-6}}}[/tex]

Answer:

ITS THE FIRST ONE

Step-by-step explanation:

THE OUTPUTS ARE THE Y-VALUES

THE Y-VALUES ARE 4, -1, 3, -3

THEREFORE, THE ANSWER IS THE FIRST OPTION. {-3, -1, 3 4}

Answer: The maximum possible value of y is 30 ;)

Answer:

THANKS FOR THE POINTS!!!

Step-by-step explanation:

Hi!

Your answer should be: (4) 28.

Hope this helps!

Yours truly,

Answer:

[tex]f(x)^{-1} =\frac{x}{4} -25[/tex]

Step-by-step explanation:

This is the inverse function of f(x)=100+4x

Answer:

another ratio is 3:5=6:10 or 9:15

Explanation:

3:5×2=6:10

3:5×3=9:15

Answer:

(9,15) aka C

Step-by-step explanation:

3 times 3 is 9 and so you multiply the same number to the y-coordinate. 5 times 3 is 15!

Answer:

Angle 2 = 48

we are going to divide 48 by 2 to get the Angle 1

Angle 1 = 24

then Angle 5 = (5×24)

Angle 5 = 120

Answer:

D. angle SWT and angle QWT are complementary

Step-by-step explanation:

The angles formed at W when the two lines, PS and RT, which are perpendicular to each other intercept at W are right angles.

Thus, let's analyse each given statements to see which is true or not true about the angle pairs formed:

Statement 1: "angle PWQ and angle QWT are complementary".

m<PWT = 90°.

m<PWQ + m<QWT = m<PWT (angle addition postulate)

m<PWQ + m<QWT = 90° (definition of complementary angles)

Therefore, statement 1 is CORRECT.

Statement 2: "angle PWR and angle TWP are supplementary".

m<PWR = 90°

m<TWP = 90°

m<PWR + m<TWP = 180° (definition of supplementary angles)

Therefore, statement 2 is CORRECT.

Statement 3: "angle RWQ and angle TWQ are supplementary".

<RWQ and <TWQ are angles on a straight line and are a linear pair.

m<RWQ + m<TWQ = 180° (definition of supplementary angles)

Therefore, statement 3 is CORRECT.

Statement 4: "angle SWT and angle QWT are complementary".

m<SWT = 90°

Therefore, m<SWT + m<QWT ≠ 90°

The sum of both angles does not give 90°. Therefore, statement 4 is INCORRECT.

Answer:

it is a horizontal line resting at 15 on the y axis

Step-by-step explanation:

because there is no x on the left side of the equation, it must be flat. it is 15, so that is where it lies

The graph of the function y=15 is the horizontal line resting at 15 on the y-axis

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The graph of the function y=15 is the horizontal line resting at 15 on the y-axis because there is no x on the left side of the equation, it must be flat. it is 15, so that is where it lies.

Therefore the graph of the function y=15 is the horizontal line resting at 15 on the y-axis. The graph is attached with the answer below.

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Answer:

46215

Step-by-step explanation: