In a sports competition, Alyssa was penalized -16 points. She received the same number of penalty points in each of the 4 events. How many points was she penalized each event?

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:

Monthly payment for choice​ 1 is $6,600

Step-by-step explanation:

We will use following formula in order to calculate the monthly payment of choice 1

Value of Loan = Monthly payment x ( 1 - ( 1 + Interest rate )^-numbers of payments / interest rate

Where

Value of Loan = $110,000

Interest rate = 6%

Numbers of Payment = 15 years x 12 payments / year = 180 payments

Placing values in the formula

$110,000 = Monthly payment x ( 1 - ( 1 + 6% )^-180 ) / 6%

$110,000 = Monthly payment x 16.6662

Monthly Payment = $110,000 / 16.6662

Monthly Payment = $6,600.18

Monthly Payment = $6,600 (Rounded to whole number)

Answer:

haha

Step-by-step explanation:

doing this for points

Answer:

jackpot

Step-by-step explanation:

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

No real solutions.

                                         there is none

Answer:

Step-by-step explanation:

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:

THANKS FOR THE POINTS!!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

I hope this helps!

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!

Answe

Step-by-step explanation:

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

:-) :-( ;-) :-P (^o^) ^o^ ^_^ :-! 8-) :-{ :-[ (-:

or

that is not an exercise. but still thanks for the points.

Answer:

Step-by-step explanation:

Remember that

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

[tex]\pi = pi \\r = radius[/tex]

They told us that for this circle, the area is [tex]144\pi m^2[/tex]

If you put it back into the formula for area of a circle we get:

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

[tex]144\pi = \pi r^2[/tex]

Divide both sides by [tex]\pi[/tex].

144 = [tex]r^2[/tex]

Now we want to solve for r (r = radius).

You need to square root each side

[tex]\sqrt{144} = \sqrt{r^2}[/tex]

[tex]12 = r[/tex]

So now we know the radius, [tex]r = 12[/tex] metres

Also remember that

Diameter = [tex]2r[/tex]

So,

Diameter = 2 times 12 = 24 metres

The required diameter of the given circle is 24 meters.

The area of the circle is given by the pie times square of the radius.

Area of circle = πr^2

Here,
The given area of the circle is 144π m²
And we know that,
Area = πr²

substitute the value of the area in the above expression,

144π = πr²
r² = 144
r = √144
r = 12 meters

Since,
Diameter = 2 × radius
Diameter = 2 × 12 = 24 meter

Thus, the required diameter of the given circle is 24 meters.

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Answer:

6,591,024,000

Step-by-step explanation:

Minutes in 24 hours=1,440

number of seconds in 24 hours=60*1440

=86,400..

number of cars made in each second=209

number of cars made in 86,400 seconds= 18,057,600

24 hours =one day

1 year =365 days

cars made in one year =365*18,057,600

=6,591,024,000

therefore, the number of cars made in one year =

6,591,024,000

The number of cars made in the factory in one year where cars are made for 24 hours every day is 150891.

The total time taken is inversely proportional to the rate of work. If a unit of work is done in total n number of days, then the total work done W in a day can is,

[tex]W=\dfrac{1}{n}[/tex]

In a factory, cars are made, where Cars are made for 24 hours every day. As, there is total 60 seconds in one minute and 60 minutes in one hour. Thus, the number of second in 24 hours is,

[tex]24\times60\times60=86400[/tex]

In the factory, a car is made every 209 seconds. Thus, the number of cars made in 86400 seconds (24 hours),

[tex]\dfrac{86400}{209}=431.4[/tex]

There is total 365 days (24 hours) in one year. Thus, the number of cars made in the factory in one year is,

[tex]431.4\times365=150891[/tex]

Thus, the number of cars made in the factory in one year where cars are made for 24 hours every day is 150891.

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Answer:

9+6i

Step-by-step explanation:

3+6=9

5+1=6

Answer:

The cube is a 8x8x8

so a side length is 8

Answer:

Pain Pain Pain Pain Pain now where is my brainliest you promised me

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

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:

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:

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:

When you divide a negative number by a positive number then the quotient is negative. When you divide a positive number by a negative number then the quotient is also negative.

Step-by-step explanation:

Hi!

Your answer should be: (4) 28.

Hope this helps!

Yours truly,

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

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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: The maximum possible value of y is 30 ;)

Answer:

i pick my answer as 3

Step-by-step explanation:

7-4=3

Answer:

11

Step-by-step explanation:

A is -7 and b is -4 if you add them it would be positive 11 because a negative plus a negative is a positive. Here's this to keep in mind:

+(+) Two like signs become a positive sign 3+(+2) = 3 + 2 = 5

−(−)                                                                         6−(−3) = 6 + 3 = 9

+(−) Two unlike signs become a negative sign 7+(−2) = 7 − 2 = 5

−(+)                                                                         8−(+2) = 8 − 2 = 6