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3 years ago

Determine if x+2 is a factor of p(x) = x4 + 3x3 +4x2 -8

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

5 0

Hello,

Yes it <em>is.

p(-2)=(-2)^4+3*(-2)^3+4*(-2)^2-8
=16-24+16-8=0

p(x)=(x+2)(x^3+x^2+2x-4)

</em>

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At one gym, there is a $12 start-up fee, and after that each month at the gym costs $20. At another gym, it costs $4 to startup,

mart [117]

Answer:

In 4 months the cost of both gyms will be the same.

Step-by-step explanation:

At first we need to model the function to calculate the cost of the 2 gyms.

Slope-intercept equation of linear function

$f(x)=mx+b$

where

$m\rightarrow$ slope of line

$b\rightarrow$ y-intercept

Let linear function to calculate total cost of gym be:

$c(n)=mn+b$

where

$c\rightarrow$ total cost of gym

$m\rightarrow$ cost per month (slope)

$n\rightarrow$ number of months

$b\rightarrow$ start-up fee (y-intercept)

For Gym 1

$m=20$ , $b=12$

$c(n)=20n+12$

For Gym 2

$m=22$ , $b=4$

$c(n)=22n+4$

In order to find the number of months the cost of both gyms will be the same, we need to equate both functions and solve for number of months $(n)$

$20n+12=22n+4$

$\\\textrm{Subtracting 22n from both sides}\\20n-22n+12=22n-22n+4\\-2n+12=4\\\textrm{Subtracting 12 from both sides}\\-2n+12-12=4-12\\-2n=-8\\\textrm{Dividing both sides by -2}\\\frac{-2}{-2}n=\frac{-8}{-2}\\n=4\textrm{ months}$

So,

In 4 months the cost of both gyms will be the same.

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3 years ago

The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is x feet, wh

Orlov [11]

6x + 1 = 13

Hope this helps!

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3 years ago

What is the value of k if 2x^3-3x^2+kx-4 is divided by x-3 and gives a remainder of -7?

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By the polynomial remainder theorem, the remainder upon dividing a polynomial $p(x)$ by $x-c$ is the same as the value of $p(c)$ .

Here $p(x)=2x^3-3x^2+kx-4$ and $c=3$ . We have

$p(3)=23+3k=-7\implies k=-10$

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3 years ago

A scatter plot with a line is shown below. Which statement is most likely correct about the line?

Savatey [412]

Answer: A

If its around the line and the dots are going the same way than its accurate.

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2 years ago

Read 2 more answers

thomas has 6.35 in dimes and quarters the number of dimes is three more than three times the number of quarters how many quarts

Feliz [49]

Answer:

11 quarters

Step-by-step explanation:

If Thomas ignores the extra 3 dimes, he can arrange his coins in groups of 3 dimes and 1 quarter, each group valued at 55¢. It takes

... 6.05/0.55 = 11

groups to bring the total value to the $6.05 remaining after ignoring the extra dimes.

Thomas has 11 quarters and 36 dimes.

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