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Assoli18 [71]
3 years ago
7

Which fraction represents this graph?

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
8 0

B. y=2x+3 is your answer



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Given the function f(x)=x^4+10x^3+35x^2+50x+24 , factor completely. Show all work and steps. Then sketch the graph.
Varvara68 [4.7K]
According to the rational root theorem, the possible rational factors, if any, of the given polynomial are the factors of 24/1=24.
Thus possible factors are
(x +/- k) where k=1,2,3,4,6,8,12,24.
Since all terms are positive, (x-k) do not exist as factors (see Descartes rule of signs) for all k.
Of the remainder, we note that the
sum of coefficients of even degree terms=1+35+24=60
sum of coefficients of odd degree terms=10+50=60
This means that (x+1) is a factor.

Divide f(x) by (x+1) =>
g(x)=f(x)/(x+1)=x^3+9x^2+26x+24 (no remainder)

We continue with x+2=0, or put x=-2 into g(x), and get
g(-2)=-8+36-52+24=0  => (x+2) is another rational factor.

Again, divide g(x) by (x+2) to get
h(x)=x^2+7x+12 (remainder=0)

We can readily factor h(x) by inspection as h(x)=(x+3)(x+4)
[from 3+4=7,3*4=12]

Therefore

f(x)=x^4+10*x^3+35*x^2+50*x+24=(x+1)(x+2)(x+3)(x+4)

6 0
3 years ago
Use the exponential function y=500(.9)^x to find the value of the video game console after 4 years.
zysi [14]

Answer:

328.05 dollars

7 years

Step-by-step explanation:

1.

y=500(.9)^4 =328.05

What is being asked in the problem and what does that mean?

We are asked to the price of the video game after 4 years.

What do I know and what does it mean? What plan am I going to try?

We know the <u>initial price is $500</u>, the <u>value depreciates 10% each year </u>because we have .9 or 90% of the price going into the next year.

- value of the video game after first year 90% of 500 so is 450

- value of the video game after second year 90% of 450 so is 405

-value of the video game after third year 90% of 405 so is 364.5

-value of the video game after <u>fourth year</u> 90% of 364.5 so is 328.05

The plan is to substitute x with 4 and calculate y, y=500(.9)^4

What is your answer and what does it mean?

The answer is $328.05, and it means that the video game that was initially worth $500 it lost its' value by 10 % each of the four years.

2.

         y= 500(.9)^x

----------------------------------------------------------------------------

x =8, y= 500(0.9)^8 = 215.234 ≈215.23, this is less than $250

x = 7, y= 500(0.9)^7 = 239.148 ≈239.15, this is less than $250

x =6, y= 500(0.9)^6 = 265.721 ≈ 265.72, this is more than $250

What is being asked in the problem and what does that mean?

We are asked to find the value of x that represents the years such that the value of the console is still under $250.

What do I know and what does it mean? What plan am I going to try?

We know the value of y has to be less that $250, we know the inequality

[500(.9)^x ] < 250, the plan is to try different values for x until we have the maximum value of x that gives us less than 250.

8 0
3 years ago
Which are solutions to the equation below?
mojhsa [17]
The answers would be E and F -6 and -3
3 0
3 years ago
Read 2 more answers
Solve the equation for x: c a−x/x−a =5x Answer: , a ≠ − 1/5
meriva

Answer:

\large\boxed{x=-\dfrac{1}{5}}

Step-by-step explanation:

\dfrac{a-x}{x-a}=5x\\\\\dfrac{(a-x)}{-(a-x)}=5x\qquad\text{cancel}\ (a-x)\\\\-1=5x\qquad\text{divide both sides by 5}\\\\-\dfrac{1}{5}=\dfrac{5x}{5}\to\boxed{x=-\dfrac{1}{5}}

7 0
3 years ago
Use the diagram shown to help you find the m∠LNM.
attashe74 [19]

Answer:

135 is your answer......

7 0
2 years ago
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