Based on the graph below, what is the solution to the equation f(x) = g(x)?graph of function f of x equals negative x plus 2.5 and graph of function g of x equals x squared plus 2 multiplied by x minus 8

Answers

Answer 1

Answer: The wording of the second function may be interpreted in several differente ways. These are some:

g(x) = (x^2 +2)(x-8)
g(x)=x^2 + 2(x-8)
g(x) x^2 +2x - 8

I will work with the last one, so my system of equation is:

f(x) = - x +2.5
g(x) = x^2 + 2x - 8

f(x) = g(x) ⇒ - x + 2.5 = x^2 + 2x - 8

x^2 + 3x - 8 - x - 2.5 = 0

x^2 + 3x - 10.5 = 0

Use the quadratic formula to solve for x:

x = [ - 3 +/- √(3^2) - 4(1)(-10.5) ]/2

x = - 5.07 and x = 2.07

Answer 2

Answer:

The solution of the equation f(x) = g(x) are x = 3.055 or x = -6.055 if the f(x) = -x + 2.5 and g(x) = x² +2(x - 8)

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) = -x + 2.5

g(x) = x² +2(x - 8)

f(x) = g(x)

-x + 2.5 = x² +2(x - 8)

After simplification:

x² + 3x - 18.5 = 0

After solving, we get:

x = 3.055 or x = -6.055

Thus, the solution of the equation f(x) = g(x) are x = 3.055 or x = -6.055 if the f(x) = -x + 2.5 and g(x) = x² +2(x - 8)

Learn more about the function here:

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Related Questions

What is the average rate of change for (0,80) and (15,10)

Answers

Answer:

-14/3

Step-by-step explanation:

formula: (y₂ - y₁) / (x₂ - x₁)

(10 - 80) / (15 - 0)

(-70) / (15)

simplify

-14/3

Y/X
10-80/15-0
-70/15
=-14/3

What is the sum of the first 50 natural numbers? How to solve it without adding 50 digits?

Answers

$1+2+3+4+5+\dots+50\n\n1;\ 2;\ 3;\ 4;\ 5;\dots;50\ are\ the\ terms\ of\ a\ arithmetic\ sequence\nwhere\ a_1=1\ and\ d=1\n\nSum:S_n=(a_1+a_n)/(2)\cdot n\n\nS_(50)=(1+50)/(2)\cdot50=51\cdot25=1275\leftarrow solution$

Look at the first one and the last one: 1 + 50 = 51
Look at the second one and the second-last one: 2 + 49 = 51
Look at the third one and the third-last one: 3 + 48 = 51

Every pair you construct in this way adds up to 51 .

There are ( 50/2 ) = 25 pairs.

They all add up to ( 25 pairs ) x ( 51 per pair ) = 1,275

In Russel Elementary School there are 50 students. At the beginning of the year, each student planted three flowers in the school yard. During the year, eight flowers withered. Which of the following expressions represents the number of flowers that remained in the school yard? A. (3 × 50) – 8 B. (50 + 3) – 8 C. (50 × 8) – 3 D. (50 × 3) ÷ 8

Answers

Answer:

option A is correct answer

Megan borrowed $50,000 at 5% simple interest for 6 years. joseph borrowed $60,000 at 4% simple interest for 8 years. using the formula who will have a greater monthly payment, m, and by how much?

Answers

Answer:

Megan will pay $78 more than Joseph.

Step-by-step explanation:

Formula: Simple Interest = P x R x T

Megan Info

Borrowed Money (P)=$50,000
Rate of interest (r)=0.05
Time (t) = 6 years

Simple interest paid by Megan = 50,000 x 0.05 x 6 = 15000

Total amount paid in 6 years = 50000 + 15000 = $65,000

Monthly payment by Megan (m) = 65000÷72 = $903

Joseph Info

Borrowed Money (P)=$60,000
Rate of interest (r)=0.04
Time (t) = 8 years

Simple interest paid by Magan = 60,000 x 0.04 x 8 = 19200

Total amount paid in 8 years = 60000 + 19200 = $79,200

Monthly payment by Joseph (m) = 79200÷96 = $825

Now we find Difference of monthly payment

⇒Megan - Joseph

⇒ 903-825

⇒ $78

Thus, Megan will pay $78 more than Joseph.

Answer:

Megan will pay approximately $78 more per month.

Step-by-step explanation:

Factor by grouping:4-12r+9r^2

i know the answer is (2-3r)^2

Can anyone explain to me how it is?

Answers

$(x-y)^2=x^2-2xy+y^2\n---------------------------\n\n4-12r+9r^2=2^2-2\cdot2\cdot3r+(3r)^2=(2-3r)^2$

$other\ method:\n\n4-12r+9r^2=4-6r-6r+9r^2=2(2-3r)-3r(2-3r)\n\n=(2-3r)(2-3r)=(2-3r)^2$

Because:
$(a-b)^2=a^2+2ab+b^2$

What is the elapsed time between 10:30 p.m. and 1:15 a.m.?3 hours
3 hours and 15 minutes
2 hours and 45 minutes
2 hours and 30 minutes

Answers

If you would like to find the elapsed time between 10:30 p.m. and 1:15 a.m., you can calculate this using the following steps:

12:00 p.m. - 10:30 p.m. = 1:30
00:00 a.m. + 1:15 a.m. = 1:15

1:30 + 1:15 = 2:45 = 2 hours and 45 minutes

The correct result would be 2 hours and 45 minutes.

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