1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Free_Kalibri [48]
3 years ago
15

Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$ Find $f(x) - g(x) + h(x).$

Mathematics
1 answer:
Viefleur [7K]3 years ago
6 0

QUESTION 1

Given that:

f(x)=2x^2+3x-9,

g(x)=5x+11,

and

h(x)=-3x^2+1

Then;

f(x)-g(x)+h(x)=2x^2+3x-9-(5x+11)+(-3x^2+1)

f(x)-g(x)+h(x)=2x^2+3x-9-5x-11-3x^2+1

Group similar terms;

f(x)-g(x)+h(x)=2x^2-3x^2+3x-5x-11-9+1

Simplify;

f(x)-g(x)+h(x)=-x^2-2x-19

QUESTION 2

Given that;

f(x)=4x-7.

g(x)=(x+1)^2

and

s(x)=f(x)+g(x)

Substitute the functions;

s(x)=4x-7+(x+1)^2

Substitute x=3

s(3)=4(3)-7+(3+1)^2

s(3)=12-7+(4)^2

s(3)=5+16

s(3)=21

QUESTION 3

Given:

f(x)=3x+2

g(x)=x^2-5x-1

f(g(x))=f(x^2-5x-1)

This implies that;

f(g(x))=3(x^2-5x-1)+2

Expand the parenthesis;

f(g(x))=3x^2-15x-3+2

f(g(x))=3x^2-15x-1

QUESTION 4

The given function is;

f(x)=3(x-6)^2+1

Let

y=3(x-6)^2+1

\Rightarrow y-1=3(x-6)^2

\Rightarrow \frac{y-1}{3}=(x-6)^2

\Rightarrow \sqrt{\frac{y-1}{3}}=x-6

\Rightarrow x=6+\sqrt{\frac{y-1}{3}}

The range is:

\frac{y-1}{3}\ge0

y-1\ge0

y\ge1

The interval notation is;

[1,+\infty)

You might be interested in
1. The expression 11x2 - 12x - 10 has ___ terms and a constant of ___.
Illusion [34]
1.  3,-10

2. 10x + y

3. 2x - 3y


6 0
3 years ago
Read 2 more answers
Find the slope and the y-intercept of the graph of the linear equation. y=-7x+12<br><br>​
Sever21 [200]
Slope = -7

Y intercept= 13
7 0
1 year ago
Read 2 more answers
Please I need help. you will get points ​
iragen [17]

Answer:

t(32) = 94

Step-by-step explanation:

a. I think s is the independent variable

b I think t or t(s) is the dependent variable since the total amount of money depends on how many treats are sold.

t(32) = 30 + 2(32)

t(32) = 30 + 64

t(32) = 94

I'm a little unsure on the dependent and independent variable but I know the function is correct.

Hope this helps :)

7 0
3 years ago
True or false don’t lie
erastovalidia [21]

Answer:

t

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
The equation of a circle is x2 + (y – 10)2 = 16. The radius of the circle is units. The center of the circle is at .
DENIUS [597]

Answer:

(0, 10)

Step-by-step explanation:

Compare:

x2 + (y – 10)2 = 16 and

(x - h)² + (y - k)² = 4²

The center of the circle is at (h, k), which in this case is (0, 10).

4 0
3 years ago
Read 2 more answers
Other questions:
  • In the rectangle below AC has a length of 28. What is the length of ED? If necessary, round your answer to two decimals places.
    15·2 answers
  • A computer sells for $995, which is marked up 35% of the selling price. the cost of the computer is:
    7·2 answers
  • Tom bought a circular mirror that has an area of 156.25 pie square inches. What is the diameter of the mirror?
    7·1 answer
  • Jasmine earns $1200 per month as a base salary, plus 3% of her total sales. Write a linear model of her monthly earnings. Then u
    8·2 answers
  • Study the following production possibility curve. The number of data points that illustrate the proper allocation of resources i
    15·2 answers
  • There are 575 fireworks to be shot off in a firework display every minute 12 new fireworks are shot off display write a verbal m
    15·1 answer
  • The volume of a cylinder is 480 cm. The height of the cylinder is 30 cm. What is the radius of the
    12·1 answer
  • What fraction is between 2/3 and 1 1/3
    9·2 answers
  • 4x2 + 3x2 = 14 Solve to three digits?
    8·1 answer
  • What is the length of AC?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!