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
Mariulka [41]
3 years ago
10

HELP OFFERING 50 points!!

Mathematics
1 answer:
expeople1 [14]3 years ago
4 0

Answer:

f(g(x)) =  5x^{2}   + 10x+ 5

Step-by-step explanation:

Here, the given functions are:

f(x)  = 5x^2\\g(x) = x+1

Now, (fg)(x)  = f (g(x))

f(g(x))= f (x+1)

\implies f(x+1)  = 5(x+1)^2

By ALGEBRAIC IDENTITY:

(a+b)^2  = a^2 + b^2  + 2ab\implies (x+1)^2  = x^{2}  + 1 + 2x

So, 5(x+1)^2   = 5(x^{2}  + 2x + 1)  = 5x^{2}   + 10x+ 5

Hence, f(g(x)) =  5x^{2}   + 10x+ 5

You might be interested in
A football is kicked toward an end zone with an initial vertical velocity of 30 ft/s. The function h(t) = -16+ 30t models the he
Ulleksa [173]

Answer:

A. The football does not reach a height of 15ft

Step-by-step explanation:

Given

h(t) = -16t^2 + 30t

Required

Determine which of the options is true

The option illustrates the height reached by the ball.

To solve this, we make use of maximum of a function

For a function f(x)

Such that:

f(x) = ax^2 + bx + c:

f(\frac{-b}{2a}) = maximum/minimum

i.e we first solve for \frac{-b}{2a}

Then substitute \frac{-b}{2a} for x in f(x) = ax^2 + bx + c

In our case:

First we need to solve \frac{-b}{2a}

Then substitute \frac{-b}{2a} for t in h(t) = -16t^2 + 30t

By comparison:

b = 30

c = -16

\frac{-b}{2a} = \frac{-30}{2 * -16}

\frac{-b}{2a} = \frac{-30}{-32}

\frac{-b}{2a} = \frac{30}{32}

\frac{-b}{2a} = \frac{15}{16}

Substitute \frac{15}{16} for t in h(t) = -16t^2 + 30t

h(\frac{15}{16}) = -16(\frac{15}{16})^2 + 30(\frac{15}{16})

h(\frac{15}{16}) = -16(\frac{225}{256}) + \frac{450}{16}

h(\frac{15}{16}) = -(\frac{225}{16}) + \frac{450}{16}

h(\frac{15}{16}) = \frac{-225 + 450}{16}

h(\frac{15}{16}) = \frac{225}{16}

h(\frac{15}{16}) = 14.0625

This implies that the maximum height reached is 14.0625ft.

So, the option that answers the question is A because 14.0625 < 15

8 0
2 years ago
An allergy drug is tested by giving 130 people the drug and 100 people a placebo. A control group consists of 70 people who were
Ksenya-84 [330]

Answer:

Need more info?

There is no icon.....

Please screenshot the table.

3 0
3 years ago
[tex]\sqrt{x} 196<br> can someone help me
Maslowich

Answer:

14

Step-by-step explanation:

√196

Calculate the square root of 196 and get 14.

14

8 0
3 years ago
Read 2 more answers
How does graphing linear inequalities differ from graphing linear equations?​
Ivan

Explanation:

When the inequality symbol is replaced by an equal sign, the resulting linear equation is the boundary of the solution space of the inequality. Whether that boundary is included in the solution region or not depends on the inequality symbol.

The boundary line is included if the symbol includes the "or equal to" condition (≤ or ≥). An included boundary line is graphed as a solid line.

When the inequality symbol does not include the "or equal to" condition (< or >), the boundary line is not included in the solution space, and it is graphed as a dashed line.

Once the boundary line is graphed, the half-plane that makes up the solution space is shaded. The shaded half-plane will be to the right or above the boundary line if the inequality can be structured to be of one of these forms:

  • x > ...   or   x ≥ ...   ⇒ shading is to the right of the boundary
  • y > ...   or   y ≥ ...   ⇒ shading is above the boundary

Otherwise, the shaded solution space will be below or to the left of the boundary line.

_____

Just as a system of linear equations may have no solution, so that may be the case for inequalities. If the boundary lines are parallel and the solution spaces do not overlap, then there is no solution.

_____

The attached graph shows an example of graphed inequalities. The solutions for this system are in the doubly-shaded area to the left of the point where the lines intersect. We have purposely shown both kinds of inequalities (one "or equal to" and one not) with shading both above and below the boundary lines.

6 0
3 years ago
Is -3+3-3+3-3+3 a arithmetic?
bezimeni [28]

Answer:

- 3 + 3 = 0 - 3 =  - 3 \\  - 3 + 3 = 0 - 3 =  - 3 \\  - 3 + 3 = 0

3 0
3 years ago
Read 2 more answers
Other questions:
  • Plz help ASAP!!!!!!!
    10·2 answers
  • What expression are 5 times as large as 184 + 213.
    15·1 answer
  • Simplify the expression (3x^4/2y^3)^2
    5·1 answer
  • An (independent or dependent) variable can be assigned any value. The variable that changes depending on the (independent or dep
    11·1 answer
  • What are the coordinates of vertex F of parallelogram FGHJ?
    13·2 answers
  • 7. Write three different fractions equivalent to 3/4. Explain how you know they are
    15·1 answer
  • fruit salad for 5 people needs 400g of melon, 120g of mango, 0.3kg of banana and 0.45kg of grapes. How much will it weigh in gra
    10·1 answer
  • Help me. this IS NOTa quiz
    12·1 answer
  • Select all of the situations which can be represented by the expression 25.75x + 10.
    9·1 answer
  • 12.<br><br>Find the Midpoint of (0,6) and (-4,8)<br><br>if you could show your work that'd be great​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!