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3 years ago

Let f(x)=x^3+3 and g(x) = 2x^2 + 2x +1. What is g(f(-2))?

Mathematics

2 answers:

emmasim [6.3K]3 years ago

5 0

Answer:

Step-by-step explanation:

This composite function can be easily solved

First solve f(-2)

f(-2)=(-2)³+3

f(-2)=-8+3=-5

Now plug -5 for x in function g(x)

=2(5)²+2(5)+1

=50+10+1

=61

romanna [79]3 years ago

5 0

9514 1404 393

Answer:

Step-by-step explanation:

g(f(-2)) = g((-2)³ +3) = g(-8+3) = g(-5)

= 2(-5)² +2(-5) +1 = 50 -10 +1

g(f(-2)) = 41

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$2,500 {(1/.005) - [1/.005(1.005)12 ×25]}

Afina-wow [57]

Answer:

-12771250

Step-by-step explanation:

We want to evaluate;

$2500( \frac{1}{0.005} - ( \frac{1}{0.005} \times 1.005 ^{12} \times 25)$

We expand to get;

$2500 \times \frac{1}{0.005} - 2500( \frac{1}{0.005} \times 1.005 ^{12} \times 25)$

$500000 - 500000 \times 1.0617 \times 25$

We multiply to get;

$500000 - 13271250$

We now subtract to get :

$= - 12771250$

6 0

3 years ago

What is the length of the hypotenuse in a right triangle if the legs are 50 and 120

miv72 [106K]

Good evening

Answer:

Step-by-step explanation:

let L represent the length of the hypotenuse :

Since we are in a right triangle case then the Pyth theorem is a valid choice to solve the problem :

the Pythagoren theorem states that :

L² = 50^2+120^2

then

L² = 16 900

then

L = √(16 900)

=130

__________________________

5 0

4 years ago

Can you conclude line Gh is congruent to line jk

4vir4ik [10]

No, I can't. That conclusion would be completely unwarranted, unsupported
as it is by any available facts. We don't know anything about either line, not
even whether they are on the same planet. Do you have a drawing or something
that might give us some information about them ?

8 0

3 years ago

Match the steps to find the equation of the parabola with focus (-1, 2) and directrix x = 5.

Archy [21]

Answer:

The matched options to the given problem is below:

Step1: Choose a point on the parabola

Step2: Find the distance from the focus to the point on the parabola.

Step3: Use (x, y).

Find the distance from the point on the parabola to the directrix.

Step4: Set the distance from focus to the point equal to the distance from directrix to the point.

Step5: Square both sides and simplify.

Step6: Write the equation of the parabola.

Step by step Explanation:

Given that the focus (-1,2) and directrix x=5

To find the equation of the parabola:

By using focus directrix property of parabola

Let S be a point and d be line

focus (-1,2) and directrix x=5 respectively

If P is any point on the parabola then p is equidistants from S and d

Focus S=(-1,2), d:x-5=0

Step1: Let P(x,y) be any point on parabola

Step2: Therefore the $d=\sqrt{(x+1)^2+(y-2)^2}\hfill (1)$

Step3: The perpendicular distance from p to d is

$\frac{|x-5|}{\sqrt{(-1)^2+2^2}}$

$=\frac{|x-5|}{\sqrt{5}}\hfill (2)$

Step4: equating (1) and (2)

$\sqrt{(x+1)^2+(y-2)^2}=\frac{|x-5|}{\sqrt{5}}$

Step5: squaring on both sides

$(x+1)^2+(y-2)^2=\frac{|x-5|^2}{5}$

$5[(x+1)^2+(y-2)^2]=(x-5)^2$

$5[x^2+2x+1+y^2-2y+4-x^2+10x-25]=0$

$12x+y^2-2y-24=0$

Step6: Equation of the parabola is

$y^2-2y+12x-24=0$

8 0

3 years ago

Can someone help me solve multiple step equations? For example (7t - 2) - (-3t + 1) = -3(1 - 3t)

artcher [175]

Answer:

t = 0

Step-by-step explanation:

(7t - 2) - (-3t + 1) = -3(1 - 3t)

because you can not do anything inside the parantheses, you distribute. there aren't any numbers on the left side of the parantheses on the left side of the equation so we just imagine the number 1. on the right side of the equation, just distribute normally

[ 1(7t - 2) -1(-3t + 1) = -3(1 - 3t) ]

will be

7t - 2 + 3t - 1 = -3 + 9t

add like terms

10t - 3 = -3 + 9t

subtract 9t from both sides

t - 3 = -3

add 3 to both sides

t = 0

3 0

3 years ago