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3 years ago

Consider these functions:

Mathematics

2 answers:

IgorLugansk [536]3 years ago

8 0

Answer:

The value of f(g(-2)) is 12.

Step-by-step explanation:

We'll start by solving g(-2):

$g(-2)\\= (-2)^2 + 2\\= 4 + 2\\= 6$

Now we can take that value and plug it into function f:

$f(6)\\= \frac{-1}{2}6^2 + 5 * 6\\= -36/2 + 30\\= -18 + 30\\= 12$

Alternatively, you can work out a new single function that in itself describes f(g())

$f(g(x)) = -\frac{1}{2}g(x)^2 + 5g(x)\\= -\frac{1}{2}(x^2 + 2)^2 + 5(x^2 + 2)\\= -\frac{1}{2}(x^4 + 4x^2 + 4) + 5x^2 + 10\\= -\frac{1}{2}x^4 - 2x^2 - 2 + 5x^2 + 10\\= -\frac{x^4}{2} + 3x^2 + 8$

and try plugging -2 into the new function

$= - \frac{-2^4}{2} + 3(-2)^2 + 8\\= -16 / 2 + 3 * 4 + 8\\= -8 + 12 + 8\\= 12$

rusak2 [61]3 years ago

8 0

Answer:

The answer is 12

Step-by-step explanation:

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Which inequality is represented by this graph

sertanlavr [38]

The right answer is of option D.

 $x \geqslant 4$ 

In the given graph, X is greater than 4 and X equals to 4.

Hope it helps.....

Good luck on your assignment

4 0

3 years ago

∠F and ∠G are supplementary angles. If m∠F is two less than six times the measure of ∠G, find the measures of both angles

Mnenie [13.5K]

Answer:

∠ G = 26°, ∠ F = 154°

Step-by-step explanation:

Express ∠ F in terms of ∠ G, that is

F = 6G - 2

and since the angles are supplementary, then

G + 6G - 2 = 180, that is

7G - 2 = 180 ( add 2 to both sides )

7G = 182 ( divide both sides by 7 )

G = 26

Thus

∠ G = 26° and ∠ F = 6(26) - 2 = 156 - 2 = 154°

4 0

3 years ago

Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.

koban [17]

Answer:

$x^2 + 4x + y^2 +8y = 0$

Step-by-step explanation:

Given

$A = (-1,-2)$

$B = (2,4)$

$AP:BP = 1 : 2$

Required

The locus of P

$AP:BP = 1 : 2$

Express as fraction

$\frac{AP}{BP} = \frac{1}{2}$

Cross multiply

$2AP = BP$

Calculate AP and BP using the following distance formula:

$d = \sqrt{(x - x_1)^2 + (y - y_1)^2}$

So, we have:

$2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

$2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

Take square of both sides

$4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2$

Evaluate all squares

$4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16$

Collect and evaluate like terms

$4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20$

Open brackets

$4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20$

Collect like terms

$4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y + 20 - 20 = 0$

$3x^2 + 12x + 3y^2 +24y = 0$

Divide through by 3

$x^2 + 4x + y^2 +8y = 0$

3 0

3 years ago

U + -5/6 = -1/3 solve for u

Phoenix [80]

Move all terms not containing U to the right side of the equation.

Exact Form:

U = 1/2

Decimal Form:

U = 0.5

8 0

3 years ago

Read 2 more answers

What is the initial value of y= 8x+7

allochka39001 [22]

Answer:

Step-by-step explanation:

The initial value is another name for the y-intercept. This equation is written in point slope form (y=mx+b). And before you think y-intercept means y, right? No that is incorrect, I got that wrong in the beginning too ;)

y=mx+b

y=8x+7

b in the point slope form equation is always the initial value or y-intercept or whatever people call it. So what substitutes b out here? 7. So 7 is the initial value!

:) Hope you understand now! Have a good day!

8 0

3 years ago