SUPER URGENT!

If f(x)=8-10x and g(x) =5x +4, what is the value of (fog)(-2)?

swat32

Answer:

68

Step-by-step explanation:

Any function is evaluated by putting the argument value where the variable is, then doing the arithmetic. When the argument is another function value, that function value is evaluated first.

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The "o" in (fog) is a stand-in for the "ring operator" (∘) which is the operator used to signify a composition. A composition is evaluated right-to-left. That means (f∘g)(x) ≡ f(g(x)). The value of g(x) is found first, and is operated on by the function f.

Writing the composition in the form f(g(x)) lets you identify the layers of parentheses. As with any expression evaluation, the Order of Operations applies. It tells you to evaluate the expression in the innermost parentheses and work your way out.

To evaluate (f∘g)(-2) = f(g(-2)), we must first evaluate g(-2). That is ...

g(x) = 5x +4

g(-2) = 5(-2) +4 = -10 +4 = -6 . . . . . put -2 where x is, do the math

Now that we know g(-2) = -6, we know this expression is ...

f(-6) = 8 -10(-6) = 8 +60 = 68 . . . . . substitute for x in 8-10x

Then the value we're looking for is ...

(f∘g)(-2) = 68

8 0

1 year ago

Write an equation in slope-intercept form for the following line:<br> (-14.1) and (13,-2)

vesna_86 [32]

Answer:

$y=-\frac{1}{9}x-\frac{5}{9}$

Step-by-step explanation:

$(-14,1)(13,-2)$

Use the slope-intercept formula:

$y=mx+b$

m is the slope and b is the y-intercept. Use the slope formula first:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} =\frac{rise}{run}$

Rise over run is the change in the y-axis over the change in the x-axis. Plug in the coordinates:

$(-14(x_{1}),1(y_{1}))\\(13(x_{2}),-2(y_{2}))$

$\frac{-2-1}{13-(-14)}$

Simplify parentheses (two negatives makes a positive):

$\frac{-2-1}{13+14}$

Simplify:

$\frac{-3}{27} =-\frac{3}{27}=-\frac{1}{9}$

The slope is $-\frac{1}{9}$ . Insert into the equation:

$y=-\frac{1}{9}x +b$

Now, to find the y-intercept, take one of the points and substitute for the x and y values of the equation:

$(13,-2)\\-2=-\frac{1}{9} (13)+b$

Solve for b, the y-intercept. Simplify parentheses:

$-\frac{1}{9}*\frac{13}{1}=-\frac{13}{9}$

$-2=-\frac{13}{9} +b$

Add $-\frac{13}{9}$ to both sides:

$-2+\frac{13}{9}=-\frac{13}{9} +\frac{13}{9} +b\\\\-2+\frac{13}{9} =b$

Simplify:

$-\frac{2}{1} +\frac{13}{9}\\\\-\frac{18}{9}+\frac{13}{9}\\ \\b=-\frac{5}{9}$

The y-intercept is $-\frac{5}{9}$ . Insert this into the equation:

$y=-\frac{1}{9} x-\frac{5}{9}$

Finito.

8 0

2 years ago

MEDAL !!! TRUE OR FALSE. Jonathan is catering an event for one of his clients. He has a maximum of $200 to spend on appetizers.

DochEvi [55]

182.5 US dollars so yes

the answer is True

5 0

3 years ago

b In a hostel. 50 students have food enough for 54 days. How many students should be added in de the hostel so that the food is

lys-0071 [83]

Everybody will one thing a day

6 0

2 years ago

DJ Giovanni is making a playlist for a friend; he is trying to decide what 12 songs to play and in what order they should be pla

Elena L [17]

Answer:

5.78×10¹⁵

Step-by-step explanation:

The playlist has 12 songs, and he wants the same number of songs for each genre, so he must pick 4 songs per genre.

The number of ways he can choose 4 country songs (ignoring the order) is ₂₂C₄ = 7315.

The number of ways he can choose 4 reggae songs (ignoring the order) is ₁₁C₄ = 330.

The number of ways he can choose 4 pop songs (ignoring the order) is ₅C₄ = 5.

The total number of combinations is 7315 × 330 × 5 = 1.21×10⁷.

Once he has his 12 songs selected, the number of ways he can arrange them is ₁₂P₁₂ = 12! = 4.79×10⁸.

So the total number of possible playlists is:

(1.21×10⁷) × (4.79×10⁸) = 5.78×10¹⁵

4 0

3 years ago