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Serjik [45]
2 years ago
10

- If f(x) = 3x² − 4 and g(x) = 2x − 6, what is g(f(2))?

Mathematics
2 answers:
koban [17]2 years ago
6 0

Answer:

g[f(2)] = 10

Step-by-step explanation:

Given functions:

\begin{cases}f(x)=3x^2-4\\g(x)=2x-6\end{cases}

Find f(2) by substituting x = 2 into function f(x):

\begin{aligned}\implies f(2)& =3(2)^2-4\\& = 3(4)-4\\& = 12-4\\& = 8\end{aligned}

Now substitute the found value of f(2) into function g(x):

\begin{aligned}g[f(2)] & = 2[f(2)]-6\\\implies g[f(2)] & =2(8)-6\\& = 16-6\\& = 10\end{aligned}

svetoff [14.1K]2 years ago
6 0

\\ \rm\Rrightarrow g(f(2))

\\ \rm\Rrightarrow g(3(2)²-4)

\\ \rm\Rrightarrow g(12-4)

\\ \rm\Rrightarrow g(8)

\\ \rm\Rrightarrow 2(8)-6

\\ \rm\Rrightarrow 16-6

\\ \rm\Rrightarrow 10

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Suppose that two cards are randomly selected from a standard​ 52-card deck. ​(a) what is the probability that the first card is
eduard
<span><span>You draw a queen on the first draw and one on the second<span><span><span>4/52 </span>∗ <span>3/51 </span>= <span>12/2652 </span>= <span>1/22 </span></span></span></span><span>
You draw something other than a queen on the first draw and a queen on the second<span><span><span>
48/52 </span>∗ <span>4/51 </span>= <span>192/2652</span>=<span>16/221</span></span></span></span></span>

So in total, the chance is:

<span><span><span>1/221 </span>+ <span>16/221 </span>= <span>17/221</span>=
<span>4/52</span></span></span>

8 0
4 years ago
What is the axis of symmetry for the function f(x)=-(x+9)(x-21)
Levart [38]

\bf \stackrel{f(x)}{0}=-(x+9)(x-21)\implies \begin{cases} 0=-x-9\implies &x=-9\\ 0=x-21\implies &21=x \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \boxed{-9}\rule[0.35em]{8em}{0.25pt}0\rule[0.35em]{5em}{0.25pt}\stackrel{\downarrow }{6}\rule[0.35em]{10em}{0.25pt}\boxed{21}


now, this parabolic graph, has two zeros/solutions/x-intercepts, at -9 and 21.

for a quadratic equation, the vertex will be right in between the x-intercepts, namely in this case between -9 and 21, right in the middle, namely at 6, and is where the axis of symmetry is at, x = 6.

6 0
3 years ago
Read 2 more answers
What is the answer for 5x-2x+8=2+6x+6?
Ede4ka [16]

5x - 2x + 8 = 2 + 6x + 6


Add like terms:

5x - 2x = 3x

2 + 6 = 8


3x + 8 = 6x + 8


To isolate the variable, subtract 6x from both sides of the equation:

3x - 6x = -3x


-3x + 8 = 8


Now subtract 8 from both sides:

8 - 8 = 0


-3x = 0


To finish, divide both sides by -3:

0 ÷ -3x = 0


The answer is x = 0


Hope this helps.

3 0
3 years ago
Read 2 more answers
Solving Inequalities (Will mark as brainliest)
svlad2 [7]

Answer:

1. x ≤ -8

2. y < -8

3. y < -11

4. n > 10

5. n ≤ -2

6. n ≤ 15

7. n ≤ -5

Step-by-step explanation:

Your goal is to get just the variable on one side of the inequality!

For example, take -2y - 4 > 18.

Add 4 to both sides. So... -2y - 4 + (4) > 18 + (4)

Now you get -2y > 22. Since y isn't by itself, let's divide both sides by -2.

So, (-2y / -2) > (22 / -2)

<u>Anytime you're dividing something by a negative, remember to FLIP THE SIGNS.</u> So instead of a greater than, it will now be a less than sign <.

Now you get, y < -11

5 0
2 years ago
What is an equation of the line that passes through the points (-6, 3) and<br> (-6, -3)?
Verizon [17]

Answer:

x = -6

Explanation:

4 0
3 years ago
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