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3 years ago

If f(x) = 4x + 8 and g(x) = (x+4, what is (fºg)(12)?

Mathematics

1 answer:

svetlana [45]3 years ago

4 0

Answer:

Step-by-step explanation:

$f(x) = 4x+8\\g(x) = x + 4\\\\1. f(g(x)) = 4(x+4) + 8\\2. f(g(x)) = 4x + 16 + 8\\3. f(g(x))=4x + 24\\\\4. f(g(12)) = 4(12) + 24\\5. f(g(12)) = 48 + 24 = 72\\$

To do these, you have to place the entire function inside the parent function's variables.

You are inputting the value of the function g(x) into f(x)

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1. Kalena was asked to prove ifx(x - 1)(x + 1) = x3 - X represents a polynomial identity. She

Verdich [7]

Answer:

C. Kalena made a mistake in Step 3. The justification should state: -x²

+ x²

Step-by-step explanation:

Given the function x(x - 1)(x + 1) = x3 - X

To justify kelena proof

We will need to show if the two equations are equal.

Starting from the RHS with function x³-x

First we will factor out the common factor which is 'x' to have;

x(x²-1)

Factorising x²-1 using the difference of two square will give;

x(x+1)(x-1)

Note that for two real number a and b, the expansion of a²-b² using difference vof two square will give;

a²-b² = (a+b)(a-b) hence;

Factorising x²-1 using the difference of two square will give;

x(x+1)(x-1)

Factorising x(x+1) gives x²+x, therefore

x(x+1)(x-1) = (x²+x)(x-1)

(x²+x)(x-1) = x³-x²+x²-x

The function x³-x²+x²-x gotten shows that kelena made a mistake in step 3, the justification should be -x²+x² not -x-x²

6 0

3 years ago

Joe likes to go fishing. He knows that the stronger the fishing line is, the larger the fish that he can catch.

Trava [24]

The answer is
B.

The size of the fish Joe can catch is a function of the strength of his fishing line.

6 0

3 years ago

Which situation represents a proportional relationship?

Natalka [10]

Answer:

B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y=kx$

The ratio between the two variables is a constant called constant of proportionality k

$k=y/x$

Verify each case

A) Julie sold 4 necklaces for $12 and 9 necklaces for $25.

$\frac{4}{12}=\frac{9}{25}$

Multiply in cross

$4(25)=9(12)\\100\neq108$

Is not true

therefore

The situation not represent a proportional relationship

B) Jack biked 5 miles in 25 minutes and 8 miles in 40 minutes.

$\frac{5}{25}=\frac{8}{40}$

Multiply in cross

$5(40)=8(25)\\200=200$

Is true

therefore

The situation represent a proportional relationship

C) Larry packed 24 apples in 6 boxes and 46 apples in 9 boxes

$\frac{24}{6}=\frac{46}{9}$

Multiply in cross

$24(9)=46(6)\\216\neq276$

Is not true

therefore

The situation not represent a proportional relationship

D) Allie put 14 pieces of candy in 2 bags and 30 pieces of candy in 4 bags

$\frac{14}{2}=\frac{30}{4}$

Multiply in cross

$14(4)=30(2)\\56\neq60$

Is not true

therefore

The situation not represent a proportional relationship

7 0

3 years ago

Please help me o have to turn this in tomorrow and I don’t want to fail

andriy [413]

B=5 units that is the answer

5 0

3 years ago

If two cards are drawn without replacement from a 52 card deck, find the probability that the second card drawn is red, given th

snow_lady [41]

Answer:

The probability that the second card drawn is red, given that the first card was a heart is 0.1225

Step-by-step explanation:

Total cards in a deck = 52

Total red cards = 26

Heart cards = 13

Probability of getting red card = $\frac{13}{52}$

Total remaining card = 51

Remaining red cards = 25

Probability of getting red card in second draw without replacement = $\frac{25}{51}$

So, the probability that the second card drawn is red, given that the first card was a heart = $\frac{13}{52} \times \frac{25}{51} =0.1225$

Hence the probability that the second card drawn is red, given that the first card was a heart is 0.1225

5 0

2 years ago