Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.

Answers

Answer 1

Answer: f(x) = x³ + 4 and g(x) = ∛(x - 4)

so, the first thing the question asks of you is to see that f(g(x)) = x. try it out, plugging g(x) in as the x-variable in the first equation:

f(g(x)) = (∛(x - 4))³ + 4

they were merciful in writing this problem, and thankfully your cube roots cancel out and don't cause you any trouble. continue solving:

f(g(x)) = (∛(x - 4))³ + 4 ... cube root and exponent cancel
f(g(x)) = x - 4 + 4 ... simplify
f(g(x)) = x

so, yep. that one worked. try out the second half of the question: g(f(x)) = x

g(f(x)) = ∛((x³ + 4) - 4) ... simplify inside your radical, cancelling out the 4s
g(f(x)) = ∛(x³) ... the cube root of x³ is x itself, so:
g(f(x)) = x

and there you are. you've confirmed that these are inverses.

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Which multiplication has a negative answer?A) (-1)(-1)
B) (-1)(-1)(-1)(-1)
C) (-1)(-1)(-1)(-1)(-1)
D) (-1)(-1)(-1)(0)

Answers

To find out quickly if multiplication will be positive or negative, count the number of negative signs in each equation. If it comes out even, it is positive. If odd, it will come out negative. Only exception is when 0 is in the mix. First equation has 2, therefore is positive because even. Second has 4, which is another positive because even. 3rd is 5, which is negative because it is odd and has NO 0. 4th has 0.

C is the answer and I hope this helped.

The answer is C. because when you multiply,exponents [-1][-1][-1][-1][-1]. the answer results in the exponent -1.hope i helped

If 2x/5y=6,what is the value of y, in terms of x ? 2. 11/4-a=3 , What is the value of a in the equation ?

Answers

$(2x)/(5y) = 6$

$2x = 6 * 5y$

$2x = 30y$

$(2x)/(30) = y$

$y = (x)/(15)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$(11)/(4) - a = 3$

$-a = 3 - (11)/(4)$

$a = (11)/(4) - 3$

$a = (11)/(4) - (12)/(4)$

$a = - (1)/(4)$

On a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam?

Answers

Answer:

89.84375

Step-by-step explanation:

Given that on a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93.

To find weighted mean.

Here weights can be considered as number of majors in each subject

$Marks x 90 85 93\nWeights 15 7 10\nProduct 1350 595 930\n$

Weighted total = 1350+595+930 = 2875

Weighted mean = weighted total/total students

$=(2875)/(32) =89.84375$

Josh spent $30 at the movies. 1/5 was spent on a drink, 45% on a ticket and the rest on food. How much did he spend on food?

Answers

Answer:

$10.5

Step-by-step explanation:

Given data

Total amount=$30

Drink = 1/5*30= $6

Ticket= 45% of 30

=45/100*30

=0.45*30

=$13.5

The remainder is for food

=30-6-13.5

=$10.5

Given Δ ABC ≅ Δ EFG, What is the value of x? A. x= 45 °
B. x= 50 °
C. x= 85 °
D. x= 135 °

Answers

Answer: The correct option is (A) 45.

Step-by-step explanation: We are given that triangles ABC and EFG are congruent to each other, where

$m\angle A=50^\circ,m\angle G=85^\circ,m\angle B=x^\circ.$

We are to find the value of x.

We know that the corresponding angles of congruent triangles have equal measures.

So, m∠A = m∠E, m∠B = m∠F and m∠C = m∠G.

Also, since the sum of three angles of a triangle is 180 degrees, so from triangle ABC, we get

$m\angle A+m\angle B+m\angle C=180^\circ\n\n\Rightarrow 50^\circ+85^\circ+x^\circ=180^\circ\n\n\Rightarrow 135^\circ+x^\circ=180^circ\n\n\Rightarrow x^\circ=180^\circ-135^\circ\n\n\Rightarrow x^\circ=45^\circ\n\n\Rightarrow x=45.$