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2 years ago

Which equation is the inverse of y = 2x2 – 8?

Mathematics

1 answer:

Marrrta [24]2 years ago

6 0

The inverse of the the function above is y = $\sqrt{\frac{x+8}{2}}$

In order to find the inverse of any function, you need to switch the x and y values. Once you've done that, you need to solve for the new y value. The resulting equation will be your inverse. The work for this one is below.

y = 2x^2 - 8 ----> Switch the terms

x = 2y^2 - 8 ----> Add 8 to both sides.

x + 8 = 2y^2 ----> Divide both sides by 2.

$\frac{x+8}{2}$ = y^2 ----> Now take the square root of both sides.

$\sqrt{\frac{x+8}{2}}$ = y

What's left is your inverse. You can change the order so that it is in a more acceptable form.

y = $\sqrt{\frac{x+8}{2}}$

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Daniel is organizing his rock collection of 18 rocks into equal groups. How many possible ways can Daniel line up his rock colle

Colt1911 [192]

Answer:

The correct options are (2, 3 and 6).

Step-by-step explanation:

It is provided that Daniel has a rock collection of 18 rocks.

He wants to organize these 8 rocks into equal groups.

The factors of 18 are:

Factor (18): {1, 2, 3, 6, 9, 18}

A group is a selection of more than 1 items. So, there cannot be 18 groups.

And there cannot be 1 group, since then Daniel would not be organizing the rocks.

So, the possible ways Daniel line up his rock collection are {2, 3, 6 and 9}.

Thus, the correct options are (2, 3 and 6).

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2 years ago

Milton is floating in an inner tube in a wave pool. He is 1.5 m from the bottom of the pool when he is at the trough of a wave.

posledela

This is the concept of sinusoidal, to solve the question we proceed as follows;
Using the formula;
g(t)=offset+A*sin[(2πt)/T+Delay]
From sinusoidal theory, the time from trough to crest is normally half the period of the wave form. Such that T=2.5
The pick magnitude is given by:
Trough-Crest=
2.1-1.5=0.6 m
amplitude=1/2(Trough-Crest)
=1/2*0.6
=0.3
The offset to the center of the circle is 0.3+1.5=1.8
Since the delay is at -π/2 the wave will start at the trough at [time,t=0]
substituting the above in our formula we get:
g(t)=1.8+(0.3)sin[(2*π*t)/2.5]-π/2]
g(t)=1.8+0.3sin[(0.8πt)/T-π/2]

3 0

2 years ago

While at a carnival, Andrew comes across a game that involves rolling a die. According to the game's rules, if the number rolled

Reptile [31]

Answer:

he can expect to lose 0.5$

Step-by-step explanation:

To solve this problem we must calculate the expected value of the game.

If x is a discrete random variable that represents the gain obtained when rolling a dice, then the expected value E is:

$E =\sum xP (x)$

When throwing a dice the possible values are:

x: 1→ -$9; 2→ $4; 3→ -$9; 4→ $8; 5→ -$9; 6→ $12

The probability of obtaining any of these numbers is:

$p=\frac{1}{6}$

The gain when obtaining an even number is twice the number.

The loss to get an odd number is $ 9

So the expected gain is:

$E=-9*\frac{1}{6}-9*\frac{1}{6}-9*\frac{1}{6} + 4*\frac{1}{6} + 8*\frac{1}{6} + 12*\frac{1}{6}\\\\E =-27*\frac{1}{6} + 24*\frac{1}{6}\\\\E=-3*\frac{1}{6}\\\\E=-$0.5$

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2 years ago

Hamid has gained weight

Aleksandr-060686 [28]

Answer:

Step-by-step explanation:

if 88 is 10% higher than his previous weight then his current weight is 110%

divide 88 by 110 then multiply it by 100 to find his previous weight

88 ÷ 110 × 100 = 80

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2 years ago

Alia needs to bring at least 25 pieces of fruit to a training practice. She suggested apples and oranges and was told to be sure

dalvyx [7]

Answer:

Just took the test, answers are:

x + y ≥ 25,

x > 10,

and y ≥ 0

4 0

2 years ago