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2 years ago

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

Mathematics

2 answers:

Novay_Z [31]2 years ago

6 0

Answer:

$g(x)=\frac{x-12}{4}$

Step-by-step explanation:

To find the inverse of y=4x+12, all you need to is swap x an y and then remake y the subject.

y=4x+12

Swap x and y:

x=4y+12

Solve for y:

Subtracting 12 on both sides:

x-12=4y

Dividing 4 on both sides:

$\frac{x-12}{4}=y$

So $g(x)=\frac{x-12}{4}$

Margarita [4]2 years ago

6 0

Answer:

[-12 + x]\4 = g(x)

Step-by-step explanation:

x = 4y + 12 [SWAP y and x]
-12 + x = 4y [Move -12 to the left side of the equivalence symbol]
[-12 + x]\4 = g(x) [Divide by 4]

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What is the surface area of a right circular cylindrical oil can, if the radius of its base is 5 inches and its height is 13 inc

valentina_108 [34]

SA = 2 pi r^2 + 2 pi r h
SA = 2 * pi * 25 + 2 pi * 5 * 13
SA = 565.2 in ^3
this is using 3.14 for pi

6 0

3 years ago

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Find S^20 if the series 1 + 1.1 ..... is a (a) arithmetic (b) geometric

quester [9]

I'm guessing S^20 is actually referring to the 20th partial sum $S_{20}$ , with

$S_{20}=1+(1+1\times0.1)+(1+2\times0.1)+\cdots+(1+18\times0.1)+(1+19\times0.1)$

in the arithmetic case, and

$S_{20}=1+1.1+1.1^2+\cdots+1.1^{18}+1.1^{19}$

in the geometric case.

(a) Combining like terms, we have

$S_{20}=20+0.1(1+2+\cdots+18+19)$

and invoking the formula

$1+2+\cdots+(n-1)+n=\dfrac{n(n+1)}2$

we end up with

$S_{20}=20+0.1\dfrac{19\times20}2=39$

(b) Multiply $S_{20}$ by 1.1, then subtract this from $S_{20}$ :

$1.1S_{20}=1.1+1.1^2+1.1^3+\cdots+1.1^{19}+1.1^{20}$

$S_{20}-1.1S_{20}=-0.1S_{20}=1-1.1^{20}$
$\implies S_{20}=\dfrac{1.1^{20}-1}{0.1}\approx57.275$

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2 years ago

If the purchase price for a house is $309,900, what is the monthly payment if you put 20% down for a 30 year loan with a fixed r

lorasvet [3.4K]

Answer:

The correct answer is A. $729.98.

Step-by-step explanation:

Given that the purchase price for a house is $ 309,900, to determine what is the monthly payment if you put 20% down for a 30 year loan with a fixed rate of 6%, the following calculation must be performed:

100 - 20 = 80

(309,900 x 0.80) x 1.06 / (30x12) = X

247,920 x 1.06 / 360 = X

262,795.2 / 360 = X

729.98 = X

Therefore, the monthly payments will be $ 729.98.

4 0

2 years ago

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Find the distance from P to l. Line l contains points (-4,2) and (3,-5).Point P has coordinates (1,2).

Annette [7]

Hello,

A=(-4,2)
B=(3,-5)
AB≡y-2=(x+4)(-7)/7==>y=-x-2

Slope of the perpendicular: 1

y-2=(x-1)1==>y=x+1 is the equation of the perpendicular.

Intersection: y=x+1 and y=-x-2 ==>(-3/2,-1/2)=Q

|PQ|²=(-1/2-2)²+(1+3/2)²=25/2
|PQ|=5√2/2≈3.5355339059....

7 0

3 years ago

Pedro has determined that the probability his shot will score in a lacrosse game is 0.30.

Igoryamba

For two shots Pedro has four outcomes:

1 shot | 2 shot

score | score

score | not score

not score | score

not score | not score

The probability Pedro's shot will score in a lacrosse game is 0.30 and the probability his shot will not score in a lacrosse game is 1-0.30=0.70. So you can count probabilities for all cases:

1. 0.3·0.3=0.09;

2. 0.3·0.7=0.21;

3. 0.7·0.3=0.21;

4. 0.7·0.7=0.49.

In total 0.09+0.21+0.21+0.49=1. The first outcomes is that what you need.

Answer: 0.09.

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2 years ago

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