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2 years ago

A function is given:

Mathematics

1 answer:

IceJOKER [234]2 years ago

5 0

Answer:

See explanations below

Step-by-step explanation:

Given the function

f(x) = 3x+12

Let y = f(x)

y = 3x+12

Replace y with x

x = 3y+12

Make y the subject

3y = x-12

y = (x-12)/3

Hence the required inverse is!

g(x) = (x-12)/3

b) To show that the functions are inverses, we must show that f(g(x)) = g(f(x))

f(g(x)) = f((x-12)/3)

Replace x in f(x) with x-12/3

f(g(x)) = 3(x-12)/3 +12

f(g(x)) = x-12+12

f(g(x)) = x

Similarly for g(f(x))

g(f(x)) = g(3x+12)

g(f(x)) = (3x+12-12)/3

g(f(x)) = 3x/3

g(f(x)) = x

Since f(g(x)) = g(f(x)) = x, hence they are inverses of each other

c) Given f(g(x)) = x

f(g(–2)) = -2

The domain is the input variable of the function. Hence the domain is -2

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Increase 400litres by 20%

Sati [7]

Answer:

480 Litres

Step-by-step explanation:

Percentage increase = 20% × 400

New value =

400 + Percentage increase =

400 + (20% × 400) =

400 + 20% × 400 =

(1 + 20%) × 400 =

(100% + 20%) × 400 =

120% × 400 =

120 ÷ 100 × 400 =

120 × 400 ÷ 100 =

48,000 ÷ 100 =

480

3 0

2 years ago

An appliance salesperson receives a monthly salary of $2,250 plus a commission of 4.5% on all sales compute total pay for a mont

tino4ka555 [31]

Answer:

the total pay for the month for appliance salesperson = $6680.25

Step-by-step explanation:

salesperson receives a monthly salary of $2,250

commission of 4.5% on all sales compute

total pay for a month and when she sold $98,450 worth of appliances

total pay = $2,250 + 4.5% of $98,450

= $2,250 + $4430.25 = $6680.25

6 0

3 years ago

Part A - Construct a circle of any radius, and draw a chord on it. The construct the radius of the circle that bisects the chord

Julli [10]

Answer:

It can be concluded that the intersection of a chord and the radius that bisects it is at right angle. The two are perpendicular.

Step-by-step explanation:

i. Construct the required circle of any radius as given in the question, then locate the chord. A chord joins two points on the circumference of a circle, but not passing through its center.

ii. Construct the radius to bisect the chord, dividing it into two equal parts.

Then it would be observed that the intersection of a chord and the radius that bisects it is at right angle. Thus, the chord and radius are are perpendicular to each other.

The construction to the question is herewith attached to this answer for more clarifications.

5 0

3 years ago

Simplify this please

Ugo [173]

Answer:

$\frac{12q^{\frac{7}{3}}}{p^{3}}$

Step-by-step explanation:

Here are some rules you need to simplify this expression:

Distribute exponents: When you raise an exponent to another exponent, you multiply the exponents together. This includes exponents that are fractions. $(a^{x})^{n} = a^{xn}$

Negative exponent rule: When an exponent is negative, you can make it positive by making the base a fraction. When the number is apart of a bigger fraction, you can move it to the other side (top/bottom). $a^{-x} = \frac{1}{a^{x}}$ , and to help with this question: $\frac{a^{-x}b}{1} = \frac{b}{a^{x}}$ .

Multiplying exponents with same base: When exponential numbers have the same base, you can combine them by adding their exponents together. $(a^{x})(a^{y}) = a^{x+y}$

Dividing exponents with same base: When exponential numbers have the same base, you can combine them by subtracting the exponents. $\frac{a^{x}}{a^{y}} = a^{x-y}$

Fractional exponents as a radical: When a number has an exponent that is a fraction, the numerator can remain the exponent, and the denominator becomes the index (example, index here ∛ is 3). $a^{\frac{m}{n}} = \sqrt[n]{a^{m}} = (\sqrt[n]{a})^{m}$

$\frac{(8p^{-6} q^{3})^{2/3}}{(27p^{3}q)^{-1/3}}$ Distribute exponent

$=\frac{8^{(2/3)}p^{(-6*2/3)}q^{(3*2/3)}}{27^{(-1/3)}p^{(3*-1/3)}q^{(-1/3)}}$ Simplify each exponent by multiplying

$=\frac{8^{(2/3)}p^{(-4)}q^{(2)}}{27^{(-1/3)}p^{(-1)}q^{(-1/3)}}$ Negative exponent rule

$=\frac{8^{(2/3)}q^{(2)}27^{(1/3)}p^{(1)}q^{(1/3)}}{p^{(4)}}$ Combine the like terms in the numerator with the base "q"

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)}q^{(1/3)}}{p^{(4)}}$ Rearranged for you to see the like terms

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(2)+(1/3)}}{p^{(4)}}$ Multiplying exponents with same base

$=\frac{8^{(2/3)}27^{(1/3)}p^{(1)}q^{(7/3)}}{p^{(4)}}$ 2 + 1/3 = 7/3

$=\frac{\sqrt[3]{8^{2}}\sqrt[3]{27}p\sqrt[3]{q^{7}}}{p^{4}}$ Fractional exponents as radical form

$=\frac{(\sqrt[3]{64})(3)(p)(q^{\frac{7}{3}})}{p^{4}}$ Simplified cubes. Wrote brackets to lessen confusion. Notice the radical of a variable can't be simplified.

$=\frac{(4)(3)(p)(q^{\frac{7}{3}})}{p^{4}}$ Multiply 4 and 3

$=\frac{12pq^{\frac{7}{3}}}{p^{4}}$ Dividing exponents with same base

$=12p^{(1-4)}q^{\frac{7}{3}}$ Subtract the exponent of 'p'

$=12p^{(-3)}q^{\frac{7}{3}}$ Negative exponent rule

$=\frac{12q^{\frac{7}{3}}}{p^{3}}$ Final answer

Here is a version in pen if the steps are hard to see.

5 0

3 years ago

Yolanda watches a carnival game in which a paper cup is tossed. It costs $1 to play the game. If the cup lands upright, the play

trapecia [35]

Answer:

Step-by-step explanation:

a. Yolanda only wins if the cup lands upright.

From the experimental data we see that the probability of winning is 5 out of 50, or

10%. Therefore, if Yolanda plays 10 times she can expect to win 10% of 10 times = 1

time. She will lose 9 times. (Note: Ten trials is a very small number of trials, so we should not be surprised if Yolanda’s results are very different from the percentages

produced by the longer experiment.)

b. If Yolanda wins 1 time and plays 10 times, she will have spent $10 to play and won

back only $5, so she would have less money at the end of 10 games.

5 0

2 years ago