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2 years ago

What is the inverse of the function g(x)=7x+3/x-5?

Mathematics

1 answer:

Ad libitum [116K]2 years ago

8 0

Answer:

g(x) = (5x + 3)/ x - 7

Step-by-step explanation:

Let g(x) = y

y = (7x + 3)/x - 5

Make x the subject

xy - 5y = 7x + 3

xy - 7x = 5y + 3

x(y - 7) = 5y + 3

x = (5y + 3)/ y - 7

Therefore, the inverse of the function = (5x + 3)/ x - 7

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Explain how the values of h and k in y=|x-h|+k affect the graph of y=|x|

Dvinal [7]

Answer:

Horizontal shift:

For the parent function f(x) and a constant h, the function given by g(x) = f(x-h) can be sketched by shifting f(x) h units horizontally.

The values of h determines the direction of shifts:

If :

h>0, the parent graph shifts h units to the right

h < 0, the parent graph shifts h units to the left.

Vertical shifts:

For the parent function f(x) and a constant k, the function given by g(x) =f(x) +k can be sketched by shifting f(x) k units vertically.

The value of k determines the direction of shifts;

if:

k > 0, the parent graph shifts k units upward, and

k < 0, the parent graph shifts k units downward.

Therefore, the values of h and k in y=|x-h|+k affect the graph of y=|x| tells us how far the graph shifts horizontally and vertically.

8 0

3 years ago

tennis balls with a diameter of 2.5in are sold in cans of three. the can is a cylender. what is the volume of the area not occup

mina [271]

Answer:

The volume of the area not occupied by the tennis balls is 12.28 cubic inches.

Step-by-step explanation:

It is given that tennis balls with a diameter of 2.5in are sold in cans of three. the can is a cylinder.

Radius of ball = Radius of can = $\frac{2.5}{2}=1.25$

Height of can = $2.5\times 3=7.5$

The volume of sphere is

$V=\dfrac{4}{3}\pi r^3$

where, r is radius of sphere.

The volume of a tennis balls is

$V=\dfrac{4}{3}\pi (1.25)^3$

$V=8.18123$

$V\approx 8.18$

Volume of three tennis balls is

$V_1=3\times 8.18=24.54$

The volume of cylinder is

$V=\pi r^2h$

The volume of can is

$V_2=\pi (1.25)^2(7.5)$

$V_2=36.81553$

$V_2\approx 36.82$

The volume of the area not occupied by the tennis balls is

Volume = Volume of cylinder - Volume of three tennis balls

= 36.82 - 24.54 = 12.28 inches

Therefore, the volume of the area not occupied by the tennis balls is 12.28 cubic inches.

3 0

3 years ago

Factorise <br> x2 + 10x + 16

d1i1m1o1n [39]

Answer:

hope this helps, (x+2) (x+8)

Step-by-step explanation:

factor x^2 + 10x+16 using the AC Method

6 0

2 years ago

Read 2 more answers

stumpy the skeleton goes for a bike ride every night in the cemetery. He rides 1/2 way around the cemetery and stops. Stumpy the

marin [14]

He bikes 13/8 of the cemetery

4 0

3 years ago

Multiply Conjugates Using the Product of Conjugates Pattern

weeeeeb [17]

Answer:

The product is the difference of squares is $\left(xy-9\right)\left(xy+9\right)={{x}^2}{{y}^2}-81$

Step-by-step explanation:

Explanation

The given expression is (x y-9)(x y+9).
We have to multiply the given expression.
Square the first term xy. Square the last term 9 .

$\begin{aligned}&(x y-9)(x y+9)=(x y)^{2}-(9)^{2} \\&(x y-9)(x y+9)=x^{2} y^{2}-81\end{aligned}$

5 0

2 years ago