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3 years ago

14

Select all the correct functions. Identify all the functions that have a greater rate of change than the function represented in

the graph. y = 2x + 7 y = 0.5x -5 y = 3x + 12 y = 1.5x - 1 y = 2.5x - 20 y = x + 7

1 answer:

RoseWind [281]3 years ago

5 0

Answer:

y=2x+7

Step-by-step explanation:

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Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

7 0

2 years ago

How many days are there in 6 weeks? Solve the related word problem to represent the inverse operation There are days in 6 weeks

expeople1 [14]

Answer:

there a 42 days in 6 weeks

Step-by-step explanation:

multiply 6 x 7= 42

3 0

2 years ago

Pls help asap thank you

Sati [7]

Use the Pythagorean theorem to find the height.

Height = sqrt(26^2-10^2)

Height = 24 cm

Volume = 20^2 x 24/3

Volume = 7,200 cm^3

7 0

2 years ago

Read 2 more answers

A survey of a group’s viewing habits over the last year revealed the following

Tom [10]

Answer:

0.52

Step-by-step explanation:

The computation of the percentage of the group in which none of the three sports watched is shown below:

= gymnastic percentage + baseball percentage + soccer percentage - gymnastic & baseball percentage - baseball & soccer percentage - gymnastic & soccer percentage + three sports percentage

= 0.28 + 0.29 + 0.19 - 0.14 - 0.12 - 0.18 + 0.08

= 0.48

Now the percentage is

= 1 - 0.48

= 0.52

7 0

3 years ago

15. The height and yolume of a cylinder are 4cm and 616cm respectively. Calculate the diameter of the base. (take t = 27 쪽 A. 7c

irakobra [83]

Step-by-step explanation:

Given that,

Height of cylinder = 4 cm
Volume of cylinder = 616 cm³

To find,

Diameter of the base = ?

Firstly we'll find the base radius of the cylinder.

$\longmapsto\rm{V_{(Cylinder)} = \pi r^2h}\\$

<u>Accordi</u><u>ng</u><u> </u><u>to</u><u> </u><u>the</u><u> </u><u>qu</u><u>estion</u><u>,</u>

$\longmapsto\rm{616= \dfrac{22}{7} \times r^2 \times 4}\\$

$\longmapsto\rm{616 \times 7 = 22 \times r^2 \times 4}\\$

$\longmapsto\rm{4312 = 88 \times r^2 }\\$

$\longmapsto\rm{\cancel{\dfrac{4312}{88}} = r^2 }\\$

$\longmapsto\rm{49 = r^2 }\\$

$\longmapsto\rm{\sqrt{49} = r }\\$

$\longmapsto\rm{7 \; cm = r }\\$

Now,

$\longmapsto\rm{Diameter = 2r }\\$

$\longmapsto\rm{Diameter = 2(7 \; cm) }\\$

$\longmapsto\bf{Diameter = 14 \; cm}\\$

The required answer is 14 cm.

4 0

2 years ago