PLEASE HELP ASAP!! CORRECT ANSWER ONLY PLEASE!!<br><br> Simplify.<br><br> 3√-50

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

17, 24, 31, 38, ... common diffrence Arithmetic Sequences

irinina [24]

Ans: 10+7n

Step-by-step explanation: there you go

8 0

3 years ago

Read 2 more answers

Mr.Eastman drew triangle JKL,with a height of 12 inches and a base of 12 inches, and triangle XLZ, with a height of 8 inches and

34kurt

Answer:

Step-by-step explanation:

Area of triangle = 1/2 × Base × Height

Mr.Eastman drew triangle JKL,with a height of 12 inches and a base of 12 inches

Area of JKL = 1/2 × 12 inches × 12 inches

= 72 Square inches

triangle XLZ, with a height of 8 inches and a base of 16 inches. Which triangle has the greater area?

5 0

3 years ago

I need help with this pleaseee!

ololo11 [35]

Probably B

STEP BY STEP

7 0

3 years ago

Amanda placed her finger on the origin of a regular coordinate plane. She marked a point after moving her finger 1 unit to the l

Lubov Fominskaja [6]

Answer:

( x , y ) = ( -1 , - 5 )

Step-by-step explanation:

Solution:-

- The rectangular coordinate system ( Cartesian ) is defined by two independent variables namely, "x and y".

- The values of both varibales lie on the horizontal and vertical line respectively, ( x & y ).

- The values on the horizontal axis also known as the x-axis is marked with a referece of x = 0 ( origin ). All the values to the right of the point of origin are denoted as positive units and all values to the left of the point of origin are denoted as negative units.

- Similarly, The values on the vertical axis also known as the y-axis is marked with a referece of y = 0 ( origin ). All the values to the above the point of origin are denoted as positive units and all values below of the point of origin are denoted as negative units.

- The axis are conventionally oriented such that 90 degrees angle is formed in between them and always denoted in the counter-clockwise direction.

In other words, if +x is pointing to the right then the +y will be pointed in the direction when +x is rotated counter clockwise to 90 degrees; hence, points upward.

- When Amanda starts off at the origin she is at the order pair ( 0 , 0 ).

- She then moves her finger 1 unit to left ( -x ) and 5 units down ( -y ). Hence, she moves 1 unit along the -x direction and then moves 5 units down along -y direction.

Hence, she is at an ordered pair ( x , y ) = ( -1 , - 5 ) .

3 0

3 years ago

PLEASE HELP ASAP!! CORRECT ANSWER ONLY PLEASE!! Simplify. 3√-50