Is 0.2 10 times 0.02<br> true or false

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

Taking an Uber ride in NYC has an initial fee of $2.55 with an additional charge of $1.75 per mile (we will ignore the small per

dmitriy555 [2]

Answer:

what exactly am i solving for ?

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

A sculpture is shaped like a sphere with 4 cones attached to it. Several dimensions of the sculpture, in feet, are shown in the

suter [353]

volume of the center sphere = 4/3*PI*r^3

r = 3 ( given in the picture)

so 4/3 * 3.14 *3^3 = 113.04 cubic feet

volume of 1 cone: pi *r^2 *h/3

r = 3 and h=3 ( given in the picture)

so 3.14 * 3^2 * 3/3 = 28.26 cubic feet

there are 4 cones so 28.26* 4 = 113.04 cubic feet

113.04 + 113.04 = 226.08 cubic feet

rounded to nearest cubic foot = 226 cubic feet

5 0

3 years ago

The perimeter of a rectangle must be greater than 70 cm, but the length cannot be greater than 30 cm and the width cannot be gre

Jlenok [28]

<span>W=15 & L=25

character requirement

</span>

3 0

3 years ago

The vertices of the image of GHJK after a translation are given. Choose the vector that describes the translation.

Lady_Fox [76]

Answer:

Option B

Step-by-step explanation:

Let's take a vertex G of quadrilateral GHJK to understand the rule for the translation,

From the graph attached,

Coordinates of G → (-5, 5)

Coordinates of the image point G' after the translation → G'(-5, 5)

Let the point G is translated 'a' units to the right and 'b' units down,

Rule for this translation,

G(x, y) → G'(x + a, y - a)

By this rule,

G(-5, 5) → G'(-5 + a, 5 - a)

-5 + a = -5 ⇒ a = 0

5 - a = 5 ⇒ a = 0

Therefore, vector that defines the translation will be,

<0, 0>

Option B is the the correct option.

8 0

3 years ago

Is 0.2 10 times 0.02 true or false