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3 years ago

11. Identify the properties below. a. 5 + 6 = 6 + 5 b. 7 + (3 + 9) = (7 + 9) + 3

Mathematics

1 answer:

jenyasd209 [6]3 years ago

5 0

A is commutative property
B is associative property
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:

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

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3 years ago

Edward was running errands on his bike first to be like from his house to the post office to pick up a package the post office i

Karo-lina-s [1.5K]

Answer:

Edward drove altogether of 16.1 miles.

Step-by-step explanation:

Given:

Edward was Running around on his bike.

Distance from home to post office = $4 \frac{4}{5} \ miles$

$4 \frac{4}{5} \ miles$ can be Rewritten as $4.8 \ miles$

Distance from home to post office = $4.8 \ miles$

Now Given:

Distance from Post office to market = 3.25 miles.

Now we will calculate Distance from Home to market.

Distance from Home to market can be calculated by adding Distance from home to post office and Distance from Post office to market.

Framing in equation form we get;

Distance from Home to market = $4.8+3.25 = 8.05\ miles$

Also Given:

his mother picked him up at the market and drove him home.

We need to find the total miles Edward drive altogether.

total miles Edward drive altogether will be equal to Sum of Distance from Home to market and Distance from market to home.

framing in equation form we get;

Total Distance Edward drove = $8.05+8.05 = 16.1\ miles$

Hence Edward drove altogether of 16.1 miles.

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2 years ago