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1 year ago

Which is an algebraic expression for the product of 10 and a

Mathematics

1 answer:

trasher [3.6K]1 year ago

5 0

the product of 10 and a

10 × a = (product)

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What is the area of Triangle II?

Nuetrik [128]

10.5625 is your answer hope i helped

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2 years ago

A construction crew is lengthening a road. The road started with a length of

raketka [301]

L = 4d + 54

after crew worked 33 days...d = 33
L = 4(33) + 54
L = 132 + 54
L = 186...so after 33 days, the crew made a road that measures 186 miles

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2 years ago

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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2 years ago

Answer like gauss 1+3+5+7+...=999

raketka [301]

1+3+5+7+...+999 =

= 1+2+3+4+...+500

+1+2+3+...+499

= 2·(1+2+3+...+499) + 500

= 2·(499·500)/2 + 500

= 499·500 + 500

= 500·(499 + 1)

= 500·500

= 250.000

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2 years ago

Which number belongs to the solution set of the equation below? 8x=120

vlabodo [156]

8x = 120
x = 120/8
x = 15

4 0

2 years ago