1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ollegr [7]
1 year ago
8

If a= 2^x and b =2^x+1; show that: 8a^3 / b^3 = 2^x+1​

Mathematics
1 answer:
kkurt [141]1 year ago
7 0

Step-by-step explanation:

Given that:

a = 2ˣ

b = 2ˣ⁺¹ = 2ˣ * 2¹ = 2.2ˣ

Now,

{(8a³)/b²}

Substitute the value of x and y in expression then

= [{8(2ˣ)³}/(2.2ˣ)²]

= [(8*2³ˣ)/{2² * (2ˣ)²}]

= {(8*2³ˣ)/(4 * 2²ˣ)}

[since, (aᵐ)ⁿ = aᵐⁿ]

= {(2 * 2³ˣ)/2²ˣ}

= {(2 * 2²ˣ * 2ˣ)/2²ˣ}

[since (2a = a+a, that means 3x = 2x + x)]

= 2 * 2ˣ

= 2ˣ⁺¹

[since (aᵐ * aⁿ = aᵐ+ⁿ)]

<u>Answer:</u> Therefore, {(8a³)/b²} = 2ˣ⁺¹ .

Please let me know if you have any other.

You might be interested in
If x is an even integer and y is an odd integer than x + y is a rational number. A) Always True B) Sometimes True C) Usually Tru
Katyanochek1 [597]
A) Always TRue
Both integers are rational, so the sum must be rational
7 0
3 years ago
Hey can some one help me with this
Leno4ka [110]
Hello!

First you have to find the surface area of what he is painting

Finding the areas of all the rectangles he is painting

14 * 8 = 112
14 * 8 = 112
12 * 8 = 96
12 * 8 = 96
12 * 14 = 168

Add all these up

112 + 112 + 96 + 96 + 168 = 584

Divide this by the amount of area a pint of paint covers

584 / 90 = 6.4888...

He needs 7 pints of paint because he needs more than 6

Multiply this by the cost of 1 pint of pint

7 * 7.98 = 55.86

The answer is $55.86

Hope this helps!
3 0
3 years ago
Read 2 more answers
You are asked to draw a triangle with side lengths of 6 inches and 8 inches. What is the longest whole number length that your t
tensa zangetsu [6.8K]
Fo sides, a,b,c
where c is the longest

c<a+b
or else you won't have a triangle

we want the longest side
this mystery side is c
other ones are a and b

c<6+8
c<14
the next largest whole number is 13

answer is 13 inches
3 0
2 years ago
Read 2 more answers
Claudia added an equilateral triangle shape that is one inch high and one inch wide to a slide in her presentation. She clicked
mr_godi [17]

The effect of Claudia's changing the height of of the triangle from 1 inch

to 3 inches is the option;

  • The height of the triangle changed to three inches but the width remained 1 inch

<h3>Which option gives the effect of changing the height?</h3>

The given dimensions of the equilateral triangle Claudia added are;

Height of the triangle = 1 inch

Width of the triangle = 1 inch

The value Claudia typed in the Shape Height box = 3

Required:

What happened to the shape after she press Enter

Solution:

By entering 3 in the Shape Height box, changes the height of the

equilateral triangle to 3 inches but the width remains 1 inches

From a similar question posted online, the correct option is therefore;

  • The height of the triangle changed to three inches but the width remained 1 inch

Learn more about triangles here:

brainly.com/question/16430835

3 0
2 years ago
the area of a rectangular photograph is 35 square inches. If the width of the photo is 5 inches how tall is the photo
Vika [28.1K]
We know that:

Area= length*width

Plug in the stuff you know.

35= length(tall)*5

Divide both sides by 5.

7= length

The photo is 7 inches tall.

I hope this helps!
~kaikers


5 0
2 years ago
Other questions:
  • Which is an equation in slope-intercept form for the line passing through (5, 1) and (–4, 7).
    5·1 answer
  • What is the best first step for solving the given system using substitution while avoiding fractions?
    6·2 answers
  • Given: f(x) = x - 7 and h(x) = 2x + 3<br><br><br> Write the rule for h(f(x)).
    10·1 answer
  • If you wanted to reduce the 8x6 rectangle by a ratio of 1/4 what would the dimensions of the new rectangle be
    14·1 answer
  • What is the solution to x2 = 225?
    12·2 answers
  • This rectangle represents the base of a rectangular prism. The height of the rectangular prism is 13 ft.
    10·2 answers
  • Given the table below, determine the initial value/y intercept. PIC IS ABOVE! ANSWER!
    13·2 answers
  • HELP ME PLEASE IM BEGGING YOU
    13·1 answer
  • Reduce las siguientes sumas sin usar calculadora
    6·1 answer
  • Dis time i needa find da rule
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!