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
melisa1 [442]
3 years ago
7

Why do you multiply 12 by 3 to find the total number cubes in the bottom 3 layers

Mathematics
1 answer:
BaLLatris [955]3 years ago
4 0

because there are 12 in one layer and there are 3 layers

You might be interested in
the length of a rectangle is 3m more than twice the width, and the area is 180m². find the dimensions of the rectangle​
Fofino [41]

The breadth (width) of a rectangle, w, is 3m less than its length, l. If the area, A, is 180m square, what is the dimension of the rectangle?

Given:

A = 180 m^2

w = l - 3 m

Find:

l

We have one unknown in this scenario, representing length, l. So, we only need to write one equation for a numerical solution.

Since we know how the area, A, of a rectangle is related to its length, l, and breadth (width), w, we can write the equation as follows:

A = lw

Substituting our given values into the equation:

180 = l x (l - 3)

180 = l^2 - 3l

0 = l^2 - 3l - 180

This is a simple quadratic equation. We can solve it by brute force using the Quadratic Formula which states:

The roots of an equation in the for Ax^2 + Bx + C = 0 are

(-B + or minus SQRT[B^2 - 4AC])/2A

But, if we are on a timed test, there is an easier way to get to this answer rapidly.

We know the length and breadth (width) are probably integers, and that they lie three spaces apart on the number line, l = w + 3. We also know the area, A = 180, so 180 = lw. Since the SQRT[A] would equal l and w if they were the same, that’s a good first approximation.

SQRT[180] = 13.4

So, w will be less than 13.4, and l will be more.

Let’s try w = 13, and l = 13 + 3 = 16. 13 x 16 = 208 > 180 No

Let’s try w = 12, and l = 12 + 3 = 15. 12 x 15 = 180 = 180 Yes

A good test taker will be able to do this math in their head, without doing any of the calculations we’ve shown here. Let’s run through the mental steps.

180 = lw

w = l + 3

SQRT[180] = 13.4 = lw so l and w straddle 13.4

the last two digits of l and w must have a product that is a multiple of ten since 180 is a multiple of ten. 2 and 5 are three apart and a multiple of 10, so try 12 x 15 = 180 Check.The breadth (width) of a rectangle, w, is 3m less than its length, l. If the area, A, is 180m square, what is the dimension of the rectangle?

Given:

A = 180 m^2

w = l - 3 m

Find:

l

We have one unknown in this scenario, representing length, l. So, we only need to write one equation for a numerical solution.

Since we know how the area, A, of a rectangle is related to its length, l, and breadth (width), w, we can write the equation as follows:

A = lw

Substituting our given values into the equation:

180 = l x (l - 3)

180 = l^2 - 3l

0 = l^2 - 3l - 180

This is a simple quadratic equation. We can solve it by brute force using the Quadratic Formula which states:

The roots of an equation in the for Ax^2 + Bx + C = 0 are

(-B + or minus SQRT[B^2 - 4AC])/2A

But, if we are on a timed test, there is an easier way to get to this answer rapidly.

We know the length and breadth (width) are probably integers, and that they lie three spaces apart on the number line, l = w + 3. We also know the area, A = 180, so 180 = lw. Since the SQRT[A] would equal l and w if they were the same, that’s a good first approximation.

SQRT[180] = 13.4

So, w will be less than 13.4, and l will be more.

Let’s try w = 13, and l = 13 + 3 = 16. 13 x 16 = 208 > 180 No

Let’s try w = 12, and l = 12 + 3 = 15. 12 x 15 = 180 = 180 Yes

A good test taker will be able to do this math in their head, without doing any of the calculations we’ve shown here. Let’s run through the mental steps.

180 = lw

w = l + 3

SQRT[180] = 13.4 = lw so l and w straddle 13.4

the last two digits of l and w must have a product that is a multiple of ten since 180 is a multiple of ten. 2 and 5 are three apart and a multiple of 10, so try 12 x 15 = 180 Check.

4 0
2 years ago
What is the sale price of jeans which regularly cost $28, but now are 10% off ?
Morgarella [4.7K]
25.20 is the final answer after you take 10% off <3
3 0
2 years ago
Read 2 more answers
A skateboarder travailing a 7.0 meters per second rolls to a stop at the top of a ramp in 3.0 seconds. What is the skateboarders
Sedbober [7]
7.0-3.0=4 the answer is 4

5 0
3 years ago
Four-fifths of a number<br> decreased by eight is four.<br> Find the number.
Norma-Jean [14]
4/5x-8 = 4
4/5x = 12
X = 15
8 0
3 years ago
Read 2 more answers
5. <br> 56°<br> 94°<br> 4.5%<br> 1.5x
dedylja [7]

Answer:

Step-by-step explanation:

jjjjjjjjjjjjj

8 0
2 years ago
Other questions:
  • 313.92 ÷ 6.4 + 200.4 What is the value of the expression?
    15·1 answer
  • Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $0.42.
    6·2 answers
  • I still am not sure how l and m are parallel
    6·1 answer
  • How to find the x with trig functions
    9·1 answer
  • anne marie needs to rent a car for 9 days to take on vacation. The cost of renting a car is $66 per day, $15.99 for insurance, a
    7·2 answers
  • What is the slope of the line passing through the points (2, −5) and (4, 1)?
    14·1 answer
  • How do you add all even numbers that are less than 123?
    10·1 answer
  • Please help.................
    13·1 answer
  • What does it mean to approximate the zeros? And how would I do that?
    14·1 answer
  • 2; 4; 6; 8; ...
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!