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Alex777 [14]
3 years ago
6

Maxwell is trying to figure out how much water he needs to fill his aquarium. He knows that his aquarium has measurements of 8 i

nches wide, 9 inches long and 12 inches high. He plans to put a solid metal chest in the bottom of the aquarium that has a base area of 30 inches and a height of 4 inches. How much water will he need to fill the aquarium.
Mathematics
1 answer:
Vladimir [108]3 years ago
4 0

Answer:23

Step-by-step explanation:

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Identify the polynomial.
Alexxandr [17]

Answer:

it's a trinomial

7 0
3 years ago
How many different perfect cubes are among the positive actors of 2021^2021
9966 [12]

Answer:

hope this helps :D

Step-by-step explanation:

Perfect cube factors:

If a number is a perfect cube, then the power of the prime factors should be divisible by 3.

Example 1:Find the number of factors of293655118 that are perfect cube?

Solution: If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

5(0 or 3)——- 2 factors

11(0 or 3 or 6 )— 3 factors

Hence, the total number of factors which are perfect cube 4x3x2x3=72

Perfect square and perfect cube

If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.

Example 2: How many factors of 293655118 are both perfect square and perfect cube?

Solution: If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.Hence both perfect square and perfect cube must have

2(0 or 6)—– 2 factors

3(0 or 6) —– 2 factors

5(0)——- 1 factor

11(0 or 6)— 2 factors

Hence total number of such factors are 2x2x1x2=8

Example 3: How many factors of293655118are either perfect squares or perfect cubes but not both?

Solution:

Let A denotes set of numbers, which are perfect squares.

If a number is a perfect square, then the power of the prime factors should be divisible by 2. Hence perfect square factors must have

2(0 or 2 or 4 or 6 or 8)—– 5 factors

3(0 or 2 or 4 or 6)  —– 4 factors

5(0 or 2or 4 )——- 3 factors

11(0 or 2or 4 or6 or 8 )— 5 factors

Hence, the total number of factors which are perfect square i.e. n(A)=5x4x3x5=300

Let B denotes set of numbers, which are perfect cubes

If a number is a perfect cube, then the power of the prime factors should be divisible by 3. Hence perfect cube factors must have

2(0 or 3 or 6or 9)—– 4 factors

3(0 or 3 or 6)  —–  3  factors

5(0 or 3)——- 2 factors

11(0 or 3 or 6 )— 3 factors

Hence, the total number of factors which are perfect cube i.e. n(B)=4x3x2x3=72

If a number is both perfect square and perfect cube then the powers of prime factors must be divisible by 6.Hence both perfect square and perfect cube must have

2(0 or 6)—– 2 factors

3(0 or 6) —– 2 factors

5(0)——- 1 factor

11(0 or 6)— 2 factors

Hence total number of such factors are i.e.n(A∩B)=2x2x1x2=8

We are asked to calculate which are either perfect square or perfect cubes i.e.

n(A U B )= n(A) + n(B) – n(A∩B)

=300+72 – 8

=364

Hence required number of factors is 364.

8 0
3 years ago
How to find the scale factor of two triangles
BabaBlast [244]

Answer:

Here's how to do it.  

Step-by-step explanation:

The two triangles must be similar, that is, corresponding angles must be equal, as in the diagram below.

1. Find a corresponding pair of sides

Assume that ∆ABC is the original and ∆DEF is its scaled image.

Then, AB and DE are corresponding sides, with lengths of 8 and 12 units , respectively.

2. Set up a ratio

Ratio = side length in image/side length in original = 12/8

3. Simplify the ratio

The simplified ratio is the scale factor (SF).

SF = 12/8 = 3/2 = 1.5

The scale factor is 1.5.

6 0
3 years ago
Lyla is shopping for school supplies. She has $20.00 to spend. She plans to buy a package of pens for $4.98. She also wants to b
Ket [755]
<h3><em><u>Question:</u></em></h3>

Lyla is shopping for school supplies. She has $20.00 to spend. She

plans to buy a package of pens for $4.98. She also wants to buy a

calculator. All calculators are being sold for 30 percent less than the

original price. write an inequality that can be used to find the original price, x, of a calculator lyla can buy.

<h3><em><u>Answer:</u></em></h3>

4.98+0.7x\leq 20 inequality that can be used to find the original price, x, of a calculator lyla can buy

<h3><em><u>Solution:</u></em></h3>

Given that,

Lyla has $ 20 to spend

So she can spend entire $ 20 or less than $ 20

Total amount she has = $ 20

She  plans to buy a package of pens for $4.98

Cost of package of pens = $ 4.98

She also wants to buy a  calculator

Let "x" be the original price of calculator

All calculators are being sold for 30 percent less than the  original price

Selling price of calculator = original price - 30 % of original price

Selling price of calculator = x - 30 % of x = x - 0.3x = 0.7x

Selling price of calculator = 0.7x

<em><u>Thus a inequality can be framed as:</u></em>

Cost of package of pens + Selling price of calculator \leq 20

4.98+0.7x\leq 20

This means that, combined cost of package of pen and selling price of calculator must be less than or equal to the amount with Lyla ( 20 $ )

Thus the inequality is found

5 0
3 years ago
Prove that; cosec²∅-2 = COS2∅ Sin2∅​
MakcuM [25]

Answer:

here you go..............

7 0
3 years ago
Read 2 more answers
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