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Slav-nsk [51]
1 year ago
6

A rectangle has length that is 5 less than 2 times the width. Write an expression for the area of the rectangle.

Mathematics
1 answer:
a_sh-v [17]1 year ago
7 0

We are given a relationship between the sides of a rectangle, that is, the length of one of its sides is 5 less two times its width, and we are asked to find an expression for the area. Let's remember that the area of a rectangle is equal to the product of the length of its side by its width. Let "w" be the length of the rectangle and "L" its lenght, then the area is given by the following formula:

A=Lw

We can use the relationship given in the problem, that is, its length being five less two times its width, that is:

L=5-2w

Replacing in the formula for the area we get:

A=(5-2w)w

Now we use the distributive law:

A=5w-2w^2

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marta [7]
The answer would be 2 I’m pretty sure
3 0
2 years ago
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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
Please give me a real answer or I will report you I dont want to friend you just put the answers in the comments
kotykmax [81]

Answer:

j = 17.32 sq rt 3  or   30

Step-by-step explanation:

sin 60 = j/20sq rt 3

0.8660 = j/20sq rt 3

j = 17.32 sq rt 3

4 0
3 years ago
2.59 is greater or less than 2.684
Dahasolnce [82]

Answer:

Less than.

Step-by-step explanation:

2.59 is less than 2.684 by 0.094

2.59 < 2.684

~

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3 years ago
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If the bases of an isosceles trapezoid have lengths of 11 and 24, what is the length of the median? A. 17.5 units B. 35 units C.
erma4kov [3.2K]

Answer:

Option A. 17.5\ units

Step-by-step explanation:

we know that

The measure of the median is the semi-sum of the bases

so

\frac{1}{2}(11+24)=17.5\ units

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3 years ago
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