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s2008m [1.1K]
3 years ago
7

What is the constant of proportionality between y and x in the graph?

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
3 0

Answer:

4

Step-by-step explanation:

Constant of proportionality refers to the slope of the line in this case, the slope of the line is (4-0)/(1-0)=4

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Is 6(6+x) equivalent to 6x+36
Ray Of Light [21]
Close enough, it would be 36+6x.
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Fred is playing tennis. For every 2 of his serves that land in, 4 serves land out. If he hit 28 serves in, how many serves lande
bija089 [108]

2 for every 4 = 1 for every two, so 28 multiplied by two. Your answer is 56.

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2 years ago
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What is the difference between -2 and -6?<br><br> 8<br> -8<br> -4<br> 4
Sedaia [141]
Hi there! The word "difference" means to subtract. -2 - -6=4. Therefore, it would be the last one.
8 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
Find the value of W that makes quadrilateral PQRS a parallelogram.
mestny [16]

to be a parallelogram its front sides must be equal to each other

so, we equalize the length of two sides that are face to face

\begin{gathered} 5w-25=w+15 \\  \\  \end{gathered}

and solve for w

\begin{gathered} 5w-w=15+25 \\ 4w=40 \\ w=\frac{40}{4} \\  \\ w=10 \end{gathered}

the value of w must be 10

6 0
1 year ago
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