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2 years ago

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Prove algebraically that the square of any number is always 1 more than a multiple of 8

1 answer:

abruzzese [7]2 years ago

7 0

Answer:

This is interesting but I don't think it's provable (unless it's just the square of odd numbers).

3² = 9, which is 1 more than a multiple of 8 (8)

4² = 16, which is not 1 more than a multiple of 8 (8)

5² = 25, which is 1 more than a multiple of 8 (24)

6² = 36, which is not 1 more than a multiple of 8 (32)

7² = 49, which is 1 more than a multiple of 8 (48)

8² = 64, which is not 1 more than a multiple of 8 (64)

9² = 81, which is 1 more than a multiple of 8 (80)

10² = 100, which is not 1 more than a multiple of 8 (96)

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Y/x^2 + y/x^3<br><br>perform the operation and express your answer as a single fraction

umka2103 [35]

Answer:

$\frac{y}{x^2}+\frac{y}{x^3}=\frac{yx+y}{x^3}$

Step-by-step explanation:

Given the expression

$\frac{y}{x^2}+\frac{y}{x^3}$

Let us perform the operation and express your answer as a single fraction

$\frac{y}{x^2}+\frac{y}{x^3}=\frac{x^3y+x^2y}{x^5}$

$=\:\frac{x^2\left(xy+y\right)}{x^5}$

$=\frac{\left(xy+y\right)}{x^3}$

Therefore, we conclude that:

$\frac{y}{x^2}+\frac{y}{x^3}=\frac{yx+y}{x^3}$

3 0

2 years ago

Marcus currently has $42 and plans to save an additional $5 each week to buy a pair of shoes. He made a table showing the total

Sidana [21]

Equation that represents therelationship between the nmber of weeks and total amount of money marcus will have saved is

Y= 5x+42

-5x +y =42

He currently has $42 with planning to save $5 each week. So, $5 per week is the slope and $42 is the y intercept.

3 0

2 years ago

Read 2 more answers

Please answer the question

Dominik [7]

Can't see it the equation is to blurry.

5 0

3 years ago

17x-3y=4 2x-4y=1 the solution to the system of equations is

Burka [1]

ANSWER

$x=\frac{13}{62}$

and

$y= \frac{-9}{62}$ e have

EXPLANATION

$17x-3y=4---(1)$

$2x-4y=1$

Let us make y the subject and call it equation (2)

$2x=1+4y$

$x=\frac{1}{2}+2y--(2)$

We put equation (2) in to equation (1)

$17(\frac{1}{2}+2y)-3y=4$

$\frac{17}{2}+34y-3y=4$

$34y-3y=4- \frac{17}{2}$

Simplify to get,

$31y= \frac{8-17}{2}$

$31y= \frac{-9}{2}$

Divide both sides by 31,

$y= \frac{-9}{2} \div 31$

$y= \frac{-9}{2} \times \frac{1}{31}$

$y= \frac{-9}{62}$

We put this value in to equation (2) to get,

$x=\frac{1}{2}+2\times -\frac{9}{62}$

$x=\frac{1}{2} -\frac{18}{62}$

We collect LCM to obtain,

$x=\frac{31-18}{62}$

$x=\frac{13}{62}$

7 0

2 years ago

How many solutions does this equation have?

Leto [7]

Answer:

The given equation having only one solution i.e., "w = 3". A further explanation is provided below.

Step-by-step explanation:

The given equation is:

⇒ $9(w-9)-2=-7w+7(w-8)$

By opening the brackets, we get

⇒ $9w-81-2=-7w+7w-56$

⇒ $9w-83=-56$

On adding "83" both sides, we get

⇒ $9w-83+83=-56+83$

⇒ $9w=27$

⇒ $w=\frac{27}{9}$

⇒ $=3$

4 0

2 years ago