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3 years ago

Explain why any number that is divisible by 9 is also divisible by 3.

Mathematics

1 answer:

slamgirl [31]3 years ago

6 0

Since 3 x 3 = 9, 9 is divisible by 3. So, 3 would be a factor of any number divisible by 9

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Please help with these problems! Will mark answer as brainliest and give 30 points. You have to show your work for each problem.

gulaghasi [49]

Answer:

1) (2x + 2)(x + 2)

2) 2(x + 1)(x - 1)

3) (x^2 + 3)(x^2 - 3)

4) 2x(x + 5)(x - 2)

5) (5x + 2y)(5x - 2y)

Step-by-step explanation:

2x^2 + 6x + 4

= 2x^2 + 4x + 2x + 4

= 2x(x + 2) + 2(x + 2)

= (2x + 2)(x + 2)

2x^2 - 2

= 2(x^ 2 - 1) (The difference of two squares)

= 2(x + 1)(x - 1)

x^4 - 9 (The difference of two squares)

=(x^2 + 3)(x^2 - 3)

2x^3 + 6x^2 - 20x

= 2x(x^2 + 3x - 10)

= 2x(x + 5)(x - 2)

25x^2 - 4y^2 (The difference of two squares)

= (5x + 2y)(5x - 2y)

4 0

3 years ago

1. What is the solution of the system?

andreyandreev [35.5K]

Answer:

The given system of equations has solutions below:

1) The solution is (2,3)

2) The solution is ( $\frac{-8}{7}, \frac{5}{7}$ )

3) The solution is infinitely many solutions

4) No solution

Step-by-step explanation:

Given system of equation are

$-x+2y=4\hfill (1)$

$-4x+y=-5\hfill (2)$

To solve equation by using elimination method

Multiply eqn (2) into 2

$-8x+2y=-10\hfill (3)$

Now subtracting (1) and (3)

$-x+2y=4$

$-8x+2y=-10$

_________________

7x=14

x= $\frac{14}{7}$

$x=2$

Substitute x=2 in equation (1)

-2+2y=4

2y=4+2

$y=\frac{6}{2}$

y=3

Therefore the solution is (2,3)

2) Given equation is

$-2x+y=3\hfill (1)$

4y-4=x

Rewritting as below

$x-4y=-4\hfill (2)$

To solve equation by using elimination method

multiply (2) into 2

$2x-8y=-8\hfill (3)$

Adding (1) and (3)

-2x+y=3

2x-8y=-8

________

-7y=-5

$y=\frac{5}{7}$

substitute $y=\frac{5}{7}$ in (1)

$-2x+\frac{5}{7}=3$

$-2x=3-\frac{5}{7}$

$-2x=\frac{21-5}{7}$

$x=-\frac{8}{7}$

Therefore the solution is ( $\frac{-8}{7},\frac{5}{7}$ )

3) Given equation is $6x+2y=10\hfill (1)$

$3x+y=5\hfill (2)$

equation (1) can be written as

2(3x+y)=10

$3x+y=\frac{10}{2}$

3x+y=5

Therefore equations (1) and (2) are same therefore it has infinitely many solutions

4) Given equation is $-x-2y=14\hfill (1)$

$-2x-4y=12\hfill (2)$

multiply equation (1) into 2

$-2x-4y=28\hfill (3)$

To solve equation by using elimination method

subtracting (2) and (3)

-2x-4y=28

-2x-4y=12

_______

$28\neq -12$

therefore it has no solution

4 0

3 years ago

2+90=? <br> please someone help asap

Oxana [17]

Answer:

92 :)

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Write an equation in point-slope form for the line that passes through each point with the given slope (-1,-2) m= 3

Vedmedyk [2.9K]

Answer:

Step-by-step explanation:

The Point-Slope form of equation of a line with slope of "m" and passing through point (x₁, y₁) is: y - y₁ = m(x - x₁)

m = 3

x₁ = -1

y₁ = -2

Therefore the equation:

y - (-2) = 3(x - (-1))

7 0

3 years ago

Kendra was given this system of equations.

iren2701 [21]

Answer:

Step-by-step explanation:

hope u enjoy

4 0

2 years ago

Explain why any number that is divisible by 9 is also divisible by 3.​

Explain why any number that is divisible by 9 is also divisible by 3.