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2 years ago

Select all of the expressions equivalent to 2(x + 9y) + 3(2x - 6y).

Mathematics

1 answer:

stiv31 [10]2 years ago

4 0

Answer:

Step-by-step explanation:

=2(x+9y)+3(2x-6y)

=2x+18y+6x-18y

=2x+6x-0y

=8x

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Write the equation of a line in slope intercept form that has a slope of 1/5 and contains (-10,6)

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Answer:

y = $\frac{1}{5}$ x + 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = $\frac{1}{5}$ , hence

y = $\frac{1}{5}$ x + c ← is the partial equation

To find c substitute (- 10, 6) into the partial equation

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3 years ago

Read 2 more answers

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3 years ago

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ANEK [815]

See below for the proof of the equation $\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)$

<h3>How to prove the equation?</h3>

The equation is given as:

$\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)$

Take the LCM

$\frac{(ax + by)(x - y) -(ax - by)(x + y)}{(x + y)(x - y)}= 2(a - b)$

Expand

$\frac{ax^2 - axy + bxy - by^2 -ax^2 - axy + bxy + by^2}{(x + y)(x - y)}= 2(a - b)$

Evaluate the like terms

$\frac{-2axy + 2bxy }{(x + y)(x - y)}= 2(a - b)$

Rewrite as:

$\frac{-2axy + 2bxy }{x^2 - y^2}= 2(a - b)$

Factorize the numerator

$\frac{2(a - b)(x^2 - y^2)}{x^2 - y^2}= 2(a - b)$

Divide

2(a - b)= 2(a - b)

Both sides are equal

Hence, the equation $\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)$ has been proved