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3 years ago

Please solve the numbers don’t worry about the graph ok, by numbers i mean Y and X..

Mathematics

1 answer:

Anvisha [2.4K]3 years ago

4 0

x y

______

10, 5

8, 4

6, 3

4, 2

2, 1

0, 0

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Nostrana [21]

Answer:

$\displaystyle \begin{cases} \displaystyle {x} _{1} = - p \\ \displaystyle x _{2} = - q \end{cases}$

Step-by-step explanation:

we would like to solve the following equation for x:

$\displaystyle \frac{1}{p} + \frac{1}{q} + \frac{1}{x} = \frac{1}{p + q + x}$

to do so isolate $\frac{1}{x}$ to right hand side and change its sign which yields:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{1}{p + q + x} - \frac{1}{x}$

simplify Substraction:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{x - (q + p + x)}{x(p + q + x)}$

get rid of only x:

$\displaystyle \frac{1}{p} + \frac{1}{q} = \frac{ - (q + p )}{x(p + q + x)}$

simplify addition of the left hand side:

$\displaystyle \frac{q + p}{pq} = \frac{ - (q + p )}{x(p + q + x)}$

divide both sides by q+p Which yields:

$\displaystyle \frac{1}{pq} = \frac{ -1}{x(p + q + x)}$

cross multiplication:

$\displaystyle x(p + q + x) = - pq$

distribute:

$\displaystyle xp + xq + {x}^{2} = - pq$

isolate -pq to the left hand side and change its sign:

$\displaystyle xp + xq + {x}^{2} + pq = 0$

rearrange it to standard form:

$\displaystyle {x}^{2} + xp + xq + pq = 0$

now notice we end up with a quadratic equation therefore to solve so we can consider factoring method to use so

factor out x:

$\displaystyle x( {x}^{} + p ) + xq + pq = 0$

factor out q:

$\displaystyle x( {x}^{} + p ) +q (x + p)= 0$

group:

$\displaystyle ( {x}^{} + p ) (x + q)= 0$

by Zero product property we obtain:

$\displaystyle \begin{cases} \displaystyle {x}^{} + p = 0 \\ \displaystyle x + q= 0 \end{cases}$

cancel out p from the first equation and q from the second equation which yields:

$\displaystyle \begin{cases} \displaystyle {x}^{} = - p \\ \displaystyle x = - q \end{cases}$

and we are done!

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3 years ago

What are the solutions of the quadratic equation? X2=-5x-3

vagabundo [1.1K]

the correct answer is x^2+5x+3=0

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3 years ago

The complement of an angle is 81° what is the measure of the angle

Fiesta28 [93]

9°, complementary angles always add up to 90°

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3 years ago

-3/2 is less than 3x solve

sweet-ann [11.9K]

Answer:

anything above 1

Step-by-step explanation:

-3/2 = -1.5.

3 x -2 = -6

Nope

3 x -1 = -3

Nope

3 x 1 = 3 Yes!!

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2 years ago

What is the solution of the equation ×-3=1/3×+5?

murzikaleks [220]

The Answer Is 14/15 Hope This Helps.

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3 years ago

Read 2 more answers