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3 years ago

(_+10)(_+-1)= 11x^2+17x-10 in factored form

Mathematics

1 answer:

Sever21 [200]3 years ago

4 0

Answer:

The factored form will be:

$11x^2+17x-10=\left(11x-5\right)\left(x+2\right)$

Step-by-step explanation:

Given the expression

$11x^2+17x-10$

Breaking the expression into groups

$=\left(11x^2-5x\right)+\left(22x-10\right)$

factoring out x from 11x²-5x

11x²-5x = x(11-5)

factoring out 2 from 22x-10

22x-10 = 2(11x-5)

so the expression becomes

$=x\left(11x-5\right)+2\left(11x-5\right)$

factoring out common term 11x-5

$=\left(11x-5\right)\left(x+2\right)$

Therefore, the factored form will be:

$11x^2+17x-10=\left(11x-5\right)\left(x+2\right)$

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3 years ago

Which value of m will create a system of parallel lines with no solution? y=mx-6 8x-4y=12 A coordinate grid with one line labele

nydimaria [60]

Answer:

A system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2

Step-by-step explanation:

The equation of the given line is 8·x - 4·y = 12

Which gives;

8·x- 12= 4·y

y = 2·x - 3

Given that the line passes through the points (0, -3) and (1, -1), we have;

$Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

When (x₁, y₁) = (0. -3) and (x₂, y₂) = (1, -1), we have;

$Slope, \, m =\dfrac{(-1)-(-3)}{1-(0)} = 2$

y - (-3) = 2×(x - 0)

y = 2·x - 3 which is the equation of the given line

For the lines 8·x - 4·y = 12, which is the sane as y = 2·x - 3 and the line y = m·x - 6 to have no solution, the slope of the two lines should be equal that is m = 2

Given that the line passes through the point (1.5, 0), we have;

y - 0 = 2×(x - 1.5)

y = 2·x - 3...................(1)

For the equation, y = m·x - 6, when m = 2, we have;

y = 2·x - 6..................(2)

Solving equations (1) and (2) gives;

2·x - 3 = 2·x - 6, which gives;

2·x - 2·x= - 3 - 6

0 = 9

Therefore, a system of parallel lines will be created where the two lines will never meet and have no common solution at a value of m = 2.

4 0

3 years ago