Mathematics, 07.07.2019 06:30 natalie2sheffield

Match the reasons with the statements. given: x2 + 6x + 2x + 12 = 0 to prove: x = -6 or x = -2 1. x2 + 6x + 2x + 12 = 0 subtraction property of equality 2. x2 + 8x + 12 = 0 distributive postulate 3. (x + 6)(x + 2) = 0 combining like terms 4. x + 6 = 0 or x + 2 = 0 zero product postulate 5. x = -6 or x = -2

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Answer from: hhh976

Given: x^2 + 6x + 2x + 12 = 0.

1. Combining like terms (here terms 6x and 2x both contain x, then we can combine them):

$x^2+(6x+2x)+12=0,\\\\x^2+8x+12=0.$

2. Distributive postulate:

x^2+8x+12=(x+6)(x+2).

The equation is

(x+6)(x+2)=0.

3. Zero product postulate (zero product postulate state that if a product of two factors is equal to zero, then first factor is equal to zero or second factor is equal to zero):

$x+6=0 \text{ or } x+2=0.$

4. Subtraction property of equality:

a) subtract 6 from the first equation:

$x+6=0\Rightarrow x+6-6=-6, \ x=-6.$

b) subtract 2 from the second equation:

$x+2=0\Rightarrow x+2-2=-2, \ x=-2.$

Answer from: brittnum9044

1.x2 + 6x + 2x + 12 = 01. Given

2.x2 + 8x + 12 = 0 2. Combining like terms

3.(x + 6)(x + 2) = 0 3. Distributive Postulate

4.x + 6 = 0 or x + 2 = 04. Zero product postulate

5.x = -6 or x = -2 5 Subtraction property of equality

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

answer: 7 x 2/5 = 2.8 hours, is your answer. your welcome! : 3

step-by-step explanation: first work out how long it took to hose 1/7 of the lawn which is 2/5 hours. times that by 7 to get the whole lawn.

sorry i don't know the other answer. i didn't learn what a proportional relationship is.

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Match the reasons with the statements. given: x2 + 6x + 2x + 12 = 0 to prove: x = -6 or x = -2 1....

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