Mathematics, 13.07.2019 17:30, tee4597

#1. factor the expression. 4g^2+21g-49 #2. factor the expression. 320y^2-80y-75 #3. 36k2 – 44k - 8 factors to (4k-4)(9k+2). true? false?

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1. You want to find factors of 4×(-49) that add to 21. Those would be +28 and -7. Replacing the term 21g with the sum 28g -7g, we get an expression that can be factored by grouping.

... (4g² +28g) + (-7g -49)

... = 4g(g +7) -7(g +7) = (4g-7)(g+7)

2. After you factor out 5, you have 5(64y² -16y -15). As in the previous problem, you're looking for factors of 64×(-15) = -960 that sum to -16. There are 14 factor pairs of 960, so it can take a little bit of effort to find the right pair. That pair is -40 and 24. As in the previous problem you replace the term -16y with the sum -40y +24y and factor by grouping.

... = 5(64y² -40y +24y -15) = 5(8y(8y -5) +3(8y -5))

... = 5(8y +3)(8y -5)

3. False. It is perhaps easiest to check this by multiplying out the offered factors. Doing that gives you 36k² -36k +8k -8. The collected k terms add to -28k, not -44k.

answered: Guest

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