Mathematics, 21.10.2019 19:00 whocares1234

Which system of linear inequalities has the point (3,-2) in its solution set?
a. y < -3
y ≤ 2/3x - 4
b. y > -3
y ≥ 2/3x - 4
c. y < -3
y ≥ 2/3x - 4
d. y > -2
y ≤ 2/3x - 4

(the answers come with graphs but sorry i couldn't find a way to put them all in)

Answers: 3

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Answers

Answer from: usagimiller

Option B.

Step-by-step explanation:

we know that

If a ordered pair is a solution of the system of inequalities

then

the ordered pair must satisfy both inequalities of the system

Verify each case

Case A) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

-2< -3 ----> is not true

therefore

The ordered pair is not a solution of the system A

Case B) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

-2 -3 ----> is true

Inequality 2

$-2 \geq \frac{2}{3} (3)-4$

$-2\geq -2$ ----> is true

therefore

The ordered pair is a solution of the system B

Case C) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

----> is not true

therefore

The ordered pair is not a solution of the system C

Case D) we have

The point (3,-2)

Substitute the value of x and the value of y in both inequalities and then compare the results

Inequality 1

-2-2 ----> is not true

therefore

The ordered pair is not a solution of the system D

Answer from: Quest

d) -1

step-by-step explanation:

Asap 25 pts + brainliest to right/best answer

Answer from: Quest

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram. we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2. so it's not a square or a rhombus.

we check the dot product of direction vectors of adjacent sides. we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular. we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

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Which system of linear inequalities has the point (3,-2) in its solution set?
a. y < -3