Question

Determine whether or not each of the following points is a solution of the inequality y< 2x²+3x-5. justify your answer. number 1 is done for you.

points
EXAMPLE 1. A(-1,6)
justification (ANSWER)
x=-1 and y=6
y<2x²+3x-5
6<2(-1)²+3(-1)-5
6<2(1)-3-5
6<2-3-5
6< -6 FALSE point (-1,6) is not a solution to the inequality y<2x²+3x-5

QUESTIONS
2. B(1,8)
3. C(-5,10)
4. D(3,6)
5. E(-3,4)
6. F(2,9)
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Answer 1

Answer:

Step-by-step explanation:

y<2x²+3x-5

Substitute B(1,8)

8< 2*1² +3*2-5

8<2+6-5

8<3 false

B(1,8) is not a solution.

Substitute C(-5,10) in y<2x²+3x-5

10<2*(-5)²+3*-5 -5

10< 50-15-5

10<30 true

C(-5,10) is a solution.

D(3,6)

6<2*3²+3*2-5

6< 18+6-5

6<19 true

D(3,6) is a solution.

E(-3,4)

4<2*(-3)²+3(-3)-5

4< 18-9-5

4<4 false

E(-3,4) is not a solution

F(2,9)

9< 2*2²+3*2-5

9< 8+6-5

9<9 false

F(2,9) is not a solution.

Answer 2

Answer:

The point $B(1,8)$ is not a solution of the given inequality.

Whereas the points $C(-5,10) \ and \ D(3,6)$ are the solutions of the given inequality.

Step-by-step explanation:

It can be found out simply by substituting $(x,y)$ values in the given equation

$y<2x^{2} +3x-5$

let us start with the point  $B(1,8)$.

here $x=1 \ and \ y=8$, therefore $y<2x^{2} +3x-5$ becomes

$8<2(1^{2} )+3(1)-5 =2+3-5=0$

that means, $8<0$, which is an incorrect inequality, therefore the point

$B(1,8)$ is not a solution of the given inequality.

similarly, for $C(-5,10)$,

$10<2(-5)^{2}+3(-5)-5 = 50+15-5=60$

that is ,$10<60$, which is correct.

therefore $C(-5,10)$ is a solution of the given inequality.

next  $D(3,6)$;

$6<2(3)^{2}+3(3)-5 = 18+9-5 = 22$

that is $6<22$, which is correct . Therefore the point D is a solution of the given inequality.

thank you