Question

medal and fan!

Answer 1

we have to draw, these lines:
\(y=3x+10\)
and
\[y = - \frac{{3x}}{4} - 1\]

Answer 2

yes!
so the region involved, is the dark region

Answer 3

now, please you have to locate the point \((8,10)\)

Answer 4

what about partA

Answer 5

for part A, we can say this:
"The solution region, is the region of all points \((x,y)\), whose y-coordinate, is Greater than \(3x+10\) and less than \( - \frac{{3x}}{4} - 1\)"

Answer 6

the points of the two lines \(don't\) belong to the solution region

Answer 7

okay

Answer 8

so now you need me to find the coordinates 8,10

Answer 9

now, for part B, please draw the point \((8,10)\) and check if such point is inside or outside the solution region

Answer 10

okay give me a second please:)

Answer 11

ok!

Answer 12

as we can see, such point is located outside the solution region
please substitute its coordinate into the first inequality:
\(y>3x+10\)
what do you get?

Answer 13

coordinates*

Answer 14

i dont understand

Answer 15

oh i think i get it let me see if it works

Answer 16

hint:
x=8, and y=10
so after substitution, we get:
\[10 > \left( {3 \times 8} \right) + 10\]
please simplify the right side

Answer 17

hint:
what is \((3 \times 8)+10=...\)

Answer 18

hold on please im not very fast when i comes to math:)

Answer 19

ok!

Answer 20

x=30?

Answer 21

noooo

Answer 22

i did it wrong

Answer 23

I got this \((3 \times 8)+10=24+10=34\), am I right?

Answer 24

34 yep!

Answer 25

ok! So we got this statement:
\(10>34\)
is it true or false?

Answer 26

false

Answer 27

that's right! That is the Mathematical proof, that the point \((8,10)\) doesn't belong to the solution region

Answer 28

okay so the hole thing would be


Part A: The solution region, is the region of all points (x,y), whose y-coordinate, is Greater than 3x+10 and less than −3x4−1"

PartB: The point is located outside the solution region
please substitute its coordinate into the first inequality:
y>3x+10 =34

So we got this statement:
10>34 = false

That is the Mathematical proof, that the point (8,10) doesn't belong to the solution region.

Answer 29

that's right!

Answer 30

please make sure to attach the graph of the solution region

Answer 31

okay thank you so much! do you mind checking two more of my questions to make sure that they are right?

Answer 32

ok!

Answer 33

i will post a new question

Answer 34

ok!