Math  /  Algebra

Question2. Select all coordinate pairs that are solutions to the inequality 5x+9y<455 x+9 y<45. A. (0,0)(0,0) B. (5,0)(5,0) C. (9,0)(9,0) D. (0,5)(0,5) E. (0,9)(0,9) F. (5,9)(5,9) G. (5,9)(-5,-9)

Studdy Solution

STEP 1

What is this asking? Which points, when plugged into 5x+9y5x + 9y, make the result less than 45? Watch out! Don't forget to check *all* the answers, some inequalities have *multiple* solutions!

STEP 2

1. Test each coordinate pair.

STEP 3

Alright, let's **kick things off** with option A, (0,0)(0, 0)!
We're going to substitute x=0x = 0 and y=0y = 0 into our inequality 5x+9y<455x + 9y < 45.

STEP 4

So, we have 50+90<455 \cdot 0 + 9 \cdot 0 < 45.
This simplifies to 0+0<450 + 0 < 45, which means 0<450 < 45.
This is **absolutely true**, so A is a solution!

STEP 5

Next up, option B: (5,0)(5, 0).
Substituting, we get 55+90<455 \cdot 5 + 9 \cdot 0 < 45, which simplifies to 25+0<4525 + 0 < 45, or 25<4525 < 45. **Another true statement!** B is a solution too.

STEP 6

Now for option C, (9,0)(9, 0): 59+90<455 \cdot 9 + 9 \cdot 0 < 45.
This becomes 45+0<4545 + 0 < 45, or 45<4545 < 45.
Hmm, 45 is *not* less than itself!
So, C is *not* a solution.

STEP 7

Let's check option D, (0,5)(0, 5): 50+95<455 \cdot 0 + 9 \cdot 5 < 45.
This gives us 0+45<450 + 45 < 45, or 45<4545 < 45.
Just like C, this is **not true**, so D is not a solution.

STEP 8

Moving on to E, (0,9)(0, 9): 50+99<455 \cdot 0 + 9 \cdot 9 < 45.
We get 0+81<450 + 81 < 45, which means 81<4581 < 45.
Definitely **not true**, so E is not a solution.

STEP 9

Time for option F, (5,9)(5, 9): 55+99<455 \cdot 5 + 9 \cdot 9 < 45.
This becomes 25+81<4525 + 81 < 45, or 106<45106 < 45. **Nope, not true**, F is not a solution.

STEP 10

Last but not least, option G, (5,9)(-5, -9): 5(5)+9(9)<455 \cdot (-5) + 9 \cdot (-9) < 45.
This simplifies to 2581<45-25 - 81 < 45, or 106<45-106 < 45.
This is **absolutely correct**!
G is a solution.

STEP 11

The coordinate pairs that are solutions to the inequality are A (0,0)(0, 0), B (5,0)(5, 0), and G (5,9)(-5, -9).

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord