<h3>3
Answers: Choice D, Choice E, Choice F</h3>
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Explanation:
The inequality 6x - 10y ≥ 9 solves to y ≤ (3/5)x - 9/10 when you isolate y.
Graph the line y = (3/5)x - 9/10 and make this a solid line. The boundary line is solid due to the "or equal to" as part of the inequality sign. We shade below the boundary line because of the "less than" after we isolated for y.
Now graph all of the points given as I've done so in the diagram below. The points in the blue shaded region, or on the boundary line, are part of the solution set. Those points are D, E and F.
We can verify this algebraically. For instance, if we weren't sure point E was a solution or not, we would plug the coordinates into the inequality to get...
6x - 10y ≥ 9
6(5) - 10(2) ≥ 9 .... plug in (x,y) = (5,2)
30 - 20 ≥ 9
10 ≥ 9 ... this is a true statement
Since we end up with a true statement, this verifies point E is one of the solutions. I'll let you check points D and F.
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I'll show an example of something that doesn't work. Let's pick on point A.
We'll plug in (x,y) = (-1,1)
6x - 10y ≥ 9
6(-1) - 10(1) ≥ 9
-6 - 10 ≥ 9
-16 ≥ 9
The last inequality is false because -16 is smaller than 9. So this shows point A is not a solution. Choices B and C are non-solutions for similar reasons.
Answer:
The cost increase for each square of carpet by 12.
Step-by-step explanation:
The given function is

It is a slope intercept form of the line

Where m is the slope and b is y-intercept.
Therefore the slope of given function is 12 and the y-intercept is 50.
It means the initial ot fixed cost of the carpet is 50 and the cost increased by 12 for each square of carpet.
Answer:
y ≈ 2.5
Step-by-step explanation:
Using the Sine rule in Δ XYZ
=
, substitute values
=
( cross- multiply )
y sin50° = 2 sin75° ( divide both sides by sin50° )
y =
≈ 2.5 ( to the nearest tenth )
1. Perfect square trinomials, are 2nd degree polynomials, of the form

so that

, which can be written as perfect squares.
2. For example

3. Thus

are perfect square trinomials.
4.

5. In the first case -b=20, so b=-20. In the second case, -b=-20, so b=20.
6. b∈{-20, 20}
Answer:
B.
Step-by-step explanation:
If you simple this expression we can see that 7/35 will simplify to 1/5 first. As for the exponents, you can write them out to make it easier to cancel, shown in the photo.