Daniel has 40 points and Zeke has 75. The opposing team has 150. It is Daniel's turn. How many points
1 answer:
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<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:
32°
Step-by-step explanation:
Given:
∠DMQ = 58º
In this circle, the radius is DM. Since AD is tangent to the circle M, at point D, and the angle between a tangent and a radius is 90°
Therefore, ∠MDQ = 90°
The total angle in a triangle is 180°. Since we have the values of ∠MDQ and ∠DMQ, ∠DQM will be calculated as:
180 = ∠DMQ + ∠MDQ + ∠DQM
Solving for ∠DQM, we have:
∠DQM = 180 - ∠DMQ - ∠MDQ
∠DQM = 180 - 90 - 58
∠DQM = 32°
The measure of ∠DQM is 32°
