<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:

Step-by-step explanation:
As the line is perpendicular to
, we know that the slope of the line is
. As it passes through
, we know that it should be
.
An arithmetic sequence has a common difference.
143 - 130 = 13
156 - 143 = 13
169 - 156 = 13
The common difference is 13.
a1 = 130
a2 = 130 + 13
a3 = 130 + 2 * 13
a4 = 130 + 3 * 13
...
an = 130 + (n - 1) * 13
an = 130 + 13(n - 1)
an = 130 + 13n - 13
an = 117 + 13n
an = 13n + 117
Answer:
k = 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 5 ← is in slope- intercept form
with slope m = - 3
Parallel lines have equal slopes, thus the 2 points have a slope of - 3
calculate the slope using the slope formula and equate to - 3
m = 
with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (k, 5)
m =
=
= - 3 ( multiply both sides by (k - 4) )
- 3(k - 4) = 6 ( divide both sides by - 3 )
k - 4 = - 2 ( add 4 to both sides )
k = 2
Answer: Median!
Step-by-step explanation: If it's easier you can just use this website so your math will be easier: https://www.calculatorsoup.com/calculators/statistics/mean-median-mode.php