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3 years ago

Question

Mathematics

1 answer:

kondor19780726 [428]3 years ago

6 0

Answer: r = 11

Step-by-step explanation:

We know that the point (-2, r) lies on the graph of:

2*x + y = 7.

Then, if we that point is on the graph of the equation, we can replace the values and we will have:

2*(-2) + r = 7

and now we solve this for r-

-4 + r = 7

r = 7 + 4 = 11

r = 11

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PL has endpoints P(4, −6) and L(−2, 1). The segment is translated using the mapping (x, y) → (x 5, y). What are the coordinates

cestrela7 [59]

The coordinates of P' is (9, -6) and L' is (3, -1).

<h2>Given that</h2>

PL has endpoints P(4, −6) and L(−2, 1).

The segment is translated using the mapping (x, y) → (x + 5, y).

<h3>We have to determine</h3>

What are the coordinates of P’ and L’?

<h3>According to the question</h3>

PL has endpoints P(4, −6) and L(−2, 1).

The segment is translated using the mapping (x, y) → (x + 5, y).

The coordinates of point P after translation using mapping is,

$\rm P(x, \ y) - P'(x+5, y)\\
\\
P(4, -6) - P'(4+5, \ -6)\\
\\
P(4, -6) - P'(9, -6)\\$

And the coordinates of point L after translation using mapping is,

$\rm L(x, \ y) - L'(x+5, y)\\\\L(-2, 1) - L'(-2+5, \ -1)\\\\L(4, -6) - L'(3, -1)\\$

Hence, The coordinates of P' is (9, -6) and L' is (3, -1).

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Second, replace the inequality sign with an equal sign so that we can solve it like a normal equation. / Your problem should look like: $\frac{3x-5}{x-5}$ = 0
Third, multiply both sides by x - 5. / Your problem should look like: 3x - 5 = 0
Forth, add 5 to both sides. / Your problem should look like: 3x = 5
Fifth, divide both sides by 3. / Your problem should look like: x = $\frac{5}{3}$
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1. For the interval x < $\frac{5}{3}$ :
Let's pick x - 0. Then, $\frac{3x0-5}{0-5}$ > 0
After simplifying, we get 1 > 0 which is true.
Keep this interval.

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