How would I solve this question

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  4)  (4, 0)

Step-by-step explanation:

I find it useful to graph the inequalities and the points.

The point on the dashed line is not in the solution set. The only point in the doubly-shaded area is (4, 0), choice (4).

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Another method of choosing the points is to try them in the inequalities. I find it easier to do the math if the inequalities are written in standard form:

  2y < x +8 . . . . . multiply the first by 2

  x -2y > -8 . . . . . add -8-2y and swap sides. This is the first inequality.

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  y ≥ -x +1

  x + y ≥ 1 . . . . .  add x. This is the second inequality

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For the four points in the first inequality, we have ...

  1) -5 -2(3) = -11  . . .  not greater than -8

  2) 0 -2(4) = -8 . . . not greater than -8

  3) 3 -2(-5) = 13 . . . greater than -8, satisfies the first inequality

  4) 4 -2(0) = 4 . . . greater than -8, satisfies the first inequality

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So, the two points that might possibly work are (3, -5) and (4, 0). Here, we try these in the second inequality.

  3) 3 -5 = -2 . . . less than 1

  4) 4 + 0 = 4 . . . greater than 1, satisfies the second inequality

The only point listed that is a solution to the system is (4, 0), point 4.

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.