This is the fifth part (questions 41-50) of the solutions of the Grade 8 MTAP 2015 Elimination Questions. You can read the solutions for questions **1-10, ** **11-20,**** 21 – 30**, and **31 – 40**. ** **

**41.)** If , what is ?

**Solution**

, .

**Answer:** – 13

**42.)** What is the equation of the line that is parallel to and passes through ?

**Solution**

Parallel lines have the same slope, so we get the slope of the given line. That is,

So, the slope of the given line is .

By the slope-intercept form, we get the equation of the line parallel to it and passing through .

Multiplying both sides by , we obtain

Simplifying, we have

**Answer:**

**43.)** What is the domain of the function ?

**Solution**

We know that we cannot have a negative square root, so . By squaring both sides and simplifying, this means that .Since we can substitute any value for except the mentioned restriction, the domain is therefore the set of real numbers greater than or equal to 1.

**Answer:** the set of real numbers greater than or equal to 1

**44.)** Find the range of the function in Item 43.

**Solution**

The minimum value for and , therefore, the range of is the set of real numbers greater than or equal to .

Answer: set of real numbers greater than or equal to -2.

**45.)** If , cm, and cm, what is when ?

**Solution**

Since corresponding sides of congruent triangles are congruent, . So,

.

**Answer:** or .

**46.)** Let be an isosceles right triangle with C as its hypotenuse, and let and be midpoints on and , respectively, such that . If and , what is the area of the trapezoid in terms of and ?

**Solution**

The area of a trapezoid is where and are the bases, and is the height. From the given we can see that , and .

Substituting we have .

This simplifies to

**Answer:**

**47.)** If and , what is ?

**Solution **

Assuming that . From the second equation . This is impossible because . So, y is negative.

This means that the second equation becomes . Now, suppose is negative, then the first equation becomes which is impossible because we have already shown that is negative. So, we are left with the systems of linear equations.

This gives us and . Therefore, .

**Answer:** 2

48.) If and , what is ?

**Solution**: To be posted later.

**Answer**: 3

49.) Let be a square. Three parallel lines , , and pass through A, B, C, respectively. The distance between l1 and l2 is 4cm, and the distance between l2 and l3 is 5cm. Find the area of the square.

**Solution**

Draw line perpendicular to and passing through .

Let be the intersection of and and be the intersection of and . Then, (Why?). If we let be the side of the square,

which means that

.

So,

**Answer**: 41

50.) At least how many numbers should be selected from the set {1, 5, 9, 13, … , 125} to be assured that two of the numbers selected have a sum of 146?

**Solution: **To be posted later.

Answer: 20