To solve for M, we have to first crossmultiply (M + m) to the left side of the equation.
This gives: H(M + m) = 16M. Now distribute H inside the parentheses, this gives: HM + Hm = 16M.
Subtract HM on both the sides to get all the ‘M’ terms on one side: Hm = 16M – HM. Take M as the common factor: Hm = M(16 – H) which gives M = Hm/ (16 – H).
2. Given the equation of a line 5x + 3y = 15. At what point does the graph of the line intersect the yaxis?
(0, 3)
(0, 5)
(3, 0)
(5, 0)
(0, 0)
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Correct answer is option  2 Explanation: To find the intersection point of the given line with the yaxis, we should plugin x = 0.
This implies: 5(0) + 3y = 15 which gives 3y = 15; y = 5.
Therefore the point (x, y) = (0, 5)
3. If ‘x’ and ‘y’ are integers, and 4x + 3y = 17, then which of the following could be the value of ‘y’.
0
1
2
3
4
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Correct answer is option  4 Explanation:
Here, substitute the values for ‘y’ and check if any of the ‘y’ values gives an integer value for ‘x’.
For instance, if we plugin y = 0, then 4x + 0 = 17, which gives x = 17/4. Clearly, here 17/4 is not an integer.
But when we plugin y = 3, then 4x + 9 = 17 which gives 4x = 8 giving x = 2 (which is an integer).
4. If the slope of a line is 1/5 and the yintercept is 2, then what is the xintercept of the same line?
2/5
10
0
5/2
10
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Correct answer is option  5 Explanation:
The equation of a straight line is y = mx + b where given m = slope = 1/5 and given b = yintercept = 2. Hence we get, y = 1/5x – 2.
xintercept of a line is the point where y = 0. Therefore, 0 = 1/5x – 2, now solve for x by adding 2 on both sides.
This gives 2 = 1/5x and by multiplying 5 on both sides, gives x = 10.
5. Which of the following side lengths will not form a right angled triangle?
8, 15, 17
5, 12, 13
9, 12, 15
12, 16, 22
3, 4, 5
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Correct answer is option  4 Explanation: Sides of a right angled triangle satisfy the Pythagorean Theorem.
The theorem states that if a, b, c are three sides of a right triangle with ‘c’ being the hypotenuse, then a^{2} + b^{2} = c^{2}.
This implies: 12^{2} + 16^{2} = 400 is not equal to 22^{2} which is 484.
6. In a classroom of 40 students, 20 students play basketball, 22 students play tennis and 4 students do not play either. How many students play both basketball and tennis?
6
7
8
9
10
Show me the answers!
Correct answer is option  1 Explanation:
4 students do not play either so 40 4 = 36 students play one sport or the other.
Let the number of students who play both be = x
Then, students who play only basketball = 20 – x
Students who play only tennis = 22 – x
Therefore, 36 = (20 – x) + (22 – x) + x
36 = 42 – x which gives x = 6
7. In triangle ABC, AM = MB and MN is parallel to BC. If the area of the triangle AMN is 6, then what is the area of the triangle ABC?
12
20
24
28
Cannot be determined with the given information
Show me the answers!
Correct answer is option  3 Explanation: Triangles AMN and ABC are similar triangles.
Therefore the similarity ratio of the sides, AM: AB = 2:1.
This gives the similarity ratio of the areas = 1^{2}: 2^{2} = 1: 4.
Given area of triangle AMN is 6, which implies area of triangle ABC = 6 * 4 = 24.
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