Find the value of x in the diagram above
10 units
15 units
5 units
20 units
Correct answer is A
Intersecting Chords Theorem states that If two chords intersect in a circle, then the products of the measures of the segments of the chords are equal.
⇒ AE * EB = CE * ED
⇒ 6 * \(x\) = 4 * (\(x\) + 5)
⇒ 6\(x\) = 4\(x\) + 20
⇒ 6\(x\) - 4\(x\) = 20
⇒ 2\(x\) = 20
∴ \(x = \frac{20}{2}\) = 10 units
Calculate the area of the composite figure above.
6048 m\(^2\)
3969 m\(^2\)
4628 m\(^2\)
5834 m\(^2\)
Correct answer is B
Area of the composite figure = Area of semi circle + Area of rectangle + Area of triangle
Area of semi circle = \(\frac{1}{2}\pi r^2 = \frac{1}{2}\times\pi\times\frac{d^2}{4} = \frac{1}{2}\times\frac{22}{7}\times\frac{42^2}{4} = 693 m^2\)
Area of rectangle = l x b = 42 x 60 =2520 m\(^2\)
Area of triangle = \(\frac{1}{2}\times b \times h = \frac{1}{2}\times 36 \times 42 = 756 m^2\)
∴ Area of the composite figure = 693 + 2520 + 756 = 3969 m\(^2\)
Solve the logarithmic equation: \(log_2 (6 - x) = 3 - log_2 x\)
\(x\) = 4 or 2
\(x\) = -4 or -2
\(x\) = -4 or 2
\(x\) = 4 or -2
Correct answer is A
\(log_2 (6 - x) = 3 - log_2 x\)
⇒ \(log_2 (6 - x) = 3 log_2 2 - log_2 x\) (since \(log_2\) 2 = 1)
⇒ \(log_2 (6 - x) = log_2 2^3 - log_2 x\) \((a log\) c = \(log\) c\(^a)\)
⇒ \(log_2 (6 - x) = log_2 8 - log_2 x\)
⇒\(log_2 (6 - x) = log_2 \frac{8}{x}\) (\(log\) a - \(log\) b = \(log \frac{a}{b})\)
⇒ \(6 - x = \frac{8}{x}\)
⇒ \(x (6 - x) = 8\)
⇒ \(6x - x^2 = 8\)
⇒ \(x^2 - 6x + 8 = 0\)
⇒ \(x^2 - 4x - 2x + 8 = 0\)
⇒ \(x (x - 4) - 2(x - 4) = 0\)
⇒ \((x - 4)(x - 2) = 0\)
⇒ \(x - 4 = 0 or x - 2 = 0\)
∴ x = 4 or 2
20
300
50
60
Correct answer is D
Let number of children's ticket at ₦250.00 each = \(x\)
∴ Number of adult tickets at ₦520.00 each = 5\(x\)
Then,
Total amount of money received from children's tickets = 250\(x\)
Total amount of money received from adult tickets = 520(5\(x\))
⇒ 250\(x\) + 520(5\(x\)) = 171,000
⇒ 250\(x\) + 2600\(x\) = 171,000
⇒ 2850\(x\) = 171,000
⇒ \(x = \frac{171,000}{2850} = 60\)
∴ 60 tickets were sold at ₦250.00 and 300 tickets were sold at ₦520.00
The line \(3y + 6x\) = 48 passes through the points A(-2, k) and B(4, 8). Find the value of k.
16
20
8
-2
Correct answer is B
The line: \(3y + 6x\) = 48
Divide through by 3
⇒ y + 2\(x\) = 16
⇒ y = -2\(x\) + 16
∴ The gradient of the line = -2
The points: A(-2, k) and B (4, 8)
m =\(\frac{y2 - y1}{x2 - x1} = \frac{8 - k}{4 - (-2)}\)
⇒ m =\(\frac[8 - k}{4 + 2} = {8 - k}{6}\)
Since the line passes through the points
∴ -2 = \(\frac{8 - k}{6}\)
⇒ \(\frac{-2}[1} = \frac{8 - k]{6}\)
⇒ 8 - k = -12
⇒ k = 8 + 12
∴ k = 20
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