A curve is such that when y = 0, x = -2 or x = 3. Find the equation of the curve.
y = \(x^2 - 5x - 6\)
y = \(x^2 + 5x - 6\)
y = \(x^2 + x - 6\)
y = \(x^2 - x - 6\)
Correct answer is A
Since the curve cuts the x-axis at x = -2 and x = 3,
(x + 2)(x - 3) = 0
\(x^2 - 3x + 2x - 6\) = 0
\(x^2 - x - 6\) = 0
Hence, the equation of the curve is
y = \(x^2 - x - 6\)
Simplify; \(\frac{2 - 18m^2}{1 + 3m}\)
\(2 (1 + 3m)\)
\(2 (1 + 3m^2)\)
\(2(1 - 3m)\)
\(2(1 - 3m^2)\)
Correct answer is C
\(\frac{2 - 18m^2}{1 + 3m}\) = \(\frac{2(1 - 9)m^2}{1 + 3m}\)
= \(\frac{2(1 + 3m)(1 - 3m)}{1 + 3m}\)
= \(2(1 - 3m)\)
If x : y : z = 3 : 3 : 4, evaluate \(\frac{9x + 3y}{6z - 2y}\)
1\(\frac{1}{2}\)
2
2\(\frac{1}{2}\)
3
Correct answer is A
If x : y : z = 3 : 3 : 4, evaluate \(\frac{9x + 3y}{6x - 2y}\)
\(\frac{x}{y}\) = \(\frac{2}{3}\) and \(\frac{y}{z}\) = \(\frac{3}{4}\)
Thus; x = \(\frac{2}{3}T_1\) and z = \(\frac{3}{5}T_1\)
y = \(\frac{3}{7}T_2\) and z = \(\frac{4}{7}T_2\)
Using y = y
\(\frac{3}{5}T_1\) = \(\frac{3}{7}T_2\); \(\frac{T_1}{T_2}\) = \(\frac{3}{7}\) x \(\frac{5}{3}\)
\(\frac{T_1}{T_2}\) = \(\frac{15}{21}\)
\(T_1\) = 15 and \(T_2\) = 21
Therefore;
x = \(\frac{2}{5}\) x 15 = 6
y = \(\frac{3}{5}\) x 15 = 9
y = \(\frac{3}{7}\) x 21 = 9 (again)
z = \(\frac{4}{7}\) x 21 = 12
Hence;
\(\frac{9x + 3y}{6z - 2y}\) = \(\frac{9(6) + 3(9)}{6(12) - 2(9)}\)
\(\frac{54 + 27}{72 - 18}\) = \(\frac{81}{54}\) = \(\frac{3}{2}\)
= 1\(\frac{1}{2}\)
If y + 2x = 4 and y - 3x = -1, find the value of (x + y)
3
2
1
-1
Correct answer is A
y + 2x = 4 .....(1)
y - 3x = -1 ......(2)
Subtract (2) from (1)
2x - (-3x) = 4 - (-1)
2x + 3x = 4 + 1
5x = 5
X = \(\frac{5}{5}\)
= 1
Substitute 1 for x in (1);
y + 2(1) = 4
y + 2 = 4
y = 4 - 2 = 2
Hence, (x + y) = (1 + 2)
= 3
If F = \(\frac{9}{5}\)C + 32, find C when F = 98.6
30
37
39
41
Correct answer is B
F = \(\frac{9}{5}\)C + 32
When F = 98.6
98.6 = \(\frac{9}{5}\)C + 32
98.6 - 32 = \(\frac{9}{5}\)C
66.6= \(\frac{9}{5}\)C
66.6 x 5 = 9C
C = \(\frac{66.6 \times 5}{9}\)
= 37