4
8
6\(\frac{2}{3}\)
9\(\frac{1}{3}\)
Correct answer is D
Let the first term and common difference = a & d respectively.
\(T_{n} = \text{nth term} = a + (n - 1) d\) (A.P)
Given: \(T_{4} = -6 \implies a + 3d = -6 ... (i)\)
\(T_{8} + T_{9} = 72\)
\(\implies a + 7d + a + 8d = 72 \implies 2a + 15d = 72 ... (ii)\)
From (i), \(a = -6 - 3d\)
\(\therefore\) (ii) becomes \(2(-6 - 3d) + 15d = 72\)
\(-12 - 6d + 15d = 72 \implies 9d = 72 + 12 = 84\)
\(d = \frac{84}{9} = 9\frac{1}{3}\)
y = 1 - x
y = 1 + x
y = x - 1
y = 3x + 3
Correct answer is A
The second graph is
\((x^{2} - 2x - 1) + (2 + x - x^{2})\)
= \(1 - x\)
For what values of x is the curve y = \(\frac{x^2 + 3}{x + 4}\) decreasing?
-3 < x \(\leq\) 0
-3 \(\geq\) x < 0
0 < x < 3
0 \(\leq\) x \(\leq\) 3
Correct answer is D
No explanation has been provided for this answer.
What is the solution of the equation x2 - x - 1 + 0?
x = 1.6 and x = -0.6
x = -1.6 and x = 0.6
x = 1.6 and x = 0.6
x = -1.6 and x = -0.6
Correct answer is A
\(x^{2} - x - 1 = 0\)
Using the quadratic formula,
\(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)
a = 1, b = -1, c = -1.
\(x = \frac{-(-1) \pm \sqrt{(-1)^{2} - 4(1)(-1)}}{2(1)}\)
\(x = \frac{1 \pm \sqrt{1 + 4}}{2} = \frac{1 \pm \sqrt{5}}{2}\)
\(x = \frac{1 + 2.24}{2} ; x = \frac{1 - 2.24}{2}\)
\(x = \frac{3.24}{2}; x = \frac{-1.24}{2}\)
\(x = 1.62 ; x = -0.61 \)
\(x \approxeq 1.6; -0.6\)
Simplify \(\frac{x - y}{x^{\frac{1}{3}} - x^{\frac{1}{3}}}\)
x2 + xy + y2
x\(\frac{2}{3}\) + x \(\frac{1}{3}\) + y\(\frac{2}{3}\)
x\(\frac{2}{3}\) - x\(\frac{1}{3}\)y\(\frac{2}{3}\)
y\(\frac{2}{3}\)
Correct answer is B
No explanation has been provided for this answer.