Simplify:
\(\frac{(x^2y^3z^{-2})^{-3}(x^{-3}yz^2)^{1/2}}{(xyz^{-3})^{5/2}}\)
\(\frac{(x^2y^3z^{-2})^{-3}(x^{-3}yz^2)^{1/2}}{(xyz^{-3})^{5/2}}\)
A\(\frac{1}{x^2y^7z^5}\)
B\(\frac{1}{x^2y^7z^3}\)
C\(\frac{1}{x^2y^5z^7}\)
D\(\frac{1}{x^5y^7z^2}\)
Mathematics · Question Bank
algebra
143 of 433 questions match · page 2 of 8. Answer in your head first, then check the solution.
Simplify the following equation:
\(\frac{5x}{2x^2+7x+3}-\frac{x+3}{2x^2-3x-2}+\frac{2x+1}{x^2+x-6}\)
\(\frac{5x}{2x^2+7x+3}-\frac{x+3}{2x^2-3x-2}+\frac{2x+1}{x^2+x-6}\)
A\(\frac{4}{x+3}\)
B\(\frac{2}{x-3}\)
C\(\frac{4}{x-3}\)
D\(\frac{2}{x+3}\)
Simplify: \(\{x^{2/3}[x^{-1/3}y^{-1/2}(x^2y^{-2})^{1/3}]^{1/2}\}^6\)
A\(\frac{y^{5/2}}{x}\)
B\(\frac{y^{3/2}}{x}\)
C\(\frac{y^{5/2}}{x^2}\)
D\(\frac{y^{3/2}}{x^2}\)
Simplify: \(7^{a+2}-8(7)^{a+1}+5(7)^a+49(7)^{a-2}\)
A\(-5a\)
B\(-3a\)
C\(-7^a\)
D\(-4a\)
Solve for \(x\): \(x=\frac{(b^2-4b+16)(b^2-16)}{b^3+64}\)
A\(b+4\)
B\(\frac{b-4}{b+2}\)
C\(\frac{b^2-4}{b+2}\)
D\(b-4\)
Solve for \(y\): \(\frac{x}{(b-c)}=\frac{y}{(a-c)}=\frac{z}{(a-b)}\)
A\(x-z\)
B\(x+z\)
C\(a+b\)
D\(a-b\)
Resolve \(\frac{x+2}{x^2-7x+12}\) into partial fraction.
A\(\frac{6}{x-4}-\frac{2}{x-3}\)
B\(\frac{3}{x-4}-\frac{5}{x-3}\)
C\(\frac{6}{x-4}-\frac{5}{x-3}\)
D\(\frac{7}{x-4}-\frac{5}{x-3}\)
Find the value of \(A\) in the equation:
\(\frac{x^2+4x+10}{x^3+2x^2+5x}=\frac{A}{x}+\frac{B(2x+2)}{x^2+2x+5}+\frac{C}{x^2+2x+5}\)
\(\frac{x^2+4x+10}{x^3+2x^2+5x}=\frac{A}{x}+\frac{B(2x+2)}{x^2+2x+5}+\frac{C}{x^2+2x+5}\)
A\(-2\)
B\(1/2\)
C\(-1/2\)
D\(2\)
Solve for \(x\) in the following equations.
\(27^x=9^y\)
\(81^y 3^{-x}=243\)
\(27^x=9^y\)
\(81^y 3^{-x}=243\)
A\(1\)
B\(1.5\)
C\(2\)
D\(2.5\)
Evaluate:
\(y=\frac{4(5^{2n+1})-10(5^{2n-1})}{2(5^{2n})}\)
\(y=\frac{4(5^{2n+1})-10(5^{2n-1})}{2(5^{2n})}\)
A\(y=5^n\)
B\(y=9\)
C\(y=5^{2n}\)
D\(y=18\)
Given: \((a^n)(a^m)=100{,}000\) and \(\frac{a^n}{a^m}=10\)
Find \(a\):
Find \(a\):
A\(12\)
B\(9\)
C\(11\)
D\(10\)
Find the value of \(k\) so that \(4x^2+6x+k\) is a perfect square.
A\(36\)
B\(2.5\)
C\(9\)
D\(2.25\)
If \(p-q=5\) and \(pq=\frac{k}{2}\), then \(p^2+q^2\) equals
A\(k\)
B\(25k\)
C\(25+k\)
D\(\frac{k}{25}\)
Find the value of \(x\) which will satisfy the following expression: \(\sqrt{x-2}=\sqrt{x}+2\)
A\(3/2\)
B\(9/4\)
C\(18/6\)
DNone of these
Simplify \(\sqrt{\frac{ab}{\sqrt[3]{ab}}}\)
A\(\sqrt[3]{ab}\)
B\(\sqrt{ab}\)
C\(\frac{ab}{\sqrt{ab}}\)
D\(\frac{ab}{\sqrt[3]{ab}}\)
Find the quotient of \(3x^5-4x^3+2x^2+36x+48\) divided by \(x^3-2x^2+6\).
A\(3x^2-4x-8\)
B\(3x^2+4x+8\)
C\(3x^2-6x-8\)
D\(3x^2+6x+8\)
Find the remainder if we divide \(4y^3+18y^2+8y-4\) by \((2y+3)\).
A\(10\)
B\(11\)
C\(15\)
D\(13\)
Given: \(f(x)=(x+3)(x-4)+4\). When \(f(x)\) is divided by \((x-k)\), the remainder is \(k\). Find \(k\).
A\(2\)
B\(4\)
C\(6\)
D\(8\)
The mean of \(x\) and \(y\) is \(a\), the mean of \(y\) and \(z\) is \(b\) and the mean of \(x\) and \(z\) is \(c\). What is the mean of \(x, y\) and \(z\)?
A\(\frac{a+b+c}{3}\)
B\(\frac{a+b+c}{2}\)
C\(a+b+c\)
D\(\frac{abc}{a+b+c}\)
The arithmetic mean of \(80\) numbers is \(55\). If two numbers namely \(250\) and \(850\) are removed, what is the arithmetic mean of the remaining numbers?
A\(42.31\)
B\(50\)
C\(38.62\)
D\(57.12\)