Determine the sum of the positive valued solution to the simultaneous equations: \(xy=15\), \(yz=35\), \(zx=21\)
A15
B13
C17
D19
🔢
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\(\frac{1}{x^5y^7z^2}\)
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\(2\)
The value of (\(3\) to \(2.5\) power) square is equal to:
A\(729\)
B\(140\)
C\(243\)
D\(81\)
Evaluate: \(64^x \cdot 4^y\)
A\(256^{xy}\)
B\(4^{x+3y}\)
C\(64^{x+3y}\)
D\(4^{3x+y}\)
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\(10\)
Give the factors of \(a^2-x^2\).
A\(2a-2x\)
B\((a+x)(a-x)\)
C\((a+x)(a+x)\)
D\(2x-2a\)
Factor the expression \(x^2+6x+8\) as completely as possible.
A\((x+4)(x+2)\)
B\((x-4)(x+2)\)
C\((x-4)(x-2)\)
D\((x+6)(x+2)\)
\((a-b)^3=?\)
A\(a^3-3a^2b+3ab^2+b^3\)
B\(a^3-3a^2b-3ab^2-b^3\)
C\(a^3+3a^2b+3ab^2-b^3\)
D\(a^3-3a^2b+3ab^2-b^3\)
Find the value of \(k\) so that \(4x^2+6x+k\) is a perfect square.
A\(36\)
B\(2.5\)
C\(9\)
D\(2.25\)
Factor the expression \(3x^3-3x^2-18x\)
A\(3x(x-3)(x+2)\)
B\(3x(x+3)(x+2)\)
C\(3x(x+3)(x-2)\)
D\(3x(x-3)(x-2)\)
If \(p-q=5\) and \(pq=\frac{k}{2}\), then \(p^2+q^2\) equals
A\(k\)
B\(25k\)
C\(25+k\)
D\(\frac{k}{25}\)