ISIP Math Grades 6-8 Computations and Algebraic Thinking. Practice it free.

The constants $7$ and $2$ are like terms: $7 + 2 = 9$. The term $m^{2}$ stays the same, so the expression is equivalent to $m^{2} + 9\textsf{.}$

Distribute 2: $2 \cdot 4x + 2 \cdot -3 = 8x - 6$.

Use a conversion factor with pounds in the numerator so stones cancel: $28 \text{ stones} \times \dfrac{14 \text{ lb}}{1 \text{ stone}} = 392 \text{ lb}$.

$3^{2} = 3 \cdot 3 = 9\textsf{.}$

The Power of a Power Property says that a power raised to another power is simplified by multiplying the exponents, written $(x^{m})^{n} = x^{m \cdot n}\textsf{.}$ So $(3^{4})^{2} = 3^{4 \cdot 2} = 3^{8}\textsf{.}$ The Quotient of Powers Property then subtracts the exponents, written $\dfrac{x^{m}}{x^{n}} = x^{m-n}\textsf{.}$ So $\dfrac{3^{8}}{3^{5}} = 3^{8-5} = 3^{3}$ and $k = 3\textsf{.}$

Substitute $t = 3$: $f(3) = 4e^{9} + 200$. Since $e^{9} \approx 8{,}103$, $f(3) \approx 4(8{,}103) + 200 = 32{,}612 \approx 3 \times 10^{4}$.

The base $7$ appears $5$ times as a factor, so $7 \times 7 \times 7 \times 7 \times 7 = 7^{5}$.

Five gallons of water is $5 \times 16 = 80$ cups. With a $9$ to $72$ ratio, $\dfrac{9}{72} = \dfrac{x}{80}$, so $72x = 720$ and $x = 10$ cups of concentrate.