ACAP Grade 8 Expressions and Equations. Practice it free.

Substitute $t = 5$: $f(5) = 6e^{10}$. Since $e^{10} \approx 22{,}026$, $f(5) \approx 6(22{,}026) = 132{,}156 \approx 1 \times 10^{5}$.

$9.3 \times 10^7 = 93{,}000{,}000$, so $c = 9.3$.

The Product of Powers Property says that powers with the same base are multiplied by adding the exponents, written $y^{m} \cdot y^{n} = y^{m+n}\textsf{.}$ Both factors have base $y$, so $y^{6} \cdot y^{3} = y^{6+3} = y^{9}\textsf{.}$

Divide coefficients and subtract exponents: $7.2 \div 1.2 = 6$ and $-5-(-2)=-3$. So the quotient is $6 \times 10^{-3}\textsf{.}$

$x = \sqrt{121} = 11$ because $11 \times 11 = 121$.

Both equations have slope $-1$ but different $y$-intercepts ($6$ and $-2$), so the lines are parallel and the system has no solution.

Rewrite in slope-intercept form: $y = -2x + 7$ and $y = x - 2$. The slopes $-2$ and $1$ are different, so the lines intersect at exactly one point.

Subtract $2x$ from both sides: $9 = 3x - 6$. Add $6$ to both sides: $15 = 3x$. Divide by $3$: $x = 5\textsf{.}$