PSAT 10 Advanced Math. Practice it free.

First write slope-intercept form: $10 = \dfrac{2}{3}(9) + b$ gives $b = 4$, so $y = \dfrac{2}{3}x + 4$. Multiplying by $3$ and rearranging gives $-2x + 3y = 12\textsf{.}$

$\sqrt{80}=\sqrt{16 \cdot 5}=4\sqrt{5}$ and $\sqrt{45}=\sqrt{9 \cdot 5}=3\sqrt{5}$. Adding like radical terms gives $4\sqrt{5}+3\sqrt{5}=7\sqrt{5}$.

The terms $2y$ and $3y$ are like terms: $2y + 3y = 5y$. The constant $6$ stays the same, so the expression is equivalent to $5y + 6\textsf{.}$

The greatest common factor of $16x^{3}$, $24x^{2}$, and $8x$ is $8x\textsf{.}$ Factoring gives $8x(2x^{2} + 3x - 1)$.

$25x^{2} - 36 = (5x)^{2} - 6^{2} = (5x - 6)(5x + 6)$.

Here $a = 1$, $b = 2$, and $c = 10$. Substituting into $b^{2} - 4ac$ gives $2^{2} - 4(1)(10) = -36\textsf{,}$ so there are $0$ distinct real roots.

Here $a = 2$, $b = 3$, and $c = -5$. Substituting into $b^{2} - 4ac$ gives $3^{2} - 4(2)(-5) = 9 + 40 = 49$.

Write $70v$ with denominator $k$: $\dfrac{35v}{k} + \dfrac{70vk}{k} = \dfrac{35v + 70vk}{k} = \dfrac{35v(1 + 2k)}{k}$.