Use synthetic division to show that x is a solution of the thirddegree polynomial equation, and use the result to factor the polynomial completely. List all the real solutions of the equation. Polynomial Equation $2 x^{3}-17 x^{2}+12 x+63=0$ Value of x $x=-\frac{3}{2}$

Find the missing term of each arithmetic sequence. $4,\square,12,\dots$

Subtract. Use models if needed. (9x - 12) - (5x - 7).

Nosotros estabamos peleando cuando yo (me estaba rompiendo / me rompi) el dedo.

Each pair of figures is similar. Find the length of x.

Negate the following sentences. If f is a polynomial and its degree is greater than 2, then $f^{\prime}$ is not constant.

Find all solutions of the equation algebraically. Use a graphing utility to verify the solutions graphically. $3+\frac{2}{x}=\frac{16}{x^{2}}$

Use the additivity of moments to find the COM of the region. Three-quarters of the unit circle (remove the part in the fourth quadrant)

A heater for boiling a saturated liquid consists of two concentric stainless steel tubes packed with dense boron nitride powder. Electrical current is passed through the inner tube, creating uniform volumetric heating q $\left(\mathrm{W} / \mathrm{m}^{3}\right)$. The exposed surface of the outer tube is in contact with the liquid and the boiling heat flux is given as $q_{s}^{\prime \prime}=C\left(T_{s}-T_{\mathrm{sat}}\right)^{3}$. It is feared that under high-power operation the stainless steel tubes would severely oxidize if temperatures exceed $T_{\mathrm{ss}, x}$ or that the boron nitride would deteriorate if its temperature exceeds $T_{\mathrm{bn}, x}$. Presuming that the saturation temperature of the liquid $\left(T_{\mathrm{sat}}\right)$ and the boiling surface temperature $\left(T_{s}\right)$ are prescribed, derive expressions for the maximum temperatures in the stainless steel (ss) tubes and in the boron nitride (bn). Express your results in terms of geometric parameters $\left(r_{1}, r_{2}\right.\left.r_{3}, r_{4}\right)$, thermal conductivities $\left(k_{\mathrm{ss}}, k_{\mathrm{bn}}\right)$, and the boiling parameters $\left(C, T_{\mathrm{sat}}, T_{s}\right)$.

Graph the linear equation.

$$8 x - 4 y = 16$$

Find the domain of the vector-valued function. r(t) = F(t) x G(t), where F(t) = t³i - tj + tk, G(t) = ∛t i + 1 / t+1 j + (t+2)k

Explain why the baking instructions on a box of cake mix are different for high and low elevations. Would you expect to have a longer or a shorter cooking time at a high elevation?

Solve by elimination.

$$\begin{array}{l}{7 x+6 y=33} \\ {2 x-6 y=-6}\end{array}$$

For each $n \in \mathbb{N}$, let $A_{n}=\{0,1,2,3, \ldots, n\}$. a. $\bigcup_{i \in \mathbb{N}} A_{i}=$ b. $\underset{i \in \mathbb{N}}{\bigcap} A_{i}=$