Find the domain, vertical asymptote, and x-intercept of the logarithmic function, and sketch its graph by hand. $y=2+\log _{10}(x+1)$

Solve each system.

$$\left\{\begin{aligned} x+y-z &=1 \\ 3 x+3 y+z &=3 \\ 2 x+2 y-2 z &=2 \end{aligned}\right.$$

Find the opposite and the reciprocal of each number. $\sqrt{3}$

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 $x=-\frac{3}{2}$

Simplify the expression.

$$\left(-5 t^{2}\right)\left(6 t^{-9}\right)$$

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

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

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

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

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.

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

A contractor purchases a bulldozer for $36,500. The bulldozer requires an average expenditure of$11.25 per hour for fuel and maintenance, and the operator is paid $19.50 per hour. (a) Write a linear equation giving the total cost C of operating the bulldozer for t hours. (Include the purchase cost of the bulldozer.) (b) Assuming that customers are charged$80 per hour of bulldozer use, write an equation for the revenue R derived from t hours of use. (c) Use the profit formula (P = R − C) to write an equation for the profit gained from t hours of use. (d) Use the result of part (c) to find the break-even point (the number of hours the bulldozer must be used to gain a profit of 0 dollars).

Graph the curve and draw an arrow specifying the direction corresponding to motion.

$$x = t ^ { 2 } , \quad y = t ^ { 3 }$$