Name one advantage of using a flow poof rather than a two-column proof.

Use the given function f to: Find the domain and the range of $f(x)=\log (-2 x)$

Solve each system by the substitution method.

$$\left\{ \begin{array} { l } { x ^ { 2 } + y ^ { 2 } = 5 } \\ { 3 x - y = 5 } \end{array} \right.$$

The formula for _ is distance divided by time.

Determine whether the given value is a solution of the equation.

$$\frac { b } { 12 } = 5 ; b = 60$$

a. Write the formula for the area of a rectangle. b. A professional basketball court is a rectangle that is 50 feet wide and 94 feet long. What is the area of the basketball court?

The function

$$f(x)=100\dfrac{(1+0.08/12)^2-1}{0.08/12}$$

Find the standard form of the equation of the ellipse with the given characteristics. Vertices: $(\pm 5,0) ;$ foci $(\pm 4,0)$

Use l’Hopital’s Rule to evaluate the following limits. $\lim _ { x \rightarrow \infty } \frac { 1 - \operatorname { coth } x } { 1 - \tanh x }$

What is the relationship between sides and angles for each type of triangle? a. isosceles b. equilateral

Let A and B be $3 \times 3$ matrices, with det A=-3 and det B=4. Use properties of determinants to compute: $\operatorname{det} A^{-1}$.

Is the total internal energy of an ideal-gas mixture equal to the sum of the internal energies of each individual gas in the mixture? Answer the same question for a real-gas mixture.

find the limit (if it exists). If the limit does not exist, then explain why. Use a graphing utility to verify your result graphically.

$$lim x→∞(3/x^2+1)$$

Solve the system by using elementary row operations on the equations or on the augmented matrix.

$$\begin{aligned} x_{1}+5 x_{2} &=7 \\-2 x_{1}-7 x_{2} &=-5 \end{aligned}$$

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