Complete the square to change the equation $y = 2 x ^ { 2 } - 4 x + 5$ into graphing form. Identify the vertex of the parabola and sketch the graph.

Apply the Gram-Schmidt orthonormalization process to transform the given basis for $R^n$ into an orthonormal basis. Use the vectors in the order in which they are given.

$$B = \left\{(1, 0, 0), (1, 1, 1), (1, 1, −1)\right\}$$

Show that each system has infinitely many solutions.

$$\left\{ \begin{array} { l } { y = 2 x - 4 } \\ { 2 x - y - 4 = 0 } \end{array} \right.$$

A right triangle is formed by the origin and the x- and y-intercepts of the line $11 x - 4 y = 22 .$ Find the area of the triangle.

What is 24xy+26xy

Let

$$f ( x ) = 2 \sqrt { 3 - x } \text { and } g ( x ) = 4 \sqrt [ 3 ] { 3 - x }.$$

Find

$$( f g ) ( x ) \text { and } \left( \frac { f } { g } \right) ( x )$$

and state the domain of each. Then evaluate

$$( f g ) ( 2 ) \text { and } \left( \frac { f } { g } \right) ( 2 ).$$

Derman has a different way to divide fractions. He explains, "To divide fractions, I get a common denominator, just as when I add them. Then, I just divide the numerators.

$$\dfrac{\frac{5}{6}}{\frac{7}{8}}=\dfrac{5}{6}\div\dfrac{7}{8}$$

I get a common denominator for 6 and 8. It's 24. So

$$\dfrac{\frac{5}{6}}{\frac{7}{8}}=\dfrac{\frac{20}{24}}{\frac{21}{24}}=\dfrac{20}{21}$$

I never use another method." Does Derman's method always work? Explain.

The analysis of a propeller that operates in water at $70^\circ F$ shows that the pressure at the tips of the propeller drops to 0.1 psia at high speeds. Determine if there is a danger of cavitation for this propeller.

The first play of a football game resulted in a loss of 12½ yards. Then a penalty resulted in another loss of 5 yards. What is the total loss or gain?

Use each NOW-NEXT rule to produce a table of values that illustrates the pattern of change from the start value through 5 stages of change. a. NEXT = NOW + 2.5, starting at 3. b. NEXT = $\frac{1}{2}$ NOW - 50, starting at 450.

Write the word or phrase from the list that completes the sentence correctly. A person who has difficulty distinguishing colors has _____. aggressive driving, carbon monoxide, central vision, chronic illness, color blindness, depth perception, disability, emotion, field of vision, fringe vision, glare recovery time, glare resistance, night blindness, peripheral vision, permanent disability, road rage, speed smear, temporary disability, tunnel vision, visual acuity.

Compute the area of a triangle (according to the formula A = ½ba) if its base and altitude are measured to equal 42.07 cm and 16.0 cm, respectively. Justify the number of significant figures in the answer.

The stage when your body adapts to the continued presence of a stressor is the a. alarm stage. b. resistance stage. c. exhaustion stage. d. adaptation stage.

Analyzing Processes Glass can conduct some energy. Double-pane windows consist of two plates of glass separated by a small layer of insulating air. Explain why a double-pane window prevents more energy from escaping from a house than a single-pane window does.