Decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem. If false, provide an example, illustration, or brief explanation of why the statement is false. The family of orthogonal trajectories for a family of parallel lines is another family of parallel lines.

plot the intercepts and sketch a graph of the plane. 5x - y - 2z = 10

In a 45°-45°-90° triangle, a leg is 15 inches long. Find the exact length of the hypotenuse.

Determine whether the given value is a solution of the equation. d - 4 = 19; d = 15___________

determine whether each ordered triple is a solution of the system of equations.{ 4x + y - z = 0 , -8x - 6y + z = -7/4 , 3x - y = -9/4 . (-3/2, 5/4, -5/4)

Find the point P on the curve y=$x^2$ that is closet to the point (18, 0). What is the least distance between P and (18, 0)?

Solve each equation for matrix X.

$$X - \left[ \begin{array} { r r } { 0 } & { 5 } \\ { 1 } & { - 2 } \end{array} \right] = 3 \left[ \begin{array} { r r } { 2 } & { - 3 } \\ { 3 } & { 1 } \end{array} \right]$$

Find the zeros of the function by rewriting the function in intercept form.

$$y=x^2-8x+16$$

Find each sum or difference.

$$- 6 \frac { 1 } { 3 } - 6 \frac { 1 } { 3 }$$

State how Watson and Crick were able to build a structural model of DNA.

Fill in the blank with an appropriate word, phrase, or symbol(s). When graphing an inequality in two variables, if the inequality contains either < or > use a(n) _ line.

What kind of clouds would you expect to form at the leading edge of a cold front, where warm air is gradually being pushed above cold air?

A hat contains 100 coins, where at least 99 are fair, but there may be one that is doubleheaded (always landing Heads); if there is no such coin, then all 100 are fair. Let $D$ be the event that there is such a coin, and suppose that $P(D) = 1/2$. A coin is chosen uniformly at random. The chosen coin is flipped 7 times, and it lands Heads all 7 times. (a) Given this information, what is the probability that one of the coins is doubleheaded? (b) Given this information, what is the probability that the chosen coin is doubleheaded?

Let f(x) = -3x + 1 and g(x) = 10x - 4. Find the indicated value. f(4) + g(-3)