Work each problem. Let \(A=\begin{bmatrix}1 & 0 & 0\\0 & 0& -1 \\0 & 1 & -1\end{bmatrix}\). Show that \(A^{3} {i}_{3}\), and use this result to find the inverse of A.

Find each unknown for problem. Check your work. \(1000−n=258\)

Write a word problem or draw a diagram that illustrates the multiplication expression \(\frac{3}{4}\cdot\frac{1}{5} .\)

Find each unknown for problem. Check your work. \(Q−40=25\)

Using a graph to find the intersection of two curves can be challenging when the point of intersection is not on gridlines or ends up off the graph. Therefore, it helps to know another way to find the intersection without using a graph. a. Name the algebraic methods you already know to solve linear systems. b. Use one of the methods you listed in part (a) to solve for the intersection of \(\displaystyle{y}={x}^{{2}}−{3}{x}−{10}\) and \(y=−2x+2\). Carefully record your steps. Be sure to collaborate with your teammates and check your results along the way. Keep your work for this problem in a safe place. You will need it later in this lesson.

Work each problem. Write \(\displaystyle{3}\sqrt{64}\) using exponents and evaluate.

Find each unknown for problem. Check your work. \(1000−m=4081\)

Find each unknown for problem. Check your work. \(3000−a=10963000−a=1096\)

Find each unknown for problem. Check your work. \(9m=549m=54\)

Work each problem. Round to the nearest tenth of a degree, if necessary. A record low temperature of \(−89.4^{\circ}C\) was recorded at the Soviet Antarctica Station of Vostok on July 21, 1983. Find the corresponding Fahrenheit temperature.

Find each unknown for problem. Check your Work. \(6m=306\)

Using a graph to find the intersection of two curves can be challenging when the point of intersection is not on gridlines or ends up off the graph. Therefore, it helps to know another way to find the intersection without using a graph.

a. Name the algebraic methods you already know to solve linear systems.

b. Use one of the methods you listed in part

(a) to solve for the intersection of \(\displaystyle{y}={x}^{{2}}−{3}{x}−{10}\) and \(y=−2x+2\). Carefully record your steps. Be sure to collaborate with your teammates and check your results along the way. Keep your work for this problem in a safe place. You will need it later in this lesson.

The problem is called self-answering problems because the answers are embedded in the question. For example, how many ways can you arrange the letters in the word “six”? The answer is six. At time \(t=0\), water begins pouring into an empty sink so that the volume of water is changing at a rate \(V′(t)=\cos t.\) For time \(t=k\), where \(0\leq k\leq\frac{\pi}{2}\) determine the amount of water in the sink.