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Lesson 2.5 Solving Equations with Absolute Value
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Terms in this set (27)
{-6, 4}
| w + 1 | = 5
{2, 4}
| c - 3 | = 1
{-3, -1}
| n + 2 | = 1
{-10, -2}
| t + 6 | = 4
{0, 4}
| w - 2 | = 2
{1, 9}
| k - 5 | = 4
{-1, 1}
| x | = 1
{-5, -1}
| x + 3 | = 2
{3, 5}
| x - 4 | = 1
{4, -4}
| x | = 4
{10, 0}
2| x - 5 | = 10
{6, -12}
2| x + 3 | = 18
{5, -3}
2| x - 1 | = 8
{5, -1}
3| x - 2 | - 5 = 4
{0, 4}
3| x - 2 | - 1 = 5
{1, 15}
| x - 8 | + 3 = 10
{0, 16}
| x - 8 | + 2 = 10
{-9, 19}
| x - 5 | - 4 = 10
no solution
| x + 8 | = -2
no solution
| x - 9 | = -7
no solution
| x | = -3
| x - 1 | = 4
Write the absolute value equation that has a solution of {5, -3}
| x - 8 | = 7
Write the absolute value equation that has a solution of {1, 15}
| x - 12 | = 4
Write the absolute value equation that has a solution of {8, 16}
| x + 3 | = 2
Write the absolute value equation that has a solution of {-5, -1}
| x + 8 | = 2
Write the absolute value equation that has a solution of {-10, -6}
| x - 1 | = 6
Write the absolute value equation that has a solution of {-5, 7}
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Verified questions
statistics
In a laboratory test of a new engine design, the emissions rate (in mg/s of oxides of nitrogen, $\mathrm{NO}_{x})$ was measured as a function of engine speed (in rpm), engine torque $\text { (in }\mathrm{ft} \cdot 1 \mathrm{b}),$ and total horsepower. (From “In-Use Emissions from Heavy-Duty Diesel Vehicles,” J. Yanowitz, Ph.D. thesis, Colorado School of Mines, 2001.) MINITAB output is presented for the following three models: $$ \begin{array}{l} \mathrm{NO}_{x}=\beta_{0}+\beta_{1} \text { Speed }+\beta_{2} \text { Torque }+\varepsilon \\ \mathrm{NO}_{x}=\beta_{0}+\beta_{1} \text { Speed }+\beta_{2} \mathrm{HP}+\varepsilon \\ \mathrm{NO}_{x}=\beta_{0}+\beta_{1} \text { Speed }+\beta_{2} \text { Torque }+\beta_{3} \mathrm{HP}+\varepsilon \end{array} $$ $$ \begin{matrix} \text{The regression equation is}\\ \text{NOx = −321 + 0.378 Speed − 0.160 Torque}\\ \text{Predictor} & \text{Coef} & \text{SE Coef} & \text{T} & \text{P}\\ \text{Constant} & \text{−320.59} & \text{98.14 } & \text{−3.27} & \text{0.003}\\ \text{Speed} & \text{0.37820} & \text{0.06861} & \text{5.51} & \text{0.000}\\ \text{Torque} & \text{−0.16047} & \text{0.06082} & \text{−2.64} & \text{0.013}\\ \text{S = 67.13} & \text{R−Sq = 51.6\\%} & \text{R−Sq(adj) = 48.3\\%}\\ \text{The regression equation is}\\ \text{NOx = −380 + 0.416 Speed − 0.520 HP}\\ \text{Predictor} & \text{Coef} & \text{SE Coef} & \text{T} & \text{P}\\ \text{Constant} & \text{−380.1} & \text{104.8} & \text{3.63} & \text{0.001}\\ \text{Speed} & \text{0.41641} & \text{0.07510} & \text{5.54} & \text{0.000}\\ \text{HP} & \text{−0.5198} & \text{0.1980} & \text{−2.63} & \text{0.014}\\ \text{S = 67.19} & \text{R−Sq = 51.5\\%} & \text{R−Sq(adj) = 48.2\\%}\\ \text{The regression equation is}\\ \text{NOx = −302 + 0.366 Speed − 0.211 Torque + 0.16 HP}\\ \text{Predictor} & \text{Coef} & \text{SE Coef} & \text{T} & \text{P}\\ \text{Constant} & \text{−301.8} & \text{347.3} & \text{−0.87} & \text{0.392}\\ \text{Speed} & \text{0.3660} & \text{0.2257} & \text{1.62} & \text{0.116}\\ \text{Torque} & \text{−0.2106} & \text{0.8884} & \text{−0.24} & \text{0.814}\\ \text{HP} & \text{0.164} & \text{2.889} & \text{0.06} & \text{0.955}\\ \text{S = 68.31} & \text{R−Sq = 51.6\\%} & \text{R−Sq(adj) = 46.4\\%}\\ \end{matrix} $$ Of the variables Speed, Torque, and HP, which two are most nearly collinear? How can you tell?
calculus
Use Version 2 of the Chain Rule to calculate the derivatives of the following functions. $$ y = \csc \left( t ^ { 2 } + t \right) $$
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If the tomato taster doesn't know how the tomatoes have been treated, is the experiment single or double-blind? How might the blinding be improved further?
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Determine $|z|$. $==-8$
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