Q40. CRITICAL THINKING Determine valu... [FREE SOLUTION]

Chapter 4: Q40. (page 166)

CRITICAL THINKING Determine values for each variable if $d = 1$ , $e = 4 d$ , $z + d = e$ , $f = \frac{x}{5}$ , $a y = 1.5$ , $x = \frac{d}{2}$ and $y = x + \frac{x}{2}$ .
$a [\begin{matrix} x & y & z \\ d & e & f \end{matrix}] = [\begin{matrix} a x & a y & a z \\ a d & a e & a f \end{matrix}]$

Short Answer

Expert verified

The values for each variable $a, d, e, f, x, y and z$ are 2, 1, 4, $\frac{1}{10}$ , $\frac{1}{2}$ , $\frac{3}{4}$ , and 3 respectively.

Step by step solution

- Solve for variables e and x

Substitute 1 for d into the equations $e = 4 d$ and $x = \frac{d}{2}$ and solve for e and x.

$\begin{matrix} e = 4 (1) \\ = 4 \end{matrix}$

And,

$\begin{matrix} x = \frac{(1)}{2} \\ = \frac{1}{2} \end{matrix}$

- Solve for variables f and y

Substitute $\frac{1}{2}$ for x into the equations $f = \frac{x}{5}$ and $y = x + \frac{x}{2}$ and solve for f and y.

$\begin{matrix} f = \frac{(\frac{1}{2})}{5} \\ = \frac{1}{10} \end{matrix}$

And,

$\begin{matrix} y = \frac{1}{2} + \frac{(\frac{1}{2})}{2} \\ = \frac{1}{2} + \frac{1}{4} \\ = \frac{3}{4} \end{matrix}$

- Solve for variable z and a

Substitute 1 for d and 4 for e into the equation $z + d = e$ and solve for z.

$\begin{matrix} z + (1) = (4) \\ z + 1 鈭� 1 = 4 鈭� 1 \\ z = 3 \end{matrix}$

Now substitute $\frac{3}{4}$ for $y$ into the equation $a y = 1.5$ and solve for a.

$\begin{matrix} a (\frac{3}{4}) = 1.5 \\ a = 1.5 脳 \frac{4}{3} \\ a = 2 \end{matrix}$

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CRITICAL THINKING Determine values for each variable if $d = 1$ , $e = 4 d$ , $z + d = e$ , $f = \frac{x}{5}$ , $a y = 1.5$ , $x = \frac{d}{2}$ and $y = x + \frac{x}{2}$ .
$a [\begin{matrix} x & y & z \\ d & e & f \end{matrix}] = [\begin{matrix} a x & a y & a z \\ a d & a e & a f \end{matrix}]$

Short Answer

Step by step solution

- Solve for variables e and x

- Solve for variables f and y

- Solve for variable z and a

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CRITICAL THINKING Determine values for each variable if d=1, e=4d, z+d=e, f=x5, ay=1.5, x=d2and y=x+x2.axyzdef=axayazadaeaf

Short Answer

Step by step solution

- Solve for variables e and x

- Solve for variables f and y

- Solve for variable z and a

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Geometry

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

CRITICAL THINKING Determine values for each variable if $d = 1$ , $e = 4 d$ , $z + d = e$ , $f = \frac{x}{5}$ , $a y = 1.5$ , $x = \frac{d}{2}$ and $y = x + \frac{x}{2}$ .
$a [\begin{matrix} x & y & z \\ d & e & f \end{matrix}] = [\begin{matrix} a x & a y & a z \\ a d & a e & a f \end{matrix}]$