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.

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

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

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

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Geometry

Mechanics Maths

Calculus

Logic and Functions

Study anywhere. Anytime. Across all devices.

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

Decision Maths

Probability and Statistics

Geometry

Mechanics Maths

Calculus

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 $y = x + \frac{x}{2}$ .
$a [\begin{matrix} x & y & z \\ d & e & f \end{matrix}] = [\begin{matrix} a x & a y & a z \\ a d & a e & a f \end{matrix}]$