Justify each step of the solution by stating the property that was used to get to each step.

Ralph bought a computer monitor with an area of 384 square inches. The length of the monitor is six times the quantity of five l

Alenkasestr [34]

Draw the picture and label the
width = w
The length of the monitor is six times the quantity of five less than half its width:
length = 6(w/2-5)
length = 3w-30
Area = (length)*(width)
384=(3w-30)*(w)
384=3w^2-30w
Answer:
the dimensions of the monitor in terms of its width is:
384=3w^2-30w

7 0

2 years ago

Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation?

Nady [450]

For this case we have the following polynomial:
$x ^ 2 = 12x - 15
$
The first thing to do is to place the variables on the same side of the equation.
We have then:
$x ^ 2 - 12x = -15
$
We complete the square by adding the term (b / 2) ^ 2 on both sides of the equation.
We have then:
$x ^ 2 - 12x + (-12/2) ^ 2 = -15 + (-12/2) ^ 2
$
Rewriting we have:
$x ^ 2 - 12x + (-6) ^ 2 = -15 + (-6) ^ 2

x ^ 2 - 12x + 36 = -15 + 36
 
(x-6) ^ 2 = 21$
$x-6 =+/- \sqrt{21}$
Therefore, the solutions are:
$x = 6 - \sqrt{21}$
$x = 6 + \sqrt{21}$
Answer:
the solution set of the equation is:
$x = 6 - \sqrt{21}$
$x = 6 + \sqrt{21}$

3 0

2 years ago

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The commission earned on the sale of a car can be represented by the equation c(p)=250+0.02p where c represents the commission a

ch4aika [34]

Answer:

1) His total commission is $1,234.3

2) The purchase of the car is $24,790.

Step-by-step explanation:

1) 21640*0.02= 432.8+ 250= 682.8

15075*0.02= 301.5+ 250= 551.5

682.8+ 551.5= 1,234.3

2) 745.8- 250= 495.8/ 0.02= 24,790

6 0

2 years ago

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A collection of 108 coins containing only quarters and nickels is worth $21. A table titled Coin Collection showing Number of Co

harina [27]

Answer:

q = 108-n

Step-by-step explanation:

Given: 108 coins containing only quarters and nickels

q = 108-n

since total number of coins is 108, and n= number of nickels

If you want to know how many of each kind of coin, read on:

First solve the number of quarters and nickels.

If all 108 coins are quarters, the value is 108*0.25 = $27

Since this value exceed the actual by 27-21 = $6,

we replace a number of quarters by nickels.

Each replacement will reduce the value by 25 - 5 = 20 cents = 0.2 dollars.

So it will take 6/0.2 = 30 replacements.

Therefore there are 108-35 = 78 quarters and 30 nickels.

8 0

2 years ago

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22 customers are eating dinner at an Italian restaurant. Of the 22 customers, 18 order pizza, 10 order a salad, and 8 order pizz

Ne4ueva [31]

Answer:

Step-by-step explanation:

P(A) = 18/22

P(B) = 10/22

P(A and B) = 8/22

P(A or B) = 18/22 * 10/22 = 0.37

4 0

2 years ago