Answer:
Width 130 ft and
Length 320 ft
Step-by-step explanation:
We are given;
- Length of the rectangular base is 70 ft less than three times the width;
- Perimeter of the rectangular base is 900 ft
We are required to determine the dimensions of the rectangular base;
Assuming the width of the rectangular base is x ft
Then length will be (3x - 70) ft
But;
Perimeter = 2L + 2W
Thus;
900 ft = 2(3x-70) + 2(x)
900 ft = 6x -140 +2x
1040 = 8x
x = 130
Thus;
Width = 130 ft
Length = 3x -70 = 320 ft
Hence the dimensions of the rectangular base are width 130 ft and length 320 ft
Answers – Daniel is 13 years old; Ben is 33 years old
WORKINGS
Let Ben’s age be ‘x’
Let Daniel’s age be ‘y’
Given: Ben is 20 years older than Daniel
x = y + 20 ….. (Equation I)
Given: Three years ago, Ben was 3 times as old as Daniel.
x – 3 = 3(y – 3) ….. (Equation II)
Substitute ‘y + 20’ for x in Equation II
x – 3 = 3(y – 3)
(y + 20) – 3 = 3(y – 3)
y + 20 – 3 = 3y – 9
y + 17 = 3y – 9
3y – y = 17 + 9
2y = 26
y = 13
Daniel is 13 years old ….. (Answer I)
Substitute 13 for the value of ‘y’ in equation I
x = y +20
x = 13 + 20
x = 33
Ben is 33 years old ….. (Answer II)
The absolute value inequality is |x - 6| < 12 and the complete points are Midpoint = 6 and Distance = 12
<h3>How to complete the inequality?</h3>
The inequality expression is given as
-6 < x < 18
The distance is calculated as:
Distance = |18 -(-6)|/2
Evaluate the difference
Distance = 12
The midpoint is calculated as:
Midpoint = 0.5 * (18 - 6)
Evaluate
Midpoint = 6
The absolute value inequality is represented as
|x - Midpoint| < Distance
So, we have
|x - 6| < 12
Hence, the absolute value inequality is |x - 6| < 12 and the complete points are Midpoint = 6 and Distance = 12
Read more about absolute value inequality at
brainly.com/question/13282457
#SPJ1
