This question is referred to two similar triangles.
One triangle has sides x and x - 2.
The other triangle has the respective sides x + x + 5 and x - 2 + x + 1
Then you can state a proportionality relation between the sides>
[x + x + 5] / x = [x - 2 + x + 1] / [x - 2]
=> [2x + 5] / x = [2x - 1] / [x - 2]
=> (2x + 5)(x - 2) = (2x - 1)x
=> 2x^2 - 4x + 5x - 10 = 2x^2 - x
=> x - 10 = - x
=> 2x = 10
=> x = 10 / 2
=> x = 5
Answer: x = 5
We can assume that the shape is a rectangular prism by the given dimensions
Volume of a rectangular prism
Volume = Area of Base × Height of prism
= Length × Width × Height of prism
Substitute!
168 = L × 7 × 3
168 = L × 21
Divide 21 on either sides to isolate L

=

21 and 21 cancels out
8 = L
L = 8 yd
Equation of a tangent line of a curve is:
y- y0 = f´ (x0) (x - x0 ). In this case: x0=1, y0=1
f´(x)=

(Derivation)
f´(x0)=

y - 1 = 1/2 ( x - 1 )
y - 1 = 1/2 x - 1/2
y = 1/2 x - 1/2 + 1
y =
to get the equation of any straight line we only need two points off of it, hmmm let's use P and Q here and then let's set the equation in standard form, that is
standard form for a linear equation means
• all coefficients must be integers, no fractions
• only the constant on the right-hand-side
• all variables on the left-hand-side, sorted
• "x" must not have a negative coefficient


Answer:
Both answers will give an area of 2400 ft2
but with x=60 we have lawn dimensions -60 ft by -40 ft so this is out
x = 10 ft width for the sidewalk
Check: New lawn dimensions
(80-2x)(60-2x) = 60(40) = 2400 ft^2
Step-by-step explanation:
Draw a diagram:
We have a rectangle inside a rectangle.
The larger outside rectangle is the original lawn: 80ft by 60 ft with area 4800 ft2
The smaller inside rectangle is (80-2x)by(60-2x) where x is width of the new sidewalk.
Area of new lawn is 2400 ft^2
(80-2x)(60-2x) = 2400
4800 - 160x - 120x + 4x2 = 2400
4x2 - 280x + 2400 = 0
Factor out a 4
x2 - 70x + 600 = 0
(x-60)(x-10) = 0
x = 60 ft or x = 10 ft