Assume that the length of the rectangle is "l" and that the width is "w".
We are given that:
(1) The length is one more than twice the base. This means that:
l = 2w + 1 .......> equation I
(2) The perimeter is 92 cm. This means that:
92 = 2(l+w) ...........> equation II
Substitute with equation I in equation II to get the width as follows:
92 = 2(l+w)
92 = 2(2w+1+w)
92/2 = 3w + 1
46 = 3w + 1
3w = 46-1 = 45
w = 45/3
w = 15
Substitute with w in equation I to get the length as follows:
l = 2w + 1
l = 2(15) + 1
l = 30 + 1 = 31
Based on the above calculations:
length of base = 31 cm
width of base = 15 cm
The lowest percentage increase in the cost of dye that would make the scarves unprofitable is 42%
<h3>How to calculate the percentage?</h3>
(Price- Unit Cost)/Price= 20% or 0.2
Price- Unit Cost= 0.2 Price
0.8 Price = Unit Cost
Let Unit Cost be x
Price = x/0.8= 1.25x
Dye is 60% of unit costs= 0.6x
Cost of remaining material= 1 - 0.6x = 0.4x
Unit Cost= Cost of Dye+ Cost of remaining material
So, in order to become unprofitable, Unit Cost must be 1.25x
Therefore
1.25x= Maximum cost of dye+ 0.4x
Maximum Cost of Dye = (1.25-0.4)x = 0.85x
Percentage change in cost of dye= {(0.85x-0.6x)/0.6x}*100= 41.66 or 42%
Therefore, theowest percentage increase in the cost of dye that would make the scarves unprofitable is 42%.
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Answer:
D
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form use the method of completing the square.
Given
f(x) = - 0.6x² + 4.2x + 240 ← factor out - 0.6 from the first 2 terms
= - 0.6(x² - 7x) + 240
To complete the square
add/ subtract ( half the coefficient of the x- term)² to x² - 7x
f(x) = - 0.6(x² + 2(- 3.5)x + 12.25 - 12.25 ) + 240
= - 0.6 (x - 3.5)² + 7.35 + 240
= - 0.6(x - 3.5)² + 247.35
with vertex = (3.5, 247.35 )
The maximum value is the y- coordinate of the vertex
Then
f(x) = - 0.6(x - 3.5)² + 247.35 has a maximum value of 247.35
The perimeter of a rectangle is 10x + 2 which is a polynomial function. Option C is the correct answer.
<h3>
What is a perimeter?</h3>
A perimeter is a closed path that outlines either a two-dimensional shape or a one-dimensional length.
Given that the length is 3x+2 and the width is 2x-1. The perimeter of a rectangle is given below.
A polynomial function is a function that involves only positive integer exponents of a variable in an equation.
Hence we can conclude that the perimeter of a rectangle is 10x + 2 which is a polynomial function. Option C is the correct answer.
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The expression that represents the surface area of the square based pyramid is 36 + 15 + 15 + 15 + 15
<h3 />
<h3>How to find the surface area of a square based pyramid?</h3>
The surface area of the pyramid is the sum of the area of the whole faces of the pyramid.
Therefore, the pyramid has 4 triangular faces and 1 square faces.
Therefore,
surface area of the pyramid = area of the square + 4(area of the triangle)
area of the square = 6² = 36
area of each triangular faces = 1 / 2 bh
where
Therefore,
area of each triangular faces = 1 / 2 × 6 × 5 = 30 / 2 = 15
Hence, the expression is as follows:
surface area of the pyramid = 36 + 15 + 15 + 15 + 15
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