Answer:
Step-by-step explanation:
From the graph,
The initial red incline is a straight line passing through the origin.
So, a straight line passing through the origin is of the form:
Where, 'm' is the slope.
Now, the slope of a given as the change in y value to change in x value.
Consider the two end points of the red line (0, 0) and (4, 6).
The slope with two points 
on the line is given as:
Plug in 
. Therefore, slope is:
Hence, the equation of the initial red incline is:
<h3>
Answer: -15 and 2</h3>
You find this through trial and error.
A much more efficient way is to solve x^2-13x-30 = 0 using the quadratic formula. You'll find the two solutions to be x = 15 and x = -2
Going from those solutions, we get x-15 = 0 and x+2 = 0 which then turn into (x-15)(x+2) = 0 through the zero product property.
Answer:
Value of stamp collection = (45b + 43) cents
Step-by-step explanation:
What we have here is as follows;
if there are x 3-cent stamps, then there are 4x 10-cent stamps
So the number of 2-cent stamps is 1 less than 3 cent stamps and that will be x-1 2 cent stamps
Number of 2 cents stamps = b
This means that x-1 = b
Thus, x = b + 1
So the value of the stamp collection is as follows;
x 3 cents stamps = 3(b+ 1) = 3b + 3 cents
4x 10 cents stamps = 10(4(b + 1)) = 10(4b + 4) = 40b + 40
value of the 2 cents stamp = 2b cents
Total value is thus;
2b + 40b + 40 + 3b + 3 = (45b + 43) cents
<h3>Given</h3>
A regular polygon with area 500 ft² and apothem 10 ft
Cost of fence is $7.95 per ft
<h3>Find</h3>
Part III The cost of fence around an area scaled to 60 times the size
<h3>Solution</h3>
You don't want to think too much about this, because if you do, you find the regular polygon has 3.087 sides. The closest approximation, an equilateral triangle, will have an area of 519.6 ft² for an apothem of 10 ft.
For similar shapes of scale factor "s", the larger shape will have an area of s² times that of the smaller one. Here, it appears the area scale factor s² is 60, so the linear scale factor is
... s² = 60
... s = √60 ≈ 7.7460
The perimeter fence of the 500 ft² area is presumed to be 100 ft long (twice the area of the polygon divided by the apothem—found in Part I), so the perimeter fence of the industrial farm is ...
... (100 ft)×7.7460 = 774.60 ft
and the cost to construct it is
... ($7.95/ft)×(774.60 ft) ≈ $6158
Given:
6 out of 15 customers order a chicken sandwich
270 customers
This is a problem of ratio and proportion:
a/b = c/d where ad = bc
6/15 = x/270
6 * 270 = 15x
1,620 = 15x
1620 / 15 = x
108 = x
The restaurant should predict to serve 108 chicken sandwich to the 270 people.
