Step-by-step explanation:
x = number of multiple choice questions
y = number of short response questions
x + y = 15
5x + 10y = 100
=>
x + 2y = 20
let's subtract the first from the second equation :
x + 2y = 20
- x + y = 15
--------------------
0 y = 5
x + y = 15
x + 5 = 15
x = 10
to graph you need to consider both equations as linear functions. and you need to transform them into e.g. a slope intercept form : y = ax + b
a is the slope, b is the y- intercept.
x + y = 15
transforms to
y = -x + 15
this line goes e.g. through the points (0, 15) and (1, 14).
and
x + 2y = 20
transforms to
2y = -x + 20
y = -x/2 + 10
this line goes e.g through (0, 10) and (2, 9).
the crossing point of both lines is the solution and should therefore be the point (10, 5) as calculated above.
37.68m this is my best guess sorry if it's wrong :)
First month's profit of the company = $2,400.
After the first month, the profit is modeled by the function
J(t) = 2.5t + 1,250, t is the number of months after the first month the shop opened.
Now, P(t) describes the total profit earned by the company.
So, P(t) = (Profit earned from first month) + (Profit earned from remaining 11 months of the year)
= 2400 + (2.5t + 1250)
<u><em>= 2.5t + 3650</em></u>
Hence, total profit earned for the year = 2.5t + 3650.
Use Pythagorean Theorem:
a² + b² = c²
"a" is one side of the right triangle.
Its length is: radius of larger circle minus radius of smaller circle: (11 - 3 = 8)
The distance between the center of the circles creates the hypotenuse (17)
8² + b² = 17²
b² = 225
b = 15
Answer: the length of the common external tangent is 15.
Answer: The answer is 1/3
