Answer:
1. y = 12
x = 7.9
2. AB = 5
AC = 5√3
Step-by-step explanation:
1. If you call the straight up line of both triangles is z, then
(9 + 7)^2 = y^2 + z^2
=> z^2 = 256 - y^2
x^2 + 7^2 = z^2
=> z^2 = x^2 + 49
so 256 - y^2 = x^2 + 49
x^2 = 207 - y^2
for the left smaller triangle: 9^2 + x^2 = y^2
y^2 = x^2 + 81
Substitute:
y^2 = (207 - y^2) + 81
2y^2 = 288
y^2 = 144
y = 12
x^2 = 207 - y^2 = 207 - 144 = 63
x = 7.9
2. Sin(30) = AB/BC
=> AB = BC x sin(30) = 10 x 0.5 = 5
Cos(30) = AC/BC
=> AC = BC x cos(30) = 10 x √3/2 = 5√3
Answer:
$48 per unit
Step-by-step explanation:
Increasing the price by $5 reduces demand by 20 units, so the slope of the curve is -4 units per dollar. This lets us write a demand equation as ...
q = -4(p -50) +184
q = -4p + 384
q = 4(96 -p)
The revenue is the product of price and demand:
r = pq = 4p(96 -p)
This is the equation of a quadratic curve that opens downward and has zeros at p=0 and p=96. The vertex (maximum) will be halfway between the zeros, at ...
p = (0+96)/2 = 48
A price of $48 per unit will yield a maximum total revenue.
Answer:
1÷27
Step-by-step explanation:
the fraction bar just means to divide so 3/4 is 3÷4
Answer:
2
4
6
8
3
6
9
12
Step-by-step explanation:
domain is the x of ordered pair or the first number in ordered pair (number on x-axis)
range is the y of ordered pair or the second number in ordered pair (number on y-axis)
9514 1404 393
Answer:
Step-by-step explanation:
These "special" right triangles have side length ratios that it is useful to remember.
<u>45°-45°-90° triangle</u>
Sides have the ratios 1 : 1 : √2. That is, x is √2 times as long as the side length shown as 18.
x = 18√2
<u>30°-60°-90° triangle</u>
Shortest to longest, sides have the ratios ...
1 : √3 : 2
That is, y is √3 times the length of the side marked 18, and z is 2 times the length of the side marked 18.
y = 18√3
z = 2·18 = 36
