Answer:
a. x = 12
b. x = 4
Step-by-step explanation:
a. RECTANGLE
ABCD is a rectangle, AC and BD are its diagonals.
Diagonals of a rectangle are congruent.
Therefore,
AC = BD
10x + 8 = 9x + 20
10x - 9x = 20 - 8
x = 12
b. RHOMBUS
Diagonal of a rectangle bisect opposite angles.
Therefore,
(5x + 3)° = (2x + 15)°
5x + 3 = 2x + 15
5x - 2x = 15 - 3
3x = 12
x = 12/3
x = 4
9514 1404 393
Answer:
- sin(θ) = (9√97)/97
- cos(θ) = (-4√97)/97
- csc(θ) = (√97)/9
- sec(θ) = (-√97)/4
- cot(θ) = -4/9
Step-by-step explanation:
The angle is in the 2nd quadrant, where the sine is positive and the cosine is negative.
tan^2(θ) +1 = sec^2(θ) = (-9/4)^2 +1 = 97/16 ⇒ sec = -(1/4)√97
cot(θ) = 1/tan(θ) = -4/9
csc^2(θ) = cot^2(θ) +1 = (-4/9)^2 +1 = 97/81 ⇒ csc = (1/9)√97
sin(θ) = 1/csc(θ) = (9√97)/97
cos(θ) = 1/sec(θ) = (-4√97)/97
Answer:
x = 12.6 pennies
Step-by-step explanation:
total number of coins = 1 + 2+ 4 + 3 = 10 coins
P(penny) =![\dfrac{1}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B10%7D)
P(nickels) =![\dfrac{2}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B10%7D)
P(dimes) =![\dfrac{4}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7B4%7D%7B10%7D)
P(quarters) =![\dfrac{3}{10}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%7D%7B10%7D)
hence average value of the coin
x = Penny x P(Penny) + nickel x P(nickel) + dimes x P(dimes) + quarters x P(quarters)
nickels = 5 pennies dimes = 10 ; and quarters = 25 pennies
![x = 1 \times \dfrac{1}{10} + 5\times \dfrac{2}{10} +10\times \dfrac{4}{10} + 25\times \dfrac{3}{10}](https://tex.z-dn.net/?f=x%20%3D%201%20%5Ctimes%20%5Cdfrac%7B1%7D%7B10%7D%20%2B%205%5Ctimes%20%5Cdfrac%7B2%7D%7B10%7D%20%2B10%5Ctimes%20%5Cdfrac%7B4%7D%7B10%7D%20%2B%20%2025%5Ctimes%20%5Cdfrac%7B3%7D%7B10%7D)
x = 0.1 + 1 + 4 + 7.5
x = 12.6 pennies
hence, the average pennies for the first draw is equal to x = 12.6 pennies
What are the following ???
Jkldmjslsjhuu hi phhenehkuuehqkheojhejekekebheeknebejejebrjbiemebekeneoeke