Answer:
x = 29
Angle A = 46.4°
Angle B = 43.6°
Step-by-step explanation:
Since it is a right angle triangle, we can find x from pythagoras theorem;
x = √(20² + 21²)
x = √(400 + 441)
x = √841
x = 29
Using trigonometric ratios we can find angles A and B.
Opposite is 20
Adjacent is 21
Thus; opp/adj = tan B
20/21 = tan B
B = tan^(-1) 0.9524
B = 43.6°
Sum of angles in a triangle is 180°. Thus;
A = 180 - (90 + 43.6)
A = 46.4°
Answer:
250+23x=y
Step-by-step explanation:
x represents the amounts of jerseys the team buys. Once that amount is known they will multiply.
y is the amount of money spent, or the sum.
2^3 = 8
11/9 = 1.22
sqrt 5 = 2.24
sqrt 20 = 4.47
sqrt 11 = 3.32
least to greatest : 11/9, sqrt 5 , sqrt 11 , sqrt 20, 2^3
Answer:
12
Step-by-step explanation:
x = number of $1 bills
y = number of $5 bills
z = number of $10 bills
We know that:
x + y + z = 25 (total amount of bills)
x + 5y + 10z = 100 (total amount of money)
y = 4z (Given)
Substitute the third equation into the first one.
x + 4z + z = 25
x = 25 - 5z
Put this into the second equation.
(25 - 5z) + 5 (4z) + 10z = 100
Simplify and solve.
25 - 5z + 20z + 10z = 100
25z + 25 = 100
25z = 75
z = 3
Substitute this into y = 4z
y = 4 * 3
y = 12
So, there are 12 $5 bills.
So, 4/3 - 2i
4/3 - 2i = 12/13 + i8/13
multiply by the conjugate:
3 + 2i/3 + 2i
= 4(3 + 2i)/(3 - 2i) (3 + 2i)
(3 - 2i) (3 + 2i) = 13
(3 - 2i) (3 + 2i)
apply complex arithmetic rule: (a + bi) (a - bi) = a^2 + b^2
a = 3, b = - 2
= 3^2 + (- 2)^2
refine: = 13
= 4(3 + 2i)/13
distribute parentheses:
a(b + c) = ab + ac
a = 4, b = 3, c = 2i
= 4(3) + 4(2i)
Simplify:
4(3) + 4(2i)
12 + 8i
4(3) + 4(2i)
Multiply the numbers: 4(3) = 12
= 12 + 2(4i)
Multiply the numbers: 4(2) = 8
= 12 + 8i
12 + 8i
= 12 + 8i/13
Group the real par, and the imaginary part of the complex numbers:
Your answer is: 12/13 + 8i/13
Hope that helps!!!