Answer:
Step-by-step explanation:
A 45 degree angle in a right triangle produces 2 equal sides. In this case z and the perpendicular line are equal. So that's were we'll start. Then you move on to the 60 degree angle to get x and y.
Finding z
z^2 + z^2 = (24√2) Combine the left
2z^2 = 24^2 * 2 Divide both sides by 2
2z^2/2 = 24^2/2
z^2 = 24^2 Take the square root of both sides
√z^2 = √24^2
z = 24
Finding x and y
The perpendicular = 24. Because it is a 60 degree angle that's given, we can do this without a calculator.
Tan 60 = opposite over adjacent
sqrt(3) = Perpendicular / z Multiply both sides by z
z*sqrt(3) = perpendicular
The above calculation tells us the perpendicular is 24
z*sqrt(3) = 24 Divide by sqrt 3
z = 24/√3
z = 24/1.73
z = 8√3
Finding x
Use Pythagoras to determine x
Perpendicular^2 + (8√3)^2 = x^2
24^2 + 8^2*3 = x^2
576 + 192 = x^2
768 = x^2
√x^2 = √768
x = 27.71
3n - 1
When n = 1,
3n - 1 = 3*1 - 1 = 3 -1 = 2
When n = 2,
3n - 1 = 3*2 - 1 = 6 -1 = 5
When n = 3,
3n - 1 = 3*3 - 1 = 9 -1 = 8
Hence, the first three terms are 2, 5 and 8.
Answer:
544
Step-by-step explanation:
The ratios of cartons are ...
B : P = 2 : 1
S : L = 2 : 1
L : B = 2 : 1
Combining these into a single set of ratios, we have ...
S : L : B : P = 8 : 4 : 2 : 1
Then the proportion of the order that is strawberry is ...
8/(8+4+2+1) = 8/15
and the number of strawberry cartons is ...
(8/15)·1020 = 544
The store ordered 544 cartons of strawberry yogurt.
Answer:
500
Step-by-step explanation:
The problem statement tells you ...
300 = 0.60×voters
Dividing by the coefficient of the variable gives ...
300/0.60 = voters = 500
500 students voted in the election.
<u>1 is a rational number</u> because 1 can go into 1 when dividing. <u>Irrational numbers are mostly decimals. </u>
