"The sum of the number 'n' and 31" . . . . . (n + 31)
"17 times the sum" . . . . . 17(n + 31)
The equation . . . . . 17(n + 31) = 357
Answer:
√5.
Step-by-step explanation:
Tan A = 1/2 means that the right triangle containing angle A has legs of length 1 and 2 units. So the hypotenuse = √(1^2 + 2^2) = √5 (using the Pythagoras theorem). The side opposite to < A = 1 unit and the adjacent side = 2 (as tan = opposite / adjacent).
so cos A = adjacent / hypotenuse = 2/√5.
and sin A = opposite / hypotenuse = 1 / √5
cos A / sin A = 2/√5 / 1/ √5 = 2.
sin A / (1 + cos A) = 1/√5 (1 + 2/ √5)
= 1 / √5 ( (√5 + 2) /√5)
= 1 / (√5 + 2)
So the answer is:
2 + 1 /(√5 + 2).
We can simplify it further by multiplying top and bottom of the fraction by the complement of √5 + 2 which is √5 - 2.
2 + 1 / (√5 + 2)
= 2(√5 + 2) + 1 / (√5 + 2 )
= { 2(√5 + 2) + 1 } / (√5 + 2)
Multiplying this by √5 - 2 / √5 - 2 we get:
(2(5 - 4) + √5 - 2) / (5 -4)
= 2 + √5 - 2 / 1
= √5.
Well using elimination is easy because they basically did it for you.
4x-5y=-6
2x+5y=12
The postive 5y and negative 5y cancel out because -5y plus 5y is zero.
so you are left with
4x=-6
2x=12
Add these together
6x=18
divide both sides by 6 and Solve to find your x
x=3
Now we have to eliminate x to find y.
we multiply the second equation by -2 so it can cancel out so
(2x+5y=12)-2
-4x-10y=24
Add the equations together
4x-5y=-6
-4x-10y=24
You are left with -15y = 30
Solve for y
y = -2
So your final answer for the elimination would be
(3,-2)
Isolate the x. First, multiply 2 to both sides
-x/2(2) < 4(2)
-x < 4(2)
-x < 8
Isolate the x. Divide - 1 to both sides (because you are dividing a negative number, flip the sign).
-x/ -1 < 8/-1
x > -8 is your answer
hope this helps
Subtract 9/4 from both sides
3/4x=6 3/4
Multiply them by 4/3
X=9
