We can't eliminate as is so we have to change something up there in the equations to get either the x values the same number but opposite signs, or the y values the same number but opposite signs. I chose to change the y values to the same number but different signs. In the first equation y is -3y and in the second one, y is -8y. The LCM of both of those numbers is 24, so we will multiply the first equation by an 8 (8*3=24) and the second equation by 3 (3*8=24) but since they are both negative right now, one of those multiplications has to involve a negative because - * - = +. Set it up like this:
8(-10x - 3y = -18)
-3(-7x - 8y = 11)
Multiply both of those all the way through to get new equations:
-80x - 24y = -144
21x +24y = -33
Now the y's cancel each other out leaving only the x's:
-59x = -177 and x = 3. Now plug that 3 into either one of the original equations to find the y value. Either equation will work; you'll get the same answer using either one. Promise. -7(3) - 8y = 11 gives a y value of -4. so your solution is (3, -4) or B above.
Answer:
approx. 3 hours
Step-by-step explanation:
14 newspapers in 20 minutes means he can deliver 42 newspapers an hour.
60/42 = 1.4285 newspapers per minute
131 x 1.4285 = 187.1335 minutes = 3.1188 hours
Answer:
A. Total number of liters = 1.25 liters
B. Milk = 0.25 liters
Step-by-step explanation:
Let
x = total number of liters ( milk + water )
Milk = 20% of x
= 0.2x
Water = 1 liter
Total number of liters = milk + water
x = 0.2x + 1
x - 0.2x = 1
0.8x = 1
Divide both sides by 0.8
x = 1 / 0.8
= 1.25
x = 1.25 liters
Total number of liters = 1.25 liters
B.
Liters of milk in the bottle = Total number of liters - liters of water
= 1.25 liters - 1 liter
= 0.25 liter
Milk = 0.25 liters
17: 900 because 3,000 + 900 + 40 +7 is 3,947 or 3,947-3,000-40-7= 900
Answer:
x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer
x = 5pi /3 + 2 pi n
Step-by-step explanation:
8 cos^2 x + 4 cos x-4 = 0
Divide by 4
2 cos^2 x + cos x-1 = 0
Let u = cos x
2 u^2 +u -1 =0
Factor
(2u -1) ( u+1) = 0
Using the zero product property
2u-1 =0 u+1 =0
u = 1/2 u = -1
Substitute cosx for u
cos x = 1/2 cos x = -1
Take the inverse cos on each side
cos ^-1(cos x) = cos ^-1(1/2) cos ^-1( cos x) =cos ^-1( -1)
x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer
x = 5pi /3 + 2 pi n
