math worksheet
1 x+2=4
2 x+3+x=7
3 find x here it is - x
Equation 1) -2x-y=-9
Equation 2) 5x-2y=18
Multiply all of equation 1 by 2, so that both equations have (2y) in them.
1) 2(-2x-y=-9)
Simplify.
1) -4x-2y=-18
2) 5x-2y=18
Subtract equations with each other.
-9x=-36
Divide both sides by -9.
x=4
Plug in 4 for (x) into equation 1.
-2x-y=-9
-2(4)-y=-9
Simplify.
-8-y=-9
Add 8 to both sides.
-y=-1
Divide both sides by -1.
y=1
(4, 1)
~Hope I helped!~
Let x = amount of 45% antifreezeLet y = amount of 70% antifreeze EQUATION 1: x + y = 150 (total of 150 gallons mixed) EQUATION 2: .45x + .75y = .55(x + y) Simplify and solve the system of equations Multiply second equation by 100 on both sides to remove the decimals 45x + 75y = 55(x + y) Combine like terms 45x + 75y = 55x + 55y 45x - 55x + 75y - 55y = 0 -10x + 20y = 0 Now we have the following system of equations: x + y = 150 -10x + 20y = 0 Multiply the first equation by -10 to get opposite coefficients for x; add the equations to eliminate x 10x + 10y = 1500 -10x + 20y = 0 ------------------------------ 30y = 1500 Solve for y 30y = 1500 y = 50 Since the total mixed gallons is 150, x = 150 - 50 = 100 So we need 100 gallons of the 45% antifreeze and 50 gallons of the 70% antifreeze
Answer: An estimate done quickly: The circumference is about 75 ft.
Step-by-step explanation:
Round π to 3, and 24 to 25. 3 times 25 is 75
A more exact value would be 75.36
3.14 × 24 = 75.36
Probability that a stone is cracked = 15/600; denote this event by 
.
Probability that a stone is discolored = 27/600; denote this event by 
.
Probability that a stone is neither cracked nor discolored = 562/600; in terms of and , this event is captured by 
.
a. We want to find 
. Use the known probability of its complement:
b. We want to find 
. By the inclusion-exclusion principle,
c. By the law of total probability,
