Answer:
x = 12
Step-by-step explanation:
Solve for x:
(-3 x)/2 - 9 = -27
Put each term in (-3 x)/2 - 9 over the common denominator 2: (-3 x)/2 - 9 = (-18)/2 - (3 x)/2:
(-18)/2 - (3 x)/2 = -27
(-18)/2 - (3 x)/2 = (-3 x - 18)/2:
(-3 x - 18)/2 = -27
Multiply both sides of (-3 x - 18)/2 = -27 by 2:
(2 (-3 x - 18))/2 = -27×2
(2 (-3 x - 18))/2 = 2/2×(-3 x - 18) = -3 x - 18:
-3 x - 18 = -27×2
2 (-27) = -54:
-3 x - 18 = -54
Add 18 to both sides:
(18 - 18) - 3 x = 18 - 54
18 - 18 = 0:
-3 x = 18 - 54
18 - 54 = -36:
-3 x = -36
Divide both sides of -3 x = -36 by -3:
(-3 x)/(-3) = (-36)/(-3)
(-3)/(-3) = 1:
x = (-36)/(-3)
The gcd of -36 and -3 is -3, so (-36)/(-3) = (-3×12)/(-3×1) = (-3)/(-3)×12 = 12:
Answer: x = 12
A.) Simplifying the equation would lead you to 15x^2-3x+9
b.) You know your answer is correct because you're adding the two polynomials together. 9x^2+6x^2 is 1tx^2. Now you have 2x-5x and since the negative is bigger, you get -3x. Then 5+4 is 9. You have no like terms therefore your answer is 15x^2-3x+9
If x = 2 than, 6(4x2)=48
-3(8x)= -24
It would equal 24
The correct answer would be C
Answers:
(a) p + m = 5
0.8m = 2
(b) 2.5 lb peanuts and 2.5 lb mixture
Explanations:
(a) Note that we just need to mix the following to get the desired mixture:
- peanut (p) - peanuts whose amount is p
- mixture (m) - mixture (80% almonds and 20% peanuts) that has an amount of m; we denote this as
By mixing the peanuts (p) and the mixture (m), we combine their weights and equate it 5 since the mixture has a total of 5 lb.
Hence,
p + m = 5
Note that the desired 5-lb mixture has 40% almonds. Thus, the amount of almonds in the desired mixture is 2 lb (40% of 5 lb, which is 0.4 multiplied by 5).
Moreover, since the mixture (m) has 80% almonds, the weight of almonds that mixture is 0.8m.
Since we mix mixture (m) with the pure peanut to get the desired mixture, the almonds in the desired mixture are also the almonds in the mixture (m).
So, we can equate the amount of almonds in mixture (m) to the amount of almonds in the desired measure.
In terms mathematical equation,
0.8m = 2
Hence, the system of equations that models the situation is
p + m = 5
0.8m = 2
(b) To solve the system obtained in (a), we first label the equations for easy reference,
(1) p + m = 5
(2) 0.8m = 2
Note that using equation (2), we can solve the value of m by dividing both sides of (2) by 0.8. By doing this, we have
m = 2.5
Then, we substitute the value of m to equation (1) to solve for p:
p + m = 5
p + 2.5 = 5 (3)
To solve for p, we subtract both sides of equation (3) by 2.5. Thus,
p = 2.5
Hence,
m = 2.5, p = 2.5
Therefore, the solution to the system is 2.5 lb peanuts and 2.5 lb mixture.
