Please solve the following simultaneous equation:
4x-3y=15
8x^2-27y^2=45
Answers
8 x² - 27 y² =45
Isolate y for 4 x - 3y = 15
4 x - 3y = 15 ( add 3y to both sides ):
4x-3y +3y = 15 + 3y
4x = 15 + 3y
Divide both sides by 4 :
4x / 4 = 15 + 3y / 4
x = 15+3y / 4
Plug the solutions x = 15+3y / 4 into : 8 x² - 27 y²=45
8 ( 15+3y / 4 )² - 27 y² = 45
1/2 ( 3y+15)² - 27 y² = 45
Multiply by LCD = 2
9 ( y+5)² - 54 y² = 90
-45 y² + 90 y + 225 = 90
- 45 y² + 90 y = 225 - 90
-45 y² + 90 y = 135 = 0
-45 ( y + 1 ) ( y - 3 ) = 0
Using the zero factor principle:
Solve ( y + 1 ) = 0
y = - 1
Solve ( y - 3 ) = 0
y = 3
y = -1 and y = 3
Plug the solution y = -1 , y = 3 into : 4 x - 3 y = 15
4 x - 3 y = 15 for - 1 :
4 x - 3 ( - 1 ) = 15
4 x + 3 = 15
4 x = 15 - 3
4 x = 12
x = 12 / 4
x = 3
For 3 :
4 x - 3 y = 15
4 x - 3 ( 3 ) = 15
4 x - 9 = 15
4 x = 15 + 9
4 x = 24
x = 24 / 4
x = 6
Therefore the final solution :
y = 3 , x = 6
y = - 1 , x = 3
hope this helps!
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Which number is irrational? A. 3/8 B. 56/8 to the fourth C. 36 to the fourth over 4 to the fourth D. 0.19 repeating
Solve each system of equations using substitution. Show all work.1) x + y = 1 2x - y = -2 2) 5x - 3y = -11 x - 2y = 2 3) x - y = 3 6x + 4y = 13
How many factors in the expression 8(x +4) (y +4) (z 2 + 4z + 7) have exactly two terms?
Answers
Answer:
x=-5.5
Step-by-step explanation:
-3(x+4)=(-x-1)
1. Distribute
-3x+(-12)=-x-1
2. Simplify
-3x-12=-x-1
-2x-12=-1
-2x=11
x=-11/2
x=-5.5
Answer:
-11/2 or 5.5
Step-by-step explanation:
Answers
long leg is from -2 to 6 value of the x line. Its measure is 8.
short leg is form 0 to 5 value of the y line. Its measure is 5.
We will use the Pythagorean theorem to get the hypotenuse or distance of two points.
a² + b² = c²
8² + 5² = c²
64 + 25 = c²
89 = c²
√89 = √c²
9.43 = c
The distance of the two points, M and H, is 9.43
Answers
Answer:
Paul filled 4 bags on Sunday.
Step-by-step explanation:
Since each bag that was filled weighed 5 pounds then we can use the following equation to solve for the amount of bags, where (x) is the number of bags filled on Saturday and (y) is the number of bags filled on Sunday.
5x + 5y = 30
Now since we are told that on Saturday Paul filled 2 bags then we would only be left with the variable y (number of bags filled on Sunday). We can solve for y
5(2) + 5y = 30
10 + 5y = 30 ... subtract 10 on both sides
5y = 20 ... divide by 5 on both sides
y = 4
Finally, we can see that Paul filled 4 bags on Sunday.
10–25 years 10 5 20 35
26–40 years 15 10 10 35
41–55 years 20 10 0 30
Total 45 25 30 100
What is the probability (rounded to the nearest whole percent) that a randomly selected person is 10 to 25 years old or prefers drinking rootbeer?
60%
55%
10%
5%
Answers
10–25 years 10 5 20 35
26–40 years 15 10 10 35
41–55 years 20 10 0 30
Total 45 25 30 100
Probability that a randomly selected person is 10-25 years old or prefers drinking rootbeer
Probability of 10-25 years old = 35/100 = 35%
Probability of drinking rootbeer = 25/100 = 25%
Probability of 10-25 years or perfers to drinking rootbeer
= 35% + 25% = 60% 1st option
Answers
Answers
Answer:
Step-by-step explanation: