Let a and b = the numbers we must find.
a + 2b = 5.....Equation A
2a + b = 13.......Equation B
We have a system of equations in two variables.
I will solve A for little a.
a + 2b = 5
a = 5 - 2b
Now I will plug 5 - 2b for a in B.
2(5 - 2b) + b = 13
10 - 4b + b = 13
-3b = 3
b = -1
To find a, replace b with -1 in EITHER A or B.
I will use Equation A.
a + 2b = 5
a + 2(-1) = 5
a - 2 = 5
a = 7
The two numbers are -1 and 7.
Understand?
X is the easy one to solve here. A triangle must have 180 degrees. Add 90 to 38 and subtract that value from 180. This results in x = 52 Degrees. Y is a little bit more difficult. Because The two lines are parallel, Angle CDB is equal to the angle just above y-12. That angle is equal to x, in other words. This angle and y-12 must equal 180 when they are added together, as this is the value for degrees of a line. So, 180= (y-12) + 52. Just solve this algebraically, and is should result in y = 140 degrees.
Tldr: y = 140, x= 52
Step-by-step explanation:
if one pump = x
the other pump = 2x
therefore
x + 2x = 8 minutes
3x = 8 minutes
Divide through by 3
x = 8/3 minutes
converting it to seconds
x = 8/3 * 60
x = 160 seconds
therefore
the first pump = 2x = 2 * 160 = 320 seconds
the second pump = x = 160 seconds
Answer:
x = 2 + sqrt(2) or x = 2 - sqrt(2) thus B. is your answer
Step-by-step explanation:
Solve for x over the real numbers:
4 x^2 - 16 x + 8 = 0
Hint: | Write the quadratic equation in standard form.
Divide both sides by 4:
x^2 - 4 x + 2 = 0
Hint: | Solve the quadratic equation by completing the square.
Subtract 2 from both sides:
x^2 - 4 x = -2
Hint: | Take one half of the coefficient of x and square it, then add it to both sides.
Add 4 to both sides:
x^2 - 4 x + 4 = 2
Hint: | Factor the left-hand side.
Write the left-hand side as a square:
(x - 2)^2 = 2
Hint: | Eliminate the exponent on the left-hand side.
Take the square root of both sides:
x - 2 = sqrt(2) or x - 2 = -sqrt(2)
Hint: | Look at the first equation: Solve for x.
Add 2 to both sides:
x = 2 + sqrt(2) or x - 2 = -sqrt(2)
Hint: | Look at the second equation: Solve for x.
Add 2 to both sides:
Answer: x = 2 + sqrt(2) or x = 2 - sqrt(2)