Answer:
x1 = 6 + 2√6 or x2 = 6 - 2√6
Step-by-step explanation:
x² - 12x + 12 = 0
We need to use formula:
a² - 2ab + b² = (a - b)².
x² - 12x = - 12
x² - 2*6x + 6²- 6² = - 12
(x - 6)² - 36 = -12
(x - 6)² = - 12 + 36
(x -6)² = 24
(x - 6) = √24 or (x-6) = -√24
(x - 6) = 2√6 or (x-6) = - 2√6
x = 6 + 2√6 or x = 6 - 2√6
Answer:
(5,1)
Step-by-step explanation:
Given :

Solution :
Equation 1 : y=x-4
Equation 2 : y = -x+6
We will use substitution method
Putting the value of y from equation 1 in equation 2
⇒
⇒
⇒
⇒
⇒
Now substituting value of x in equation 1 to get value of y
⇒
⇒
⇒
Thus the solution of given system of equations is (5,1)
We have also solved it by graphing the equations
You can refer the attached figure.
Answer:
f ^-1 (x) = 2x+28
Step-by-step explanation:
f(x) = 1/2x-14
Replace f(x) with y
y = 1/2 x -14
Exchange x and y
x = 1/2 y -14
Solve for y
Add 14 to each side
x+14 = 1/2 y -14+14
x+14 = 1/2 y
Multiply each side by 2
2(x+14)= 1/2 y*2
2x+28 = y
The inverse function is
f ^-1 (x) = 2x+28
Answer:
The z-score for Michael's exam grade is 0.50
Step-by-step explanation:
Data
- standard deviation, σ = 2.0
- Michael's exam grade is the value of interest, x = 86
From definition, z-score is computed as follows:
Z = (x - μ)/σ
Z = (86 - 85)/2.0
Z = 0.50
Answer:
19gallons
Step-by-step explanation:
Given parameters:
Mike's car rate = 21miles per gallon
Distance = 400 miles
Unknown:
Number of gallons of gas = ?
Solution:
The rate of fuel consumption by Mikes car is given as;
Rate =
Number of gallons =
Number of gallons =
= 19gallons