Answer:
x=1+2√2 or x=1−2√2
Step-by-step explanation:
Let's solve your equation step-by-step.
3x2−6x=21
Step 1: Since the coefficient of 3x^2 is 3, divide both sides by 3.
3x2−6x
3
=
21
3
x2−2x=7
Step 2: The coefficient of -2x is -2. Let b=-2.
Then we need to add (b/2)^2=1 to both sides to complete the square.
Add 1 to both sides.
x2−2x+1=7+1
x2−2x+1=8
Step 3: Factor left side.
(x−1)2=8
Step 4: Take square root.
x−1=±√8
Step 5: Add 1 to both sides.
x−1+1=1±√8
x=1±√8
x=1+2√2 or x=1−2√2
Answer: the number of students that were surveyed is 40
Step-by-step explanation:
Let x = total number of students that were surveyed about their favorite colors
1/4 of the students preferred red.
This means that the number of students that preferred red is 1/4 × x = x/4
1/8 of the students preferred blue.
This means that the number of students that preferred blue is 1/8 × x = x/8
The remaining number of students will be the total number of students - the sum of the number of students that preferred red and the number of students that preferred blue. It becomes
x - (x/4 + x/8) = x - 3x/8 = 5x/8
3/5 of the remaining students were for green. This means that the number of students that preferred green is 3/5 × 5x/8 = 3x/8
if 15 students prefer green, then
3x/8 = 15
3x = 120
x = 120/3 = 40 students
$19,802.5 I hope this helps and I'm sorry I didn't reply sooner.
Since this is a linear function, filling in the minimum and maximum of the domain is sufficient.
f(-4) = -16 + 9 = -7
f(2)= 8 + 9 = 17
So the range of the function (given the domain) :
R = {-7, 17}
