Answer:
x=-3 or x=3/2
Step-by-step explanation:
We are given the following equation:
2x^2+5x-9=2x
We are asked to find the roots. That means just solve it for x.
2x^2+5x-9=2x
Subtract 2x on both sides:
2x^2+3x-9=0
Let's see if we can put this in factored form.
Compare
2x^2+3x-9=0
and
ax^2+bx+c=0.
a=2, b=3 , c=-9
We have to find two numbers that multiply to be ac and add up to be b.
ac=-18
b=3
What are two numbers that multiply to be -18 and add to be 3?
Say -3 and 6.
So we are going to factor 2x^2-3x+6x-9=0
The first two terms have a common factor of x.
The last two terms have a common factor of 3.
2x^2-3x+6x-9=0
x(2x-3)+3(2x-3)=0
Now we can factor the (x-3) out of those 2 terms there since they share that common factor:
(x+3)(2x-3)=0
(x+3)(2x-3)=0 implies x+3=0 or 2x-3=0.
So we must solve x+3=0 and 2x-3=0
x+3=0
Subtract 3 on both sides:
x=-3
2x-3=0
Add 3 on both sides:
2x=3
Divide both sides by 2:
x=3/2
The solutions are x=3 or x=-3/2
First, define what it is that is being asked.
"of" in mathematics usually means that the numbers or values described are being multiplied.
And so the word problem becomes:
126 employees = 3% * x employees
Solve:
126 = .03 * x
x * .03 = 126
(x * .03) / .03 = 126 / .03
x = 4200 employees
Thus your answer is 4200 employees.
The two lines will intersect at the point (2, 3).
We can find this by setting the two equations equal to eachother, as the point at which they intersect is the point where they share the same x and y value. First, we have to get both equations in the form y = mx + c, so:
-x - y = -5
+ y
-x = -5 + y
+ 5
y = -x + 5
Now we can set -x + 5 equal to x + 1 and solve to find the x coordinate:
-x + 5 = x + 1
+ x
5 = 2x + 1
- 1
4 = 2x
÷ 2
2 = x
With the x coordinate, we can substitute it in to one of the equations and find our y coordinate:
y = 2 + 1 = 3
So the final answer is (2, 3).
I hope this helps!
-x + 5 = x + 1
Answer:
(-9)(2)= -18
Step-by-step explanation:
since there are no signs in this expression, we will multiply. always remember, a negative times a positive will always be negative. just multiply 9 and 2 and you get 18. then add a negative sign. -18