Answer:
The factors are (5x + 3) and (2x + 1)
Step-by-step explanation:
When you need to factor a quadratic, and the coefficient of the x² is not 1, use the slide and divide method.
The general form of a quadratic is ax² + bx + c
Factor: 10x² + 11x + 3
Here a = 10, b = 11, and c = 3
Step 1: Multiply ac, we SLIDE a over to c. Notice the 10 is gone for now..
x² + 11x + 30
Step 2: Factor this (this step will always factor)
x² + 11x + 30 = (x + 5)(x + 6)
So the factors are (x + 5)(x + 6), but we now need to DIVIDE by a, since we multiplied it into c before. We divide the constants in the factors...
(x + 5/10 )(x + 6/10 )
Now reduce the fractions as much as possible...
(x + 1/2 )(x + 3/5)
*If they don't reduce to a whole number, SLIDE the denominator over as a coefficient of x....
(2x + 1)(5x + 3) *2 slide over in front of x, 5 slide over in front of x, the fractions are gone!
These are our factors!
Answer:
The dependent variable is the amount of money he received for birthday.
Step-by-step explanation:
After his birthday, Benjamin has decided to donate a third of the money he received as a gift from his relatives to a foundation. Considering the variables amount of money received by Benjamin and amount of money that Benjamin will donate. to. What is the dependent variable in this situation.
Here, the money he received for the birthday is x.
So, he donated x/3.
The variable is the money which he gets, so the dependent variable is amount of money he received for the birthday.
Answer:
Step-by-step explanation:
f(x) = x^2 + 3x - x/2
f(x) = x^2 + 2.5x
- 3x - 1/2x =
- 6x/2 - 1/2x =
- 5x/2 =
- 2.5x
f(6) = 6^2 + 2.5*6
f(6) = 36 + 15
f(6) = 51
Answer:
$2000:$1500:$1000
Step-by-step explanation:
So in order to split $4500 into that proportion, we need to multiply the value by the corresponding ratios to split it properly.
There are 4 + 3 + 2 = 9 total parts to the ratio.
We know that we want the first part of the ratio to be 4/total. So we can say that:
$4500 x 4/9 = $2000. This is the first part of the ratio.
We then know the middle part of the ratio is 3/total. So we can say that:
$4500 x 3/9 = $1500. This is the middle part of the ratio.
Finally, we know that the last part of the ratio is 2/total. So we can say that:
$4500 x 2/9 = $1000. This is the last part of the ratio.
Put it all together, and we get $2000:$1500:$1000.
I hope this helps!
