Answer:
The value of f(x) - g(x) is:
f(x) - g(x) = 2x² + 6x - 4
Step-by-step explanation:
Given
f(x) = 3x² + x - 3
g(x) = x² - 5x + 1
To determine
f(x) - g(x)
Using the formula
f(x) - g(x) = 3x² + x - 3 - ( x² - 5x + 1)
= 3x² + x - 3 - x² + 5x - 1
= 2x² + 6x - 4
Therefore, the value of f(x) - g(x) is:
f(x) - g(x) = 2x² + 6x - 4
Answer:
The solution of the system can be given as (5,-8).
Step-by-step explanation:
Given system of equations:
To solve the given system of equations:
Solution:
We will use substitution to solve the given system.
We will substitute the 
values in terms of 
from the equation into the other equation to solve for
Substituting into .
We have:
<em>Using distribution.</em>
<em>Combining like terms.</em>
Adding 6 both sides.
Dividing both sides by 3.
∴ 
<em>Plugging in into .</em>
We have,
∴ 
The solution of the system can be given as (5,-8).
Answer:
3/50
Step-by-step explanation:
There are 5 + 4 + 2 + 6 + 3 = 20 marbles in the bag
P(draw a black) = 6/20 = 3/10
If the black marble is replaced, then there are 20 marbles in the bag again.
P(draw a blue) = 4/20 = 1/5
P(draw a black and blue with replacement) = (3/10)(1/5) = 3/50
Answer:
c = 24.34
Step-by-step explanation:
Here, we can use the cosine rule
Generally, we have this as:
a^2 = b^2 + c^2 - 2bcCos A
12^2 = 14^2 + c^2 - 2(14)Cos 19
144 = 196 + c^2 - 26.5c
c^2 - 26.5c + 196-144 = 0
c^2 - 26.5c + 52 = 0
We can use the quadratic formula here
and that is;
{-(-26.5) ± √(-26.5)^2 -4(1)(52)}/2
(26.5 + 22.23)/2 or (26.5 - 22.23)/2
24.37 or 2.135
By approximation c = 24.34 will be correct
