Given:
The leading coefficient of a polynomial is 8.
Polynomial roots are 1 and 2.
The graph passes through the point (4,5).
To find:
The 3rd root and the equation of the polynomial.
Solution:
The factor form of a polynomial is:
Where, a is a constant and 
are the roots of the polynomial.
Polynomial roots are 1 and 2. So, 
and 
are the factors of the polynomial.
Let the third root of the polynomial by c, then 
is a factor of the polynomial.
The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:
The graph passes through the point (4,5). Putting 
, we get
Divide both sides by 48.
Therefore, the 3rd root on the polynomial is 
.
Answer:
The number of men was 
The number of women was 
Step-by-step explanation:
The question in English is
Having organized a bingo has raised $1900. For the entrance of men $15 and women $10 and an attendance of 150 people has been reported. Determine the number of men and the number of women who participated in the bingo.
Let
x----> the number of men
y----> the number of women
we know that
-----> equation A
-----> equation B
substitute equation A in equation B and solve for y
Find the value of x
therefore
The number of men was
The number of women was
Answer:
i wanna say -80?
Step-by-step explanation: so when you go from -8 to -11 its counts by 3 -11 to -14 its 3 so count up to get our answer. i just seen how many was in each 5 set which was 12 so i did -20 -12 so then i just added up and got -80
Answer:find the solution to the system of equations below.start by adding the equation
{-2x+2y=-8
{2x+y=5
Step-by-step explanation:The given system of equation are:
1---- y= x -4
2----- y=4 x+2
Equation (1) - Equation (2)
→0= x -4 - (4 x+2)
→0= -3 x -6-----[Adding and subtracting like terms]
Adding 3 x on both sides
→3 x= -6
Dividing by 3 on both sides
→x = -2
→Substituting the value of x in equation 1, we get
y= -2 -4
y =-6
→Solution set =(x,y)=(-2, -6)
Don't used the graph to find the solution.
Answer:
Step-by-step explanation:
f(x) is quadratic function and g(x) is linear (since AP in the right column).
<u>Find the equation of the function f(x), use the points on the graph:</u>
- c = 5 as the y-intercept is (0, 5)
- a(-1)² + b(-1) + 5 = 0 ⇒ a + 5 = b
- a(5²) + b(5) + 5 = 0 ⇒ 25a + 5b + 5 = 0 ⇒ 25a + 5a + 25 + 5= 0 ⇒ a = -1 ⇒ b= 4
<u>The function is:</u>
Find the equation of g(x)
<u>Find the slope of g(x):</u>
- m = (1 - 7)/(-1 + 4) = -2
<u>Use (-4, 7) to find its equation:</u>
- y - 7 = -2(x + 4)
- y = -2x + 7 - 8
- y = -2x - 1
<h3>See the required comparison below</h3>
<u>The y-intercepts:</u>
- f(x) ⇒ 5,
- g(x) ⇒ -1
- -5 < - 1
<u>Values at x = 3:</u>
- f(3) = -3² + 4(3) + 5 = 8
- g(3) = -2(3) - 1 = - 7
- 8 > 7
<u>Average rate of change in the interval [2,5]:</u>
- f(x) ⇒ (0 - 9)/(5 - 2) = -3
- g(x) ⇒ (-11 + 5)/ (5 - 2) = -2
- -3 < -2
<u>Max of function in the interval [-5, 5];</u>
- f(x) ⇒ 9, vertex of the function
- g(x) ⇒ g(-5) = -2(-5) - 1 = 9, taken the least point of x as it is a decreasing function
- 9 = 9
