Answer:
f(x) = x^3 - x^2 -2x
Step-by-step explanation:
If x = a is a zero of a polynomial, then x-a is a factor of the polynomial. Given the factors of a polynomial, the polynomial can be obtained by multiplying the factors.
The factors of the given polynomial are;
x - 2
x + 1
x
Multiplying the first two factors;
(x-2)(x+1) = x^2 + x -2x -2
= x^2 -x -2
We finally multiply this result by x to obtain our polynomial;
f(x) = x ( x^2 -x -2)
= x^3 - x^2 -2x
which is a cubic polynomial since it has 3 roots.
Answer:
1st → 1st
2nd → 3rd
3rd → 2nd
Step-by-step explanation:
just divide the first set of student wishes to the second set of students in the same question. the 1st for example
x-ray to all students is 6/ 36= 1/6 = 1:6
for all students, you add all the students in the table
So it wants you to write two equations, one for the number of fruit and another for the money spent. gather your important information first:
20 fruits for $11.50
apples cost $0.50
bananas cost $0.75
let's do the cost equation first. it's $0.50 per apple, so 0.50a, and $0.75 per banana, so 0.75b. the total cost is $11.50. put all of this information together:
0.50a + 0.75b = 11.50 ... so, the cost of apples bought plus the cost of bananas bought equals 11.50
note what your variables stand for. a represents the number of apples, b represents the number of bananas. to write an equation for how many fruits bought, you simply have to add these two and set them equal to 20 (the total number of fruits bought).
a + b = 20
and your other equation
0.50a + 0.75b = 11.50
these are your two equations. to solve the system of equations, you first want to get one variable alone; the first equation will be easier.
a + b = 20
a = 20 - b
now take this equation and plug it into the second equation.
0.50(20 - b) + 0.75b = 11.50 ... you'll notice that you only have one variable left: b. solve for it. the first step is to distribute 0.50 to the parentheses
10 - 0.50b + 0.75b = 11.50 ... combine like terms
10 + 0.25b = 11.50 ... subtract 10
0.25b = 1.5 ... divide by 0.25
b = 6
6 bananas were purchased. plug this back into an equation to find out how many apples were purchased.
a + 6 = 20 ... subtract 6
a = 14
14 apples and 6 bananas were bought.
46m - 33m = -28 - 11
13m = -39
m =-3
Answer:
Area of ΔQRS = 2.3 square inches
Step-by-step explanation:
From the given information,
<S + <Q + <R =
51 + 44 + <R =
95 + <R =
<R = - 95
=
<R =
Applying the Sine rule, we have;
= =
Using =
=
r =
= 2.9483
r = 2.9 inches
Also, =
=
q =
= 2.0559
q = 2.0 inches
From Herons formula,
Area of a triangle =
s =
= 3.6
Area of ΔQRS =
= 2.2895
Area of ΔQRS = 2.3 square inches