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
.
The <em><u>correct answers</u></em> are:
B- x + y ≤ 10
; and D- x ≥ 4
Explanation:
The illusionist needs at least 4 female volunteers. This means he could use 4 or more; this means x, the number of female volunteers, is greater than or equal to 4:
x ≥ 4
The total of number of volunteers needed is up to 10. This means the illusionist can use 10 or fewer people; this means the total is less than or equal to 10.
The number of female volunteers is x and the number of male volunteers is y; together they create the expression x+y. This gives us
x+y ≤ 10
Answer:
The value of x is 12 feet
Step-by-step explanation:
The shape in question is a composite shape. We can see that x is both the base of the triangle and the breadth of the rectangle.
To get the area of the shape, we will have to add the area of the rectangle to the area of the triangle.
Area of rectangle = length X breadth
Area of triangle = 1/2 base X height.
However, to calculate the area of the triangle, we need to find its height first.
The next step is to get the height of the triangle. Observing the shape properly, we can see that we can get the height by subtracting the length of the rectangle from the overall length of the shape.
Height of triangle = 16 ft - 10 ft = 6 ft
recall area = 156 square feet.
We now have most of our missing dimensions
We can now set up an equation as follows:

Therefore the value of x is 12 feet
The answer is c 10 #s are greater than 110