Answer:
x = –7, x = 2, or x = 4 are factors of f(x).
Step-by-step explanation:
Given : f(x) = 5x³ +5x²-170x +280 and x + 7 is one factor .
To find : What are all the roots of the function.
Solution : f(x) = 5x³ +5x²-170x +280 .
We have given that x + 7 is factor that mean x = -7 is factor of f(x )
When we divide f(x) by x +7 we get
5x² -30x +40 =0
Taking common 5 from equation
5( x² -6x +8) =0
On dividing by 5 both sides
x² -6x +8 = 0
On factoring
x² -2x -4x +8 = 0.
Taking common x from first two terms and -4 from last two terms
x ( x -2) -4 (x -2) = 0
On grouping
(x-2) (x-4) = 0
x -2 =0
x =2
x-4 =0
x = 4
Therefore, x = –7, x = 2, or x = 4 are factors of f(x).
<span>The table shows the outputs, y, for different inputs, x:
Input (x) 1 3 5 7
Output (y) 8 6 5 4
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Yes, the data in the table represent a function. The reason is that given an input (value of x), in the domain of the function (which is 1, 3, 5, 7), you can state the correspondent output (value of y) without ambiguity.
Part B: Compare the data in the table with the relation f(x) = 4x + 8. Which relation has a greater value when x = 3? (2 points)
x = 3 => f(3) = 4(3) + 8 = 12 + 8 = 20
While the image of 3 in the data is y = 6.
So, the function f(x) = 4x + 8 has a greater value when x = 3.
Part C: Using the relation in Part B, what is the value of x if f(x) = 76? Be sure to show all your work.
f(x) = 76 = 4x + 8 => 4x = 76 - 8 = 68
=> x = 68/4 = 17</span>
Answer:
The length of the TV is 45 inches and the height is 28 inches.
Answer:
Step-by-step explanation:
f(x) = -1/3x + 1:
-7=z/2+1
What you first need to do is to multiply both sides of the equation by 2
-14=z+2
Now you move the variable to the left side and change within it’s own sign
-z-14=2
Into
-z=2+14
Now you then add the numbers
-z=16
The last part you do is change the sign on both sides in this equation
z=-16
Therefore, z=-16 is your answer in number 16.
