Answer: 20/7
Step-by-step explanation: It’s still 20/7 because you can’t simply the 7.
Answer:
a=2, b=0
Step-by-step explanation:
Given:
f(x) = x^3 + x^2 - ax +b is divisible by (x^2 -x)
Need to find:
Values of a and b.
Solution:
Factor
(x^2-x) = (x)(x-1)
if x^3 + x^2 - ax +b is divisible by (x)(x-1), then
both x and (x-1) are roots to f(x), therefore
x=0 or x=1 are roots to f(x).
Using the factor theorem,
f(x=0) = 0 => 0+0-0+b = 0 => b=0
f(x=1)=0 => 1+1-a+b=0 => 1+1-a+0 = 0 => a=2
That is a=2, b=0
Now factor f(x) with a=2, b=0
f(x) = x^3 + x^2 - ax +b
= x^3 + x^2 - 2x
= x (x^2 + x - 2)
= x (x+2) (x-1)
Thus both x and (x-1) are factors... checks.
Answer:
y : x: = 5 : 4
Step-by-step explanation:
x to y = 4 to 5
Rewrite;
x:y = 4:5
Remember, a ratio is another way of representing a fraction, hence one can do the same operations that one could do with a fraction. Therefore, one can take the cross products of a ratio;
x : y= 4 : 5
5x = 4y
Inverse operations;
5x = 4y
x = y
Now substitute this into the equation y:x
y : y
Rewrite as a fraction;
Simplify;
Rewrite as a ratio;
y : x = 5 : 4
Rolling 1 die and flipping a coin 2 times would be the correct method.
There are 24 candidates so we need an experiment that has 24 different outcomes. To find the total number of outcomes, you multiply the number of outcomes for each individual part of the trial.
A dice has 6 outcomes and each coin has 2.
6 x 2 x 2 = 24
Answer:
The graph stretches horizontally by a factor of 4 and shifted up by 1 unit.
Step-by-step explanation:
Given:
The function is given as:
The function is given as:
The function 'g' can be rewritten as:
So, the 'x' value of 'f' is multiplied by and 1 unit is added to the function to get the function 'g'.
Therefore, as per transformation rules:
1.
- If C > 1 ⇒ The graph compresses in the x direction.
- If 0 < C < 1 ⇒ The graph stretches in the x direction by factor of 1/C.
2.
- If C > 0 ⇒ The graph shifts up by 'C' units.
- If C < 0 ⇒ The graph shifts down by 'C' units.
Therefore, the graph of stretches in the x direction(horizontally) by a factor of 4 and shifts up by 1 unit to get .