Answer:
That (blank) is 9.
Step-by-step explanation:
Please write 8x^2 - 48x = -104, with " ^ " indicating exponentiation. Thanks.
This sounds like a perfect example of "completing the square."
First, factor 8x^2 - 48x = -104: 8(x^2 - 6x = -13).
If we focus SOLELY on x^2 - 6x = -13, it's just a little easier to "complete the square." Take half of the coefficient of x (which here is -6), and square that result (which here is (-3)^2, or 9. Now add 9 both sides of x^2 - 6x = -13:
x^2 - 6x + 9 = -13 + 9. Note: The "blank" in the problem statement is 9.
We could go ahead and solve this, tho' we weren't asked to do so. Rewrite x^2 - 6x + 9 as (x - 3)^2:
x^2 - 6x = -13 then becomes (x - 3)^2 = 4. To solve for x, take the sqrt of both sides of this latest result, obtaining x - 3 = plus or minus 2. Add 3 to both sides to isolate x: x = 3 plus or minus 2.
Thus, x = 5 or x = 1.
Answer:
Step-by-step explanation:
To find the zeros of the quadratic function f(x)=6x^2 + 12x – 7 we need to factorize the polynomial.
To do so, we need to use the quadratic formula, which states that the solution to any equation of the form ax^2 + bx + c = 0 is:
So, the first thing we're going to do is divide the whole function by 6:
6x^2 + 12x – 7 = 0 -> x^2 + 2x - 7/6
This step is optional, but it makes things quite easier.
Then we using the quadratic formula, where:
a=1, b= 2, c = -7/6.
Then:
So the zeros are:
Answer:
Step-by-step explanation:
The problem relates to filling 8 vacant positions by either 0 or 1
each position can be filled by 2 ways so no of permutation
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 256
b )
Probability of opening of lock in first arbitrary attempt
= 1 / 256
c ) If first fails , there are remaining 255 permutations , so
probability of opening the lock in second arbitrary attempt
= 1 / 255 .
since the triangles are similar
angle DEC = 60 degrees
3 angles inside a triangle equal 180 degrees
BAC = DCE = 64
CBA = EDC = 56
DEC = 180 -56 -64 = 60 degrees
used angle-angle theorem
Answer:
B
Step-by-step explanation:
