Answer:
x = 1091.63315843
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Setting Up:
7 = ln ( x + 5 )
ln translates to "log" with an "e" as the base or subscript ( a small "e" at the bottom right of the "g" in log).
You take the base of the log and put it to the power of "7" ( "7" is the natural log of ( x + 5 ) in this problem ).
The value of which the logarithm is calculated is set equal to the base of the logarithm to the power of the calculated logarithm of the value.
e^7 = x + 5
Solving</span>:
e = 2.71828182846
Natural logarithms are logarithms to the base of the constant 'e'.
e^7 = x + 5 ( simplify e^7 )
<span>1096.63315843 = x + 5
</span>
Subtract 5 from each side.
1091.63315843 = x
I assume that the parabola in this particular problem is one whose axis of symmetry is parallel to the y axis. The formula we're going to use in this case is (x-h)2=4p(y-k). We know variables h and k from the vertex (1,20) but p is not given. However, we can solve for p by substituting values x and y in the formula with the y-intercept:
(0-1)^2=4p(16-20)
Solving for p, p=-1/16.
Going back to the formula, we can finally solve for the x-intercepts. Simply fill in variables p, h and k then set y to zero:
(x-1)^2=4(-1/16)(0-20)
(x-1)^2=5
x-1=(+-)sqrt(5)
x=(+-)sqrt(5)+1
Here, we have two values of x
x=sqrt(5)+1 and
x=-sqrt(5)+1
thus, the answers are: (sqrt(5)+1,0) and (-sqrt(5)+1,0).
Answer:
(4t − 3) (t − 6)
Step-by-step explanation:
Using AC method:
Given a quadratic ax² + bx + c, find factors of ac that add up to b. Divide those factors by a and reduce. The denominators become the coefficients and the numerators become the constants.
Here, a = 4, b = -27, and c = 18.
ac = 4 × 18 = 72
Factors of 72 that add up to -27: -3 and -24
Divide factors by a: -3/4 and -24/4
Reduce: -3/4 and -6/1
So the factored expression is:
(4t − 3) (t − 6)
F(2)= 4(16) - 6(4) + 8(2) - 15
F(2)= 64 -24 + 16 - 15
F(2)= 41
