Answer:
x = 2 ±sqrt( 97)
Step-by-step explanation:
log10(x^2 -4x+7) =2
Raise each side to the base 10
10 ^ log10(x^2 -4x+7) =10^2
x^2 -4x +7 = 100
Subtract 7 from each side
x^2 -4x+7-7 = 100-7
x^2 -4x = 93
Complete the square
-4/2 = -2 (-2)^2 = 4
Add 4 to each side
x^2 -4x+4 = 93+4
(x-2)^2 = 97
Take the square root of each side
sqrt((x-2)^2 )=±sqrt( 97)
x-2 = ±sqrt( 97)
Add 2 to each side
x = 2 ±sqrt( 97)
The interval is the value (-∞,2)
We have given that,
f(x)=x-3
g(x)= - 0.5x
<h3 /><h3>What interval is the value of (f-g)(x) negative?</h3>
First, calculate the (f-g)(x)
Since f(x)=x-3
g(x)= - 0.5x
So, (f-g)(x) = x-3-(- 0.5x)
⇒(f-g)(x) = x-3+ 0.5x
⇒(f-g)(x)
=1.5x-3
Now we are supposed to find the interval for which (f-g)(x) is negative.
So, (f-g)(x) =1.5x-3 <0
⇒1.5x<3
Thus for (f-g)(x), negative x must be less than 2
Thus the interval is(-∞,2)
Hence option B is correct.
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Answer:
The equation of the parabola is;
(y-3)^2 = 20(x-2)
Step-by-step explanation:
Here, we want to find the equation of the parabola given the focus and the vertex of the said parabola
Mathematically, we can have the equation represented as;
(y-k)^2 = 4a(x-h)
As we can see that the focus and the vertex lie on the same horizontal line of y = 3
In this case, a = 7-2 = 5
The coordinates of the vertex is (h,k) = (2,3) in this case
where h = 2 and k = 3
So the equation of the parabola will be;
(y- 3)^2 = 4(5)(x-2)
(y-3)^2 = 20(x-2)
Answer:430.2
Step-by-step explanation:
Step-by-step explanation:
1)a) 925×4.25=3931,25
b) 1806.25:4.25=425
I don't know second one.
3)a 55×1.12=61.6
b)