Step-by-step explanation:
factor 4 out of the variable terms, as this helps.
but my approach is simply to define the target and then calculate "backwards".
we want to find
(ax + b)² = a²x² + 2abx + b²
and now we compare with the original equation :
a²x² = 4x²
a² = 4
a = 2
2abx = 16x
2×2×bx = 16x
4b = 16
b = 4
b² = 16, but we have only 3, so we need to subtract 16-3 = 13 from the completed square.
so, our equation is
(2x + 4)² - 13 = 0
(2x + 4)² = 13
2x + 4 = sqrt(13)
2x = sqrt(13) - 4
x = sqrt(13)/2 - 2
Answer:
6.25π cm²
Step-by-step explanation:
pi = π
Circumference = 5πcm
Now first we should find radius(r)
2πr = 5π cm
pie will be cancelled and we get here
r = 5/ 2 cm
Therefore r = 2.5 cm
Now
Area (A) = πr²
= π * 2.5²
= 6.25π cm²
<span>The correct answer is D) g(x) = -(x + 2)^2. The given formula F(x) = x^2 creates a parabola that is open at the top. To reflect this figure across the x-axis and have it open at the bottom, the y-position of the figure on the coordinate system for every x value, which is F(x) = y = x^2 has to be inverted. This is done by negating y and respectively x^2, so to reflect the figure on the x-axis the formula would now look like this: F(x) = -y = -x^2. To move any parabola two units to the left and thereby have its root be at -2, you would simply subtract -2 from every x-position of the figure in the coordinate system. For an inverted parabola like this one the value to move it on the x-axis has to be added instead and this results in the formula from answer D: g(x) = -(x+2)^2</span>
X=number of adults, y= number of students
x+y=12
18x+12y=162
You can simplify the second equation by dividing by six: 3x+2y=27
Rearrange the first equation: y= 12-x. Plug y into the simplified second equation:
3x+2(12-x)=27
3x-2x+24=27
x=3.
Plug the now known x value into y=12-x. So y= 9.
Therefore, there are 3 adults and 9 students.
I think 3.16 I said I think
