Answer:
Step-by-step explanation:
The shape of an arch corresponds to a parabola.
the general equation for a parabola is:
we're given three coordinates: (-7,-13),(7,-13) and (0,0)
so we can plug these values in the general equation to make 3 separate equations:
(x,y) = (-7,-13)
(x,y) = (7,-13)
(x,y) = (0,0)
so we have three equations. and we can solve them simultaneously to find the values of a,b, and c.
we've already found c = 0, let's use substitute it to other equations.
we can solve these two equation using the elimination method, by simply adding the two equations
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Now we can plug this value of a in any of the two equations.
We have the values of a,b, and c. We can plug them in the general equation to find the equation of the arch.
This our equation of the arch!
Answer:
Let the number be x
3.06% = 0.0306
The above statement is written as
0.0306x = 0.86
Divide both sides by 0.0306
x = 0.86/0.0306
<h2>x = 28.10</h2>
Hope this helps you
Answer:
$3.45
Step-by-step explanation:
The tip is 15% of his breakfast, that means 15% of 23
That is 15%* 23= 15*23/100= 3.45 $
The tip is $3.45
Have a good day.
Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
