Answer:
x
=
5 and (
5
,
−
9
)
Explanation:
The equation of a parabola in vertex form is.
2
2
y
=
a
(
x
−
h
)
2
+
k
2
2
Where (
h
,
k
) are the coordinates of the vertex and a is a multiplier
f
(
x
)
=
(
x
−
5
)
2
−
9 is in this form
with (
h
,
k
)
=
(
5
,
−
9
)
⇒
vertex =
(
5
,
−
9
)
the axis of symmetry passes through the vertex is vertical with equation
x
=
5
← axis of symmetry graph{(y-x^2+10x-16)(y-1000x+5000)=0 [-20, 20, -10, 10]}
Answer:
y - 5
12x + 18y
Step-by-step explanation:
6) five less than y
y - 5
7) six times the quantity of<u> two x plus 3 y</u>
2x + 3y
six times the above exp
6(2x + 3y)
= 12x + 18y
Answer:
F(x) = 45*x - (5/2)*x^2 + C
Step-by-step explanation:
Here we want to find the antiderivative of the function:
f(x) = 45 - 5*x
Remember the general rule that, for a given function:
g(x) = a*x^n
the antiderivative is:
G(x) = (a/(n + 1))*a*x^(n + 1) + C
where C is a constant.
Then for the case of f(x) we have:
F(x) = (45/1)*x^1 - (5/2)*x^2 + C
F(x) = 45*x - (5/2)*x^2 + C
Now if we derivate this, we get:
dF(x)/dx = 1*45*x^0 - 2*(5/2)*x
dF(x)/dx = 45 - 5*x
Answer:
3.41 feet
Step-by-step explanation:
Area = Length × Breath
Area of the rectangular lawn = 100 × 50
= 5000 feet²
The sidewalk must occupy an area no more than 10% of the total lawn area.
So, the area of the sidewalk would be not more than = 10% × 5000
= 0.10 × 5000
= 500 feet²
Let the width of the sidewalk = x feet
area of the side walk = (L×W of the long way) + ((L-x)×W of the short way)
(100 × x) + ((50 - x) × x) < 500
100x + (50-x)(x) < 500
-x² + 150x < 500
-x² + 150x = 500
-x² + 150x - 500 = 0
By using quadratic formula
or 
x = 3.41089 ≈ 3.41 feet or x = 146.58
Therefore, width of the sidewalk would be 3.41 feet.
Answer:
n=9
Step-by-step explanation:
