What are the vertex, focus, and directrix of the parabola with equation y = x^2 – 10x + 33?
Answers
Answer:
Vertex:(5,8)
Focus:(5,8.25)
Directrix: y=7.75
Step-by-step explanation:
For the equation of the parabola in the form:
(x - h)² = 4p(y - k), where p≠ 0
The vertex of this parabola is at (h, k).
The focus is at (h, k + p).
The directrix is the line y = k - p.
Converting the equation y=x²-10x+33 in the above form
y=x²-10x+25+8
y=(x-5)²+8
(x-5)²=(y-8)
On comparing this equation with the above equation, we see that
h=5 k=8 and 4p=1
or p=1/4
Vertex=(5,8)
Focus=(5,8+1/4)
=(5,8.25)
Directrix: y=8-1/4
y= 7.75
(x-h)^2=4P(y-k)
complete the square with the x term
take 1/2 of -10 and square it and add that to both sides
y+25=x^2-10x+25+33
factor perfect square
y+25=(x-5)^2+33
minus 33 both sides
y-8=(x-5)^2
force factor out a 4
4(1/4)(y-8)=(x-5)^2
(x-5)^2=4(1/4)(y-8)
vertex is (5,8)
distance from directix is P or 1/4 or 0.25
since opens up, directix is ycoordinate-0.25 aka y=7.75 is directix
focus=(5,8+0.25)=(5,8.25)
vertex=(5,8)
directix: y=7.75
focus: (5,8.25)
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Answers
Answer:
It means something mathematical
Step-by-step explanation:
The slashed zero glyph is often used to distinguish the digit "zero" ("0") from the Latin script letter "O" anywhere that the distinction needs emphasis, particularly in encoding systems, scientific and engineering applications, computer programming (such as software development), and telecommunications.
Answers
Answer:
HERE
Step-by-step explanation:
To calculate the percent of tax on an item priced at $135, we need to find the percentage of $8.10 in relation to the original price.
To do this, we divide the tax amount by the original price and then multiply by 100 to find the percentage:
($8.10 / $135) * 100 = 0.06 * 100 = 6%
Therefore, the tax on the item priced at $135 is 6%.
If you are looking for the nearest whole percentage, it would be 6%
B. $648.71
C. $657.97
D. $661.55
Answers
A = P * eᵃˣ
A - the future value
P - the principal
a - the rate
x - the period of time
We know:
A = ?
P = $500
a = 4% = 4%/100% = 0.04
x = 7
A = P * eᵃˣ
A = 500 * e⁰.⁰⁴*⁷
A = 661.55
Evaluate the expressions:
h(x)=12/x
h(-2)
h(a)
Answers
Answer:
h(-2) = -6, h(a) = 12/a
Step-by-step explanation:
h(-2)
It says that you are supposed to do 12 divided by the number in the parentheses, so you have 12 / -2 = -6.
h(a)
Again, you have to do 12 divided by the number in the parentheses, so you have 12/a.
Answers
Of the provided graphs, the second would be the correct answer.
Functions occur when the input only has one possible output (though the output can be recieved through multiple inputs)
The relation shown in the 2nd diagram is a function. The reason for this is that one and only one y-value is associated with each x-value.
Note that this is not true of the first diagram. If x=0, there are two separate y vaues associated: -1 and 2. This clearly states that the first diagram does not represent a function.
Answers
Answer:
Mr Juan is 48 years old and Eric is 16 years old
Step-by-step explanation:
let Eric's age be x, then his father is 3x ( three times as old as Eric )
the sum of their ages is 64 , that is
x + 3x = 64 ( simplify left side )
4x = 64 ( divide both sides by 4 )
x =
, that is
x = 16
and 3x = 3 × 16 = 48
Mr Juan is 48 and Eric is 16