A parabola is a mirror-symmetrical U-shape.
The equation of the parabola is [tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]The focus is [tex]\mathbf{Focus = (80, -1760)}[/tex]The directrix is [tex]\mathbf{y = \frac{1}{640}}[/tex]The axis of the symmetry of parabola is: [tex]\mathbf{x = 80}[/tex]From the question, we have:
[tex]\mathbf{Vertex: (h,k) = (80,10)}[/tex]
[tex]\mathbf{Origin: (x,y) = (0,0)}[/tex]
The equation of a parabola is:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
Substitute the values of origin and vertex in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]
[tex]\mathbf{0 = a(0 - 80)^2 + 10}[/tex]
[tex]\mathbf{0 = a(- 80)^2 + 10}[/tex]
[tex]\mathbf{0 = 6400a + 10}[/tex]
Collect like terms
[tex]\mathbf{6400a =- 10}[/tex]
Solve for a
[tex]\mathbf{a =- \frac{1}{640}}[/tex]
Substitute the values of a and the vertex in [tex]\mathbf{y = a(x - h)^2 + k}[/tex]
[tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]
The focus of a parabola is:
[tex]\mathbf{Focus = (h, \frac{k+1}{4a})}[/tex]
Substitute the values of a and the vertex in [tex]\mathbf{Focus = (h, \frac{k+1}{4a})}[/tex]
[tex]\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}[/tex]
[tex]\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}[/tex]
[tex]\mathbf{Focus = (80, -11\times 160)}[/tex]
[tex]\mathbf{Focus = (80, -1760)}[/tex]
The equation of the directrix is:
[tex]\mathbf{y = -a}[/tex]
So, we have:
[tex]\mathbf{y = \frac{1}{640}}[/tex] ----- the directrix
The axis of symmetry is:
[tex]\mathbf{x = -\frac{b}{2a}}[/tex]
We have:
[tex]\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}[/tex]
Expand
[tex]\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}[/tex]
Expand
[tex]\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}[/tex]
[tex]\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }[/tex]
A quadratic function is represented as:
[tex]\mathbf{y = ax^2 + bx + c}[/tex]
So, we have:
[tex]\mathbf{a = -\frac{1}{640}}[/tex]
[tex]\mathbf{b = \frac{1}{4}}[/tex]
Recall that:
[tex]\mathbf{x = -\frac{b}{2a}}[/tex]
So, we have:
[tex]\mathbf{x = -\frac{1/4}{2 \times -1/640}}[/tex]
[tex]\mathbf{x = \frac{1/4}{1/320}}[/tex]
This gives
[tex]\mathbf{x = \frac{320}{4}}[/tex]
[tex]\mathbf{x = 80}[/tex]
Hence, the axis of the symmetry of parabola is: [tex]\mathbf{x = 80}[/tex]
Read more about parabola at:
https://brainly.com/question/21685473
I need help pleaseeeee
Answer:
b
Step-by-step explanation:
5 5/16
Answer:
5 and 5/16
Step-by-step explanation:
70+2e+3e=180° answere me
Answer:
2e+3e=180-70
5e=110
e=110÷5
e=22
Write the equation of the parabola in vertex form.
vertex (3,1), point (2, - 4).
f(x)=
)
w
Realiza los siguientes problemas de Tanto Por Ciento.
1. Se desplaza un camión consumiendo el 60% de su combustible, si el tanque
lleno tiene 45 litros de gasolina ¿Cuántos litros ha consumido?
2. En un gimnasio una persona se pesa y tiene 78 kilogramos de peso, si el peso ideal (100%) para una persona de su edad es de 62 kilogramos ¿Cuales el porcentaje de peso que tiene la persona?
3. Un cohete lunar ha consumido el 20% de su tiempo de vida útil, el cual es de 15 años (100%) ¿Cuânto tiempo de vida útil ha consumido el cohete lunar?
4. El volcán de Pacaya incremento su altitud en 25 metros en su ultima erupción de ceniza, si el volcán mide 2,552 metro ¿Qué porcentaje de altura incremento?
5. Beni tiene el 40% de la edad de su hermano Aarón que tiene 24 años ¿Que edad tiene Beni?
Answer:
1. 27 liters
2. 125.8%
3. 3 years
4. 0.98%
5. 9.6 years
Step-by-step explanation:
1. (60%)(45) = 27 liters
2. Percentage of weight relative to ideal weight = (100%)(78/62) = 125.8%, rounded to nearest 10th of a percent.
3. (20%)(15) = 3 years
4. Assume that the beginning height is 2552 meters and the height increases 25 meters. Then, the percentage increase = (100%)(25/2552) = 0.98%, rounded to the nearest 100th of a percent.
5. Beni's age = (40%)(24) = 9.6 years
According to the graph, what is the value of the constant in the equation below?
Answer:
0.8
Step-by-step explanation:
just use guess and check. Divide each of the constants by the width of one point. When you find a constant that matches, try that out with all the other widths, if it works with the other widths, then you found the right constant!
A radio station requires DJs to play 2 commercials for every 10 songs they play. What is the unit rate of songs to commercials.
Answer:
5 : 1 or 10 : 2
Step-by-step explanation:
A teacher tells her students she is just over 1 and billion seconds old.
1. Write her age in seconds using scientific notation.
Step-by-step explanation:
Words Decimal Representation Scientific Notation
ten million 10,000,000 1 x 107
one hundred million 100,000,000 1 x 108
one billion 1,000,000,000 1 x 109
ten billion 10,000,000,000 1 x 1010
7
10 points
One force of magnitude 48 acts on an object. Another force of magnitude 90 acts on the object at a right angle, what is the magnitude of the resultant force on the object?
Type your answer...
Nathan usually drinks 38 ounces of water per day. He read that he should drink 71 ounces of water per day. If he starts drinking 71 ounces, what is the percent increase?
Answer:
104
Step-by-step explanation:
Answer:
87%
Step-by-step explanation:
Which polynomial function has a leading coefficient of 1, roots -2 and 7 with multiplicity 1, and root 5 with
multiplicity 2?
Of(x) = 2(x + 7)(x + 5)(x - 2)
Of(x) = 2(x-7)(x - 5)(x + 2)
Of(x) = (x + 7)(x + 5)(x + 5)(x - 2)
of(x) = (x-7)(x-5)(x - 5)(x + 2)
Mark this and return
Save and Exit
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Sb
Answer:
of(x) = (x-7)(x-5)(x - 5)(x + 2)
Step-by-step explanation:
Given: WX congruent yz
Prove: WYXZ
Answer:
Segment Addition
Step-by-step explanation:
1. WX ≅ YZ Given
2. XY = XY Reflexive
3. WX + XY ≅ YZ + YZ Addition
4. WY ≅ XZ Substitution/ Segment addition
I need help pleaseeeee
No links
maths giving 10 point asap 1 question only
Find the value of P
Answer:
p=7
Step-by-step explanation:
pqrs equal to tuv perimeters =60
triangle=20×3
60
Trapezium=(p+8)+12+12+3p
60=4p+32
4p=28
p=7
Find the equation in slope-intercept form that describes line.
A line through (-1, 1) and (2,3)
Answer:
y = 2/3 x + 5/3.
Step-by-step explanation:
Slope m = (3-1)/(2-(-1)) = 2/3.
y - y1 = m(x - x1)
y - 1 = 2/3(x - (-1))
y - 1 = 2/3(x + 1)
y - 1 = 2/3 x+ 2/3
y = 2/3 x + 5/3.
Tìm hàm số bậc nhất,biết đồ thị đi qua điểm (3;−2), song song với đường thẳng
′:3−2+1=0
20234555446698382636
What is the GCF of x^3y^5z^2 and x^4yz^5?
If your are confused the question is also in the picture down below
Solve: (x - y)/(sqrt(x) + 1) = 2 + (sqrt(x) - 5)/3
Solve for the unknown.
HELP PLEASEEEEEEE!!!!
Step-by-step explanation:
answer/ explanation is in the picture
Answer:
2.02units
Step-by-step explanation:
tan68°=[tex]\frac{5}{x}[/tex]=2.4750868534163,so x ≈2
HELPOOPPPOOPFOLFMTMR ME
Answer:
1.) 2y 2.) 14y
Step-by-step explanation:
You’ve decided to open a checking account. You know there are a number of differences with individual banking institutions. Name at least 3 good questions to ask to get started, and explain why knowing this information is helpful. Use complete sentences.
Answer:
1. Can I use the Atm for free?
2. What happens if I withdraw more money than I have in my account?
3. Does my account pay me intrest?
Step-by-step explanation:
1.ATMs allow you to withdraw money from your checking account without visiting a bank branch. But some withdrawals could cost you. Many banks charge you to use machines operated by other banks or third parties, and those fees can add up quickly.
2. Withdrawing more than your account contains is called an overdraft. Bank overdraft services generally allow your transaction to go through, but you will be charged a fee. Some banks prevent you from overdrafting when swiping your debit card and may let you request that all transactions are declined when your account doesn’t contain enough funds.
3. Generally, if checking accounts pay interest, the rate is very low. High-yield checking accounts offer higher interest but typically require higher balances. Savings accounts offer higher rates, but because the accounts are intended for saving, they’re subject to different rules
t (x) = 5x^2- 3x+4, what is the value t (-3)?
PLEASE HELP!!! 20 POINTS
Justify each step of the solution by stating the property that was used to get to each step.
Given: 2(10 − 13)+ 9 −5 = −34 + 55
Step 1: 2(10 −13) +9 = -34 + 60
Step 2: 20 — 26x + 9x = -34x + 60
Step 3: -17x = -34x + 40
Step 4: 17x =40
Step 5: x = 40/17
Answer:
Step-by-step explanation:
Properties used in each step are as below-
2 (10 -13x) + 9x = -34x +60
Step 1: -Associative property
Step 2: - Additive property of equality.
Step 3: - Additive property of equality.
Step 4: - Division property of equality
The expression -7y is a
a. term
b. variable
c. constant
Answer:
the answer is a) term
Step-by-step explanation:
hope this helps! :)
brainliest?
PLEASE HELP WILL MARK BRAINLIEST TO BEST ANSWER
Answer:
option D
[tex] {10x}^{2} + 3x - 8[/tex]
Answer:I would say A I found out 2X^2+-1 first
Step-by-step explanation:2x
2
+−1
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax
n
is nax
n−1
.
2×2x
2−1
Multiply 2 times 2.
4x
2−1
Subtract 1 from 2.
4x
1
For any term t, t
1
=t.
4x
Then I saw that 6-2 making 4 so I chose the first one
Andy is scuba diving. He starts at sea level and then descends 10 feet in 2 1/2 minutes.
Part A. How would you represent Andy’s descent as a unit rate ? Express your answer in an integer.
Part B.If he continues at this rate , where will Andy be in relation to sea level after 6 minutes?
Answer:
A. -4 feet per minute (FPM)
B. -24 feet below sea level.
Step-by-step explanation:
2)
Where is the opposite of -10 located on a number line?
ght
X
A)
to the left of o
he
ning
1.28
Cools
B)
to the right of 0
C)
to the right of 12
D
to the left of -10?
Answer:
B
Step-by-step explanation:
the opposite of -10 is 10
10 being bigger than 0 would therefore be to the right of 0
Answer:
B
Step-by-step explanation:
The opposite is positive 10. Negative 10 is the left to 0 and positive is always to the right of 0. Hope that helps <3
Identify the domain and range of the following relation. {(7,-2), (7,4), (7,6), (7,-4), (7,1)
Answer:
look at explanation
Step-by-step explanation:
domain= all the 7s
range: -2, 4, 6, -4, 1
Work out the value of 3.14
157/5....................
hey uhm can someone answer this for 12 points
[tex] \frac{0.2x - 3.2}{5} = 1.8 \\ 0.2x - 3.2 = 1.8 \times 5 \\ 0.2x - 3.2 = 9 \\ 0.2x = 9 + 3.2 \\ 0.2x = 12.2 \\ x = \frac{12.2}{0.2} \\ \boxed{ x = 61}[/tex]