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:
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HELP ME PLEASE I legit suck at rounding
Answer:
Alright, this is a lot, here are the answers.
Round to the nearest thousand:
1. 14,000
2. 30,000
3. 3,000
4. 10,000
5. 56,000
6. 90,000
Round to the nearest ten thousand:
1. 20,000
2. 40,000
3. 150,000
4. 20,000
5. 300,000
6. 80,000
Round to the nearest ten:
1. 90
2. 2,680
3. 270
4. 510
5. 100
6. 2,750
Round to the nearest hundred:
1. 800
2. 3,000
3. 5,000
4. 300
5. 5,500
6. 600
One More!
Round to the nearest hundred thousand:
1. 900,000
2. 100,000
3. 1,000,000
4. 800,000
5. 200,000
6. 400,000
There those are the final answers! Let me know if any are incorrect and I'll fix them!
Brainliest are appreciated!
a scarf is made of 65% cotton.If the scarf weighs 18 ounces,then how much cotton is in the scarf( STEPS PLEASEE)
Answer: 11.7 ounces
Step-by-step explanation:
65% of 18 is:
0.65*18=11.7
Therefore, the answer is 11.7 ounces.
Answer:
There are 11.7 oz of cotton in this scarf.
Step-by-step explanation:
The scarf weighs 18 oz. We are told that 65% of the makeup of the scarf is cotton. To determine how much cotton is in the scarf, we multiply the scarf's full weight, 18 oz, by 0.65 (0.65 is the decimal fraction equivalent of 65%):
0.65(18 oz) = 11.7 oz
There are 11.7 oz of cotton in this scarf.
In a school annual Day 60 students involved is Science Exhibition, 75 involved in Mathematics Exhibition, 20 involved in both Exhibitions, and the rest of 285 students are not involved in any exhibition. Illustrate the above information in a Venn- diagrom. How many students took part in Schools Annual Day? How many of them involved in only one exhibition ?
Answer:
440 man its so easy just add up all the numbers
Step-by-step explanation:
440
Answer:
1) See the explanation
2) 400 Students
3) 95 Students
Step-by-step explanation:
1) As can be known from the question
Then, draw the venn diagram according to the known conditions.
2) 60 + 75 - 20 = 115 { Draw a venn diagram to calculate }
115 + 285 = 400
3) 60 - 20 + 75 - 20 = 95 ( Draw a venn diagram to calculate }
PLSSS HLEPP ME OUTT ITS URGENTTTT
Answer:
[tex]P(B) = \frac{4}{18} = \frac{2}{9} = 0.2[/tex]
Step-by-step explanation:
Sample space 2+5+7+4=18
Answer:
4/18 or 2/9
Step-by-step explanation:
The total number of balls = 2 + 5 + 7 + 4 = 18
4 out of the 18 balls are blue ∴ the probability is 4/18 or 2/9
Hope this helps!
help fast pleaseee
NO RANDOMS
Answer:
a)-30
b)-60
c)98
d)-54
Step-by-step explanation:
320/-4
-180/3
-14X-7
6X-9
Solve the quadratic equation 2x^2-4x+1=0
Answer:
Step-by-step explanation:
= 2 ± 2 √ 2
Please help with this linear equation question. Image Attached.
There is no image, and without the image, no answer.
PlsSSS answer this is due at 11 am today and i dont know
Answer:
where is the question???..............
Please answer this question
Answer:
it is C
Step-by-step explanation:
What is the P (getting a number less than 8)?
Answer:
2/3
Step-by-step explanation:
there's 6 total and 4 numbers less than 8 so probability is 4/6 simplify and u get
2/3
Which shows where the function is decreasing?
O A only
O Conly
O C and D
O A and C
What is the length of the segment
Answer:
9 units
Step-by-step explanation:
There are 15 pieces of the same size candy in a bag. Four are banana flavored, three strawberry flavored, six cherry flavored, and two orange flavored. What would be the probability of picking a banana, cherry, or a strawberry flavored candy from the bag? Write your answer as a simplified fraction in a/b form.
Answer:
(Hope this helps can I pls have brainlist (crown)☺️)
Step-by-step explanation:
In pic
The dinner check for Lee's family was $79.30. Estimate a 15% tip.
Answer:
$11.90
Step-by-step explanation:
79.30 times 0.15
Answer:
The answer is 11.895. That's the exact answer.
Step-by-step explanation:
Original price X Discount %
A. Annie is correct. Keegan did not regroup properly. B. Keegan is correct. Annie did not regroup properly. C. Keegan is correct. Annie did not line up the decimals correctly. D. Annie is correct. Keegan did not line up the decimals correctly.
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The Correct choice is C
Keegan is correct, Annie didn't line up the decimals correctly.
Alan has forgotten his 4-digit PIN code.He knows it begins with a 6 and the 4 digits make an even number.How many different sets of 4 digits could it be?
Answer:
500.
Step-by-step explanation:
The last digit must end with 0, 2, 4, 6, 8 for the Pin code to be even.
The middle 2 digits may be any numbers.
So if the last number is 0 Then there are 10*10 = 100 possible PIN codes.
So as there are 5 possible last digits , the total possible sets of digits
= 5 * 100
= 500.
Help out pleassseeeeeee
Step-by-step explanation:
bro, MO bisects into 2 equal halves. ..
so, there will be
Angle AMO is equal to angle BMO.__(A)
MO is common side ___( S)
Angle AOM is equal to angle MOB___(A)
hence ,
∆AMO is congrent to ∆BMO
hence proved
211-0 + (-71-9)
.
Simplify
0 0
-3,12
-3
0 -3
DONE
Answer:
-3, -
Step-by-step explanation:
I took the test
cancelout the v^-6
21/-7
-3
Answer:
Step-by-step explanation:
[tex]\dfrac{21y^{-6}}{-7y^{-6}}= (-3) *y^{-6 -[-6]} = (-3)*y^{6+6}=-3*y^{0} = -3*1 = -3[/tex]
pleases help me! with my math hw!!! please do 2-26 evens only!!!! thx!! will give brainliest and extra points!!
how do you solve y=x+12 y=-18
Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values.
please help
The Finance Committee: Nine members of a finance committee could not get together for an emergency meeting. However, during the next three days, each member talked to each other member on the telephone. What is the minimum number of phone calls needed to accomplish this?
The Merry-Go-Round: On a merry-go-round, 12 horses are evenly spaced on the outside perimeter. It takes four seconds for the fourth horse to reach Abe,starting when the first horse is opposite him. How long will it take the merry-go-round to go around once?
Answer:
1) How does "Abe" relate to the merry-go-round? (The problem doesn't seem to say.)
2) How many people did each person provide for? So how many dozens were brought? How many are in a dozen? So how many cookies were brought?
Step-by-step explanation:
nm the top
There are n seats on a merry- go-round. A boy takes n rides. Between each ride, he moves clockwise a certain number of places to a new horse. Each time he moves a different number of places. Find all n for which the boy ends up riding each horse.
2) So if there are n horses, first the boy could move by one place then he could move by n+1 places then by 2n+1 so on and so forth, until he moves (n−2)n+1 places, in which case he'd would have been ridden each horse only one time and taken unique number of steps, which implies that all n's satisfy given condition.
1) I don't know how to cancer this let me resheerch and ill get back to you
P>S let this be help only if you need to annotate or reword thx
Express the interval shown on the number line in inequality notation.
G
T-
10 12
-12
-6
6
-10
8
-8
-2 0
24
-4
A
U
>>
Al
00
IA
00
or
D.
[]
(,) || ()
I
Inequality Notation:
Answer:
Umm Where's The Answer?
WHAT IS THE MEASURE OF ANGLE #5
WHAT IS THE MEASURE OF ANGLE #6
WHAT IS THE MEASURE OF ANGLE #7
WHAT IS THE MEASURE OF ANGLE #8
Answer:
5)42º
6)112º
7)112º
8)38º
Step-by-step explanation:
m<6 180-68=112
m<5 180=26+112+x 42=x
m<7 is congruent to m<6
m<8 180=30+112+x 38=x
Shyla Cuts 6 strips of ribbon to make her hair bows when she is done she realizes that each strip is 1/8 too short how does the total length of strips compared to what their total length should have been?
10 yd
5 yd
7 yd
2 yd
Perimeter:
Area:
Answer:
p= 24
a=50
Step-by-step explanation:
p= rectangle l+b+l+b or square l+l+l+l
a= rectangle lxb or square lxl
answer pls for 30 points and brainliest
Answer:
your answer will be letter B
Step-by-step explanation:
You went grocery shopping with $40.65. You left the
store with $5.10. Write an equation you can use to find
the cost c of the groceries.
C
Answer:
$40.65 - c = $5.10
Step-by-step explanation: You will subtract $5.10 from both sides to get the answer to C
The cost of the groceries is $35.55.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total amount = $40.65
Amount left = $5.10
The equation for the cost of groceries C.
40.65 - C = 5.10
Solve for C.
40.65 - 5.10 = C
C = 35.55
Thus,
The cost of the groceries is $35.55.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
Is -92.41 an integer
Answer:
No
Step-by-step explanation:
Because it is a decimal, it can't be an integer. Integers are whole numbers and can be positive or negative.
Hope this helps!
Please tell me the answer by process
Answer:
1680/10= 168
168/2= 84
84 is the answerStep-by-step explanation:
1680/10 bc u have to get rid of the volume height and that leaves two bases
168/2 bc u only need one side NOT two bc of the book covers one base not two
PLZZZ LOOK AT THE PHOTO PROVIDE HELPPPP I NEEED HELPPPPPPPPPOPP
Answer:
OH MY GOSH I DON'T KNOW BUT GL! WISH YOU THE BEST AAAAA-
Step-by-step explanation:
Answer:
ITS A
trust me it's quite simple. you just need to find the overall pattern of the sequence