The original Volkswagen Beetle follows
a quadratic curve, write an equation if
the height is 5 feet long and the length
is 14 feet long. Show your work in the
sketchpads below.
Answers
Answer:
[tex]y= -\frac{5}{49}x^{2}+5[/tex]
Step-by-step explanation:
In order to solve this, we need to start by drawing a sketch of what the problem looks like (see attached picture).
From the picture, we can see that the graph of the equation should be a parabola with a vertex located at the point (0,5) and x-intercepts located at (-7,0) and (7,0) respectively.
So, there are two ways in which we can build a quadratic equation:
Standard form:
[tex]y=ax^{2}+bx+c[/tex]
or
Vertex form:
[tex]y=a(x-h)^{2}+k[/tex]
Since we already have the vertex and two points on the equation, we can directly use the vertex form. Where vertex is located at the coordinates (h,k)
So in this case: h=0 and k=5, which simplifies our equation a lot:
[tex]y=a(x-0)^{2}+5[/tex]
[tex]y= ax^{2}+5[/tex]
So we only need to find the value of a for our equation to be complete. We can use either x-intercept to find this. Let's use the point (7,0) so we get:
[tex]0=a(7)^2+5[/tex]
and now we can solve for a:
[tex]-5=49a[/tex]
[tex]a=-\frac{5}{49}[/tex]
so this completes our equation:
[tex]y= -\frac{5}{49}x^{2}+5[/tex]
whose graph looks like the one in the attached picture.
Related Questions
A 6.50% coupon bond with 18 years left to maturity is offered for sale at $1,035.25. What yield to maturity [interest rate] is the bond offering? Assume interest payments are paid semi-annually, and solve using semi-annual compounding. Par value is $1000.
Answers
Answer:
The yield to maturity is 6.3974%
Step-by-step explanation:
The computation of the yield to maturity is as follows
Given that
NPER = 18 × 2 = 36
PMT = $1,035.25 × 6.50% ÷ 2 = $33.65
PV = $1,035.25
FV = $1,000
The formula is shown below:
=RATE(NPER;PMT;-PV;FV;TYPE)
The present value comes in negative
AFter applying the above formula, the yield to maturity is
= 3.1987% × 2
= 6.3974%
Hence, the yield to maturity is 6.3974%
4/5 divided by 1/5 in unit form
Answers
Answer:
answer to your question is 4
What is the y intercept of y =4x
Answers
Answer:
origin of the graph (0)
Step-by-step explanation:
because it does not have a b value it is zero if there is no plus or minus a number at the end it is always 0 when dealing with the y=mx+b equation
Jason and his twin brother, Seth, are painting the walls in their bedroom. It took Jason 50 minutes to paint a 160-square-foot wall. It took Seth 30 minutes to paint a 120-square-foot wall. Who painted faster?
Answers
Answer:
Jason
Step-by-step explanation:
Answer:
It's Seth
Step-by-step explanation:
An above-ground garden is in the shape of a rectangular prism measuring 5 feet by 8 feet by 1.5 feet. The organic soil costs $1.20 per cubic foot. How much will it cost to fill the above-ground garden fully?
Answers
Answer:$72.00
Step-by-step explanation: To find the volume you do 5×8×1.5 which equals 60. Then you multiply 60 by 1.20 to find your total cost. Answer is 72
What’s the common factor for 72 and 84
Answers
Answer:
Step-by-step explanation:
This is the general method for doing this problem. First factor these numbers into primes.
72: 2 * 2 * 2 * 3 * 3
84: 2*2 * 3 * 7
Now each number has at least two 2s
Each number has at least one 3
The highest common factor is 2 * 2 * 3 = 12
Solve the inequality
Answers
need help asap
Google maps determines that a destination is 50 miles away and that the average speed of a car in this area is 23.2 miles/hour. How long should Google maps predict it will take you to drive to your destination?
Answers
Answer:
2 hours, 9 minutes (and 19 seconds if u wanna be exact)
Step-by-step explanation:
Abbey receives a $40 gift card for downloading music and wants to determine how many songs she can purchase. Each downloaded song costs $2.89 a. Let m represents the number of songs downloaded. Write an inequality that represents this given situation? b. What is the maximum number of songs Abbey can download?
Answers
Answer:
A. $2.89(m)=$40
B. 13 songs
Step-by-step explanation:
$2.89(m)=$40
m=$40/$2.89
m=13.84
She can download a maximum of 13 songs
Check:
$2.89 (13 songs)=$37.57
$40-$37.57=$2.43 left on her gift card
m=13.84, check that 0.84 of the cost of a song is left over 0.84*$2.89=$2.43
Answer:
13 songs
Step-by-step explanation:
40 divided by 2.89 is 13.84. DO NOT ROUND TO 14
So its a maximum of 13 songs, otherwise it will cost 40.46 for 14 songs
20) Solve the problem. Suppose that 12 unique names are put into a hat and drawn at random without
replacement. How many different ways can you draw all of the names from the hat? Remember that
"without replacement" means that the names are not returned to the hat after they are chosen. Write your
answer in factorial notation.
SHOW WORK: None to be shown
A) 12!
B) 11!
C) 10!
D) 12! - 1
Answers
the answer would be A) 12 because there are only twelve names
The number of different ways is 12! you can draw all of the names from the hat without replacement option (A) 12! is correct.
What are permutation and combination?
A permutation is the number of different ways a set can be organized; order matters in permutations, but not in combinations.
It is given that:
Number of unique names = 12
That 12 unique names are put into a hat and drawn at random without
replacement.
"Without replacement" means that the names are not returned to the hat after they are chosen.
Number ways (without replacement) = 12x11x10x9x8x7x6x5x4x3x2x1
Number ways (without replacement) = 12!
Thus, the number of different ways is 12! you can draw all of the names from the hat without replacement option (A) 12! is correct.
Learn more about permutation and combination here:
https://brainly.com/question/2295036
#SPJ2
You have $500, sale price is $435. How much change will you get
Answers
I’m sorry if this is wrong it’s two in the morning
I guess this is what college does to u....
Answer:
go to sleep its 11:23 also u will get
$65 dollars pls mark me brainleist
Step-by-step explanation:
Evaluate the
determinant.
Answers
Answer:
I think it's 21
Step-by-step explanation:
Hellllp please asap
Answers
Between the hours of 10pm and 6am, the temperature decreases an average of 3/4 of a degree per hour. How long will it take for the temperature to decrease by 5 degrees?
Answers
Answer: it take for the temperature to decrease by 5 degrees 5 weeks
Step-by-step explanation:10pm and 6am, the temperature decreases an average of 3/4 of a degree per hour.
3,000 ÷ 50=300 ÷ 5 =?
Answers
Write an Equivalent Expression by combining like terms for 2x+3x+y+2y
Answers
Answer:
5x+3y
Step-by-step explanation:
2x+3x=5x since they have the same variable.
y+2y
1y+2y u can put a 1 so that would be 3y
5x+3y
3. Simplify the following inequalities.
Answers
Answer:
7x+7 > 23-x
group like terms
7x+ x > 23-7
8x > 16
we divide both side by
8x > 16
8 8
so 8 cancelled out 8 living
x > 16
8
x > 2
8
we
Given the points P(2, –6) and R(8, 3), what is the component form of Vector PR?
- ⟨6, -3⟩
- ⟨10, -3⟩
- ⟨6, 9⟩
- ⟨10, 9⟩
Answers
Answer:
the third one
Step-by-step explanation:
jsut took it
Answer:
It’s C
Step-by-step explanation:
(1 point) A pond contains 100 fish, of which 40 are carp. If 20 fish are caught from the lake, what are the mean and variance of the number of carp among those 20
Answers
Answer:
E(X) = 6
Var(X) = 3.394
Step-by-step explanation:
Let X represent the number of carp caught out of the 20 fishes caught. Now, if we are to assume that each
of the (100, 20) ways to catch the 20 fishes will be equally likely.
Thus, we can say that X fulfills a hypergeometric
distribution with parameters as follows;
n = 20, N = 100, k = 30
Formula for expected mean value in hypergeometric distribution is;
E(X) = nk/N
E(X) = (20 × 30)/100
E(X) = 6
Formula for variance is;
Var(X) = (nk/N) × [((n - 1)(k - 1)/(N-1))) + (1 - nk/N)]
Var(X) = ((20 × 30)/100) × [((20 - 1)(30 - 1)/(100 - 1)) + (1 - (20 × 30/100)]
Var(X) = 6 × 0.5657
Var(X) = 3.394
What is 1.452 rounded to the nearest hundredth
Answers
Answer:
1.450
Step-by-step explanation:
what grade ar4e you in I'm guessing 4th or 5th
A barrel of 20 apples has 2 rotten apples and 18 good apples. 7 apples are selected at random from the barrel. What is the expected number of good apples selected
Answers
Answer:
Expected value = 7 x 0.9 = 6.3
Step-by-step explanation:
Probability of getting a good apple is 18/20 = 0.9
Probability of getting a bad apple is 2/20 = 0.1
This follows a binomial distribution because either you get a good apple or a bad apple.
The expected value of a binomial distribution is given as n*p where n is number of trials and p is the probability of success.
In this case our number of trials is 7 and the probability of success is 0.9, since the trials are for getting good apples.
Hence
n = 7
p = 0.9
Expected value = 7 x 0.9 = 6.3
HELP NOW
Write an equation of the parabola that passes through the point (62,−490) and has x-intercepts −8 and 72. Then find the average rate of change from x=−8 to x=2.
Answers
Answer:
y = 0.7(x^2 - 64x - 576)
Average rate of change = -49.
Step-by-step explanation:
As the x intercepts are -8 and 72 we can write the equation
y = a(x + 8)(x - 72) where a is some constant to be found.
As it passes through point (62, -490) we have, substituting:
-490 = a(62+8)(62-72)
-490 = - 700a
a = 0.7
So the equation of the parabola
y = 0.7(x + 8)(x - 72) or
y = 0.7(x^2 - 64x - 576).
Average rate of change between x = -8 and x = 2
= [0.7(2+ 8)(2 - 72) - 0.7(-8+8)(-8-72)] / (2 - -8)
= -490 - 0 /10
= -49
Where is most of Earth’s fresh water found?
in the ground
near the poles
in lakes and streams
in the air as water vapor
Answers
Answer:
B: near the poles
Step-by-step explanation:
got it right on edge 2020
Answer:
near the poles
Step-by-step explanation:
trust me I know
Help me I’m not sure the answe
Answers
Answer:
i believe it would be the last option.
Step-by-step explanation:
In an election for school president, the loser received 70% of the winner's votes. If 969 votes were cast, how many did each receive?
Answers
Answer:
The ans would be 291 (however we can round this off to 290 as no can partially vote as 0.1)
Step-by-step explanation:
We can easily find the loser's vote by-
70% of 969= 678.9
now, all we need to do is find the winners vote
we know that the total no. of votes= 969 & we know the no. of votes loser got
so, subtracting the losers vote from 969 would give us the remaining no. of votes (the winner's votes)....so,
969-678.9=290.1
we can round this off to 290
Over which of the given intervals does g have an average rate of change of zero?
Choose 1 answer:
3<3<9
B
2 <3 <4
-9 <<-5
D
--2 <<3
Answers
Answer:
I think is c 2 hope that works
Step-by-step explanation:
please give brainliest :D
expand 2 + 4 how do i do this
Answers
Answer:
6
Step-by-step explanation:
You could expand t to 1+1+1+1+1+1 which would give you 6.
Answer:
2+4=6
Step-by-step explanation:
write the fraction of 15/25 in its simple form
Answers
Answer:
3/5
First you would need to find the greatest common factor of 15 and 25
which is 5
Then divide the numerator and denominator by the GCF
15 divided by 5
25 divided by 5
Then simplify your answer is
3/5
A seven-person relay team completed a race in 84.7 seconds. On average, what was each runner's time?
Answers
Answer:
12.1 seconds
Step-by-step explanation:
84.7/7 = 12.1
Answer:
12.1
Step-by-step explanation:
Divide the 84.7 by the # of people on team (7)
1. Explain the difference between circumscribed angles and inscribed angles in relationship to a circle.
2. Explain, in your own words, the steps required to convert any equation of a circle into standard form be completing the square.
3. Explain/define the following terms, or draw a picture and label the terms.
a. radius
b. diameter
c. chord
d. secant
e. tangent
f. point of tangency
Answers
9514 1404 393
Explanation:
1. Consider the attachment. Angle CDF is a circumscribed angle. It is formed at the intersection of two tangents to the circle. Angles BCE, CBE, and BEC are inscribed angles. Their vertices are on the circle, and they are formed by two chords.
If a chord degenerates to zero length, the ray it represents with respect to an inscribed angle becomes a tangent. That is, angles BCD and ECD can also be considered to be inscribed angles. Similarly, straight angle DFG at tangent point F can be considered to be a degenerate case of both an inscribed angle and a circumscribed angle. (Some authors may not include degenerate cases in their definitions. YMMV)
__
2. The general form of the equation of a circle is ...
Ax² +Ay² +Dx +Ey +F = 0
Any equation of a circle can be put in this form. If we divide by A, this can be written as ...
x² +y² -2hx -2ky +c = 0 . . . . where h = -D/(2A), k = -E/(2A), c = F/A
and the equation can be further transformed to the standard form ...
(x -h)² +(y -k)² = r² . . . . . where r² = h² +k² -c
The last equation is the result of "completing the square" by adding h² and k² to both sides of the second equation shown. The values of h and k are as shown above, given the coefficients of the general form equation.
__
3. Again refer to the attached diagram.
a) a radius is a line segment with the circle center at one end and a point on the circle at the other end. AB and AC are radii.
b) A diameter is a line segment whose ends are on the circle and whose midpoint is the center of the circle. BC is a diameter.
c) A chord is a line segment whose end points lie on the circle. BC, BE, and CE are chords.
d) A secant is a line containing two points of the circle. Lines CG and CE are secants.
e) A tangent is a degenerate case of a secant in which the two points of intersection merge to one point of intersection. It is a line that touches the circle at exactly one point, the point of tangency. DG and DC are tangents.
f) The point of tangency is the single point where a tangent intersects a circle. A radius to the point of tangency (such as AC) is always perpendicular to the tangent line (DC).
