The spider's movement is an illustration of a parabola.
The equation of a parabola is: [tex]\mathbf{y = -\frac{1}{160}(x - 40) + 10}[/tex]The focus of a parabola is: (40,-30)The axis of symmetry is: [tex]\mathbf{x = 40}[/tex]The directrix is:[tex]\mathbf{y = 50}[/tex](a) The equation
The spider passes through the origin.
So, we have:
[tex]\mathbf{(x,y) = (0,0)}[/tex]
The spider jumps to a maximum height of 10mm, midway 80mm.
So, the vertex is:
[tex]\mathbf{(h,k) = (40,10)}[/tex]
The equation of a parabola is:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
So, we have:
[tex]\mathbf{0 = a(0 - 40)^2 + 10}[/tex]
Subtract 10 from both sides
[tex]\mathbf{a(0 - 40)^2 =- 10}[/tex]
[tex]\mathbf{1600a =- 10}[/tex]
Solve for a
[tex]\mathbf{a =- \frac{1}{160}}[/tex]
Substitute [tex]\mathbf{a =- \frac{1}{160}}[/tex] and [tex]\mathbf{(h,k) = (40,10)}[/tex] in [tex]\mathbf{(h,k) = (40,10)}[/tex]
[tex]\mathbf{y = -\frac{1}{160}(x - 40) + 10}[/tex]
(b) The focus, directrix and the axis of symmetry
The focus of a parabola is:
[tex]\mathbf{Focus= (h, k + p)}[/tex]
Where:
[tex]\mathbf{p = \frac{1}{4a}}[/tex]
So, we have:
[tex]\mathbf{p = \frac{1}{4 \times -1/160}}[/tex]
[tex]\mathbf{p = -\frac{160}{4}}[/tex]
[tex]\mathbf{p = -40}[/tex]
So, we have:
[tex]\mathbf{Focus = (40,10-40)}[/tex]
[tex]\mathbf{Focus = (40,-30)}[/tex]
The axis of symmetry is:
[tex]\mathbf{x = h}[/tex]
So, we have:
[tex]\mathbf{x = 40}[/tex]
The directrix is:
[tex]\mathbf{y = k - p}[/tex]
[tex]\mathbf{y = 10 + 40}[/tex]
[tex]\mathbf{y = 50}[/tex]
Read more about parabolas at:
https://brainly.com/question/25237745
Please help me thank you
Answer:
C. The product of 12 and √17
Step-by-step explanation:
Because it gives a number that isn't a repeating or terminating decimal.
What is the answer for this question:12+2c+6d-8c+d
Answer:
12+10c+7d
Step-by-step explanation:
There is no possible way to really describe the value of the variables, so I simplified it.
Can someone solve this and thanks
Given the function f(x)=x^2+2x+1, find each value of the function
Answer:
1 9/16
Step-by-step explanation:
F(1/4) means u plug in 1/4 for x
so the equation would be
f(1/4)=1/4^2+2 1/4 + 1
f(1/4)=1/16+1/2+1
f(1/4)= 9/16 +1
f(1/4)= 1 9/16
its not nine teen its one and 9 over 16 just clarification
Suppose Felipe has 9.24 pounds of seed if it takes 6.6 pounds of seed to plant on acre of grass how many acres of grass can be planted?
Answer:
1.4 acres of grass can be planted.
Step-by-step explanation:
He has 9.24 pounds of seeds.
If one acre of grass needs 6.6 pounds of seeds we can divide 9.24 pounds by 6.6 pounds to find how many acres of grass he can plant.
9.24 lbs × [tex]\frac{1acre}{6.6 lbs}[/tex] = 1.4 acres
13 For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a
coordinating response. Be sure to clearly label each part of your response as Part A Part B, and Part C.
Part A: Jamal has $35 to spend at the mall. If pairs of shorts are $9.99, how many can he buy?
Part B: Round your answer to an appropriate number.
Part : In a short paragraph, explain in your own words your work for Steps A and B.
Answer:
35 / 9.99 = can buy 4 rounded
paragraph: To find how many pairs of shorts we can buy, we must divide our total money with the cost. We are diving because we need to find how many times 35 can go into 9.99 to find our number. 35 / 9.99 = 3.5035035035035. Our answer must be rounded now because shorts are in whole numbers and can't be in decimals. Take the tenth place of the decimal and round it to the nearest number. 5 is closer to 10 than 0 so we just round it to 4 and there is our answer.
Robin earned $4,581 in 9 weeks. How much does he earn per week?
Answer:
$509 per weekStep-by-step explanation:
Well, in order to find the unit rate we simply do the following steps:
4,581 ÷ 9 = 509
So to answer the question, each week Robin earns $509.
Hope this helps! : )
Answer:
they earn 509 a week
Step-by-step explanation:4581 divided by 9
Question 1
Tim is a car salesman and earns a 5% of the price of the cars he
sells: Last month he sold 8 cars for a total of $152,558.75.
Estimate the amount Tim earned last month.
Answer:
152558.75*5%=7627.9
Step-by-step explanation:
What is the slope of the line on the graph?
Enter your answer in the box.
Answer: The slope of the line is 6.
You can use the distance formula to find the slope (Y2-Y1/X2-X1). You can plug in any two points seen on the graph into the formula. I will use (0,-1) and (1,5). When I plug in the values, 5-(-1)/1-0=6/1=6. So the slope of the line is 6.
:)
HELP HELP! Will give brainliest
Answer:
2347897876 my number
Step-by-step explanation:
Mr. Mole's burrow lies 5 meters below the ground. He started digging his way deeper into the ground, descending 3 meters each minute. Graph the relationship between Mr. Mole's elevation relative to the ground (in meters) and time (in minutes).
coordinates please!
Answer:
See the graph attached
Step-by-step explanation:
Every minute = 3m
At time zero, the depth is zero
Giving coordinates of (0, 0)
At time 1 minute, the depth is 3m
Giving coordinates of (1, 3)
This gives a linear equation
Slope = Δy/Δx
= (3-0)/(1-0)
= 3/1
= 3
Take any general point (x, y)
The equation of the line is:
(y-0)/(x-0) = 3
y/x = 3
y = 3x
See the plot which goes up to a depth of 5m
-x + 2y = 5
5x - 10y = 11
Solve for x and y they have to be equal
Answer:
Sorry for the late notice but I
Ig1000+log342 - 1 -123
Answer:
log(342) - 121
Step-by-step explanation:
-121 + log(342) is a transcendental number
-115.165189262937394847783249972808918485...
For brainily please help
Answer:
Yes
Step-by-step explanation:
Use a property of equality to solve this equation:
4.5x = 18
x =
Answer:
4
Step-by-step explanation:
x= 18÷4.5=4
hope it helps
f) create a residual plot for your data.
g) does your residual plot show that the linear model from the regression calculator is a good model?
h) using your equation estimate the gpa of a student who studies for 15 hours a week.
PLSSSSS NEED HELP
Answer: Consider the plot created from the residuals of a line of best fit for a set of data. Does the residual plot show that the line of best fit is appropriate for the data? Yes, the points have no pattern.
Step-by-step explanation:
HELP ME PLEASE!!!!! I NEED THIS BRAINIEST IF CORRECT ANSWER!!!!!
Answer:
- 3/4 feet per hour
Step-by-step explanation:
Rate of change is the slope.
Take two points on the graph and use the slope formula.
Points:
(0, 9) and (4, 6)The slope is:
m = (6 - 9)/(4 - 0) = -3/46 find the missing length
Answer:
C) 143
Step-by-step explanation:
GL/FL = NL/ML
36/39 = 132/ML
39/36 = ML/132
(39/36) x 132 = ML
143 = ML
Hope This Helps! •v•
(14.7+9.3) times (1/2)2
Answer:
24
Step-by-step explanation:
4.5 kg equals times one gram
Answer:
4500 gr
Step-by-step explanation:
4.5 kg equals some number (n) times one gram. Solve this for n:
4.5 kg = n(1 gr)
Recall that 1 kg = 1000 gr. Because of this, the equation above becomes
4.5 kg (4.5)(1000 gr)
n = --------------- or ------------------- or 4500 gr
1000 gr 1 gr
if kathy had 1700 apples and split with her 4 friends. and then one friend give her back 15 apples. and she gives then 1 apple back. how. much does she have.
Answer:
439
Step-by-step explanation:
1700/4=425
15-1=14
425+14=439
I WILL GIVE BRAINLYEST
Answer:
0.93
Step-by-step explanation:
3. The first row shows s(1) = 0.5. What does this mean in words?
Answer:
this means it shows half as a fraction turned into a decimal
Step-by-step explanation:
1/2=fraction form
0.5=decimal form
50%=percent form
half=word form
HELP PLEASE THIS IS DUE TOMORROW 1. Mr. Connors drives his car 11 miles each day to and from work. Is the distance Mr. Connors drives commuting to work proportional to the number of days he works? How do you know?
Answer:
short answer Yes and No
Step-by-step explanation:
long answer
let's say he drives to and from work 5 days a week that's 110 hours driving to and from work. But let's say he only drives to work and from work 2 days a week that only 44 hours driving to and from work. But now let's say he only drives 2 days a week but has to keep driving to and back from work because he forgets something at his house or at work and say he hasto drive and extra 77 hours because he forgot something that's now 99 hours he drove to and from work but only worked 2 days out of the week
Hope this helped :)
which expression has the fewest number of significant figures?
a. 360
b. 18.3
c. 296.54
d. 5,280
Answer:
A has two significant figures
The others have at least three
the average age of teacher at school is 36 years.mr Smith age is 11/9 of the average. how old is Mr Smith?
Answer: 44
Step-by-step explanation:
I'm positive this is right! Have a good day! Hope this helps! Please give brainliest, i would help a lot if you did, but its fine if you don't Just have a good rest of the day!
Solve the math problem
Answer: Slopes
Step-by-step explanation:
1. slope is [tex]\frac{4}{3}[/tex]
2. slope is [tex]\frac{1}{2}[/tex]
3. Slope is [tex]\frac{4}{2}[/tex] or 2
4. slope is [tex]\frac{3}{2}[/tex]
Olivia deposits $6,952 in a savings account paying 3.72% interest. To the nearest dollar, how much money does Olivia have in total after sixteen years?a.$4,138b.$8,568c.$11,090d.$29,901
Answer:
11090
Step-by-step explanation:
6952x.0372=258.61
258.61x16=4137.83
4137.83+6952=11090
Answer:
C on EDGE 2021
Step-by-step explanation:
The map shows the location J of Jose's house, the location of Tyrell's house, and the
location Fof the football field. Jose is going to Tyrell's house and then the two of them are
going to the football field for practice. How far did Jose travel to football practice?
Using distance between two points, it is found that Jose traveled 25 units of length to football practice.
The distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:
[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
First, Jose goes from his house, at (-6,8), to Tyrell's house, at (6,8), thus:
[tex]D_1 = \sqrt{(6 - (-6))^2 + (8 - 8)^2} = \sqrt{12^2} = 12[/tex]
Then, he goes from Tyrell's house, at (6,8), to the football field, at (6, -5), thus:
[tex]D_2 = \sqrt{(6 - 6)^2 + (-5 - 8)^2} = \sqrt{13^2} = 13[/tex]
The total distance is:
[tex]D = D_1 + D_2 = 12 + 13 = 25[/tex]
Jose traveled 25 units of length to football practice.
A similar problem is given at https://brainly.com/question/22532602
When or how do you use them to solve for the answer
Answer:
a) Δt = vf - vi ÷ a
b) (a × Δt) + vi = vf
