The total distance in d,in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, is the time in seconds. At a time of 10. 0 seconds the total distance is traveled by the objects is 50. 0 meters and at a time of 20. 0 seconds the total distance traveled by the object is 200. 0 meters if the object was at a distance of 0 meters when t=0 then what is the total distance traveled in meters, by the object after 30. 0 seconds
Answers
Let's denote the total distance traveled by the object as `d` and time as `t`.
We can use the given information to set up a system of equations:
When t = 10.0 seconds, d = 50.0 meters
50.0 = a(10.0)^2 + b(10.0) + c (Equation 1)
When t = 20.0 seconds, d = 200.0 meters
200.0 = a(20.0)^2 + b(20.0) + c (Equation 2)
When t = 0 seconds, d = 0 meters
0 = a(0)^2 + b(0) + c (Equation 3)
Simplifying Equation 3, we get c = 0.
Substituting c = 0 in Equations 1 and 2, we get:
50.0 = 100a + 10b (Equation 4)
200.0 = 400a + 20b (Equation 5)
We can solve Equations 4 and 5 simultaneously to get the values of `a` and `b`:
From Equation 4, we get:
10b = 50 - 100a
b = 5 - 10a
Substituting this value of `b` in Equation 5, we get:
200.0 = 400a + 20(5 - 10a)
200.0 = 400a + 100 - 200a
200.0 = 200a + 100
100.0 = 200a
a = 0.5
Substituting this value of `a` in Equation 4, we get:
50.0 = 100(0.5) + 10b
50.0 = 50 + 10b
b = 0
Therefore, the quadratic function that models the total distance traveled by the object is:
\(d = 0.5t^2\)
To find the total distance traveled by the object after 30.0 seconds, we can substitute `t = 30.0` in the above equation:
\(d = 0.5(30.0)^2\)
d = 450.0 meters
Therefore, the object will travel a total distance of 450.0 meters after 30.0 seconds.
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Related Questions
1) Louis is dilating triangle ABC at right. He
multiplied each x-coordinate and y-coordinate of
triangle ABC by -2.
a. What are the new coordinates of the points?
Answers
To find the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2, we can use the following formulas:
New x-coordinate = -2 * old x-coordinate
New y-coordinate = -2 * old y-coordinate
Let's apply these formulas to each point in triangle ABC:
Point A: (-3, 4)
New x-coordinate of A = -2 * (-3) = 6
New y-coordinate of A = -2 * 4 = -8
New coordinates of A: (6, -8)
Point B: (1, 1)
New x-coordinate of B = -2 * 1 = -2
New y-coordinate of B = -2 * 1 = -2
New coordinates of B: (-2, -2)
Point C: (5, -2)
New x-coordinate of C = -2 * 5 = -10
New y-coordinate of C = -2 * (-2) = 4
New coordinates of C: (-10, 4)
Therefore, the new coordinates of the points after Louis multiplied each x-coordinate and y-coordinate of triangle ABC by -2 are:
A: (6, -8)
B: (-2, -2)
C: (-10, 4)
Image transcription textSuppose the following two simple statements are true.
The scroll is open.
The writings are visible.
Determine which of the following compound statements would also be true. Select all that apply.
Answer
The scroll is not open or the writings are visible.
" The scroll is open or the writings are not visible.
The scroll is open or the writings are visible.
1 The scroll is not open or the writings are not visible.... Show more
Answers
Based on the given simple statements, "The scroll is open" and "The writings are visible," we can determine which compound statements would also be true.
The scroll is not open or the writings are visible.
This compound statement would be true. Since the first simple statement states that the scroll is open, the negation of this statement would be that the scroll is not open. The second simple statement states that the writings are visible, which aligns with this compound statement. Therefore, this compound statement is true.
The scroll is open or the writings are not visible.
This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, the second part of this compound statement contradicts the given information.
The scroll is open or the writings are visible.
This compound statement would be true. It directly matches the given simple statements, where both the scroll being open and the writings being visible are mentioned. Therefore, this compound statement is true.
The scroll is not open or the writings are not visible.
This compound statement would not be true. Both simple statements state that the scroll is open and the writings are visible. So, neither part of this compound statement aligns with the given information.
The compound statements that would be true are:
The scroll is not open or the writings are visible.
The scroll is open or the writings are visible.
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Based on the given five balances what is the average balance for the 5 day period
Answers
The average balance for the 5 day period is 27.
The average of anything is given by adding all the numbers and dividing the sum of total number of items. The average daily balance is given by adding up your balances from all of the days throughout the period, dividing them by the total number of days during the period.
Now, Adding the all five balances, we get
Sum = (-21)+(-55)+102+125+(-16)
= -21-55+102+125-16
= 135
Now, Dividing the sum by total number of days i.e. 5,
Average \(=\frac{135}{5}\)
= 27
Hence, the average balance for the 5 day period is 27.
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WILL GIVE 30 POINTS
It costs $100 to rent the bowling alley, plus $4 per person. The cost for any number (n) of people can be found using the expression 100 + 4n. The cost for 15 people equals $ ___.
Answers
Answer:
Step-by-step explanation:
Cost of renting bowling alley = $ 100
Additional cost of renting bowling alley per person = $ 4
⇒ Total Cost for n no. of people = 100 + 4 × n
So, Cost for 15 people = Fix $100 for bowling alley
+ $4 for each 15 people
= 100 + 4 × 15
= 100 + 60
= 160
Therefore, The cost for 15 people equals to $ 160.
A school principal wants to buy some book cases for the school library. She can choose between two types of book case. Type A costs $10 and it requires 0.6 m2 of floor space and holds 1.2 m3 of books. The maximum floor space available is 7.2 m2 and the budget is $140 (but the school would prefer to spend less). What number and type of bookcases should the principal buy to get the largest possible storage space for books?
Answers
The principal should buy 8 of type A and 3 of type B to get the largest possible storage space for books
How to determine the number and type of book cases?Let x represent type A and y represent type B,
So, we have the following table:
x y Available
Floor space 0.6 0.8 7.2
Budget 10 20 140
Book hold 0.8 1.2
Using the above table, we have the following linear model
Objective function Min Z = 0.8x + 1.2y
Subject to
0.6x + 0.8y ≤ 7.2
10x + 20y ≤ 140
x, y > 0
Using a graph, the solution to the above system of inequalities is:
(x,y) = (8,3)
Hence, the principal should buy 8 of type A and 3 of type B to get the largest possible storage space for books
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Use the Law of Sines to find mZE.
Round to the nearest degree.
D
30 mi
18 mi
78°
F
E
Answers
Answer:
Step-by-step explanation:
recall law of Sines : Sin(A) / a = Sin(B) / b
where F can be A, in above equation, and then a = 30
we want to find E so that can be B, and b = 18
Sin(78) / 30 = Sin(B) / 18
solve the parts you can
0.03260 = Sin(B) / 18
18 * 0.03260 = Sin(B)
0.5868885 = Sin(B)
use arcSin() to find angle of B
arcSin(0.586885) = arcSin( Sin(B)) [ b/c arcSin is the inverse of Sin those go away, they cancel each other out ]
35.9365 = B
36° = B ( and B = E in the given triangle )
∠E = 36°
W
4. A chef at a restaurant buys 50 pounds of
red potatoes for $27.50 and 30 pounds
of sweet potatoes for $22.50. Which kind
of potato costs more per pound? How
much more?
Answers
Consequently, a restaurant pays $27.50 for 50 pounds of red potatoes and $22.50 for 30 pounds of sweet potatoes, with the red potatoes costing $0.485 more per pound.
what is cost per pound ?The cost function's generic formula is C(x)=F+V. (x) F is the sum of all fixed costs, V is the sum of all variable costs, x is the number of units, and C(x) is the sum of all production costs.
given
50 pounds of red potatoes are purchased by a restaurant for $27.50.
The price of 30 pounds of sweet potatoes is $22.50,
hence the price per pound of red potatoes is = 50/27.50 = $1.818
while the price per pound of sweet potatoes is = 30/22.50 = $1.33 .
The red potatoes are therefore more expensive per pound by the amount of $1.818 - $1.33 = $0.485.
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a student applies for ten different scholarships to various universities. seven of the scholarships pay for books. four scholarships include a meal ticket. two of the scholarships exclude meals and books. how many scholarships pay for both books and meals? use a venn diagram to illustrate and help solve this problem
Answers
The number of scholarships that pay for both books and meals is 1.
To solve this problem, we need to use the concept of set intersection. Let B be the set of scholarships that pay for books, and M be the set of scholarships that include a meal ticket. We want to find the number of scholarships that pay for both books and meals, which is the size of the set intersection B ∩ M.
From the problem statement, we know that:
|B| = 7 (seven scholarships pay for books)
|M| = 4 (four scholarships include a meal ticket)
We can use the inclusion-exclusion principle to find |B ∩ M|:
|B ∩ M| = |B| + |M| - |B U M|
We need to find the size of the union of the sets B and M, which includes all scholarships that pay for books, all scholarships that include a meal ticket, and possibly some scholarships that pay for both. From the problem statement, we know that there are two scholarships that exclude both meals and books, so we can subtract that from the union:
|B U M| = |B| + |M| - |B ∩ M| + 2
Substituting the known values, we get:
|B ∩ M| = |B| + |M| - |B U M| + 2
|B ∩ M| = 7 + 4 - (7 + 4 - |B ∩ M| + 2) + 2
|B ∩ M| = 1 + |B ∩ M|
Solving for |B ∩ M|, we get
|B ∩ M| = 1
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The given question is incomplete, the complete question is:
A student applies for ten different scholarships to various universities. seven of the scholarships pay for books. four scholarships include a meal ticket. two of the scholarships exclude meals and books. how many scholarships pay for both books and meals?
how to do expected frequency for chi^2 goodness fit test
Answers
Pearson's chi-square goodness of fit test statistic is: - where Oj are observed counts, Ej are corresponding expected count and c is the number of classes for which counts/frequencies are being analysed.
...
Chi-square Goodness of Fit Test.
Value Observed frequency Expected frequency
3 29 14.96
4 8 5.61
Step-by-step explanation:
So basically you're going to start with your (expected value - observed value) squared
(O-E)²
You're then gonna divide that by your expected value that you just used
(O-E)²/E
Determine the length of the line segment shown.
graph of line segment from negative 3 comma negative 2 to 0 comma 2
4 units
5 units
10 units
25 units
Answers
Answer:
I think the answer is 5
Step-by-step explanation:
Answer:
(b) 5 units
Step-by-step explanation:
You want to know the length of the segment from (-3, -2) to (0, 2).
DistanceThe formula for the distance between two points is based on the Pythagorean theorem. The distance is the root of the sum of the squares of the horizontal distance and the vertical distance.
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
ApplicationFor the given points, the distance is computed to be ...
\(d=\sqrt{(0-(-3))^2+(2-(-2))^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}\\\\d=5\)
The line segment is 5 units long.
__
Additional comment
The numbers (3, 4, 5) comprise a "Pythagorean triple", a set of three integers that satisfy the Pythagorean relation. You will see the 3-4-5 right triangle a lot in algebra and geometry problems, along with its multiples, such as 6-8-10.
You don't have to go to the trouble of using the formula. You can count grid squares on the graph to see the triangle is a 3-4-5 triangle.
17x - 45 + 7(5x-2) = 5x - 3(x-17)
SOLVE FOR X
Answers
Answer:
The solution to the problem is 11/5.Work:
17x - 45 + 7(5x - 2) = 5x - 3(x - 17)=> 17x - 45 + 35x - 14 = 5x - 3x + 51=> 52x - 59 = 2x + 51=> 52x - 2x = 59 + 51=> 50x = 110=> 5x = 11=> x = 11/5Hence, the solution to the problem is 11/5.
Hoped this helped.
\(BrainiacUser1357\)
A manufacturer determines that the cost of making a computer component is4.161616 $. Write the repeating decimal cost as a fraction and as a mixed number.
Answers
Answer:
$4.161616 =
As a fraction
= $[(4 × 62500) + 10101]/62500
= $(260101/62500)
As a mixed number =
$\(4\frac{10101}{62500}\)
Step-by-step explanation:
Cost of making a computer component = $4.161616
= $4 + $0.161616
6 numbers after the decimal , hence
0.161616 × 1000000/1000000
= 161616/1000000
= 10101/62500
We are told in the question to write the repetiting decimal cost as a fraction and as a mixed number
$4 + $0.161616 = $4 + 10101/62500
As a fraction
= $[(4 × 62500) + 10101]/62500
=$260101/62500
As a mixed number = \($4\frac{10101}{62500}\)
How much almonds will each person get if 20 people share 2 2/5 kilograms of almond?
Answers
Therefore, each person will get 12 grams of almonds when 20 people share 2 2/5 kilograms (or 12 grams/person when 20 people share 2.4 kilograms) of almonds.
To determine how much almonds each person will get when 20 people share 2 2/5 kilograms of almonds, we need to divide the total amount of almonds by the number of people.
First, let's convert 2 2/5 kilograms to a single fraction. We can rewrite it as 12/5 kilograms.
Now, we can calculate the amount of almonds per person:
Amount of almonds per person = Total amount of almonds / Number of people
Amount of almonds per person = (12/5) kilograms / 20 people
To simplify the calculation, we can convert kilograms to grams:
Amount of almonds per person = (12/5) * 1000 grams / 20 people
Amount of almonds per person = 240 grams / 20 people
Amount of almonds per person = 12 grams/person
please help me with this quickly
Answers
Answer:
is this 190/3?
if so ur answer is 60.3333333
if it's \(\sqrt[3]{190}\)?
then ur answer is 5.74889707894
Step-by-step explanation:
Eight friends shared ⅙ kg of nuts equally. What fraction of a kg of nuts did each friend eat?
Answers
Answer:
all u would have to do is multiply eight by 1/6 then divide the answer by eight
Step-by-step explanation:
hope i helped
A recipe uses 5 cups of flour for every 2 cups of sugar. How much sugar is used for every cup of flour?
Answers
A recipe uses 5 cups of flour for every 2 cups of sugar. How much sugar is used for every cup of flour?
2/5 = 0.4
so there is 0.4 cups of sugar used for every one cup of flour.
Please Help me - You will get 60 points for the rapid reply- Use isosceles trapezoid ABCD to determine the following measurements-
Answers
Answer:
1) AD = 9 in
2) DE = 9.25 in
3) ∠EDC = 36°
4) ∠AEB = 108°
5) 11.5 in
Step-by-step explanation:
1) AD = BC = 9in
2) AC = BD (diagonals are equal)
⇒ BD = 14.25
⇒ BE + DE = 14.25
⇒ 5 + DE = 14.25
DE = 9.25
3) Since AB ║CD,
∠ABE = ∠EDC = 36°
4) ∠ABE = ∠BAE = 36°
Also ∠ABE + ∠BAE + ∠AEB = 180 (traingle ABE)
⇒ 36 + 36 + ∠AEB = 180
∠AEB = 108
5) midsegment = (AB + CD)/2
= (8 + 15)/2
11.5
Alicia read 1/3 of a book in the morning, and she read some more at night. By the end of the day, she still had 1/4 of the book left to read. How much of the book did Alicia read at night?
Answers
Alicia read 1/3 of a book in the morning and still had 1/4 of the book left to read by the end of the day. Alicia read 5/12 of the book at night.
The question asks how much of the book Alicia read at night.
Let's assume the total book is represented by the unit "1." Alicia read 1/3 of the book in the morning, leaving 2/3 of the book unread. By the end of the day, she still had 1/4 of the book left to read, which is equal to 1/4 of the original 2/3.
To find out how much Alicia read at night, we need to subtract the remaining fraction from the initial 2/3.
2/3 - 1/4 = 8/12 - 3/12 = 5/12
Therefore, Alicia read 5/12 of the book at night.
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If AB = C and A = 2i and B
-6i, what is C?
Answers
Answer:
12
Step-by-step explanation:
2i * (-6)i
-12i^2
-12(-1)
12
10. a? = 3,600
algebra solve each equation
Answers
Answer:
a=360
Step-by-step explanation:
3600 divided by 10 is 360
Kelly ordered birthday pencils. It cost $25 per box plus $3 for shipping. If Kelly can spend up to at most $200, what is the greatest number of boxes she can purchase?
Answers
Answer:7
Step-by-step explanation: 25 x 7 = 175 now 3 x 7 = 21 175 + 21 =196 r 4 :)
Which of the following statements are true? Select all that apply.
Answers
Answer:
a,d
Step-by-step explanation:
Question 1
What is the approximate circumference of a plate with a diameter of 11 inches? Use 3.14 for . Round to the nearest
hundredth if necessary.
Answers
Answer:
34.54 in
Step-by-step explanation:
The approximate circumference of a plate with a diameter of 11 inches can be calculated using the formula C = πd, where C is the circumference and d is the diameter .
So, substituting the given value of diameter d = 11 inches and taking π to be approximately 3.14, we get:
C = πd = 3.14 x 11 = 34.54 inches (approx.)
Therefore, the approximate circumference of the plate is 34.54 inches.
Since it is required to round the answer to the nearest hundredth, we get the rounded answer as 34.54 rounded off to two decimal places, which is 34.54 (no rounding needed).
Answer: For circumference, you simply multiply the diameter by pi, so the answer you are looking for is 34.54
Step-by-step explanation:
If you add the digits in a number, how many numbers between 0 and 10,000 will have a sum of 10? (For example, 334 is one such number because 3 + 3 + 4 = 10)
Answers
Answer: I think 100,000
Step-by-step explanation:
find median of data 7 5 2 11 14 6 8 12 10
pls fast..
Answers
Answer:
the median is 8
Step-by-step explanation:
hope this helps!
2,5,6,7,8,10,11,12,14
Answer:
8
Step-by-step explanation:
Rearrange to 2 5 6 7 8 10 11 12 14 in ascending order
Take the center number
Solve each for the missing variable
1. 9x + 15 = 96
Answers
Answer:
81
Step-by-step explanation:
my friend theres nothing on the world that will say that 96 - 15 = 9x
because 96-15= 81 and 81 + 15 equals 96
Sergio and Linnea live on the same street. Their houses are shown on the diagram below. If the length of each square represents 1 yard, how far is the point in the middle of Linnea's house from the point in the middle of Sergio's house?
Answers
Answer:
11 yards
Step-by-step explanation:
The distance between both houses area 11 yards.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
As per the attached graph, the coordinates of Sergio's house are (-7,4), and the coordinates of Linnea's house are (4, 4).
Hence the distance between two coordinates (-7,4) and (4,4),
The two points have the same y-coordinate, which means they lie on a horizontal line.
Therefore, the distance between them is simply the difference between their x-coordinates:
Distance = |4 - (-7)| = |4 + 7| = 11
So the distance between (-7,4) and (4,4) is 11 units.
Since the length of each square represents 1 yard
Thus, the distance between both houses area 11 yards.
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A farmer has asked you for advice on the best strategy for planting wheat and corn on her 500-acre farm. To make it through harvest time, each acre of wheat she plants will require 1 person-day of labor and other expenses of $20. Each acre of corn she plants will require 5 person-days of labor and expenses of $30. The farmer has $11,400 and 1480 person-days of labor available, and she expects to make a profit of $90 per acre of wheat and $120 per acre of corn. If x = acres of wheat and y = acres of corn, which of the following is NOT a constraint?
x + y ≤ 500
20x + 30y ≤ 11,400
y ≥ 5x + 30
x + 5y ≤ 1480
Answers
The constraint that is NOT valid is " \(y > = 5x + 30\) "
To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.
To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.
The constraints are as follows:
\(x + y < = 500\) : This constraint ensures that the total planted area does not exceed the farm size.\(20x + 30y < = 11,400\) : This constraint represents the budget limitation.\(y > = 5x + 30\) : This constraint is NOT valid because it suggests that the number of acres of corn must be greater than or equal to 5 times the number of acres of wheat plus 30. However, there is no information provided to support this relationship.\(x + 5y < = 1480\) : This constraint limits the total available person-days of labor.By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.
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A social media influencer charges $50 per hour for a public appearance plus $250 for the ownership rights of the photos taken at the event. A second influencer charges $75 per hour for their appearance plus a $100 travel fee.
Which equation can be solved to determine x, the number of hours after which the costs would be the same?
(A) 50 + 100x = 75 + 250x
(B) 50x + 100 = 75x + 250
(C)50 + 250x = 75 + 100x
(D) 50x + 250 = 75x + 100
Answers
Answer:
its d
Step-by-step explanation:
x is the number of hours he charges for
Rewrite, using the distributive
property.
16b-8b = ([?]-8)b = [?]b
![Rewrite, using the distributiveproperty.16b-8b = ([?]-8)b = [?]b](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/9Tmzv11947B9UtnbF6DBvWJp63YQcon7.png)
Answers
Answer:
8b
Step-by-step explanation:
You can factor the b-term out since b-term exists for all terms in the expression. By factoring out, you are basically dividing the factored term off and put it outside of the bracket, thus:
\(\displaystyle{16b-8b=\left(16-8\right)b}\)
Then evaluate and simplify:
\(\displaystyle{\left(16-8\right)b=8\cdot b}\\\\\displaystyle{=8b}\)