Marion is observing the velocity of a cyclist at different times. After two hours, the velocity is 18km/h. After four hours, the velocity of the cyclist is 4km/h.
Part A: write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used.
Part B: how can you graph the equations obtained in part A for the first 8 hours?
Answers
To solve this problem,
we assume that velocity is a linear function of time:
v(t) = m t + b
where
v = velocity
t = time
m = slope of line
b = y-intercept of line equation
When t = 2 hours, v =
18 km/h, therefore:
2 m + b = 18 (1)
When t = 4 hours, v = 4 km/h, therefore
4 m + b = 4 (2)
Subtract (1) from (2) to obtain
4 m – 2 m = 4 - 18
2 m = -14
m = -7
From (1), calculate
for b:
b = 18 – 2(-7) = 32
Part A. The
equation in standard form is therefore:
v = -7 t + 32
Part B. To graph
the equation for the first 8 hours, we create a table as shown below. Assign
values of t from 0 to 8 hours then calculate the corresponding velocity.
v, km/h: 32 25 18 11 4 -3 -10 -17 -24
From the table, the velocity becomes negative between t=4 and t=5. This means that between this time, Marion already came to rest. Note that when the velocity is zero, t is equivalent to
32 - 7t = 0
7t = 32
t = 4.57
The new table is below and we plot it.
t: 0 1 2 3 4 4.57 5 6 7 8
v: 32 25 18 11 4 0 0 0 0 0
Related Questions
Determine the domain of the function. f(x) is equal to four divided by x squared.
A. x ≥ 0
B. All real numbers except 0
C. All real numbers except 3
D. All real numbers
Answers
Think what values of x give real values of f(x)
negative numbers are Ok andso are positive ones
What about x = 0? What is the value of 4 / (0)^2 ?
What is the ratio of the area of sector ABC to the area of sector DBE?
I am not quite sure how to do this. So far, since there are variables instead of numbers, I have got (pi)(r)^2:(pi)(3r)^2, but I know that is definitely wrong.
Answers
[tex]\bf \cfrac{\triangleleft ABC}{\triangleleft DBE}\qquad \cfrac{\frac{\beta \pi (2r)^2}{360}}{\frac{3\beta \pi (r)^2}{360}}\implies \cfrac{\beta \pi (2r)^2}{360}\cdot \cfrac{360}{3\beta \pi (r)^2}\implies \cfrac{\beta \pi 2^2r^2}{360}\cdot \cfrac{360}{3\beta \pi r^2} \\\\\\ \cfrac{\beta \pi 4r^2}{3\beta \pi r^2}\implies \cfrac{4}{3}[/tex]
Answer:
4/3
Step-by-step explanation:
rewrite 7/11 as a division problem
Answers
Sandy has earned $290. That is 20% of the cost of the new computer she wants to buy. What is the total amount of money she needs to buy the computer?
Answers
Hope the explanation helped!
Answer:
1450
Step-by-step explanation:
simply just multiply 290 by 5 and u get 1450 hope this helps you
The three sides of sail A are each half the length of the three sides of sail B. How do the areas of the two sails compare?
Answers
Area of sail A is 1/4 of area of sail B
Answer:
Step-by-step explanation:
It is B
Ajay analyzed two companies and has formulated tables to model each company’s growth, where x represents the age of the companies in years and y represents growth in terms of number of employees. Company 1 Company 2
Table 1 Table 2
x l y x l y
0 l 0 0 l 1
1 l 6 1 l 6
2 l 12 2 l 36
3 l 18 2 l 216
4 l 24 4 l 1,296
If the number of employees is an indicator of a successful business, in which company should Ajay invest? company 1 because it is adding six employees each year while company 2 is multiplying its number of employees by six each year company 1 because it is multiplying its number of employees by six each year while company 2 is adding six employees each year company 2 because it is adding six employees each year while c
Answers
Answer:
Company 2 because it is gaining six times the number of employees, while Company 1 is only adding 6 employees every year.
Step-by-step explanation:
Looking at the table, the number of employees in Company 1 goes up by 6 employees per year.
The number of employees in Company 2 is multiplied by 6 every year; this means they gain more employees after the first year than Company 2 does (they go from 6 to 36, which is a gain of 30, while Company 1 goes from 6 to 12, a gain of 6).
If we are looking strictly at the number of employees, Company 2 is the better choice.
Answer:
company 2 is multiplying
Step-by-step explanation:
Ian has 120 folders to file. So far, he has filed 36 of the folders. What percent of the folders does he have left to file?
Answers
Hope the explanation helped!
The 70 percent of the folders, he have left to file.
What is a fraction?A fraction represents a part of a number or any number of equal parts.
We are given that Ian has 120 folders to file. So far, he has filed 36 of the folders.
The fraction of the amount of folders Ian did not file out of 120 ;
84/120
= 21/30
In order to convert this into a percent, we have to divide both the numerator and the denominator by 1.2.
we will get 70/100.
This new fraction as a percent is 70%.
Therefore, he has 70% of folders left to file.
Learn more about fraction;
https://brainly.com/question/729654
#SPJ2
Suatu jenis roti memerlukan 150 gram tepung dan 50 gram mentega. Roti jenis lain memerlukan 75 gram tepung dan 75 gram mentega, produksi roti membuat sebanyak roti dan dua jenis roti itu. Bahan yang tersedia 2.250 gram tepung dan 1.250 gram mentega, berapakah banyak roti masing masing yang dibuat?
Answers
The second type of the bread be bread B
Let the flour be 'f' and the butter be 'b'
We need 150f + 50b for bread A and 75f + 75b for bread B
We can compare the amount of flour and bread needed for each bread and write them as ratio
FLOUR
Bread A : Bread B
150 : 75
2 : 1
We have a total of 2250gr of flour, and this amount is to be divided into the ratio of 2 parts : 1 part. There is a total of 3 parts.
2250 ÷ 3 = 750 gr for one part then multiply back into the ratio to get
Bread A : Bread B = (2×750) : (1×750) = 1500 : 750
BUTTER
Bread A : Bread B = 50 : 75 = 2 : 3
The amount of butter available, 1250 gr is to be divided into 2 parts : 3 parts.
There are 5 parts in total
1250 ÷ 5 = 250 gr for one part, then multiply this back into the ratio
Bread A: Bread B = (2×250) : (3×250) = 500 : 750
Hence, for bread A we need 1500 gr of flour and 500 gr of butter, and for bread B, we need 750 gr of flour and 750 gr of butter.
The amount of Bread Type 1 is 10 pieces
The amount of Bread Type 2 is 10 pieces
Further explanationSimultaneous Linear Equations can be solved using one of the following methods :
Elimination MethodSubstitution MethodGraph MethodLet's try to solve the problem now.
Let :
Amount of Bread Type 1 = A
Amount of Bread Type 2 = B
1 piece of bread type 1 requires flour as much as 150 grams and 1 piece of bread type 2 requires flour as much as 75 grams, while the total amount of flour is as much as 2250 grams, then:
[tex]150A + 75B = 2250[/tex]
[tex]2A + B = 30[/tex]
[tex]\boxed{B = 30 - 2A}[/tex] → Equation 1
1 piece of bread type 1 requires butter as much as 50 grams and 1 piece of bread type 2 requires butter as much as 75 grams, while the total amount of butter is as much as 1250 grams, then:
[tex]50A + 75B = 1250[/tex]
[tex]2A + 3B = 50[/tex]
[tex]2A + 3(30 - 2A) = 50[/tex] ← Equation 1
[tex]2A + 90 - 6A = 50[/tex]
[tex]2A - 6A = 50 - 90[/tex]
[tex]-4A = -40[/tex]
[tex]A = -40 \div -4[/tex]
[tex]\large {\boxed{A = 10}}[/tex]
[tex]B = 30 - 2A[/tex]
[tex]B = 30 - 2(10)[/tex]
[tex]B = 30 - 20[/tex]
[tex]\large {\boxed{B = 10}}[/tex]
Conclusion :The amount of Bread Type 1 is 10 pieces
The amount of Bread Type 2 is 10 pieces
Learn morePerimeter of Rectangle : https://brainly.com/question/12826246Elimination Method : https://brainly.com/question/11233927Sum of The Ages : https://brainly.com/question/11240586?Answer detailsGrade: High School
Subject: Mathematics
Chapter: Simultaneous Linear Equations
Keywords: Elimination , Substitution , Graph , Method , Linear , Equation , Simultaneous
The ratio of girls to boys is 5 to 6. If there are 72 boys, how many girls are there?
Answers
If the ratio of girls to boys is 5 to 6, it can be written as 5/6. You can use cross multiplication to figure out how many girls there are if there are 72 boys by setting the number of girls equal to x and dividing it by 72 like so: [tex] \frac{5}{6}= \frac{x}{72}[/tex]
After multiplying 5 and 72, and 6 and x, you get the equation [tex]360=6x[/tex]. To find the number of girls, all you have to do is divide by 6, which leaves you with [tex]x=60[/tex], meaning there are 60 girls when there are 72 boys based on the ratio 5:6 (girls to boys).
Identify each function as a constant, direct variation, absolute value, or greatest integer function.
g (x)=x+3
Answers
It's not a constant function, because it is not equal to a constant (something that isn't a variable)
It doesn't show direct variation, because it can't be represented in the form
y = kx.
It isn't an absolute value function because the absolute value isn't taken anywhere.
If it was an absolute value function it would look something like this:
[tex]g(x) = |x+3|[/tex]
It isn't a greatest integer function, because the greatest integer isn't taken anywhere.
If it was a greatest integer function it would look something like this:
[tex]g(x) = \left \lfloor{x + 3}\right \rfloor[/tex]
Are you sure you typed that question right?
Find the coordinates of point l that lies along the directed line segment from N(14,4) to M(2,8) and partitions the segment in the ratio of 1:3
Answers
Let these perpendiculars intersection be point A, with coordinates (2, 4).
[clearly A will have x coordinate equal to the x coordinate of M, and y coordinate equal to the y coordinate of N]
2. Let P be the point on NM such that |NP|/|PM|=1/3
3. Drop the perpendiculars from point P to AN and AM. Let the foot of these perpendiculars be points P' and P'' respectively.
4. By Thales theorem: |NP'|/|P'A|=1/3 and |AP''|/|P''M|=1/3
so let |NP'|=b, |P'A|=3b, |AP''|=c, |P''M|=3c, as shown in the figure
5. |AN|=14-2=12.
|AN|=4b so b=12/4=3
the x coordinate of P'=2+3b=2+9=11
the x coordinate of P= the x coordinate of P'=11
similarly |AM|=8-4=4
|AM|=4c so c=1
the y coordinate of P'' is 4+c=4+1=5
the y coordinate of P = the y coordinate of P''=5
Answer: (11, 5)
There are 40 vehicles in a parking lot.Twenty percent of the vehicles are pickup trucks.How many pickup trucks are in the parking lot?
Answers
20% of 40....turn ur percent to a decimal..." of " means multiply
0.20(40) = 8.....there are 8 pickup trucks <==
A pearl is formed in one of every 10,000 oysters what percent of oysters make pearls
Answers
1/10000
this is equal to 0.0001
moving the decimal point 2 points to the right, you would get
0.01%
x%=x/100
1 in 10000
1/10000=x/100
times both sides by 100
100/10000=x
1/100=x
0.01=x
0.01% of all oysters make perls
A scientist measures the angle x and the distance y between the Earth and the moon. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Earth and the Sun.
Answers
From the trigonometric rules:
tan(theta)=opposite/adjacent
In this case: theta=x , opposite=y and adjacent=z
tan(x)=y/z
All terms in the equation are known except for 'z'.
therefore the distance between the earth and the sun denoted by the symbol 'z' is equal to: y/tanx
tan =opposite/adjacent
In this case: tan =X , opposite=Y and adjacent= D
tan(x)=Y(opposite) /D(adjacent)
All terms in the equation are known except for 'D the distance'.
So the distance between the earth and the sun indicate by the symbol 'D' is equal to: y/tan(x)
find the area and circumference of a circle with radius 4 in.
Answers
area = 3.14159 * 4 ^ 2
area = 3.14159 * 16
area = 50.26544 square inches
circumference = 2 * PI * radius
circumference = 2 * 3.14159 * 4
circumference = 25.13272 inches
Answer is provided in the image attached.
Which expression is equivalent to am ÷ an?
am − n
am + n
am ⋅ n
am ÷ n
Answers
just because you're dividing an from am
so you're taking away n .
Either that or am divided by n.
not 100% sure but this is my suggestion
The equivalent expression is a^m − n
What are properties of exponents?The properties of exponents are mentioned below.
Law of Product: a^m × a^n = a^m+nLaw of Quotient: a^m/a^n = a^m-nLaw of Zero Exponent: a^0 = 1Law of Negative Exponent: a^-m = 1/a^mLaw of Power of a Power: (a^m)^n = a^mnLaw of Power of a Product: (ab)^m = a^m*b^mLaw of Power of a Quotient: (a/b)^m = a^m/b^mGiven expression:
am ÷ an
Now, using the law of exponents we have
a^m ÷ a^n
=a^(m-n)
Hence, the equivalent expression is a^m − n
Learn more about exponents and powers here:
https://brainly.com/question/15722035
#SPJ2
Suppose you add two linear equations that form a system, and you get the result y = −2. how many solutions does the system have?
Answers
** if it were to end like 0 = 4, or 2 = -3....no variables and numbers that dont equal....this means no solutions.
** if u were to end up with 5 = 5, or -9 = -9...no variables and numbers that do equal, then u will have infinite solutions
** but if u end with y = -2 or x = 5...a variable equaling a number, then u will have 1 solution
In early spring, you are wanting to purchase 6 potted rose plants. The plants to choose from come in 8-inch pots that sell for $12 and 10-inch pots that sell fro $15. If you spend $78, which of the following are the equations for this scenario? Let x= number of 8 inch pots and let y = number of 10 - inch pots.
A. y+15y=6
12x+x=78
B. x+y=6
12x+15y=78
C. x+y=78
12x +15y=6(78
D. x+y=6
15x+12y=78
E. No solution
Answers
Six total pots = # of 10" + # of 8"
$78 total = cost of 10" + cost of 8"
So:
6 = x +y
and
78 = x*(cost of x) + y * (cost of y)
78 = x*12 + y*15
We need:
x+y=6 AND 12x+15y=78
So our answer can only be B.
why is a stem and leaf plot called a stem and leaf plot?
Answers
Stem = the first digit, or digits
Leaf = the last digit
Ex: The stem of 32 would be 3 and the leaf would be 2.
A stem-and-leaf plot gets its name from the way the data is structured. The 'stem' represents the highest place value digits of the numbers in the dataset, and the 'leaf' represents the lower place value digits. These plots keep the actual numerical data intact, providing more detail than other data representations like bar graphs or histograms.
Explanation:The term stem-and-leaf plot, also known as a stemplot, originates from the way data is structured in this type of graphical representation. The 'stem' in a stem-and-leaf plot stands for the highest place value digits of the numbers in the dataset, similar to the stem of a plant that holds up the leaves. The 'leaf' stands for the lower place value digits, similar to the leaves that extend from the stem. For example, in a dataset [23, 24, 33, 35], 2 and 3 would be stems, and the various units (3, 4 for 2 and 3, 5 for 3) would be leaves.
One of the main purposes of a stem-and-leaf plot is that it keeps the actual numerical data intact, as opposed to other graphical representations like bar graphs or histograms which group data into classes, thus providing a more detailed view of the data distribution.
Learn more about stem-and-leaf plot here:https://brainly.com/question/32830750
#SPJ12
When two balanced dice are rolled, there are 36 possible outcomes. what is the probability that the sum of the numbers on the dice is 6 or 10?
Answers
The probability of having a sum of either 6 or 10 is [tex]\frac{2}{9}[/tex]
The sample space has the size [tex]|S|=36[/tex]
Let
[tex]A=\text{the event of having a sum of 6}\\B=\text{the event of having a sum of 10}[/tex]
then
[tex]A=\{(1,5),(2,4),(3,3),(4,2),(5,1)\}\\|A|=5[/tex]
and
[tex]B=\{(4,6),(5,5),(6,4)\}\\|B|=3[/tex]
then, the probability of having a sum of either 6 or 10 will be
[tex]P(A\cup B)=P(A)+P(B)[/tex]
since [tex]A[/tex] and [tex]B[/tex] are mutually exclusive events. Substituting
[tex]P(A\cup B)=P(A)+P(B)\\=\frac{|A|}{|S|}+\frac{|B|}{|S|}\\=\frac{2}{9}[/tex]
Learn more about probability here: https://brainly.com/question/17136647
When two balanced dice are rolled, there are 36 possible outcomes. To find the probability that the sum of the numbers on the dice is 6 or 10, count the favorable outcomes and divide it by the total outcomes.
Explanation:When two balanced dice are rolled, there are 36 possible outcomes. To find the probability that the sum of the numbers on the dice is 6 or 10, we need to count the favorable outcomes and divide it by the total outcomes.
For the sum of 6, there are 5 possible outcomes: (1,5), (2,4), (3,3), (4,2), (5,1). For the sum of 10, there are 3 possible outcomes: (4,6), (5,5), (6,4). Therefore, there are 8 favorable outcomes out of 36 total outcomes.
The probability is calculated as:
Probability = Favorable outcomes / Total outcomes = 8 / 36 = 2 / 9
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
Lou’s Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers. Determine which equation represents how much Kayla will spend on sandals after the discount.
Answers
The equation represents how much Kayla will spend on sandals after the discount is $13.50 = 0.75x.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Lou’s Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers.
The equation can be written as:-
$13.50 = 0.75x.
To know more about an expression follow
https://brainly.com/question/13462254
#SPJ6
simplify 4x+5/6x^2-x-12 subtract 5x/6x^2-x-12
Answers
= (4x + 5 - 5x)/(6x^2-x-12)
= (-x + 5) / (2x - 3)(3x +4)
answer
-x + 5
---------------------
(2x - 3)(3x +4)
The value of a treadmill bought new for $1000 decreases 5% each year. Use a graph to predict the value of the treadmill in 5 years.
A) ≈ $773.78
B) ≈ $857.38
C) ≈ $902.50
D) ≈ $814.50
Answers
V (t)=V0 (1-r)^t
V (t)?
V0 1000
R 0.05
T 5 years
V (5)=1,000×(1−0.05)^(5)=773.78
The predicted value of the treadmill after 5 years, with an annual depreciation rate of 5%, is approximately $773.78. This calculation uses the exponential decay formula and corresponds to option A).
To predict the value of a treadmill in 5 years that was bought new for $1000 and decreases 5% each year, we can use the formula for exponential decay:
V = [tex]P(1 - r)^t[/tex]
Where:
V is the future value of the treadmill,
P is the original value ($1000),
r is the rate of decay (5% or 0.05), and
t is the time in years (5 years).
By substituting the values we have:
V = $1000(1 - 0.05)⁵
V = $1000(0.95)⁵
V = $1000(0.77378) = $773.78
Therefore, the predicted value of the treadmill after 5 years is approximately $773.78, which corresponds to option A).
(03.01)
A newly made car will have a model number, a parts number, and a serial number. A model number is assigned by the manufacturer to identify each type of car. A parts number identifies one part of the smaller parts that make up the car. A serial number is unique to each car produced and identifies it.
Which relation is a function?
(parts number, serial number)
(model number, parts number)
(serial number, model number)
(serial number, part number)
Answers
Answer:
Hi!
The corrects answers are:
•(serial number, model number)
Step-by-step explanation:
First, you have to understand the meaning of a function, that is an a relation but have the condition:
The input must be relationed with only one output.
The question says:
"A serial number is unique to each car produced and identifies it." so this will be you input, and will be related with only one model number.
end behavior of F(x)=-x^(3-)2x^(2)+7x-10
A. The graph of the function starts high and ends high
B. The graph of the function starts low and ends low
C. The graph of the function starts high and ends low
D. The graph of the function starts low and ends high
Answers
if trapezoid jklm is translated according to the rule (x,y) ,(x+8,y-3) what are the coordinates of point L
Answers
-5 + 8 = 3
-2 - 3 = -5
New coordinates of L: (3, -5)
Hope this helps :)
Please give brainliest
With the given translation rule, to find new coordinates of a point L in trapezoid JKLM, apply it to the original coordinates by moving right by 8 units and down by 3 units. If original coordinates of L were (2,5), new coordinates will be (10,2).
Explanation:In geometry, a translation is a type of transformation that slides a figure along a straight line. In this case, the translation rule given is (x, y) -> (x+8, y-3). This means that every point in the trapezoid is being moved 8 units to the right (increase in x-coordinate) and 3 units down (decrease in y-coordinate).
Per your question, to find the new coordinates of point L after the translation, you simply need to apply this rule to the original coordinates of point L. If for example, the original coordinates of point L were (2, 5), its new coordinates after the translation would be calculated as follows: (2+8, 5-3) = (10, 2).
This is how you find the new coordinates of a point after a translation in geometry.
Learn more about Translation in Geometry here:https://brainly.com/question/32226769
#SPJ3
simplify 6√1,000m^3n^12
Answers
The simplified expression is 60mn⁶.
What is factorization?Factorization is a process to simplify the expression by finding the factors of that expression.
And to find the same expression from factors, you have to reverse the process.
Given that the expression is 6√1,000m³n¹².
We can simplify this expression by breaking down 1,000 into its prime factorization:
1,000 = 2³ x 5³
Then we can rewrite the expression as:
6√(2³ x 5³ x m³ x n¹²)
Using the properties of radicals, we can separate the factors inside the radical:
6√2³ x √5³ x √m³ x √n¹²
Simplifying each square root term:
6 x 2 x 5 x m x n⁶
= 60mn⁶
Therefore, the simplified expression is 60mn⁶.
To learn more about the factorization;
https://brainly.com/question/29474540
#SPJ2
Find the area of the shaded region.
Answers
To find the area of a rectangle, multiply base times height.
5 x 10 = 50
Now we need to subtract the area of the non-shaded part.
2 x 2 = 4
50 - 4 = 46
The answer is 46
Hope this helps! :)
Hope the explanation helped!
Which sequence of transformations will result in an image that maps onto itself?
Answers
The correct transformation to get result in an image that maps onto itself will be;
''Reflect over the y axis and then reflect again over the y axis''.
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The statement is,
'' A sequence of transformations will result in an image that maps onto itself''.
Now,
Since, We know that after two reflections over the same axis we get the original image.
Thus, we get;
The correct transformation to get result in an image that maps onto itself will be;
''Reflect over the y axis and then reflect again over the y axis''.
Learn more about the transformation visit:
https://brainly.com/question/2689696
#SPJ2
A local newspaper compiles data on the number of days, X, people in a neighborhood receive the newspaper. The probability distribution for the data is shown in the table below. What is the probability that a randomly chosen person receives the newspaper at least one day per week?
Answers
x 0 1 2 5 7
P(x) 17% 16% 14% 12% 41%
Where x is number of days that a person receives the newspaper per week
and P(x) is the probability that a person will receive the newspaper according to the number of days per week
We are asked for the probability that a person receives the newspaper at least one day per week
So,
16% + 14% + 12% + 41%
= 83%
There is 83% probability that a person will receive the newspaper at least one day per week.
Answer: D 83% is the answer