3. Plot 2 ordered pairs on the initial climb (first part of the rollercoaster going up) and determine the slope.
Points: Work to find Slope: Slope: ________
4. What is the equation of the line in slope-intercept form that represents your initial climb (first part of the rollercoaster going up)?
Equation: ___________
5. What is the domain and range of your entire roller coaster? (HINT: use compound inequalities)
Domain: Range:
6. a) Plot 2 ordered pairs at the top and the bottom of each hill (not the loop).
Hill 1 points: _________ Hill 2 points: _________
b) Find the rate of change going down each hill.
Work for Hill 1: Work for Hill 2:
Rate of change down Hill 1: _______ Rate of change down Hill 2: _______
c) Which hill is steeper? How do you know that hill is steeper?
Hill 1 or Hill 2 (circle/underline/pick one)
Explanation:
7. Is the roller coaster a function? Why or why not?
Function: YES or NO (circle/underline/pick one)
Explanation:
Answers
Using function concepts, it is found that:
3. Two ordered pairs are: (0, 0) and (130,260). The slope is of 2.
4. The equation of the line is of y = 2x.
5. The domain is 0 ≤ length ≤ 400, and the range is 0 ≤ height ≤ 260.
6. a)
For Hill 1, we have that:
The bottom point is (130,260).The top point is (170,60).For Hill 2, we have that:
The bottom point is (400,0).The top point is (360,80).6. b) The rate of change down Hill 1 is of -5, while it is of -2 for Hill 2.
6. c) Due to the higher rate of change, Hill 1 is steeper.
7) The roller coaster is not a function, as for lengths between 190 ft and 240 ft, there are vertically aligned points on the graph.
What are the two ordered pairs on the initial climb, what is the slope, and what is the equation of the line?Two ordered pairs are: (0, 0) and (130,260).
The slope is given by change in y divided by change in x, hence:
m = (260 - 0)/(130 - 0) = 2.
Considering the slope and the intercept(which is of 0, as when x = 0, y = 0), we have that:
The equation of the line is of y = 2x.
What are the domain and the range of the graph?The domain of a function is the set that contains all possible values of the input. In the graph, it is all the values assumed by the horizontal axis.The range of a function is the set that contains all possible values of the output. In the graph, it is all the values assumed by the vertical axis.Hence:
The domain is 0 ≤ length ≤ 400, and the range is 0 ≤ height ≤ 260.
Bottom and top of the hills:For Hill 1, we have that:
The bottom point is (130,260).The top point is (170,60).For Hill 2, we have that:
The bottom point is (400,0).The top point is (360,80).The rates of change(change in height divided by change in length) are given as follows:
Hill 1: (-200)/40 = -5.Hill 2: -80/40 = -2.Due to the higher rate of change, Hill 1 is steeper.
Is the graph a function?A graph is a function if it has no vertically aligned points, that is, each value of the input is mapped to only one value of the output.
Hence:
The roller coaster is not a function, as for lengths between 190 ft and 240 ft, there are vertically aligned points on the graph.
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Related Questions
50 points
add and write the fraction in its simplest form.
-7/8 + (-2 1/6) =
Answers
Answer:-3 1/24
Step-by-step explanation:
Solve the equation.
2|2x+3|=|x-3|
There should be two solutions.
Please show the steps and give an explanation on how to solve it and why.
Answers
Answer:
x= -3
Step-by-step explanation:
[tex]2(2x + 3) = x - 3 \\ 4x + 6 = x - 3 \\ 4x = x - 3 - 6 \\ 4x - x = - 3 - 6 \\ 3x = - 9 \\ x = \frac{ - 9}{3} \\ x = - 3[/tex]
Answer:
[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]
Step-by-step explanation:
Given absolute value equation:
[tex]2|2x+3|=|x-3|[/tex]
The absolute value of a number is its positive numerical value.
Therefore, the expressions inside the bars should be set to both positive and negative. Rewrite the absolute value equation as four equations without absolute value bars and simplify:
[tex]\textsf{Positive = Positive}: \quad 2(2x+3)=x-3[/tex]
[tex]\textsf{Positive = Negative}: \quad 2(2x+3)=-(x-3)[/tex]
[tex]\begin{aligned}\textsf{Negative = Positive}: \quad -2(2x+3) &=x-3\\ \implies 2(2x+3) &=-(x-3)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Negative = Negative}: \quad -2(2x+3) &=-(x-3)\\ \implies 2(2x+3)&=x-3\end{aligned}[/tex]
From inspection of the equations:
Positive = Positive is equal to Negative = Negative, and Negative = Positive is equal to Positive = Negative,so there are only two unique equations to be solved.
Equation 1
[tex]\begin{aligned}2(2x+3) & =x-3\\4x+6 & = x-3\\4x+6-x&=x-3-x\\3x+6&=-3\\3x+6-6&=-3-6\\3x & =-9\\\dfrac{3x}{3} & = \dfrac{-9}{3}\\ x&=-3 \end{aligned}[/tex]
Equation 2
[tex]\begin{aligned}2(2x+3)&=-(x-3)\\4x+6&=-x+3\\4x+6+x&=-x+3+x\\5x+6&=3\\5x+6-6&=3-6\\5x &=-3\\ \dfrac{5x}{5}&=\dfrac{-3}{5}\\x &=-\dfrac{3}{5} \end{aligned}[/tex]
Therefore, the solutions are:
[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]
Write each number as a percent.
1(2/5)
Answers
You buy a new car for $22,000. The value of the
car decreases by 12.5% each year.
Answers
Answer:
Thus the value of the car decreases by $2,750 every year.... Making it $19,250 in the first year and $16,500 in the second
Step-by-step explanation:
12.5/100×22,000
2750
Jan and Dinah both ran for 20 seconds, each at a constant speed. Jan ran 50 mefers and Dingh ran 60 meters. 1. Who was moving faster? Explain how you know. 2. How far did each person move in 1 second?
Answers
By calculating speed of each person we can find who is faster.
What is Speed?Speed can be defined as the distance covered with respect to time. It is a scalar quantity. It is calculated as follows
Speed = Distance / Time taken
The time taken by each person is 20 seconds.
Distance covered by Jan = 50 meter
Speed of Jan = Distance / Time taken
Speed of Jan = 50 / 20
Speed of Jan = 2.5 meters per second
Distance covered by Dingh = 60 meter
Speed of Dingh = Distance / Time taken
Speed of Dingh = 60 / 20
Speed of Dingh = 3 meters per second
Since the speed of Dingh is more than Jan, we can say that Dingh is faster.
Distance = Speed × Time taken
Here, time taken = 1 second
This implies Distance Covered = Speed
Therefore, Jan covers 2.5 meters in one second while Dingh covers 3 meters in one second.
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how to do:
5n - 7n = 14
Please show the step by step process! (:
Answers
Answer: n=-7
Step-by-step explanation:
5n - 7n = 14
(5-7)n=14
-2n=14
-2n/(-2)=14/(-2)
n=14/(-2)
n=-7
The equation is,
→ 5n - 7n = 14
Solving for the value of n,
→ 5n - 7n = 14
→ -2n = 14
→ n = -(14//2)
→ [ n = -7 ]
Thus, the value of n is -7.
Chen buys 11 books for $77. Each book has the same price. What is the price of each book? Show the multiplication or division fact you used to solve the problem?
Answers
Answer: $7 per book
Step-by-step explanation:
$77 for 11 books, so we do 77 ÷ 11 = 7
Tyrone needs 50 volunteers for a concert.
Tyrone has 20% more volunteers than
he needs. Tyrone assigns 15% of the total
volunteers to the stage area. How many
volunteers does Tyrone assign to the
stage area?
Answers
Answer:
go
Step-by-step explanation:
i don't understand this shirty app
Answer: 9
Step-by-step explanation:
20% of 50 is 10. So, he has a total of 60 volunteers. He uses 15% of that for the stage area, and 15% of 60 is 9. So, Tyrone assigned 9 volunteers to the stage area.
can someone please help me
Answers
for the first one x = 12
second one is 2
Answer:
x = 12
x = 2
Step-by-step explanation:
Basically the triangles are congruent. Therefore, the sides are equal to each other. Set both equations equal to each other and solve for x.
Determine whether each sequence is geometric. If so, find the common ratio. 10,4,1.6,0.64, . . . . .
Answers
The given sequence is geometric, with common ratio = 0.4.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Now, Given: 10, 4, 1.6, 0.64, ....
Here, [tex]\frac{4}{10}=\frac{1.6}{4}=\frac{0.64}{1.6}=0.4[/tex]
That is, the given sequence follows the only necessary condition for a sequence to be geometric.
Hence, The given sequence is geometric, with common ratio = 0.4.
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Figure ABCD is a rhombus. Find the
value of x.
B
5x-8
D
A
3x + 10
x = [?]°
Answers
A Figure ABCD is a rhombus. The angles of A and C are equal by alterenate interior angle. The value of x in the figure ABCD rhombus is 9 degree.
What is a rhombus?We know that rhombuses are a particular type of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal.
The Solution to an equation is finding values of the variable in the considered equation for which the equation considered evaluates to be true.
For a solution, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, thus solution to a system is the intersection of all its equation at single point
WE know that the diagonals of a rhombus bisect each other, we know that triangle DEC is a right triangle.
Since the side lengths of a rhombus are equal, so the angles of A and C are equal by alterenate interior angle.
Now, 5x-8 = 3x + 10
i.e. 5x - 3x = 10 + 8
i.e. 2x = 18
i.e. x = 9
Therefore the value of x in the figure ABCD is 9 degree.
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Write the equation of the circle that passes through the given point and has a center at the origin. (Hint: You can use the distance formula to find the radius.) (-2,3)
Answers
The equation of the circle that passes through the point (-2 , 3) and has a center at the origin is x^2 + y^2 = 13.
Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (-2 , 3).
radius = distance = √(x2 - x1)^2 + (y2 - y1)^2
radius = √(-2 - 0)^2 + (3 - 0)^2
radius= √4 + 9
radius = √13
The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.
Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (0 , 0)
r = √13
(x - 0)^2 + (y - 0)^2 = (√13)^2
x^2 + y^2 = 13
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Add or subtract as indicated.
25.32 + 109.2 + 8.574
Answers
Determine the following attributes of the graph below please i only have 8 mins to turn this in 20 points pleaseeee
Answers
For the following function, we have that:
The domain is 0 < x ≤ 4.The range is -2 ≤ y ≤ 2.The x-intercepts are x = 1 and x = 3, that is, points (1,0) and (3,0).The y-intercept is y = 2, that is, point (0,2).The maximum value on the interval [1,4] is of 2, at point (4,2).The minimum value on the interval [1,4] is of -2, at point (2,-2).What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.Hence, for the graph in this problem, we have that:
The domain is 0 < x ≤ 4.The range is -2 ≤ y ≤ 2.What are the intercepts of a function?The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.Hence:
The x-intercepts are x = 1 and x = 3, that is, points (1,0) and (3,0).The y-intercept is y = 2, that is, point (0,2).What is the maximum and the minimum value?We have to look at the values of y on the interval, hence:
The maximum value on the interval [1,4] is of 2, at point (4,2).The minimum value on the interval [1,4] is of -2, at point (2,-2).More can be learned about functions at https://brainly.com/question/24808124
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The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $13 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part a.
Answers
Answer:
Step-by-step explanation:
The telephone company offers two billing plans for local calls. Plan 1 charges $30 per month for unlimited calls and Plan 2 charges $15 per month plus $0.04 per call.
a. Use an inequality to find the number of monthly calls for which Plan 1 is more economical than Plan 2.
b. Explain the meaning of the answer to part
Nicolas has 1400 pokemon cards. Of these cards, 40% are water pokemon and 15% are considered rare pokemon, the rest are rock pokemon. How many rock pokemon cards does Nicolas have? (I have completely forgotten this skill)
Answers
Answer:
630 rock cards
Step-by-step explanation:
aight so 40 % of 1400 is 560 , and 15% of 1400 is 210 . add those and you get 770 . so you got 770 water and rare . you subtract that by 1400 and you got 630 !!
Answer: 476 rock type pokemon cards
Step-by-step explanation: Let's do this! 40% of 1400 is 560, and 15% of 560 is 84. 560 - 84 = 476.
The larger of two numbers is 7 more than 5 times the smaller. If the sum of the two numbers is 31, what are the two numbers
Answers
Answer: x=27 y=4
Step-by-step explanation:
Let the larger of two numbers is x and the smaller of two numbers is y
Hence,
[tex]\displaystyle\left \{ {x-5y=7} \atop {x+y=31}} \right.\\\\\left \{ {{x-5y=7} \atop {x+y-y=31-y}} \right. \\\\\left \{ {{x-5y=7\ \ \ \ \ (1)} \atop {x=31-y}\ \ \ \ (2)} \right. \\[/tex]
Substitute equation (2) into equation (1):
[tex]31-y-5y=7\\31-6y=7\\31-6y+6y=7+6y\\31=7+6y\\31-7=7+6y-7\\24=6y\\[/tex]
Divide both parts of the equation by 6:
[tex]4=y\\Hence,\\x=31-4\\x=27[/tex]
Rob has $1.65 in nickels and dimes.He has 25 coins in all. How many of each kind of coin are there
Answers
rob has 8 dimes and 17 nickels in $1.65
WHAT ARE LINEAR EQUATION ?There is only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All the points fall on the same line when the values that together make a linear equation true are determined and plotted on a coordinate grid.
CALCULATIONLet n represent nickels & d dimes
given: n + d = 25 #1 (number of coins)
given: .05n + .10d = 1.65 #2 (amount in dollars)
n = 25 - d #3 (rewrite of #1)
.05(25 -d) + .10d = 1.65 (substitute #3 in #2)
1.25 - .05d + .10d = 1.65 (multiply out the left side)
.05d = .40 (collection of like terms)
d = 8 (divided both sides by.05)
n + 8 = 25 (substitute answer for d in #1)
n = 17 (subtract both sides by 8)
There are 8 dimes and 17 nickels.
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help me number 2 please
Answers
The following volume quantities are listed below:
a) 2 pints, 1 qt
b) 12 pints, 6 qt
c) 5 pints, 2.5 c
d) 6.75 pints, 3.375 fl oz
How to convert an unit to another by using unit conversions
In this question we must transform a quantity in a unit to another quantity in a unit of the same kind. For instance, if we have a quantity in a mass unit, then we only can convert it into another mass unit.
Herein we have four unit conversion cases for volumes, both pints and quarts are volume units commonly used in the United States. There are the following equivalencies:
1 quart = 2 pints = 4 cups = 32 fluid ouncesNow we proceed to convert each quantity to pints and quarts by cross multiplication:
a) 32 fl oz × 2 pints / 32 fl oz = 2 pints, 32 fl oz × 1 qt / 32 fl oz = 1 qt
b) 24 c × 2 pints / 4 c = 12 pints, 24 c × 1 qt / 4 c = 6 qt
c) 10 c × 2 pints / 4 c = 5 pints, 10 c × 1 qt / 4 c = 2.5 c
d) 108 fl oz × 2 pints / 32 fl oz = 6.75 pints, 108 fl oz × 1 qt / 32 fl oz = 3.375 fl oz
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The geometric mean of a number and four times the number is 22 . What is the number?
Answers
If 22 is the geometric mean of a number and four times the number, then the number is 11.
Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.
To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.
The formula for the geometric mean is given by:
GM = n√x1 x2 . . . xn
Let x = x1 = unknown number
y = x2 = four times the number = 4x
Using the formula in solving geometric mean, plug in the values and variables.
GM = n√x1 x2 . . . xn
22 = √xy
22 = √x(4x)
22 = √4x^2
22 = 2x
x = 11
y = 4x
y = 44
Hence, the number is 11. 22 is the geometric mean of 11 and 44.
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I Need help pls i forgot what to do with this math problem
Answers
Answer:
-8^3/7^3 = -512/343
Step-by-step explanation:
3√ (-512/343) = 3√-(8/7)^3 = -8/7
-8^3/7^3 = -512/343
Number 7 is the one I need help with please
Answers
Answer:
23
Step-by-step explanation:
Find the sum of each finite series. Σ⁸ n=1 (7-n)
Answers
The sum of the finite series [tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex] is 20
Given a finite series:
[tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex]
Recall the properties of summation notation:
Σₙ b. f(n) = b Σₙ f(n) where b is a constant.
Σ (a + b) = Σ a + Σ b
[tex]\sum\limits^p_{n=1} {b} =b.p[/tex] where b is a constant
Using the above summation properties, we can write:
[tex]\sum\limits^{8}_{n=1} {(7-n)}=\sum\limits^{8}_{n=1} {7}-\sum\limits^{8}_{n=1} {n}[/tex]
=7 . 8 - (1+2+3+ ...+8)
= 56 - 8/2 (1+8)
= 56 - 4 . 9
= 56 - 36 = 20
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What is the value of this product
Answers
Answer:
The value of the product is 2²
Over the last 3 evenings, Heather received 61 phone calls at the call center. She received 7 more calls on the second evening than on the first evening. On the third evening, she received 2 times as many calls as the second evening. How many phone calls did she receive each evening?
Answers
Answer:
for real even great Britain cant get this because ya
Step-by-step explanation:
You want to buy a new iPhone 50 that costs $1330 including taxes(13%). How many hours will you have to work to be able to buy this new phone if you make minimum wage which is $14.25 per hour?
Answers
Answer:
105.47 hours
Step-by-step explanation:
1300x0.13=172.9
172.9+1300=1502.9
1502.9/14.25=105.47
Which example illustrates public scientific communication?
A scientist collaborates with other scientists to plan an experiment.
A scientist sends a preview copy of a journal article to some colleagues.
A federal government agency holds a press conference to describe the response to and the dangers of a new virus epidemic.
A federal government agency publishes an article in a professional scientific journal detailing technical details of a new virus.
Answers
The example that illustrates public scientific communication is D. a federal government agency publishes an article in a professional scientific journal detailing technical details of a new virus.
What is communication?Communication simply had to do with how messages are passed from the sender to the audience or the other party.
In this case, the example that illustrates public scientific communication is a federal government agency publishes an article in a professional scientific journal detailing technical details of a new virus.
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Evaluate x³ for x = 2.
06
02
08
Answers
Answer:
8
Step-by-step explanation:
x³; x = 2
2³ or 2 × 2 × 2 = 8
I hope this helps!
Paul collects comic books. He has 20 books in his collection, and he adds 3 per month. In how many months will he have a total of 44 books in his collection?
F. 5
G. 6
H. 8
J. 15
Answers
In 8 months he will have a total of 44 books in his collection.
The correct answer is an option (H)
In this question,
Paul collects comic books. He has 20 books in his collection, and he adds 3 per month.
We need to find the number of months required to have a total of 44 books in his collection.
Let n be the required number of months.
From given information, we get an equation,
20 + 3n = 44
We solve above equation to find the required number of months.
20 + 3n - 20 = 44 - 20
3n = 24
n = 8
Therefore, in 8 months he will have a total of 44 books in his collection.
The correct answer is an option (H)
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The average professional hockey player makes $2.78 million a year.
They play an average of 82 games.
How much does the average hockey player make per game?
A. $33,900.00
B. $3,390.00
C. $34,000.00
D. $3,400.00
E. None of the above
Answers
Answer:
$34,000.00
Step-by-step explanation:
[tex]2,780,000/82 = 33,902.439\\33,902.439 ~ 34,000.00[/tex]
The average hockey player makes per game is an amount of $34,000.00 which is the correct option would be option (A).
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.
For example 4/2 = 2
The average professional hockey player makes $2.78 million a year.
$2.78 million = $2,780,000
They play an average of 82 games.
The average hockey player makes per game = 2,780,000 / 82
Apply the division operation to get the answer.
The average hockey player makes per game = 33,902.439
The average hockey player makes per game = $33,900.00
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