Answers
Answer:
Horizontal distance = 0 m and 6 m
Step-by-step explanation:
Height of a rider in a roller coaster has been defined by the equation,
y = [tex]\frac{1}{3}x^{2}-2x+8[/tex]
Here x = rider's horizontal distance from the start of the ride
i). [tex]y=\frac{1}{3}x^{2}-2x+8[/tex]
[tex]=\frac{1}{3}(x^{2}-6x+24)[/tex]
[tex]=\frac{1}{3}[x^{2}-2(3x)+9-9+24][/tex]
[tex]=\frac{1}{3}[(x^{2}-2(3x)+9)+15][/tex]
[tex]=\frac{1}{3}[(x-3)^2+15][/tex]
[tex]=\frac{1}{3}(x-3)^2+5[/tex]
ii). Since, the parabolic graph for the given equation opens upwards,
Vertex of the parabola will be the lowest point of the rider on the roller coaster.
From the equation,
Vertex → (3, 5)
Therefore, minimum height of the rider will be the y-coordinate of the vertex.
Minimum height of the rider = 5 m
iii). If h = 8 m,
[tex]8=\frac{1}{3}(x-3)^2+5[/tex]
[tex]3=\frac{1}{3}(x-3)^2[/tex]
(x - 3)² = 9
x = 3 ± 3
x = 0, 6 m
Therefore, at 8 m height of the roller coaster, horizontal distance of the rider will be x = 0 and 6 m
Related Questions
-) Ms. Cohen is buying supplies for her kindergarten classroom. She can spend at most $30.
She wants to buy boxes of crayons that cost $2 per box. She also buys a poster for $5.
Ms. Cohen wants to know how many boxes of crayons she can buy.
1) Let b be the number of boxes of crayons Ms. Cohen buys.
Write an inequality that represents the situation.
+
30
5
2
b.
Yes I give brainless!!
Answers
Answer:
Step-by-step explanation:
Identify the rule for fg when f(x) = –3x – 6 and g(x) = x2 – x – 6.
Answers
Answer:
f(g) = -3( x^2 -x-6) -6 = -3x^2+3x+12
The store Matilda works at bought a pair of leggings for $12. They plan on selling them for $20. What percent are the leggings marked up?
Answers
Answer:
67%
Step-by-step explanation:
difference between the numbers = $8
8 ÷ 12 X 100 = 67%
HELP! WORTH 25 POINTS. Which sets of ordered pairs represent functions from A to B? (Select all that apply.)
A = {0, 1, 2, 3} and B = {−2, −1, 0, 1, 2}
A. {(0, 2), (3, 0), (1, 1)}
B. {(0, 0), (1, 0), (2, 0), (3, 0)}
C. {(0, −1), (2, 2), (1, −2), (3, 0), (1, 1)}
D. {(0, 1), (1, −2), (2, 0), (3, 2)}
Answers
Answer:
C. {(0, −1), (2, 2), (1, −2), (3, 0), (1, 1)}
hope it helps you
A rectangular pool at Andy's gym measures 25 meters by 50 meters. How many meters would Andy swim in order to swim diagonally across the pool?
Answers
Answer:
625 meters
Step-by-step explanation:
25 multiplied by 50 equals 1250 divided by 2 is 625 meters.
A pair of Converse Chuck Taylor Sneakers originally cost $50, but they are on sale for 20% off. If the sales tax is 7.5% what is the final cost?
Answers
Answer:
$43.75
Step-by-step explanation:
The area of square ABCD is 144 square units. The area of square EFGH is 64 square units. H∈ AB and G∈ BC . The blue area is three times the red area. Find the area of △HBG.
Answers
Answer:
24
Step-by-step explanation:
RSM
evaluate the function when x = -3
Answers
Answer:
10
Step-by-step explanation:
f(-3)=-2(-3)+4=6+4=10
SOMEONE HELP PLEASE
Answers
Answer:
We cant see what you are talking about we cant see the equation
Step-by-step explanation:
Step-by-step explanation:
106+94+135+5 = 340
540-340=200
200/2= 100
X = 100
ahh can someone help me please
Answers
4 + 195
199
Answer: $199
Complete the function table for y=2.5x−8 .
Answers
Answer:
x=3.2
Step-by-step explanation:
The value of the function at x =1 is -5.5.
What is a function?The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.
Given that the function is y = 2.5x - 8. The value of the function will be calculated as,
At x = 1 the value of y will be,
y = 2.5 x - 8
y = ( 2.5 x 1 ) - 8
y = 2.5 - 8
y = -5.5
To know more about function follow
https://brainly.com/question/10439235
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Learning Task 3
Solve the word problems
1. The sides of the quadrilateral are consecutive numbers.
how long is each side?
2. Inzo is 10 years older than Migz. Five years ago Mig
Inzo. What are their present ages?
3. An express train travels 100 kph from station A to
travelling at 45 kph, takes 45 minutes longer for the
is station A from station B.
4. The sum of two consecutive even integers is less tha
Find at least 3 pairs of numbers
5. The perimeter of the square is less than 152 m. Find
sides of the square.
Answers
Answer:
1. The sides are: 38.5, 39.5, 40.5 and 41.5
2. Presently, Inzo is 15 years old and Miz is 10 years old
3. [tex]Distance = 3682km[/tex]
4. Possible pairs are: (12, 14), (16, 18) and (20, 24)
5. [tex]L < 38m[/tex]
Step-by-step explanation:
The question has lots of missing details. See the comment section for complete question
Solving (a):
Given
Shape: Quadrilateral
Sides: Consecutive
[tex]Perimeter = 160[/tex]
Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.
So, the perimeter is:
[tex]Perimeter = x + x + 1 + x + 2 + x + 3[/tex]
This gives:
[tex]160 = x + x + 1 + x + 2 + x + 3[/tex]
Collect Like Terms
[tex]160 -1-2-3= x+x+x+x[/tex]
[tex]154= 4x[/tex]
Divide both sides by 4
[tex]38.5 = x[/tex]
[tex]x =38.5[/tex]
So, the sides are: 38.5, 39.5, 40.5 and 41.5
Solving (b):
Given
Presently: [tex]Inzo = 10 + Miz[/tex]
Five years ago: [tex]Miz - 5= \frac{1}{3} * (Inzo-5)[/tex] --- (Missing from the question)
Required: Determine their present ages
Substitute [tex]10 + Miz[/tex] for Inzo in the second equation
[tex]Miz - 5 = \frac{1}{3} * (10 + Miz - 5)[/tex]
[tex]Miz - 5 = \frac{1}{3} * (Miz + 5)[/tex]
Multiply both sides by 3
[tex]3Miz - 15 = Miz + 5[/tex]
Collect Like Terms
[tex]3Miz -Miz = 15 + 5[/tex]
[tex]2Miz= 20[/tex]
Divide both sides by 2
[tex]Miz = 10[/tex]
Substitute 10 for Miz in [tex]Inzo = 10 + Miz[/tex]
[tex]Inzo = 10 + 5[/tex]
[tex]Inzo = 15[/tex]
So presently, Inzo is 15 years old and Miz is 10 years old
Solving (3):
Given
Express Train:
[tex]Speed = 100kph[/tex]
[tex]Time = t[/tex]
Local Train:
[tex]Speed = 45kph[/tex]
[tex]Time = t + 45[/tex]
Required: Determine the distance between A and B
Distance is calculated as:
[tex]Distance = Speed * Time[/tex]
For the express train:
[tex]Distance = 100 * t[/tex]
For the local train
[tex]Distance = 45 * (45 + t)[/tex]
Distance between both stations are equal; So,
[tex]100 * t = 45 * (45 + t)[/tex]
[tex]100 t = 2025 + 45t[/tex]
Collect Like Terms
[tex]100 t -45t= 2025[/tex]
[tex]55t= 2025[/tex]
Divide by 55
[tex]t = 36.82[/tex]
Substitute 36.82 for t in [tex]Distance = 100 * t[/tex]
[tex]Distance = 100 * 36.82[/tex]
[tex]Distance = 3682km[/tex]
Solving (4):
Let the even numbers be: n and n + 2.
Sum greater than 24: [tex]n + n + 2 > 24[/tex]
Sum less than 60: [tex]n + n + 2 < 60[/tex]
So, we have:
[tex]n + n + 2 > 24[/tex]
[tex]2n + 2 > 24[/tex]
Collect Like Terms
[tex]2n > 24-2[/tex]
[tex]2n > 22[/tex]
[tex]n > 11[/tex]
[tex]n + n + 2 < 60[/tex]
[tex]2n + 2< 60[/tex]
Collect Like Terms
[tex]2n < 60-2[/tex]
[tex]2n < 58[/tex]
Divide by 2
[tex]n<29[/tex]
So, we have:
[tex]n > 11[/tex] and [tex]n < 29[/tex]
So, possible pairs are: (12, 14), (16, 18) and (20, 24)
Solving (5):
Given
[tex]Perimeter < 152m[/tex]
Required: Find the possible lengths
Let the length be L.
Perimeter is calculated as:
[tex]Perimeter =4 * L[/tex]
[tex]Perimeter =4 L[/tex]
So, we have:
[tex]4L < 152m[/tex]
Divide through by 4
[tex]L < 38m[/tex]
Hence, length is less than 38m (e.g. 37m)
For the expression 2 x squared + 28 x + 93 Over (x + 6) cubed, which sum represents the correct form of the partial fraction decomposition?
Answers
Answer:
Option-3
Step-by-step explanation:
got-it-lol
also-keyboard-broke:(
70.3 rounded to one decimal place
Answers
Answer:
The answer will be 70
Step-by-step explanation:
Hope this Helped
9514 1404 393
Answer:
70.3
Step-by-step explanation:
The number already has one decimal place. No adjustment is needed.
70.3
rewrite the following polynomials in standard form
Answers
Answer:
x^2+3x+1/3
Step-by-step explanation:
the term with the highest degree comes first, then alphabetical order based on variables, then normal terms.
When Alexis adopted her puppy, the puppy weighted 12 pounds. One year later, the puppy weighted 60 pounds. By what percent did the puppy's weight change in one year?
Answers
Answer:
400%
Step-by-step explanation:
Original wieght = 12
New weight = 60
Change = 60- 12= 48
Change percent = change / original x 100 = 48 / 12 x 100 = 400 %
I hope its right!!!! :)
anyone tell me the answer
Answers
Answer:
a. Pop
b. 30 CDs
c. 230 CDs
Step-by-step explanation:
Given that "O" represents 20 CDs
a. The CD that was the mode is the CD that has as much "O", which is Pop.
Mode = Pop
b. Number of Rock CDs = 3 × 20 = 60 CDs
Number of Classical CDs = 1½ × 20 = 30 CDs
Therefore, 30 more CDs of Rock were sold than Classical CDs were sold
c. Pop = 5*20 = 100 CDs
Jazz = 2*20 = 40 CDs
Classical = 1½*20 = 30 CDs
Rock = 3*20 = 60 CDs
Total sold altogether = 100 + 40 + 30 + 60
= 230 CDs
can someone answer this one for me?
Answers
Answer:
it would be 540 degrease i just took the qiuz in first pd. an got it right lol
Step-by-step explanation:
6 - 3x = -6 PLEASE ANSWER FAST I NEED HELP!!!
Answers
Answer:
4
Step-by-step explanation:
Subtract 6 to both sides so you can get -12. Next divide -3 from x and -12. Finally your answer should be positive 4. Mark me brainily please if it is correct
What do Geometry teachers use to decorate their floors?
Answers
The solution to the riddle, Geometry teachers use to decorate their floors is Area rugs.
What is the area of a figure?The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters, square feet, square inches, and other similar units are used to measure area.
The problem is actually, a riddle(Joke) and the solution to the problem is Area rugs.
Thus, the solution to the riddle, Geometry teachers use to decorate their floors is Area rugs.
Learn more about the Area:
https://brainly.com/question/11952845
In a race in which 6 automobiles are entered and there are no ties, in how many ways can the first three finishers come in?
Answers
Answer:
Step-by-step explanation:
number of ways=6×5×4=120
somebody help me ASAP!!! No joking
Answers
Answer:
it is given that. a^2 + b^ 2 = c^2
then we need to find b
then formula will
b= √(c^2 - a^2)
hence 3600 - 1296
=. √{ 1296}
=. 48
a triangle has sides with lengths of 3 miles 4 miles and 5 miles is it a right angle
Answers
Answer:
yes
Step-by-step explanation:
pls give me brainlest
What is the total cost of a $12 t-shirt if the sales tax is 6.5%?
Answers
What’s the area of this parallelogram
Answers
Answer:
360%
if not u question isnt correct
hope this might help you
Answer: Multiply the base by the height
for example A=B x H
Step-by-step explanation:
2x²-26x+84 (Factor COMPLETELY)
Answers
[tex]\tt{} {2x}^{2} - 26x + 84[/tex]
[tex]\tt{}2 {(x}^{2} - 13x + 42)[/tex]
[tex]\tt{}2 {(x}^{2} - 6x - 7x + 42)[/tex]
[tex]\tt{}2( x \times (x - 6) - 7(x - 6))[/tex]
[tex]\tt{}2(x - 6) \times (x - 7)[/tex]
what is the coefficient of the c-term algebraic expression 14a-72r-c-34c
Answers
Miss Van invested some money by using the app e-trade. She tracks her
gains and losses using the app on her phone. Miss Van receives a daily
notification that updates her on all her transactions from the previous day.
This morning, her notification read as follows: Yesterday's investment
activity included a loss of $500, a gain of $740, and another gain of $120.
Log in now to see your current balance. Write an integer to represent the
highlighted box.
Answers
Answer:
$360
Step-by-step explanation:
Gains represents additions to her account while losses represent substractions
-$500
+740
+120 ________
$360
Find the value of r(q(-5)).
Answers
Answer:
=−5qr
Step-by-step explanation:
please help quick i will give brainlist!!!!!!
Answers
Answer:
a) 75/3=25/1
Step-by-step explanation: