A portion of a roller coaster track is in the shape of a parabola. Write and graph a quadratic function the models this portion of the roller coaster with a maximum height of 90 feet, represented by a vertex of (25, 90), passing through the point (50, 0).
Answers
The equation of a parabola is: \(y = a(x - h)^2 + k\) where (h,k) represents the vertex.
The equation of the parabola is: \(y = \frac{18}{625}(x - 25)^2 + 90\)
We have:
\((h,k) = (25,90)\) --- the vertex
\((x,y) = (50,0)\) -- one of its point.
Recall that:
\(y = a(x - h)^2 + k\)
Substitute \((h,k) = (25,90)\)
\(y = a(x - 25)^2 + 90\)
To solve for a, we substitute \((x,y) = (50,0)\)
\(0 = a(50 - 25)^2 + 90\)
\(0 = a(25)^2 + 90\)
Collect like terms
\(a(25)^2 = 90\)
\(625a = 90\)
Solve for a
\(a = \frac{90}{625}\)
\(a = \frac{18}{125}\)
Recall that:
\(y = a(x - 25)^2 + 90\)
Hence, the equation of the parabola is:
\(y = \frac{18}{625}(x - 25)^2 + 90\)
See attachment for the graph of \(y = \frac{18}{625}(x - 25)^2 + 90\)
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Related Questions
B. What is each piece measurement if the angle is cut into 9 equal
lengths? Kerf width is 0.125.
Answers
Each piece Measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.
When a particular angle is cut into nine equal parts, the measure of each piece needs to be calculated.
Therefore, it is essential to first calculate the total angle measure and then divide it by the number of parts into which it is being cut.
What is an Angle?
An angle is a geometrical shape that consists of two rays sharing a common endpoint. The common endpoint is known as the vertex, and the two rays are known as the arms of the angle. An angle can be measured in degrees, radians, or gradians. Degrees are the most commonly used unit of measuring angles.How to Calculate Each Piece Measurement of an Angle if Cut into 9 Equal Lengths
To determine each piece measurement of an angle if cut into nine equal lengths, we will need to carry out the following steps:
Step 1: Calculate the total angle measure Suppose the angle being cut into nine equal lengths is an obtuse angle measuring 120 degrees. In that case, the total angle measure will be 120 degrees.
Step 2: Divide the total angle measure by the number of parts into which it is being cut.120 degrees ÷ 9 = 13.3333 degrees
Step 3: Add the kerf width to the piece measurements.0.125 x 9 = 1.125 degrees13.3333 + 1.125 = 14.4583 degrees
Therefore, each piece measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.
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-11=-11a+33 what is the answer I’m stuck
Answers
The work behind it
-11a+33= -11
-33 -33
-11a=-44
Divide both sides by -11
-44/-11=a
A=4
if a adult grey whale weigh an average 50 -55 tons about how many pounds does an adult grey whale weigh
a ton equals 2000 pounds
A 500,000 - 550-000 pounds
B 10,000 - 11,000 pounds
C 1, 000,000 - 1, 100, 000 pounds
D 50,000 - 50,500 pounds
E 100,000 - 110,000
Answers
Answer:
E. 100,000-110,000
Step-by-step explanation:
50×2,000=100,000 pounds
55×2,000=110,000 pounds
So the answer is 100,000-110,000 pounds
Answer:
E. 100,000-110,000
Step-by-step explanation:
2000 x 50=100,000
2000 x 55=110,000
Mai's class volunteered to clean a park with an area of square mile. Before they took a lunch break, the class had cleaned of the park. How many square miles had they cleaned before lunch?
Answers
The class had cleaned x × A square miles before lunch.
Let's assume that the area of the park is A square miles, and the portion of the park cleaned by Mai's class before the lunch break is represented by x (a fraction or decimal between 0 and 1).
If the class had cleaned x portion of the park, then the area they had cleaned is x times the total area of the park:
Area cleaned before lunch = x × A
Since x represents a fraction or decimal, multiplying it by the total area A gives us the corresponding portion of the park that was cleaned.
Let's say the park has an area of A square miles, and the area that Mai's class cleaned up before lunch is denoted by the number x (a fraction or decimal between 0 and 1).
If the class had cleaned a certain percentage of the park, their cleaned area would be x times the park's overall area:
Before lunch, the area was cleaned = x A
We may calculate the proportion of the park that was cleaned by multiplying x by the entire area A because it indicates a fraction or decimal.
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A survey of 450 randomly chosen US adults found that 35% of the 200 men and 40% of the 250 women attended a college football game during the past month. Do these data provide statistical evidence at the α = 0.01 level that men are more likely than women to attend football games? Be sure to state the parameter, check conditions, perform calculations, and make conclusion(s). (10 points)
Answers
Answer:100,000
Step-by-step explanation:
The following are the temperatures of 10 days in winter in °C.
0
,
−
2
,
4
,
4
,
−
1
,
0
,
8
,
2
,
−
1
,
9
Work out the mean temperature.
Answers
The mean temperature is 3.1 °C.
How is the mean calculated?The sum of the observations divided by the total number of observations is the definition of the mean formula in statistics for a collection.The mean can be calculated in two steps: Add up all of the data set's values. By the total number of values, divide this number.Mean = Sum of n observations /nTo calculate the mean temperature of the temperatures for 10 days in winter in °C.
Mean Temperature = (0+2+4+4+1+0+8+2+1+9) /10
= 31 / 10
= 3.1 °C
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While working at a bakery, you are responsible for decorating cakes. You would like to add a string of flowers to the border of a round cake you are decorating. The cake has a radius of 14 inches.
What is the length, to the nearest inch, of the string of flowers you will need?
Answers
Answer:
88 inches
Step-by-step explanation:
we need to find the circumference of the cake and the formula is 2rPi
The diameter is 28 and that times pi is about 88
Hopes this help please mark brainliest
what is answer plz help
Answers
Answer:
y=1
Step-by-step explanation:
When x= -4, y=1, i don't know how else to explain it. Find the y value of the graph at that point.
Answer:
y=1
Step-by-step explanation:
if we look at the graph at x-axis where x= -4 and go to meet the line graph , now look at the y -axis and see y= 1
the following pair of triangles are similar. find the value of x 10 x x+2 x+14
Answers
The numerical value of x in the similar pair of triangle is 10.
What is the numerical value of x?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
From the diagram,
Side A of the small triangle = 10
Side B of the small triangle = x + 2
Side A of the Big triangle = 10 + x
Side B of the big triangle = x + 14
Hence;
Ratio of Side A to Side B of the small triangle = 10 / x + 2
Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14
Since the triangle area similar, equate the two ratio and solve for x.
10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )
Cross multiply
10( x + 14 ) = ( 10 + x )( x + 2 )
Expand using FOIL method
10x + 140 = 10x + 20 + x² + 2x
10x + 140 = x² + 12x + 20
x² + 12x + 20 = 10x + 140
x² + 12x + 20 - 10x - 140 = 0
x² + 2x - 120 = 0
Factor the left side of the equation
( x - 10 )( x + 12 ) = 0
Hence;
x - 10 = 0 and x + 12 = 0
x = 10 and x = -12
Since the dimension of the triangle cannot be negative,
x = 10
Therefore, the value of x is 10.
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Solve the second equation to find the coordinate of point B. Show your work step by step. (2 points) 2.5= -2B+6
Answers
Answer:
1.75
Step-by-step explanation:
-2b+6 = 2.5
-2b = 2.5-6
-2b = -3.5
b = -3.5 \ -2
b = 1.75
The Sea Wharf Restaurant would like to determine the best way to allocate a monthly advertising budget of $1000 between newspaper advertising and radio advertising. Management decided that at least 25% of the budget must be spent on each type of media, and that the amount of money spent on local newspaper advertising must be at least twice the amount spent on radio advertising. A marketing consultant developed an index that measures audience exposure per dollar of advertising on a scale from 0 to 100, with higher values implying greater audience exposure. If the value of the index for local newspaper advertising is 50 and the value of the index for spot radio advertising is 80, how should the restaurant allocate its advertising budget in order to maximize the value of total audience exposure?
a. Formulate a linear programming model that can be used to determine how the restaurant should allocate its advertising budget in order to maximize the value of total audience exposure.
b. Solve the problem using the graphical solution procedure.
Answers
Answer:
Step-by-step explanation:
to find the answer you will want to gather the indenpent varible and dependent varrible. SO when you look at the problem you see 25%. You have to find the amount of money on each thing they bought. The budget and how much they have to spend.
How many grams are in 7.4 x10 19 atoms of Copper? round the the thousandths place
Answers
There are 0.09779 grams in 7.4 x 10^19 Atoms of copper.
The number of grams in a given number of atoms of an element, we need to use the concept of molar mass and Avogadro's number.
The molar mass of an element represents the mass of one mole of that element. For copper (Cu), the molar mass is approximately 63.546 grams per mole.
Avogadro's number, denoted as N<sub>A</sub>, is the number of atoms or molecules in one mole of a substance. It is approximately 6.022 x 10^23 atoms/molecules per mole.
To calculate the mass of a given number of atoms, we can use the following steps:
Step 1: Determine the number of moles of copper atoms.
Given: 7.4 x 10^19 atoms of copper
Number of moles = (Number of atoms) / (Avogadro's number)
Number of moles = (7.4 x 10^19) / (6.022 x 10^23)
Step 2: Calculate the mass using the molar mass of copper.
Mass = (Number of moles) x (Molar mass)
Mass = (7.4 x 10^19) / (6.022 x 10^23) x 63.546
Now, we can perform the calculations:
Mass ≈ 0.09779 grams
Therefore, there are approximately 0.09779 grams in 7.4 x 10^19 atoms of copper.
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Simplify 3(x+2) + 2x + 5
Answers
Answer:
\(5x+11\)
Step-by-step explanation:
Step 1: Distribute
\(3x+6+2x+5\)
Step 2: Add like terms
\(5x+11\) < your answer
PLS HELP ILL GIVE YHU BRAINLEST!!
Answers
Answer:
C - 0.75, -0.5, -3, 1.5, 2
Step-by-step explanation:
Becayse 0.75 is the lowest, and 2 is the highest. If you put both up on a number line you would put -0.75 at the end and 2 at the end. Hope this helps :)
Suppose that y varies directly with x, and y=4 when x = 10.
(a) Write a direct variation equation that relates and y Equation: y =
Answers
Answer:
y = 0.4x
Step-by-step explanation:
given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = 4 when x = 10 , then
4 = 10k ( divide both sides by 10 )
\(\frac{4}{10}\) = k , that is
k = 0.4
y = 0.4x ← equation of variation
Describe the graph of y = 3 x squared and compare it with the graph of y = x squared
Answers
Answer:
\(y=3x^{2}\) has a higher vertical scaling compared to \(y=x^{2}\)
Step-by-step explanation:
Graph it! (:
Answer:
Both graphs are parabolas and they both open upward and pass through 0, 0. The first graph is more narrow than the second graph.
Step-by-step explanation:
This was the possible answer provided :)
figure below represents a floor covered with white tiles and gray tiles. KEY = 1 square unit
Answers
According to the information, we can infer that the correct expression is (10 * 7) + (2 * 7) (option D).
How to find the correct expression?To find the correct expression we must look at the graph and interpret the information it has. In this case, some tiles are white and others are gray, so they would represent different elements. In this case, the white area is 10 * 7 tiles, so this would be the first part of the expression.
On the other hand, the second part of the expression would be 7 * 2, which represents the length, length and width of the gray area. According to the above, the correct expression would be (10 * 7) + (2 * 7), the first part in parentheses represents the white area and the second part in parentheses represents the gray area.
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consider a two-factor factorial design with three levels for facts a, three levels for factor b, and four replicates in each of the nine cells
a. how many degrees of freedom are there in determining the A variation and the factor B variation
b. how many degrees of freedom are there in dreaming the interaction variation
c. how many degrees of freedom are there in determining the random variation
d. how many degrees of freedom are there in determining the total variation
Answers
In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.
What is a two-factorial design?A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.
Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.
From the data given:
a.
In calculating the factor A variation, there are two degrees of freedom.
In determining the variation of factor B, there are two degrees of freedom.
b.
Finding the degree of freedom using the interaction variation, there are four degrees of freedom.
c.
In finding the random variable, there are 9(4-1) = 27 degrees of freedom.
d.
In calculating the total variable, there are 9*4-1 =35 degrees of freedom.
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The ratio of the measures of the angles of a triangle is 7:5:8. What is the measure of the largest angle
Answers
Answer:
72° is the largest angle, 63°, 45°
Step-by-step explanation:
7x + 5x + 8x = 180
20x = 180
20x/20 = 180/20
x = 9
I set the equation equal to 180 because there are 180 degrees in a triangle.
Now find the largest angle, which will be the 8x, since 8 is bigger than 5 and 7.
8x
8(9)
72° is the largest angle
If you need the other two angle measures:
7x
7(9)
63°
5x
5(9)
45°
Please help!!
One thousand people stood in a very large circle. Each person wore a sign on their back
with a numeral from 1 to 1000, in a clockwise sequence. They began counting off. The
first person, person A, said "one-in," and remained in the circle. Person B, the person to
the left of A, said "two-out," and left the circle. The person to the left of B, person C, said
"three-in," and remained in the circle. The person to the left, person D, said "four-out,"
and stepped out of the circle.
So it continued with each person wearing an odd number saying "in," and remaining in
the circle, and with every person wearing an even numeral leaving the circle.
It was easy to visualize who remained in the circle when the count off made it all the way
around back to the first person. Since the last person said "one thousand-out," person A,
the first person, said "one-in," and stayed in, while person C, now the next person, said
"three-out," and left the circle. This process would keep going on and on until only one
person was left in the circle.
Who was the last person standing?
Answers
The person who gets to say the last number, 1000, will be Person 6.
Here, we have,
In this scenario, we have seven people sitting in a circle and counting clockwise. The goal is to determine which person will say the last number when they reach 1000. To solve this problem, we can use the concept of modular arithmetic.
When dividing 1000 by the total number of people (7), we get a quotient of 142 and a remainder of 6 (1000 = 142*7 + 6). This means that after completing 142 full rounds of counting, the group will have reached the number 994 (142*7). In the next round, they will continue counting from 995 to 1000.
Since the remainder is 6, it indicates that the last number (1000) will be spoken by the person sitting 6 positions after the first person in the circle (clockwise). In other words, Person 1 says numbers 1, 8, 15, and so on, while Person 6 will say 6, 13, 20, and so on.
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complete question:
10) Seven people sit in a circle and begin counting clockwise starting from 1.Each person in the group is keeping track of the numbers she is saying (e.g. 1,8, 15...) If they continue in this way, counting on and on, until they reach 1000, which person will get to say the last number
will give brainliest if correct
Answers
Answer:
d
Step-by-step explanation:
as x→-∞ , y→+∞
as x→∞ , y→-∞
Reduce this fraction: 5/25x
Answers
Answer:
1/5x
Step-by-step explanation:
1/5x
Pablo deposits $5000 into an account that pays simple interest at a rate of 3% per year. How much interest will he be paid in the first 6years?
Answers
Answer:
$5900
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Simple Interest Rate Formula: A = P(1 + rt)
P is principle amountr is ratet is time (in years)Step-by-step explanation:
Step 1: Define
Identify variables
P = 5000
r = 3% = 0.03
t = 6
Step 2: Find Interest
Substitute in variables [Simple Interest Rate Formula]: A = 5000(1 + 0.03 · 6)(Parenthesis) Multiply: A = 5000(1 + 0.18)(Parenthesis) Add: A = 5000(1.18)Multiply: A = 5900Complete this puzzle using each of these numbers only once : 2, 4, 5, 7, 8, 11, 13, 14, 16 Put the even numbers in the squares and the odd nurmbers in the circles. Each row of three numbers must add up to 26.
Answers
Here is one solution to the puzzle:
Squares: 2, 8, 16
Circles: 5, 7, 14
Total: 26
You can verify that each row of three numbers adds up to 26: 2 + 8 + 16 = 26, 5 + 7 + 14 = 26.
What are even and odd numbers?An even number is a number that can be divided into two equal groups. An odd number is a number that cannot be divided into two equal groups. Even numbers end in 2, 4, 6, 8 and 0 regardless of how many digits they have. Odd numbers end in 1, 3, 5, 7, 9.
Therefore, the correct answer is as given above
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how many ft is equal to 1.66m
Answers
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
sam rented a truck for one day there was a base fee of 18.99 and there was an additional fee of 79 cents for each mile driven. Sam had to pay 213.33 when he returned the truck how many miles did he drive the truck.
Answers
Sam drove approximately 246 miles.
Let's start by subtracting the base fee from the total amount Sam paid to find the additional fee he incurred for the miles driven:
213.33 - 18.99 = 194.34
We know that the additional fee is 79 cents per mile, so we can set up an equation to find the number of miles Sam drove:
194.34 = 0.79x
where x is the number of miles driven.
To solve for x, we can divide both sides of the equation by 0.79:
x = 194.34 / 0.79 ≈ 246
Therefore, Sam drove approximately 246 miles.
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Identify the independent and dependent variables in the following situation: Julie notices that her plant grows one inch for every liter of water that it receives.
Answers
Answer:
third choice the independent variable is the amount of water given, dependent is the height of the plant
There are 52 playing cards in a standard deck. Each card is assigned to one of four suits: diamonds, hearts, spades, or clubs. Within each suit, there are 13 ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King.
pls help
Answers
Answer:
Plzzzz answer fast......
If 2 cards are selected from a standard deck of 52 cards.The first card is placed back in the deck before the 2nd card is drawn.What is the probability that a heart and a club will be drawn ?
Answers
There are 13 cards of each suit.
Picking a heart would be 13/52 which reduces to 1/4
Then replacing the card and picking a club would be the same : 1/4
Picking a heart then a club would be 1/4 x 1/4 = 1/16
Answer: 1/16
HELPPP ME PRECAL CLASS
Answers
the answer is g(x)= (x+6).
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
from the given , we get,
f(x)=x^4
and, f(g(x))= (x+6)^4
hence, the answer is g(x)= (x+6).
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