On solving the linear equations we get the result as
x1 + x2 − 2x3 + 3x4 + 2x5 = 6
3x1 + 3x2 − x3 + x4 + x5 = 12
2x1 + 2x2 − x3 + x4 − 2x5 = 5
4x1 + 4x2 + x3 +0x4 − 3x5 = 16
8x1 + 5x2 − 2x3 − x4 + 2x5 = 29
where ,
x1 = 5,x2 = -1, x3 = 3 ,x4 = 2 , x5 = 1
Finding the value of an equation's unknown variable can be done by solving the equation. If an equation contains a "equal to" sign, it is considered to be balanced. This equation so shows that the two quantities on both sides of it are equal. Left hand side and right hand side are the two sides of the equation (Right hand side).
One equation is x - 4 = 5, for instance. It illustrates that x - 4 (LHS) = 5. (RHS). Here, x is an unknowable quality or variable. Therefore, in order to determine the value of x, we must solve this equation.
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4 divided by 5/9 wrote in simplest form need it by 12/2/22 -12/4/22
Answer:
Step-by-step explanation:
First write the reciprocal of 5/9 which it is 9/5 then multiply by 5 which it equal to 36/5
PLSSSSSSSS HELP!!!!!!
Samuel currently has 18 rocks in his collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week. Part A: Set up a system of equations to show how many rocks each has in their collection. You must write two equations for this. (2 points) Part B: After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Write out the equation used and show all work. (1 point) Part C: How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? Show work on how this is found. (1 point)
Answer:
Part A:
Samuel: y=4x+18
Lewis: y=3x+30
Part B: 12 weeks
Part C: 66 rocks
Step-by-step explanation:
Part A:
X represents the number of weeks. With the current amounts, you add that to the equation.
Part B/C:
1. Have both equations equal to each other
4x+18 = 3x+30
2. Solve for x
x = 12
3. Substitute the given variable, x, into the equation y=4x+18
y=4(12)+18
4. Solve for y
y=66
x=12
y=66
X is a normally distributed random variable with mean 51 and standard deviation 13. What is the probability that X is between 38 and 90? Use the 0.68-0.95-0.997 rule and write your answer as a decimal. Round to the nearest thousandth if necessary.
Therefore, by using mean and standard deviation the required probability is P( 38 ≤ x ≤ 90) = P(-1<x<3) = 0.83999
In math, what is the mean?The mean (also known as the arithmetic mean, as opposed to the geometric mean) of a dataset is the sum of all values divided by the total number of values. It's the most commonly used measure of central tendency and is often referred to as the "average.
What is a standard deviation?A standard deviation (or) is a measure of how dispersed the data is in relation to the mean. A low standard deviation indicates that data are clustered around the mean, whereas a high standard deviation indicates that data are more spread out.
Given:
mean = μ = 51
Standard deviation = σ = 13
as per the question, the probability that X is between 38 and 90 will be
P( 38 ≤ x ≤ 90)
By using the 0.68 - 0.95 - 0.997 rule
P( 38 ≤ x ≤ 90) = P((x-μ)/σ≤z≤(x-μ)/σ)
P( 38 ≤ x ≤ 90) =P((38-51)/13≤z≤(90-51)/13)
from z standard normal table
P(x<-1) = 0.15866
P(x>3) = 0.0013499
Therefore, by using mean and standard deviation the required probability is
P( 38 ≤ x ≤ 90) = P(-1<x<3) = 0.83999
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Stephen's current hourly pay is $10.30. If he receives a 4.5% hourly pay increase each year, what will his hourly pay be in two years?
$14.94
$11.25
$10.76
$15.00
Answer:
$11.25
Step-by-step explanation:
If Stephen receives a 4.5% hourly pay increase each year, his hourly pay will be $10.30 + (4.5% * $10.30) = $10.30 + $0.465 = $10.765 after the first year.
In the second year, his hourly pay will be $10.765 + (4.5% * $10.765) = $10.765 + $0.486 = $11.251.
Therefore, in two years, Stephen's hourly pay will be $11.251. This is closest to the answer choice of $11.25, so it is the correct answer.
What are the vertex and range of y = |4x + 8| − 1?
The vertex and range of y = |4x + 8| - 1 will be (-2, -1) ; -1 ≤ y < ∞ respectively. Using the concept of function -
What is function?According to the function, every value in the domain is associated to exactly one value in the range, and they have a predetermined domain and range. This specific sort of connection is what it is called.
Given that,
y = |4x +8| - 1
To get the vertex of y = |4x +8| - 1 as follows.
Where the absolute values are zeros are the vertex points of the absolute value function.
or, |4x +8| = 0
or, 4x +8= 0
or, 4x = -8
or, x = -2
Substitute the value into an original function,
y = |4(-2) + 8| - 1
y= 0 - 1
y = - 1
As a result, the vertex is at (-2, -1)
Remember that the domain is specified in the range of (-∞, ∞) while determining the range.
Given that |4x + 8| ≥ 0 , (absolute value is always 0 or positive)
The result of adding -1 to the inequality's two sides is
|4x + 8| - 1 ≥ - 1
But since |4x + 8| - 1 is identical to f(x) = y, we have y = f(x) - 1, which means that the range is specified for all values larger than -1.
So the range is -1 ≤ y < ∞
Thus,the vertex and range of y = |4x + 8| - 1 will be (-2, -1) ; -1 ≤ y < ∞ respectively.
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Which of the relations given by the following sets of ordered pairs is a function?
O ((-2,5), (7, 5), (-4, 0), (3, 0), (1, — 6)}
O ((3, 3), (3, — 1), (3, 1), (3, 3), (3,5)}
O {(1, 2), (2, 3), (3, 4), (5, 6), (2, 1)}
O {(2,8), (1,-4), (0, 0), (1, 4), (2,8)}
Step-by-step explanation:
be a function, there needs to be one unique
value of +y+ for every +x+
-----------------------------
The 1st set has 5 different values of +y+
for +x+=+1+ and violates definition
--------------
The 2nd set is a function
-----------------------
The 3rd set has
( 1,2 ) & ( 1,1 )
( 2,3 ) & ( 2,2 )
( 3,4 ) & ( 3,3 )
Each of these pairs violates the definition
----------------
The 4th set has ( 2,-7 ) & ( 2,0 ) which
violate definition
Need help making a frequency table
Here is the frequency table based on the data:
1 - 200 7
201 - 400 1
401 - 600 2
601 - 800 3
801 - 1000 1
1001 - 1200 1
1201 - 1400
1401 - 1600 1
1601 - 1800 1
What is a frequency table ?A frequency table is a table that is used to compress a large dataset into a smaller format that can be easily interpreted. A frequency table is usually made up of a class interval and frequency.
A class is the group of a numbers. The frequency of the class is the total number of times that numbers within the class appear in the dataset. For example in the class 100 - 200, there are 7 numbers in the dataset that have a value between 100 and 200. This means that the frequency of 100-200 is 7.
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The height of a tower on a scale drawing is 14 centimeters. The scale is 2 cm : 13 m. What is the actual height of the tower?
Using the cross-multiplication method, we know that the actual height of the building is 91 m.
What is the cross-multiplication method?One might cross-multiply an equation between two fractions or rational expressions in mathematics, more specifically in elementary arithmetic and elementary algebra, to make the equation simpler or to find the value of a variable.
To cross-multiply two fractions, multiply the first fraction's numerator by the second denominator and the second fraction's numerator by the first fraction's denominator.
So, we know that:
The height of the building scale is 14 cm.
The scale is 2 cm and the actual height is 13 m.
Now, the actual height of the building will be:
14/x = 2/13
Use cross-multiplication method as follows:
14/x = 2/13
2x = 14 * 13
2x = 182
x = 182/2
x = 91 m
Therefore, using the cross-multiplication method, we know that the actual height of the building is 91 m.
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Divide
(-21yx+31y²x⁴) ÷ (-4y²x⁴)
Simplify your answer as much as possible
Solution:
Given:
(-28yx+ 31y²[tex]x^{4}[/tex])/(-4y²[tex]x^{4}[/tex])
[tex]\frac{-28yx}{-4y^{2}x^{4} }[/tex] + [tex]\frac{31y^{2}x^{4}}{-4y^{2} x^{4} }[/tex]
[tex]\frac{7}{x^{3} y}[/tex] + [tex]\frac{31}{4}[/tex]
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After dividing the given equation, the answer in the simplest form is [tex]\frac{7}{x^{3} y}- \frac{31}{4}[/tex]
What do you mean by simplest form?
A fraction with a denominator and numerator that are both relatively prime has the simplest form. It indicates that the fraction's numerator, which is the portion at the top of the fraction, and denominator, which is the portion at the bottom, do not share any factors other than one.
An amount that represents a fraction of a whole is called a fraction. A fraction's reduced form is another name for its simplest form. A fraction with a common factor of one, such as 34, has the simplest form. Although 2/4 can be further simplified and written as 12, it is not the most basic form. The fractions 12 and 2/4 are equivalent in this case, we can also say.
Given:
⇒(-28yx+ 31y²[tex]x^{4}[/tex])/(-4y²[tex]x^{4}[/tex])
⇒ [tex]\frac{-28yx}{-4x^{4}y^{2}}[/tex] + [tex]\frac{31y^{2}x^{4}}{-4y^{2} x^{4} }[/tex]
⇒ [tex]\frac{7} {x^{3} y}[/tex] - [tex]\frac{31}{4}[/tex]
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A party rental company has chairs and tables for rent l. The total cost to rent 5 chairs and 6 tables is $53. The total cost to rent 3 chairs and 2 tables is $21. What is the cost to rent each chair and each table?
For the given word problem, the cost to rent each chair is $5.25 and each table is $2.625
What is a word problem?
A word problem is a short passage presenting a "real-life" situation where an issue needs to be solved using math. The word problem for groups is a classic example, but there are numerous additional examples as well. This question is in many significant circumstances undecidable, which is a profound conclusion of computational theory.
Let C be the cost per chair
Let T be the cost per table
The total cost to rent 5 chairs and 6 tables is $53.
Then, 5C+6T=42 ................ (i)
The total cost to rent 3 chairs and 2 tables is $21.
Then, 3C+2T=21 ................. (ii)
Now, by solving both equations, multiply (ii) by 3 and subtract (i), we get
9C - 5C = 63 - 42
or, 4C = 21
or, C = $5.25
Then, T = (21-3*5.25)/2 = $2.625
Hence, the cost to rent each chair is $5.25 and each table is $2.625
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Which of the following are solutions to the equation |6x −1| = 17?
Select all that apply.
Answer: 3,-3
Step-by-step explanation:
|6x-1| = 17
For absolute value problems there is always two solutions. They will both be the same number, one positive and one negative.
6x-1 = 17
Add 1 to both sides.
6x-1 +1 = 17+1
6x=18
Now, divide by 6.
6x/6=18/6
x = 3
The two answers that would be correct are 3,-3.
Ginny and Bob are both locksmiths.
Ginny uses the function f(x)=60x+80 to determine the charge to her customers, where x represents the number of hours of labor.
The table shows what Bob charges a customer for x hours of labor.
x (hours) 0 1 2 3 4
cost ($) 60 140 220 300 380
Which locksmith charges less for an initial fee for a service call?
Drag a value or name to the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Ginny charges Response area for an initial fee, and Bob charges Response area for an initial fee. Response area charges less for an initial fee.
Ginny charges $80 for an initial fee, and Bob charges $60 for an initial fee. Bob charges less for an initial fee.
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
f(x)=60x+80 is function that represents the charge to Ginny's customers, where x represents the number of hours of labor.
To find initial fee, put x = 0 in the given function.
Put x = 0 in f(x) = 60x + 80:
f(0) = (60×0) + 80
f(0) = 80
The initial fee is $80.
From the table,
When x = 0, cost = $ 60.
The initial fee is $60.
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In an analysis of variance with a between-groups population variance estimate of 30 and a within-groups estimate of 25, the F ratio is A) 25 / (30–25) = 5.00
B) (30–25) / 30 = 0.17 C) 25 / 30 = 0.83
D) 30 / 25 = 1.20
The F ratio is 1.2.
What is statistic?
The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem.
30/25 = 1.2
In an ANOVA, this statistic is used in the F test to test the hypothesis that the group means are not equal to one another. The F ratio is calculated as follows:
Fobs=MSB/MSW
30/25 = 1.2
Where MSB is the mean square between the groups and MSW is the mean square within the groups.
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Hi can you help me with this problem?and explain it to me thanks!
-
Euromart Tile Company borrowed $40,000 on April 6 for 66 days. The rate was 14% using the ordinary interest method. On day 25 of the loan, Euromart made a partial payment of $15,000, and on day 45 of the loan, Euromart made a second partial payment of $10,000.
a.
What was the new maturity value of the loan?
b. What was the maturity date of the loan?
Answer:
A. The new maturity value of the loan would be $15,000
B. The maturity data of the loan would be June 20
Step-by-step explanation:
N/A
The volume of a particular die is 7200 mm³. Use the fact that 10 mm equals 1 cm to convert this volume to cm³. Round your answer to the nearest tenth.
Answer: 720.0 cm³
Step-by-step explanation:
To convert the volume of the die from millimeters to centimeters, we need to divide the volume by the conversion factor that relates millimeters to centimeters. Since 10 millimeters is equal to 1 centimeter, the conversion factor is 10.
To convert the volume to centimeters, we can divide it by the conversion factor:
7200 mm³ / 10 = 720 cm³
This means that the volume of the die is 720 cm³. Rounded to the nearest tenth, the volume of the die is 720.0 cm³.
5x +6 (x-2) -8 (x-3) please help
Answer:
3x + 12
Step-by-step explanation:
5x + 6(x - 2) - 8(x - 3) ← distribute parenthesis
= 5x + 6x - 12 - 8x + 24 ← collect like terms
==(5x + 6x - 8x) + (- 12 + 24)
= 3x + 12
What shapes use the area formula A = lw ?
O Parallelogram
O Triangle
O Trapezoid
O Rectangle
Answer:
Rectangle
Step-by-step explanation:
Welcome to Brainly! :]
A rectangle uses A=lw to calculate area
Where l is length and w is width
Hope this helps,
:]
will mark brainliest to whoever is correct
Complete the inequalities for the domain and range of the solution set to equation below.
y=8 x-4
Where x is the number of days and y is the weight of the plant.
the domain = [1,∞) and range = [4 , ∞) for the given equation.
What is domain and range?
The set of all doable values that qualify as inputs to a operate is understood because the domain of the operate, or it may also be outlined because the entire set of values doable for freelance variables.
The set of all the outputs of a operate is thought because the vary of the operate or when subbing the domain, the whole set of all values attainable as outcomes of the variable.
Main body:
Given equation =
y=8x-4
as x is the number of days
and,y is the weight of the plant.
so x can not be negative
hence the domain of x = [1,∞)
As x is positive , y can not be negative as well.
Hence the domain = [1,∞) and range = [4 , ∞)
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Natasha's Flowers, a local florist, purchases fresh flowers each day at the local flower market. The buyer has a budget of $1,000 per also a maximum amount the shop can sell. Based on past experience the shop has estimated the following NPV of purchasing each
Roses
Lilies
Pansies
Orchids
NPV per bunch
$1
$10
$4
$20
Cost per bunch
$21
$29
$33
$76
Max.
Bunches
25
10
10
5
What combination of flowers should the shop purchase each day?
The profitability index for each choice is: (Round to three decimal places.)
Roses
NPV per bunch
$1
Cost per bunch
$21
Max.
Bunches
25
Profitability Index (per bunch)
1. Based on the profitability index per bunch, the combination of flowers to purchase each day is 10 Lilies, 10 Pansies, and 5 Orchids, costing $1,000. On any other day, the florist can purchase 25 Roses.
2. The profitability index per bunch is as follows:
Roses = 1.0476Lilies = 1.345Pansies = 1.121Orchids = 1.270.What is the profitability index?The profitability index can also be described as the profit investment ratio or value investment ratio.
The profitability index shows the ratio of the investment's payoff and the investment cost.
The profitability index is computed as the net present value added to the initial cost and divided by the initial investment.
The profitability index is the quotient of the present value of future cash flows and the initial investment cost.
NPV Cost Max. Total Total
per bunch per bunch Bunches NPV Costs
Roses $1 $21 25 $25 $525
Lilies $10 $29 10 $100 $290
Pansies $4 $33 10 $40 $330
Orchids $20 $76 5 $100 $380
Total budget per day = $1,000
Profitability index = (NPV + Cost)/Cost
Roses = 1.0476 ($1 + $21)/$21
Lilies = 1.345 ($10 + $29)/$29
Pansies = 1.121 ($4 + $33)/$33
Orchids = 1.270 ($20 + $74)/$74
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Biologists stocked a lake with 800 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 6600 . The number of fish grew to 1020 in the first year.
a) Find a logistical model for the number of fish P(t) after t years
P(t)=
b) How long will it take for the population to increase to 3300 hhalf of the carrying capacity)?
It will take years.
Answer:
Below
Step-by-step explanation:
from 800 to 1020 is a 220/800 * 100% = 27.5% increase each year
P(t) = 800 ( 1 + .275)^t
3300 = 800 ( 1+.275)^t
3300 / 800 = 1.275 ^t LOG both sides
.615423 / LOG 1.275 = t = 5.83 years
A 12-sided die is rolled. The set of equally likely outcomes is
{1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a 4.
Answer: 1/12
Reason:
There's one side we want (rolling the "4") out of 12 sides total. Each side has a probability of 1/12 of occurring since each side is equally likely.
Suppose you send aboui 12 text messaqes a day, and your older sister sends
more text messages than you do. Together, you send a total of about 26 messages per day. About how many text messages does she send a day? Write an equation and solve for the unknown value.
Answer:
Step-by-step explanation:
if you send 12 messages a day.
and your sister sends and unkown number of texts per day but together you both send 26 number of total texts.
Then, suppose your sister sends X number of texts.
Then
X + 12 = 26
X = 26 - 12
X = 14
What is a residual for a multiple regression model and the data that is used to create it? select one.
Option d is correct
What is the "multiple regression" model:y=β0+β1x1+β2x2+β3x3+........+βkxk+ε
Where y is the "independent" variable and 0 to k are the "regression" coefficients. In a "multiple linear regression" model, the "independent" variables are x1, x2, x3,..., xk, and the "residual" or "error" term is.
The "residual" for the regression model is calculated using the following formula.
Residual=y-ŷ
Where y is the "independent variable's" "actual" value and is the "independent variable's" "predicted" value.
The "difference" between the "actual" value of the "dependent" variables and the corresponding "predicted" value when employing the "multiple regression" model is referred to as the "residual" in the "residual" formula.
A statistical technique for evaluating the relevance of a "multiple regression" model is the "F test." Linear models are A linear model is a statistic that explains the “relationship” between “response” and “predictor” variables. Using the “multiple regression” model, the “predicted” value of the “response” variable is denoted by ŷ.
hence option 4 is correct
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I understand you mean:
What is a residual for a multiple regression model and the data that is used to create it? Select one:
1.A statistic that is used to evaluate the significance of the multiple regression model
2.A statistic that explains the relationship between response and predictor variables
3.The predicted value of the response variable using the multiple regression model
4.The difference between the actual value of the response variable and the corresponding predicted value (regression error) using the multiple regression model
Teddy has two piggy banks. The difference in the amount of money between the two banks is no more than $10. One piggy bank has $7.31 in it. Select the choices that make the inequality and statement about the possible amount of money in the other piggy bank correct.
The inequality and statement about the possible amount of money in the other piggy bank is 0 ≤ PB₂ ≤ 2.69.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Teddy has two piggy banks. The difference in the amount of money between the two banks is no more than $10.
∴ PB₁ + PB₂ ≤ 10.
One piggy bank has $7.31 in it.
∴ 7.31 + PB₂ ≤ 10.
PB₂ ≤ 2.69.
So, The amount in PB₂ can be 0 ≤ PB₂ ≤ 2.69.
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How much would you need to deposit in an account now in order to have $4000 in the account in 15 years? Assume the account earns 2% interest compounded monthly.
2,985/- need to deposit in an account.
To calculate the interest we use one type of formula which is
A=P(1+r/n)^(t n)------------------(1)
In the above formula:
A = Accrued amount.
P = Principal amount.
r = Annual nominal interest rate as a decimal.
n = number of compounding periods per unit of time.
t = time in decimal years.
I = Interest amount.
ln = natural logarithm.
Given That
A=4000 t=15 r=2% n=2
changing the r in % into decimal we get 0.02.
Now we substitute the values in the above Formula, and we get
A=P(1+r/n)^(t n)
4000=P(1+.02/2)^(15*2)
4000=P(1.01)^(30)
4000=P(1.34)
4000/1.34=P
2,985=P
Principal = $2,985
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a researcher is performing a two-way anova using two factors. the first factor has 4 levels and the second factor has 9 levels. in the anova summary table, the degrees of freedom for the interaction between the first and second factors will be 24 27 32 36
In a two-way ANOVA, the two independent variables are known as factors. Two variables, or factors, are supposed to influence the dependent variable.
First, let's understand what is 2-way ANOVA using 2 factors.
To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilized. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.
To evaluate if there is a statistically significant difference between the means of three or more independent groups that have been divided on two factors, a two-way ANOVA is utilized.
Given is that the first factor has 4 levels and the second factor has 9 levels.
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Simplify each of the following expressions:
-5 + 2 + 8 =
Compare the square root of 26 and twenty eight sixths using >, <, or =.
twenty eight sixths is less than the square root of 26
the square root of 26 is less than twenty eight sixths
twenty eight sixths is greater than the square root of 26
the square root of 26 is equal to twenty eight sixths
The numbers, square root of 26 and twenty eight sixths can be compared using the known values of the square root of a number near to 26, such as 25, and inequality symbols, which indicates;
Twenty eight sixths is less than the square root of 26What is an inequality in mathematics?An inequality is a comparison between values that have different measures or magnitude, such that one values may be less than, <, greater than, >, or not equal to, ≠, the other value in the comparison.
The square root of 26 is √(26)
Twenty eight sixths is [tex]\dfrac{28}{6}[/tex]
26 is a larger number than 25, therefore;
√(26) > √(25) = 5
The square root of 26, is larger than 5; √(26) > 5
Expressing the fraction of twenty eight sixths as a proper fraction, indicates
[tex]\dfrac{28}{6} = 4\frac{4}{6} =4\frac{2}{3}[/tex]
Twenty eight sixths is four and two thirds, therefore;
Four and two thirds is less than 5, therefore;
[tex]4\frac{2}{3} < 5[/tex]
Substituting twenty eight sixths with four and two thirds, indicates;
[tex]\dfrac{28}{6} = 4\frac{2}{3} < \sqrt{26} > 5[/tex]
[tex]\dfrac{28}{6} = 4\frac{2}{3} < 5 < \sqrt{26}[/tex]
[tex]\dfrac{28}{6} < \sqrt{26}[/tex]
The correct option is therefore;
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Example 2
3. FOOTBALL The flight of a football thrown by a quarterback can be
modeled by an interval of a function. Sketch a nonlinear graph that
shows the height of a football y, in feet, as a function of time x, in
seconds.
Positive: between 0 seconds and 5 seconds
Negative: for time greater than 5 seconds (represents time after
the ball hits the ground)
Increasing: for time less than 2 seconds
Decreasing: for time greater than 2 seconds
Relative Maximum: at 2 seconds, when the height of the football is 9 feet
Height of Football (ft)
End Behavior: As time increases, the height of the football decreases.
Symmetry: The height of the football for time between 0 seconds and 2 seconds
is the same as the height for time between 2 seconds and 4 seconds.
The quadratic function that models the path of the ball is given as follows:
y = -(x - 2)² + 9.
The graph of this quadratic function is given by the image shown at the end of the answer.
How to define the path of ball?The ball is increasing, and then later it decreases, meaning that it is defined by a concave down quadratic function.
The ball has a positive height until 5 seconds, hence one of the roots of the quadratic function is of 5, that is, when x = 5, y = 0.
The vertex of the quadratic function is given as follows:
(2,9).
Hence the vertex form definition of the quadratic function is given as follows:
y = a(x - 2)² + 9.
When x = 5, y = 0, hence the leading coefficient a is obtained as follows:
0 = a(5 - 2)² + 9
9a = -9
a = -1.
Hence the quadratic function is given as follows:
y = -(x - 2)² + 9.
More can be learned about quadratic functions at https://brainly.com/question/24737967
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