Option (C) is the correct one and the only true statement is
The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }.
Given, a table of values for y = f(x)
x -2 -1 0 1 2 3 4 5 6
y 7 8 9 10 11 5 6 12 13
We have to find the correct statements,
as the range of the function f(x) is { 4, 8, 9, 10, 11, 5, 6, 12, 13 }
the image of 5 in the function is 6 i.e. f(5) = 6.
The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }
the image of -1 in the function is 8 i.e. f(-1) = 8.
Hence, only the option (C) is the correct one and the only true statement is
The domain of the function f(x) is { -2, -1, 0, 1, 2, 3, 4, 5, 6 }.
Learn more about Functions here https://brainly.com/question/26209640
#SPJ1
PLEASE HELP SOLVE!!!
Answer:
positive, positive, zero, zero, negative, negative, positive
Step-by-step explanation:
The derivative is positive when a function is increasing.
The derivative is zero when a function is neither increasing nor decreasing.
The derivative is negative when the function is decreasing.
A neighborhood planner uses a coordinate plane to design a new neighborhood. The coordinates A(1,−1) , B(1,−2) , and C(2,−1) represent House A, House B, and House C. The planner decides to place a playground centered at the origin, and moves the houses to make space. House A is now located at A′(3,−4) . What are the new coordinates of House B and House C when each house is moved using the same translation?
The new coordinates of House B and House C are
B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively
What is Translation?
A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
Given data ,
Let the 3 houses be A , B ,C
The coordinate of House A = A ( 1 , -1 )
The coordinate of House B = B ( 1 , -2 )
The coordinate of House C = C ( 2 , -1 )
Now , the houses are relocated to new coordinates with
The new coordinate of House A = A' ( 3 , -4 )
The translation of Point A can be expressed in the form of x and y coordinate as there is a translation occurred with a scale factor
So ,
A ( x₁ , y₁ ) to A' ( x₂ , y₂ )
A ( 1 , -1 ) to A' ( 3 , -4 )
x₂ = x₁ + 2
y₂ = y₁ - 3
From the figure , we can clearly see that the coordinates of the houses A , B and C are translated by a scale factor and the new coordinates are
x₂ = x₁ + 2
y₂ = y₁ - 3
Therefore ,
B ( x₁ , y₁ ) to B' ( x₂ , y₂ )
B' ( x₂ , y₂ ) = B' ( 3 , -5 )
C ( x₁ , y₁ ) to C' ( x₂ , y₂ )
C' ( x₂ , y₂ ) = C' ( 4 , -4 )
Hence , the new coordinates of House B and House C are B' ( 3 , -5 ) and C' ( 4 , -4 ) respectively
To learn more about translation click :
https://brainly.com/question/19007400
#SPJ1
At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation:
s=64t-16t^2
In how many seconds does the object reach its maximum height?
The time it takes the object to attain maximum height is 2 seconds
Time to Attain Maximum HeightTo find the time it takes the object to attain maximum height, we have to use the quadratic equation to do so. The formula can be given as
t = -b/2a
But let's write and define our quadratic equation with it's variables.
S = 64t - 16t²
To attain maximum height;
t = -b/2a
a = -16, b = 64,c = 0
Substituting the values
t = -64/2(-16)
t = 2
The time is 2 seconds
Learn more on maximum height here;
https://brainly.com/question/9573062
#SPJ1
The cost to replace a water pump in a sports car was $899. This included $365 for the water pump and $89 per hour for labor. How many hours of labor were required to replace the water pump?
By solving a linear equation we will see that there were 6 hours of labor.
How many hours of labor were required?We know that the total cost is composed by a fixed amount of $365 plus $89 per hour of labor, so if there are x hours of labor, the total cost will be:
c(x) = $365 + x*$89
We know that the total cost is $899, then we can write the linear equation:
$899 = $365 + x*$89
$899 - $365 = x*$89
($899 - $365)/$89 = x = 6
So there were 6 hours of labor.
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
See question in screenshot below:
The value of P is $2,000.
The value of r is 2.8%
The value of n is 4.
The amount of money that Allision will have in 8 years is $2,500.19.
How much will he have in 8 years?When the account is compounded quarterly, it means that the amount invested and the interest that has already been earned would increase in value four times in a year. A compound growth rate can be modelled as an exponential equation.
The equation that can be used to determine the future value with quarterly compounding is:
S(t) = P( 1 + r /n)^(n x t)
Where:
P = amount deposited r = interest rate n = number of compounding t = number of yearsS(t) = 2,000 x ( 1 + 0.028 / 4)^(4 x 8)
S(t) = 2,000 x 1.007^32 = $2,500.19
To learn more about compound interest, please check: https://brainly.com/question/26367706
#SPJ1
30 POINTS AND BRAINLIEST!! PLEASE HURRY I HAVE 20 MIN LEFT. <3 tysm (:
25. doubled
26. doubled
27. increases 4 times
28. remains unchanged
29. increases 6 times
PLS HELP GUYS LIKE FR I NEED HELP THIS IS MY LAST PROBLEM FOR MY SHEET. SHOW THE DRAWING PLS
Answer/Step-by-step explanation:
Use the given drawing and scale to find out how big the building is in real life. See image. Then use the scale they asked for to make the new drawing. See image.
The functions r and s are defined as follows.
r(x) = 2x+1
s(x) = -x²
Find the value of r (s (4)).
r(s(4))=
Answer:
[tex]33[/tex]
Step-by-step explanation:
Define functions:
[tex]r(x) = 2x+1\\s(x) = -x^2[/tex]
Substitute [tex]s(x)[/tex] into [tex]r(x)[/tex]:
[tex]2(-x^2) + 1[/tex]
Solve for value:
[tex]= 2((-4)^2)+1\\= 2(16) + 1\\= 32 + 1\\= 33[/tex]
** assuming that the function of [tex]s(x)[/tex] the x value is squared with the negative sign.
Find the savings plan balance after 2 years with an APR of 3% and monthly payments of $300.
The balance is $
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answer:
Step-by-step explanation:
The balance of the savings plan after 2 years will be=$7,410.85 at 3% compounded monthly.
The balance of the savings plan after 2 years will be=$7,407.95 at 3% compounded annually.
The formula you use to calculate this is:FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD, Where R=Interest rate per period, N=number of periods, P=periodic payment, FV=Future value.
friendly and kind personality and likes to help people but like Hyde, he becomes mysterious and violent
Rewrite the equation in vertex form. (Include fractions in final answer).
y=-3x^2 -7x+4
For the given equation y = 3x² -7x + 4 the vertex form is given by
( 7/6, -1/12).
As given in the question,
Equation is given by :
y = 3x² -7x + 4
Standard form of the equation to get the vertex form is given by :
y = a ( x - h )² + k
Where ( h, k ) represents the vertex of the equation,
Now,
Simplify the given equation y = 3x² -7x + 4 into standard form to get vertex form,
y = 3x² -7x + 4
⇒ y = 3 [x² -2×(7/6)] + 4
⇒ y = 3 [ x² - 2×(7/6) + (49/36) - (49/36) ] + 4
⇒ y = 3 [ x² - 2×(7/6) + (49/36) ] - 3(49/36) + 4
⇒ y = 3 [x - (7/6)]² - (49/12) + 4
⇒ y = 3[x - (7/6)]² - (1/12)
Compare it with standard form ,
a = 3, h = (7/6) , k = -(1 /12)
Vertex form ( h, k) = ( 7/6 , -1/12 )
Therefore, for the given equation y = 3x² -7x + 4 the vertex form is given by ( 7/6, -1/12).
Learn more about vertex form here
brainly.com/question/13921516
#SPJ1
Can some one please help me do these work sheets before I fail my class♀️
Answer of the given question are respectively,
[tex]-x^2y , 2w ,\\\\h^6 , -14a^5b^2\\x^6 , 4m^8\\9x^4/14 , y^2\\-5/x^2 , 1/2k\\7 , 1[/tex]
Exponent:
A quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.
Example:
[tex]2^3[/tex] = 2 × 2 × 2
Combine like term:
1. [tex]9x^2y -10x^2y[/tex] = [tex]-x^2y[/tex]
2. Subtract 6w from 8w
8w -6w = 2w
Rule:
[tex]x^{a} * x^{b} = x^{a+b} \\\\[/tex]
1.
[tex]h^2 * h^4 = h^{2+4} \\ \\\\= h^6[/tex]
2.
[tex](-2a^2b).(7a^3b)\\\\-14 a^{2+3} b^{1+1} \\\\= -14 a^5 b^2[/tex]
Rule:
[tex](x^a)^b = x^{ab}[/tex]
1. [tex](x^2)^3 = x^6[/tex]
2.
[tex](-2m^3)^2 * m^2 \\\\4m^6*m^2\\\\4m^8[/tex]
Rule:
[tex]x^a/x^b = x^{a-b}[/tex]
1.
[tex]27x^5/42x\\\\= 9x^4 /14[/tex]
2.
[tex](y^3)^2/y^4\\\\y^6/y^4\\\\y^2\\[/tex]
Rule:
[tex]x^{-a}= 1/x^a[/tex]
1.
[tex]-5x^{-2} \\\\= -5/x^2[/tex]
2.
[tex]4k^2/8k^3\\\\= k^{-1} /2\\\\= 1/2k[/tex]
Rule:
[tex]x^0 =1[/tex]
1.
[tex]7x^0\\\\= 7[/tex]
2.
[tex](w^4)^2/w^8\\\\w^8/w^8\\\\w^0\\\\=1[/tex]
To learn more about Exponent visit: https://brainly.com/question/15993626
#SPJ9
Karen, a 52-year-old female, bought a $75,000, 20-year life insurance policy through her employer. Karen is paid weekly.
How much is deducted from her paycheck for life insurance? (Use the table.)
ABC Term Life Insurance Company
Annual premium
Age at issue
Male Female 10-year
per $1000 of coverage
20-24 23-27 $2.50
25-29 28-32 $3.25
30-34 33-37 $3.82
35-39 38-42 $4.55
40-44 43-47 $5.78
45-49 48-52 $7.53
20-year
$3.80
$5.84
$7.93
$10.33
$13.68
$17.56
As Karen age is 52- year old and she is a female and her life insurance policy is for 20- years , then amount to be deducted from her life insurance paycheck is equal to $1317.
As given in the question,
Information given about Karen,
Age = 52- year old
Gender = female
Policy = 20 -year life insurance policy
Annual premium given per $1000 for coverage
Karen policy amount = $75,000
From the table it is given that,
Amount deducted per $1000 for 20year policy in the age limit of 48 -52
= $17.56
⇒ $1000 = $17.56
⇒ $75,000 = $( 17.56 × 75,000)/ 1000
= $1317.
Therefore, as Karen age is 52- year old and she is a female and her life insurance policy is for 20- years , then amount to be deducted from her life insurance paycheck is equal to $1317.
Learn more about deducted here
brainly.com/question/3158031
#SPJ1
If tan(t)=3/4 what’s cos(t)
well, let's notice our tangent is positive, that only happens on the 1st and 3rd Quadrants
[tex]tan(t )=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{4}}\hspace{5em} \textit{now let's find the hypotenuse} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{4^2 + 3^2}\implies c=5\hspace{5em} \stackrel{I~Quadrant}{cos(t)= \cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{5}}}\qquad \stackrel{III~Quadrant}{cos(t)=-\cfrac{4}{5}}[/tex]
Consider the relationship 9r+2t=9 .
a. Write the relationship as a function r=f(t) .
Enter the exact answer.
f(t)=
b. Evaluate f(−9) .
f(−9)=
c. Solve f(t)=5 .
t=
1. The relationship as a function r = f(t) is: r = (9 - 2t)/9.
2. The numeric value at t = -9 is: f(-9) = 3.
3. The value of t for which f(t) = 5 is t = -18.
What are the desired measures?The relationship is given as follows:
9r + 2t = 9.
To write the relationship as a function of t, we have to isolate the variable r as a function of the variable t, hence:
9r = 9 - 2t
r = (9 - 2t)/9.
To find the numeric value at t = -9, we replace the lone instance of t in the relationship by -9, hence:
r = (9 - 2(-9))/9 = 27/9 = 3.
To find when f(t) = 5, we have to find t for which f(t) = 5, hence:
9r = 9 - 2t
2t = 9 - 9r
2t = 9 - 9(5)
2t = -36
t = -36/2
t = -18.
More can be learned about functions at https://brainly.com/question/24808124
#SPJ1
During one hour of running, Jeff can run 5.5 miles. The number of miles Jeff runs and the number of hours are in a proportional relationship. This is represented by y=5.5x .
The slope of the graph is 5.5.
Given:
During one hour of running, Jeff can run 5.5 miles. The number of miles Jeff runs and the number of hours are in a proportional relationship. This is represented by y=5.5x .
slope:
Slope is the steepness of a line as it moves from LEFT to RIGHT. Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line. The slope of a line is always constant .
compare the y = 5.5x with standard equation y = mx + c
m = 5.5 and c =0
m is nothing but slope:
so slope m = 5.5
= 11/2.
Therefore The slope of the graph is 5.5.
Learn more about the slope here:
https://brainly.com/question/3605446
#SPJ1
7. For the piecewise defined function {f(x)=1 x<3
{1/2x+7 x_>3
(1) 7
(2) 10
3x-1 x<3
[//x+7 _x23²)
(3) 17
(4) 27
which of the following is the value of f(6)?
Answer:
I think it's 10 idek I just search it
The scatter plot shows the winning times, in seconds, in a 50-meter race over eight consecutive years.
Scatter plot with x axis labeled Time in Years and y axis labeled Winning Time with points at 1 comma 5 and 4 tenths, 2 comma 5, 3 comma 4 and 6 tenths, 4 comma 4 and 9 tenths, 5 comma 4 and 1 tenth, 6 comma 3 and 9 tenths, 7 comma 3 and 6 tenths, and 8 comma 3 and 3 tenths.
Which of the following is an appropriate line of best fit?
y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
y hat equals 29 hundredths times x plus 5 and 67 hundredths.
y hat equals negative 45 hundredths times x plus 7 and 69 hundredths.
y hat equals 45 hundredths times x plus 7 and 69 hundredths.
Answer:
[tex]\hat{y}=-0.29x+5.67[/tex]
Step-by-step explanation:
Given points on the scatter plot:
(1, 5.4)(2, 5)(3, 4.6)(4, 4.9)(5, 4.1)(6, 3.9)(7, 3.6)(8, 3.3)Plot the given points and draw a line of best fit (see attachment).
As the y-values decrease as the x-values increase, the slope of the line of best fit is negative.
From inspection of the plotted line of best fit, we can see that the y-intercept is approximately 5.7.
Therefore, the equation that is appropriate for the line of best fit is:
[tex]\boxed{\hat{y}=-0.29x+5.67}[/tex]
Answer:
y hat equals negative 29 hundredths times x plus 5 and 67 hundredths.
Step-by-step explanation:
i took the test :)
Question content area top
Part 1
Arrivals to a bank automated teller machine (ATM) are distributed according to a Poisson distribution with a mean equal to per minutes. Complete parts a and b below.
The probabilities, using the Poisson distribution, are given as follows:
a) Three customers in five minutes: 0.1805 = 18.05%.
b) Fewer than two customers in ten minutes: 0.0916 = 9.16%.
What is the Poisson distribution?The probability mass function of the Poisson distribution is presented as follows:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters of the Poisson distribution are:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval or range of values of the input parameter.The mean is of two arrivals per five minutes, hence:
[tex]\mu = 2[/tex]
The probability of exactly three arrivals in five minutes is:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 3) = \frac{e^{-2}2^{3}}{(3)!} = 0.1805[/tex]
For ten minutes, the mean is given as follows:
[tex]\mu = 2 \times 2 = 4[/tex]
The probability of fewer than two arrivals is:
P(X < 2) = P(X = 0) + P(X = 1).
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-4}4^{0}}{(0)!} = 0.0183[/tex]
[tex]P(X = 1) = \frac{e^{-4}4^{1}}{(1)!} = 0.0733[/tex]
Then:
P(X < 2) = P(X = 0) + P(X = 1) = 0.0183 + 0.0733 = 0.0916 = 9.16%.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
More can be learned about the Poisson distribution at https://brainly.com/question/7879375
#SPJ1
Which graph represents the function f(x) = -x] -2?
The third graph or option 3 represents the function f(x) = - l x l - 2.
Given:
f(x) = - l x l - 2
Table
x y = - l x l - 2
0 -2
1 -3
2 -4
3 -5
-1 -3
-2 -4
-3 -5
On plotting above points or the above points shown in figure 3 or third graph.
Therefore the third graph or option 3 represents the function f(x) = - l x l - 2.
Learn more about the graph here:
https://brainly.com/question/17267403
#SPJ1
Read the problem below on the picture. It's Geometry by the way. Also if u can answer my other one its in my profile.
Answer:
x = 18. y = 54
Step-by-step explanation:
first we we figure out the degrees of the spot where N is.
(I know N references the line but ill be using it to call the spot)
72 + N = 90
subtract 72 from both sides
N = 18
So since opposite angles are the same
2x + N = 3x
2x + 18 = 3x
subtract 2x from both sides
18 = 1x
divide by 1 both sides
18 = x
______
now we add all the angles from the left sides to make 180
2x + N + 72 + y = 180
we know x is equal to 18 and N is also 18
2(18) + 18 + 72 + y = 180
simplify
36 + 18 + 72 + y = 180
add
126 + y = 180
subtract both sides by 126
y = 54
Prizes in a raffle are determined by taking a ball from a bag. There are 15 balls in the bag, 12 of them are green, two of them with black stars. There are two silver balls, one with a black star, and one gold ball. If you draw the green ball, without the black star, you win a small prize. If you get a green ball with the black star, you get a medium prize. If you get the silver ball without the star, you get a large prize. If you get the silver ball with the black star, you get the extra-large prize. If you get the gold ball, you get the super deluxe prize.
If you get a ball, what is the probability of getting the green with the black star?
The probability of getting the green ball with the star is
a.) 0.1333
b.) 0.1133
c.) 0.0123
d.) 0.0333
This is an example of:
a.) a joint event
b.) an elementary event
The probability of winning the small prize is:
a. 0.7666
b. 0.6666
c. 0.6667
d. 0.6777
This is an example of:
a.) a joint event
b.) an elementary event
What is the probability of winning the super deluxe prize?
The probability of winning the super deluxe prize is:
a.) 6.6677
b.) 0.6667
c.) 0.7667
d.) 0.0667
This is an example of:
a.) a joint event
b.) an elementary event
Answer:
a. )
Step-by-step explanation:
There are 15 balls ...... two are green with a star
2 out of 15 = 2/15 = .1333
Graph g(x) = |x − 3|.
Answer: x+3
Step-by-step explanation:
since it has the absolute value, it will be x+3 and you can graph that in your calculator!
Brad wants to have $14832 available as a down payment for a house in 3 years. How much must he deposit now at
9.3% compounded monthly to reach that goal?
Round final answer to the nearest cent (2 decimal places)
Answer:
P = $11233.08
Step-by-step explanation:
Another word for deposit is the principal and the compounded monthly indicates we're working with compound interest.
The formula for compound interest is:
[tex]A(t)=P(1+\frac{r}{n} )^{rt}[/tex], where P is the principal ("deposit"), r is the rate, n is the number of compounding periods, and t is the time.
Before solving, we will need to convert the percentage to a decimal (9.3% to 0.093) and remember that n = 12, since there are 12 months in a year.
Thus, we will need to solve for P to find Brad's deposit:
[tex]14832=P(\frac{0.093}{12})(^{12*3})\\14832=P(1.00775)^{36} \\14832=1.32038641P\\11233.07532=11233.08=P[/tex]
- Jacob Elementary School had a book drive. On
Monday, the students collected 95 books. They
collected 78 more books on Tuesday. How many
books did the students collect?
The students collected
books.
The Grover family went on a spring vacation. Th
cabin is 305 miles away. If they drive 98 miles
first day, how many more miles do they have to
Step-by-step explanation:
1. 95+78 as its asking how many bools all together. 173 books
2. 305-98 ita asking how many miles LEFT.
A student 6ft tall is standing 20ft away from a 35ft tall flagpole.
The flagpole is 60ft away from a building.
From the students point of view, the flagpole is lined up perfectly with the top of the building.
What's the height of the building?
PLEASE HELP MEEEE!!!!!
A student 6ft tall is standing 20ft away from a 35ft tall flagpole.
The flagpole is 60ft away from a building.
From the students point of view, the flagpole is lined up perfectly with the top of the building.
What's the height of the building?
1.e a jupiter day is about 3/8 of an earth day. about how many hours are there is jupiter their in jupiter day
1.f on the moon a person weight is about 1/6 of their weight on earth about how many kilograms would a person weigh on the moon if their weight on earth is 54kg
The number of hours that are there in Jupiter is 9 hours.
The kilograms that a person weigh on the moon is 9kg.
How to calculate the days?It is important to note that there are 24 hours in a day. Therefore, when Jupiter day is about 3/8 of an earth day. The number of hours will be:
= 3/8 × 24
= 9 hours
Also, a person weight is about 1/6 of their weight on Earth. The kilograms that a person weigh on the moon if their weight on earth is 54kg will be:
1/6 × 54
= 9kg
Learn more about Jupiter on:
brainly.com/question/15044627
#SPJ1
A poster measuring 150cm by 180cm is enlarged in the ratio 8:5. Find the length and breadth of the enlarged poster
Answer:
240 cm by 288 cm
Step-by-step explanation:
You want the dimensions of a 150 cm by 180 cm poster enlarged by the ratio 8:5.
SolutionThe enlargement ratio, expressed as a fraction, multiplies each of the original dimensions to get the new dimensions. The new dimensions are ...
(8/5)·150 cm by (8/5)·180 cm = 240 cm by 288 cm
A dog breeder is planning to buy more dog food. He makes a table showing how
many pounds of food he will have after shopping. The table is based on how much he
spends and how much food he already has. Which equation generates the table?
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
x=y-4
y=8x-4
x=8y +4
y=x+4
The equation that generates the table is
y = (2/5)x + 4.
What is an equation of a line?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
We can have the following points from the table.
(0, 4), (20, 12), (40, 20), and (60, 28).
Now,
Choose two points:
(0, 4) and (20, 12)
m = (12 - 4) / (20 - 0)
m = 8 / 20
m = 2/5
Now,
(0, 4) = (x, y)
y = mx + c
4 = (2/5) x 0 + c
4 = c
c = 4
Now,
The equation is given as,
y = mx + c
y = (2/5)x + 4
The equation that generates the table is
y = (2/5)x + 4.
Learn more about equation of a line here:
https://brainly.com/question/23087740
#SPJ1
#11 i
PROBLEM SOLVING The table shows the heights y of a competitive water-skier x seconds after jumping off a ramp.
Time (seconds), x 0 0.25 0.75 1 1.1
Height (feet), y
22 22.5 17.5 12 9.24
Write a function that models the height of the water-skier over time.
The function y =
Interpret the y-intercept.
B
22
I U
models the height.
T' T₂
When is the water-skier 5 feet above the water? Round your answer to the nearest hundredth.
70°F
Cloudy
The skier is 5 feet above the water after about
second(s).
O Search the web
J
O
L
D
(
1/10000 Word L
The function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.
A competitive water skier's heights y, x seconds after soaring off a ramp.
For x = 0, y = 22
for x = 0.25, y = 22.5
For x = 0.75, y = 17.5
For x = 1, y = 12
For x = 1.1, y = 9.24
The general equation of a quadratic equation is y = [tex]ax^{2} + bx +c[/tex]
Putting x = 0 and y = 22 in the equation, we get :
[tex]y = ax^{2} +bx +c[/tex]
c = 22
Now, putting x = 1 and y =12, we get,
12 = a*1 + b*1 + 22
a +b = 12 - 22 = -10 equation (1)
Putting x = 0.25, y = 22.5,
22.5 = a* [tex]22.5^{2}[/tex] +b*22.5 +22
506.25 a +22.5b = 0.5 equation(2)
Solving equation (1) and equation(2), we get :
a = -16 and b = 6 and c = 22
So, the quadratic equation becomes,
[tex]y = -16x^{2} + 6x +22[/tex]
Now, Time when the skier is 5 feet above the water,
[tex]x = \frac{3 +\sqrt{281} }{16} = 1.23 seconds[/tex]
Hence, the function modelled for the given condition is [tex]y = -16x^{2} + 6x +22[/tex] and the time after which the skier is 5 feet above the water is 1.23 seconds.
To read more about functions, visit https://brainly.com/question/21145944
#SPJ1