Answers
To find a sequence is arithmetic, we are going to find its common difference: [tex]d=a_{n}-a_{n-1}[/tex]
where
[tex]d[/tex] is the common difference
[tex]a_{n}[/tex] is the current term in the sequence
[tex]a_{n-1}[/tex] is the previous term in the sequence
To find if a sequence is geometric, we are going to find its common ratio:
[tex]r= \frac{a_{n}}{a_{n-1}} [/tex]
where
[tex]r[/tex] is the common ratio
[tex]a_{n}[/tex] is the current term in the sequence
[tex]a_{n-1}[/tex] is the previous term in the sequence
1) 3,4,6,10,18
For [tex]a_{n}=4[/tex] and [tex]a_{n-1}=3[/tex]:
[tex]d=a_{n}-a_{n-1}[/tex]
[tex]d=4-3[/tex]
[tex]d=1[/tex]
For [tex]a_{n}=6[/tex] and [tex]a_{n-1}=4[/tex]:
[tex]d=6-4[/tex]
[tex]d=2[/tex]
For [tex]a_{n}=4[/tex] and [tex]a_{n-1}=3[/tex]:
[tex]r= \frac{a_{n}}{a_{n-1}} [/tex]
[tex]r= \frac{4}{3} [/tex]
For [tex]a_{n}=6[/tex] and [tex]a_{n-1}=4[/tex]:
[tex]r= \frac{6}{4} [/tex]
[tex]r= \frac{3}{2} [/tex]
We can conclude that the sequence is neither arithmetic nor geometric.
2) [tex] \frac{25}{4} , \frac{5}{2} ,1...[/tex]
For [tex]a_{n}= \frac{5}{2} [/tex] and [tex]a_{n-1}= \frac{25}{4} [/tex]:
[tex]d=a_{n}-a_{n-1}[/tex]
[tex]d=\frac{5}{2}-\frac{25}{4}[/tex]
[tex]d=- \frac{15}{4} [/tex]
For [tex]a_{n}=1[/tex] and [tex]a_{n-1}= \frac{5}{2} [/tex]:
[tex]d= 1-\frac{5}{2}[/tex]
[tex]d= -\frac{3}{2} [/tex]
For [tex]a_{n}= \frac{5}{2} [/tex] and [tex]a_{n-1}= \frac{25}{4} [/tex]:
[tex]r= \frac{a_{n}}{a_{n-1}} [/tex]
[tex]r= \frac{\frac{5}{2} }{\frac{25}{4} } [/tex]
[tex]r= \frac{2}{5} [/tex]
For [tex]a_{n}=1[/tex] and [tex]a_{n-1}= \frac{5}{2} [/tex]:
[tex]r= \frac{1}{\frac{5}{2}} [/tex]
[tex]r= \frac{2}{5} [/tex]
We have a common ratio, we can conclude that the sequence is geometric.
3) [tex] \frac{2}{3} , \frac{4}{6} , \frac{8}{9} ...[/tex]
For [tex]a_{n}=\frac{4}{6}[/tex] and [tex]a_{n-1}= \frac{2}{3}[/tex]:
[tex]d=\frac{4}{6}-\frac{2}{3}[/tex]
[tex]d=0[/tex]
For [tex]a_{n}=\frac{4}{6}[/tex] and [tex]a_{n-1}= \frac{2}{3}[/tex]:
[tex]r= \frac{\frac{4}{6}}{\frac{2}{3}} [/tex]
[tex]r=1[/tex]
For [tex]a_{n}=\frac{8}{9}[/tex] and [tex]a_{n-1}= \frac{4}{6}[/tex]:
[tex]r= \frac{\frac{8}{9}}{\frac{4}{6}} [/tex]
[tex]r= \frac{4}{3} [/tex]
We can conclude that the sequence is neither arithmetic nor geometric.
4) 3,15,75...
For [tex]a_{n}=15[/tex] and [tex]a_{n-1}=3[/tex]:
[tex]d=15-3[/tex]
[tex]d=12[/tex]
For [tex]a_{n}=75[/tex] and [tex]a_{n-1}=15[/tex]:
[tex]d=75-15[/tex]
[tex]d=60[/tex]
For [tex]a_{n}=15[/tex] and [tex]a_{n-1}=3[/tex]:
[tex]r= \frac{15}{3} [/tex]
[tex]r=5[/tex]
For [tex]a_{n}=75[/tex] and [tex]a_{n-1}=15[/tex]:
[tex]r= \frac{75}{15} [/tex]
[tex]r=5[/tex]
We have a common ratio, we can conclude that the sequence is geometric.
5) 5,-11,-27
For [tex]a_{n}=-11[/tex] and [tex]a_{n-1}=5[/tex]:
[tex]d=-11-5[/tex]
[tex]d=-16[/tex]
For [tex]a_{n}=-27[/tex] and [tex]a_{n-1}=-11[/tex]:
[tex]d=-27--11[/tex]
[tex]d=-27+11[/tex]
[tex]d=-16[/tex]
We have a common difference, we can conclude that the sequence is arithmetic.
Related Questions
how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of 30% alcohol solution
Answers
To solve this, set up the following equation using the given values: that you have some quantity of a 20% solution, a quantity of a 50% solution, and that you need to have 12 gallons of a 30% solution. We will use a variable, x, together with the "goal" quantity of 12 gallons to solve this problem with only one unknown, even though we really have two unknowns (the quantity of 20% solution and that of the 50% solution).
Remember that when writing out percentages, a 20% solution is also a 0.2 solution, and a 50% solution is a 0.5 solution.
Let x = an unknown quantity of the 20% (or 0.2) solution. We therefore have 0.2x, since we have x gallons of the 20% solution. (Remember that "of" is a key word that denotes multiplication).
Therefore, 12 - x is the other unknown and is multiplied by the 0.5 (50%) solution, since we have this quantity of the 50% solution. Really, we could say that we have 0.5y (if we want to introduce another variable; however, it is much simpler to put the other quantity in terms of x, which is easy to do, since we know that the two unknown quantities must amount to 12 gallons). Now, we must multiply our second unknown, 12 - x, by 0.5. This gives us 0.5(12 - x).
Our two unknown quantities, 0.2x and 0.5(12 - x) add up to 12 gallons of a 30% solution. Putting all the words together to form an equation we get:
0.2x + 0.5(12 - x) = 0.3(12)
Now we expand the equation (call it distributing out the parentheses).
0.2x + 6 + 0.5x = 3.6
Combine like terms:
-0.3x + 6 = 3.6
Solve for x:
-0.3x = -2.4
x = 8
Plug x = 8 back into the equation to check that this is possible.
x = 8, and 12 - x = 4
0.2(8) + 0.5(12 - (8)) = 0.3(12)
0.2(8) + 0.5(4) = 0.3(12)
3.6 = 3.6
Check
To create 9 gallons of a 30% alcohol solution, mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution by setting up and solving a system of equations based on volumes and concentrations.
Explanation:To find out how many gallons of 20% alcohol solution and 50% alcohol solution must be mixed to get 9 gallons of a 30% alcohol solution, we can set up a system of equations based on the volumes and concentrations of the solutions. Let's let x represent the volume of the 20% solution and y represent the volume of the 50% solution.
Since the total volume of the mixture should be 9 gallons, we have our first equation:
x + y = 9Next, we consider the concentration of alcohol in the final mixture. The amount of pure alcohol from the 20% solution is 0.20x gallons, and from the 50% solution, it is 0.50y gallons. The final mixture has a concentration of 30%, so the total amount of alcohol in the 9 gallons mixture is 0.30 * 9 gallons. This gives us our second equation:
0.20x + 0.50y = 0.30 * 9Now we have a system of two equations with two variables that can be solved using methods such as substitution or elimination. After solving, we find that x = 6 gallons and y = 3 gallons. Therefore, to obtain 9 gallons of a 30% alcohol solution, you'd need to mix 6 gallons of the 20% alcohol solution with 3 gallons of the 50% alcohol solution.
PLEASE HELP!!!! THIS LINEAR EQUATIONS!!!
Answers
[tex]120x + 60y \geqslant 600[/tex]
We use the 'more than or equal sign' as the consultant needs to make at least $600 - so exactly $600 or more than $600
Marta wants to use her mothers recipe. Her mother's recipe makes enough soup for 10-12 people, but Marta wants to make only 1/3 of that amount. If the original recipe requires 2 1/2 pounds of chicken, how many pounds of chicken will Marta need for her soup?
Answers
However, first we need to turn 2 1/2 into an improper fraction to make the multiplication simpler. To do this, we should multiply the unit (2) by the denominator (2) and add the numerator (1).
2*2=4, 4+1 = 5, therefore, 2 1/2 = 5/2
Now, we have to multiply 5/2 by 1/3. To do this, we just multiply the two numerators and the two denominators together.
5/2 * 1/3 = 5*1/2*3=5/6
Therefore, Marta needs to use 5/6 pounds of chicken for the recipe.
Hope this helps!
If all of the diagonals are drawn from a vertex of a hexagon, how many triangles are formed?
Answers
There are 5 different triangles formed by drawing all of the diagonals from a vertex of a hexagon.
Explanation:To find the number of triangles formed by drawing all of the diagonals from a vertex of a hexagon, we need to determine the number of different combinations of vertices that can form triangles.
For a hexagon, there are 4 vertices that can be chosen as one of the vertices of the triangle. The other 2 vertices can be chosen from the remaining 5 vertices. The order in which the vertices are chosen doesn't matter, so we need to divide by 2 to avoid overcounting.
Using the combination formula, we get:
C(5, 2) / 2 = 10 / 2 = 5
Therefore, there are 5 different triangles formed by drawing all of the diagonals from a vertex of a hexagon.
Dynatashia has a list of items she needs to buy at the store. She has written down the items and the advertised prices as shown: Hamburger – $3.99 per pound Hamburger buns – $1.29 2-liter soda – 3 for $2.00 Dynatashia buys 1.5 pounds of hamburger, 1 package of buns and 3 of the 2-liter bottles of soda. Her receipt is shown below. 2-ltr soda 2@3/$2 $1.34 Hambrg 1.5 lb@3.99 $5.99 Hbuns 1@1.69 $1.69 2-ltr soda 1@3/$2 $0.67 Determine if Dynatashia's receipt is correct. a. Yes, Dynatashia's receipt is correct. b. No, Dynatashia paid too much for soda. c. No, Dynatashia paid too much for hamburger. d. No, Dynatashia paid too much for buns.
Answers
Answer:
D. No, Dynatashia paid too much for buns.
Step-by-step explanation:
We are given that,
The actual cost of the items are,
Items Cost
Hamburger $3.99 per pound
Buns $1.29 per packet
2-liter soda $2 per 3 bottle
As, she bought 1.5 pounds of hamburgers, 1 packet of buns and 3 bottles of 2-liter soda.
So, she has to pay,
For hamburger = 1.5 × 3.99 = $5.99
For buns = 1.29 × 1 = $1.29
For soda bottles = $2
But from the receipt, we see that she pays,
For hamburger = 1.5 × 3.99 = $5.99
For buns = 1.69 × 1 = $1.69
For soda bottles = 1.34 + 0.67 = $2
That is, she has to pay $1.29 for the packet of the buns but she paid $1.69 for the buns.
Hence, the receipt is not correct as Dynatashia paid too much for the buns.
Answer: D
Step-by-step explanation:
edg
Explain why the equation (x-4)^2-10=15 has two solutions. Then solve the equation to find the solutions.
Please show all your work! (30 points)
Answers
Let's solve it first so that we can understand whats going on in the equation
(x-4)²-10=15
add 10 to both sides
(x-4)²=25
square root both sides
(Okay, so here is where the problem can have 2 solutions. Because the square root of 25 could be (5*5) or it could be (-5*-5). If it's positive five then...
x-4=5
add 4 to both sides
x=9
if it's negative 5 then...
x-4=-5
add 4 to both sides
x=-1
So the answer could be x=-1 or x=9.
It has two solutions because there are two possibilities for the answer to the square root of 25.
I hope this help, and if you have any more questions, please feel free to ask me.
Have a nice day!
What is the mode of these numbers? A 40. B 43. C 26 and 31. D. 31 and 43
Answers
hello can you please help me posted picture of question
Answers
you just have to find the solution to Y.
[tex]( \frac{-b}{2a},y( \frac{-b}{2a})) [/tex]
b = coefficient of x term = 8
a = coefficient of squared term = 2
So,
[tex] \frac{-b}{2a}= \frac{-8}{4}=-2 [/tex]
and
[tex]y(-2)=2(-2)^{2}+8(-2)+1=-7 [/tex]
Therefore, the vertex occurs at (-2, -7)
So, the correct answer is option C
A cutlery manufacturer producer produces 200 units of output at a total cost of $1,500. if total variable costs are $500, the average variable cost (per unit) is ______. $2.5 $3.00 $2.00 $1.00 $7.50
Answers
(variable cost)/(number of units)
=500/200
=$2.5 dollars per unit
Answer: A] $2.5
Since there are 200 units and variable costs are $500, we do a simple division, like this:
500/200 = 2.5.
So the answer is: 2.5
Hope this helped! c:
Use multiplying by 1 to find an expression equivalent to 3/14 with a denominator of 14 y.
Answers
now, "same" could be anything whatsoever, you name it, a whole polynomial, a whole anything whatsoever.
[tex]\bf \cfrac{\sqrt{2}}{\sqrt{2}}=\cfrac{\sqrt{3}}{\sqrt{3}}=\cfrac{100000000}{100000000}=\cfrac{eggs}{eggs}=\cfrac{miles}{miles}=\cfrac{\frac{\quad \sqrt{3}}{\sqrt[5]{17}}\quad }{\frac{\sqrt{3}}{\sqrt[5]{17}}}=\cfrac{whatever}{whatever}=1[/tex]
now, that said, let us use 1 in this case then ... hmmmm we simply need a "y" in the denominator, so we simply multiply the denominator AND numerator by "y", y/y = 1 btw.
[tex]\bf \cfrac{3}{14}\cdot \cfrac{y}{y}\implies \cfrac{3y}{14y}[/tex]
If a+5=b, then what is the value of (b−a)^4?
Answers
(b-a)^4
((a+5)-a)^4
Simplification, as follows:
((a+5)-a)^4
(5)^4 the a’s cancel
625
The value of (b-a)^4 when a+5=b is 625.
ILL MARK YOU THE BRAINLIST PLS HELP a man who is 6 feet tall casts a shadow that is 15 feet long. A tree casts a similar shadow is 22 FT how tall is the tree?
Answers
Answer: 13
Here are the steps:
First we subtract 15 from 22 and then got 7
15 - 22 = 7
Finally we Add 7 + 6 = 13
Which is our final answer
I hope I helped
-Chris.
pleae help thanks a bunch
Answers
You use the Pythagorean theorem to solve this
[tex] a^{2} + b^{2} = c^{2} [/tex]
Put in the values it tells you to
[tex]a^{2} + 4.4^{2} = 5.5^{2} [/tex]
Square the numbers
[tex]a^{2} + 19.36 = 30.25[/tex]
Subtract 19.36 from both sides
[tex] a^{2} = 10.89[/tex]
Take the square root of both sides
a = 3.3
The answer is 3.3
Hope this helps!
Mrs. Daly's reading classes were surveyed about their reading preferences. the data is summarized in the table below.
given that a student is in 9th grade, what is the probability that they like to read non-fiction novels, based on this data?
Answers
Answer:
0.60
Step-by-step explanation:
A boat can travel 511 kilometers on 102.2 liters of gasoline. how far can it travel on 91.3 liters?
Answers
Which expression is equivalent to 10x^6y^12/-5x^-2y^-6? Assume .x=0.y=0.
Answers
(10x ^ 6y ^ 12) / (- 5x ^ -2y ^ -6)
Rewriting we have:
(10 / -5) * ((x ^ 6y ^ 12) / (x ^ -2y ^ -6))
(-2) * ((x ^ 6y ^ 12) / (x ^ -2y ^ -6))
Then, for power properties:
(-2) * (x ^ (6 - (- 2)) and ^ (12 - (- 6)))
(-2) * (x ^ (6 + 2) and ^ (12 + 6))
(-2) * ((x ^ 8y ^ 8)
For x = 0, y = 0, we have:
(-2) * ((0 ^ 8) (0 ^ 8))
0
Answer:
An expression that is equivalent when x = 0 and y = 0 is:
0
Answer:B on edge
Step-by-step explanation:
Joseph buys a bag of 60 pieces of taffy. In the bag, there are 6 cinnamon pieces, 18 raspberry pieces, 12 key lime pieces, and the rest are candy apple pieces. If he randomly draws one piece of taffy, what is the probability that it is a piece of key lime taffy?
A. 0.1
B. 0.4
C. 0.02
D. 0.2
Answers
# of key lime taffies 12
total # of taffies = 60
12/60 = 1/5
1/5 = 0.2
Joseph has a 0.2 probability of picking a key lime taffy.
Answer:0.2
Step-by-step explanation:
What are the zeros of the polynomial function f(x) = (x – 6)(x – 2)(x + 7)?
Answers
So,
x - 6 = 0
⇒ x = 6
x - 2 = 0
⇒ x = 2
x + 7 =0
⇒ x = -7
Thus the zeros of the given function are x = 6, x = 2 and x = -7
I WILL MARK BRAINLIEST PLEASE HURRY
Answers
according to the given equation the centre of this circle is in the poit (6;7) and its radius =4 units.
Using this data, it is possible to define right choice: D.
answer: graph D.
PLZ HURRY!!
If a Professional basketball player earns $3 million playing 125 games per year and plays an average of 40 minutes per game, how much does he earn per second of playing time?
Answers
24,000/40= 600 per minute
600/60= 10 per second
$10 per second.
A bookstore costs $90 a day to keep open, and spends $12 for each book it sells. the store charges $18 for each book it sells. If n represents the number of books sold, which equation represents the revenue function for this bookstore?
Answers
Answer:
[tex]R=6n-90[/tex]
Step-by-step explanation:
Let
R------> the revenue function
n------> the number of books sold per day
we know that
In this problem
[tex]18n[/tex] -----> represent the profit
[tex](12n+90)[/tex] -----> represent the cost
so
The revenue is equal to the profit minus the cost
[tex]R=18n-(12n+90)[/tex]
[tex]R=n(18-12)-90[/tex] ------> equation that represent the revenue function
Simplify
[tex]R=6n-90[/tex]
Lupe has 14 stickers that she wants to give to 2 friends. She wants each friend to have the same number of stickers. Select the three statements that describe how Lupe should give the stickers to her friends. Each friend gets 14÷2 stickers. Each friend gets 2 of the 14 stickers. Each friend gets 142 stickers. Each friend gets 7 of the 14 stickers.
Answers
Answer:
The correct options are 1, 3 and 4.
Step-by-step explanation:
It is given that Lupe has 14 stickers that she wants to give to 2 friends.
Total number of stickers Lupe has is 14.
The number of friends is 2.
She wants each friend to have the same number of stickers. It means each friend will get half of 14.
The number stickers Lupe should give to her friends is 14 divided by 2.
[tex]\text{Number of stickers}=14\div 2[/tex]
Write this value in fraction form.
[tex]\text{Number of stickers}=\frac{14}{2}[/tex]
[tex]\text{Number of stickers}=7[/tex]
It means the correct statements are
1. Each friend gets 14÷2 stickers.
3. Each friend gets (14)/2 stickers.
4. Each friend gets 7 of the 14 stickers.
Hence correct options are 1, 3 and 4.
how many ounces of 30% hydrochloric acid solution and 80% hydrochloric acid solution must be mixed to get 10 oz of 50% hydrochloric acid solution
Answers
This diagram tells you the constituents 80% and 30% solution are in the proportion 20:30 or 2:3 or 4:6 to make the mix having 50% hydrochloric acid. Note that the numbers 4 and 6 add to 10, the number of ounces of solution we want.
4 ounces of 80% solution must be mixed with 6 ounces of 30% solution to make 10 ounces of 50% solution.
What is the surface area of a cylinder with a radius of 5 ft and a height of 2 ft?
Answers
Answer:
Its B.
Have a great day! OwO
After being rearranged and simplified, which two of the following equations could be solved using the quadratic formula?
Answers
1. degree = 2 (i.e. the highest power equals exactly two)
2. the linear term (e.g. 4x, or -5x...) and constant term (e.g. 5, -30, pi, etc.) may or may not be present.
Now let's simplify and examine the given equations, and see if each can be solved with the quadratic formula:
A.
[tex]5x^3+2x-4=2x^2[/tex]
[tex]5x^3+-2x^2+2x-4=0[/tex]
The degree (highest power) is three, so it is not "exactly two". NO.
B.
[tex]5x^2-3x+10=2x^2+21[/tex]
[tex]3x^2-3x-11=0[/tex]
The degree (highest power) is two, so it is "exactly two". YES.
C.
[tex]5x^2-3x+10=5x^2[/tex]
[tex]0x^2-3x+10=0[/tex]
[tex]-3x+10=0[/tex]
The degree (highest power) is one, so it is not "exactly two". NO.
D.
[tex]x^2-6x-7=2[/tex]
[tex]x^2-6x-9=0[/tex]
The degree (highest power) is two, so it is "exactly two". YES.
Note that it is very important to simplify the equations before checking the degree.
If you need further explanations, please feel free to post in comments.
Answer:
The Answer will Be B and D
Step-by-step explanation:
1.
Find the amount of the annuity.
Amount of Each Deposit: $6,200
Deposited: Semiannually
Rate per Year: 6%
Number of Years: 5
Type of Annuity: Ordinary
$79,408.36
$81,720.90
$71,076.06
$73,208.36
Answers
where
[tex]FV[/tex] is the future value
[tex]P[/tex] is the periodic payment
[tex]r[/tex] is the interest rate in decimal form
[tex]n[/tex] is the number of times the interest is compounded per year
[tex]k[/tex] is the number of payments per year
[tex]t[/tex] is the number of years
We know for our problem that [tex]P=6200[/tex] and [tex]t=5[/tex]. To convert the interest rate to decimal form, we are going to divide the rate by 100%:
[tex]r= \frac{6}{100} =0.06[/tex]
Since the deposit is made semiannually, it is made 2 times per year, so [tex]k=2[/tex].
Since the type of the annuity is ordinary, payments are made at the end of each period, and we know that we have 2 periods, so [tex]n=2[/tex].
Lets replace the values in our formula:
[tex]FV=P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ][/tex]
[tex]FV=6200[ \frac{(1+ \frac{0.06}{2} )^{(2)(5)} -1}{ \frac{0.06}{2} } ][/tex]
[tex]FV=71076.06[/tex]
We can conclude that the correct answer is $71,076.06
How to solve this please?
2x - 5 = 4
Answers
2x-5=4
First lets get the 2x by itself so we have to add 5 on both sides.
2x-5=4
+5 +5
2x=9
Now we need to get the X by itself so divide each side by 2
[tex] \frac{2x}{2} = \frac{9}{2} [/tex]
Now we are left with the following
X=[tex] \frac{9}{2} [/tex]
We must simplfy the fraction
2 will go into 9 four times with 1 left over. So the mixed fraction answer would be:
x=[tex]4 \frac{1}{2} [/tex]
As a decimal you would just divide 9 and 2
x=4.5
Hope this helped!
Or in decimal form, 4.5
Hope this helps. - M
At Jason's car rental shop it costs a flat rate of $100 to rent a car, which covers the cost of driving up to 75 miles. For every mile over 75 it costs an additional $0.10. Write a piecewise function modeling this situation, where x represents the miles driven and y represents the total cost.
Answers
For a test of : p 0.50, the sample proportion is 0.36 based on a sample size of 100. use this information to complete parts (a) through (c) below.
Answers
The question involves hypothesis testing for proportions. The p-value is calculated using the normal distribution for proportions. In this case, the p-value is found to be 0.0417.
The question involves hypothesis testing for proportions. The null and alternative hypotheses need to be defined for the study.
The p-value is calculated using the normal distribution for proportions.
In this case, the p-value is found to be 0.0417. We can conclude that there is sufficient evidence to reject the null hypothesis and conclude that there is a difference between the proportions of households in the two communities.
Andrew drove 55 mph on his trip. Which of the following equations best represents the distance he drove if x stands for the number of hours?
Answers
X= The hours
I hope this helps!!
Answer
Using speed formula:
[tex]\text{Speed} = \frac{\text{Distance}}{\text{Time}}[/tex]
Let y represents the distance in miles and x represents the time in hours.
As per the given statement:
Andrew drove 55 mph on his trip.
Using formula;
we have;
[tex]55 = \frac{y}{x}[/tex]
Multiply both sides by x we have;
[tex]y = 55x[/tex]
Therefore, the equation best represents the distance he drove is [tex]y = 55x[/tex]