Answers
Angle C is congruent with angle X, angle D is congruent with angle Y, angle A is congruent with angle Z
Related Questions
Emi computes the mean and variance for the population data set 87, 46, 90, 78, and 89. She finds the mean is 78. Her steps for finding the variance are shown below. What is the first error she made in computing the variance? Emi failed to find the difference of 89 - 78 correctly. Emi divided by N - 1 instead of N. Emi evaluated (46 - 78)2 as -(32)2. Emi forgot to take the square root of -135.6.
Answers
The first error Emi made was dividing by N - 1 instead of N when computing the population variance.
The first error in computing the variance is Emi divided by N - 1 instead of N. In Emi's calculations for the data set, which includes the numbers 87, 46, 90, 78, and 89, the correct method should be to divide by N, because she is dealing with a population data set, not a sample.
For the population variance, we divide the sum of squared differences from the mean by the total number of data points in the population, which is N. However, Emi incorrectly divided by N - 1, which would only be correct if she were calculating the sample variance to estimate the population variance based on a subset of the population data.
A square garden has side lengths of 8 inches. Jackie makes a rectangular garden with the same area as the square garden .which of these could be the dimensions of the rectangular garden. a-10 inches by 6 inches, b7 inches by 9 inches, c 8 inches by 12,d 16 inches by 4 inches.
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When you multiply 16 by 4 you get 64. 8 times 8 is also 64.
If ∆XYZ = ∆KLM, then < Y = Please help due today
Answers
∠X = ∠K
∠Y = ∠L
∠Z = ∠M
So ∠Y = ∠L
I hope this helps!
Calculator Problem You downloaded a video game to your computer. You have a 60 -minute free trial of the game. It take 5 minutes to set up the game and 7minutes to play each level. You want to find out how many levels you can play for free. Let ll l l represent the number of levels played. Write an inequality to determine the number of levels you can play in 60 minutes.
Answers
S = setup = 5 minutes.
L = Levels = x
T = Time / L = 7 minutes / Level.
Formula
S + x * T ≤ 60 minutes
Substitute and solve.
5 + 7*x ≤ 60 Subtract 5 from both sides.
7x ≤ 60 - 5
7x ≤ 55 minutes Estimated, the answer is almost x = 8 but not quite. Divide by 7
x ≤ 55/7
x ≤ 7 . He almost makes it through the 8th game but not quite
x ≤ 7 Answer.
The inequality 5 + 7l ≤ 60 represents the scenario where a student has a 60-minute free trial of a game that requires 5 minutes to set up and 7 minutes to play each level, where 'l' denotes the number of levels the student can play.
Explanation:The subject of this question is about setting up an inequality to represent a scenario. The student has a 60-minute free trial of a game and it takes 5 minutes to set up the game and another 7 minutes to play each level. Let's denote 'l' as the number of levels the student can play. The total time spent both setting and playing the game cannot exceed 60 minutes. Therefore, the inequality to determine the maximum number of levels the student can play would be: 5 + 7l ≤ 60.
To explain this further, the '5' is the time spent setting up the game and '7l' is the total time spent playing the levels. As we want to find out the maximum number of levels that can be played within a constraint of 60 minutes, thus we use the less than or equal to symbol ('≤').
Learn more about Inequalities here:https://brainly.com/question/30231017
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Functions f(x) and g(x) are described as follows: f(x) = −5x2 + 9 x g(x) 0 0 1 4 2 8 3 4 4 0 Which statement best compares the maximum value of the two functions?
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To compare the maximum values of function, which is a discrete function with given values, we find that C ) It is 3 units lower for f ( x ) than g ( x )
To compare the maximum values of functions f(x) and g(x), we first analyze each function separately. The quadratic function f(x) = -4x2 + 5x has a vertex form which reveals its maximum value at x = 1/3, and since g(x) is a discrete function defined by its values at certain points, we look directly at the given values to find its maximum.
Function g(x) reaches its maximum at g(2) = 8. Comparing this to f(x), whose vertex form shows that its maximum is f(1/3), we need to compute f(1/3) = -4(1/3)2 + 5(1/3) to find its specific value. After calculation, f(1/3) is found to be higher than 8, which is the maximum of g(x).
Thus,
g ( x ) maximum value = 8
f ( x ) maximum value = 5
g ( x ) max - f ( x ) max = 8 - 5 = 3
Complete Question:
Functions f(x) and g(x) are described as follows:
f(x) = -4x2 + 5
x g(x)
0 0
1 4
2 8
3 4
4 0
Which statement best compares the maximum value of the two functions? A. It is equal for both functions. B. It is 3 units higher for f(x) than g(x). C. It is 3 units lower for f(x) than g(x). D. It is 4 units lower for f(x) than g(x).
Julia has 3 hand bags in her closet in how many ways can the bags be arranged
Answers
There are 6 ways the bags can be arranged.
Explanation:The number of ways the bags can be arranged is equal to the number of permutations of the bags. In this case, Julia has 3 handbags in her closet, so we need to find the number of permutations of 3 objects taken from a set of 3. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects being selected.
Plugging in the values, we get 3P3 = 3! / (3-3)! = 3! / 0! = 3 x 2 x 1 / 1 = 6.
Therefore, there are 6 ways the bags can be arranged.
The number of ways to arrange 3 handbags is 6.
The arrangement of objects where the order matters is a permutation problem. To find the number of permutations of n distinct objects, one uses the factorial of n, denoted as n!. The factorial of a non-negative integer n is the product of all positive integers less than or equal to n.
In this case, Julia has 3 handbags, so n = 3. We want to find the number of permutations of these 3 handbags, which is given by 3!.
Calculating 3!:
3! = 3 × 2 × 1 = 6
Therefore, there are 6 different ways to arrange the 3 handbags in Julia's closet.
At the candy store, a chocolate bar costs c dollars and a vanilla bar costs 2 dollars more than a chocolate bar. Jamie buys a chocolate bar and three vanilla bars, and Kevin buys five chocolate bars. How much money, in total, do Jamie and Kevin spend at the candy store in terms of c?
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Jamie: c + 3(c + 2)
Kevin: 5c
c + 3(c + 2) + 5c; Simplify
c + 3c + 6 + 5c; combine like terms
9c + 6 represents the amount they would spend.
The probability that a student correctly answers on the first try (the event
a.is p(a) = 0.2. if the student answers incorrectly on the first try, the student is allowed a second try to correctly answer the question (the event b). the probability that the student answers correctly on the second try given that he answered incorrectly on the first try is 0.5. find the probability that the student answers the question on the first or second try.
a.0.90
b.0.40
c.0.10
d.0.70
e.0.60
Answers
We're given that [tex]P(A)=0.2[/tex] and [tex]P(B\mid A^C)=0.5[/tex]. From the first probability, we know that [tex]P(A^C)=1-0.2=0.8[/tex]. By definition of conditional probability,
[tex]\mathbb P(B\mid A^C)=\dfrac{\mathbb P(B\cap A^C)}{\mathbb P(A^C)}[/tex]
[tex]\implies\mathbb P(B\cap A^C)=0.5\cdot0.8=0.4[/tex]
We're interested in the probability of either [tex]A[/tex] or [tex]B[/tex] occurring, i.e. [tex]\mathbb P(A\cup B)[/tex]. Apply the inclusion-exclusion principle, which says
[tex]\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)-\mathbb P(A\cap B)[/tex]
We know the probability of intersection is 0, and we know [tex]\mathbb P(A)[/tex]. Meanwhile, by the law of total probability, we have
[tex]\mathbb P(B)=\mathbb P(B\cap A)+\mathbb P(B\cap A^C)=\mathbb P(B\cap A^C)[/tex]
so we end up with
[tex]\mathbb P(A\cup B)=0.2+0.4=0.6[/tex]
The probability that the student answers the question on the first or second try is 0.60.
Given
P(A) = 0.2
[tex]\rm P(B|A^c)=0.5[/tex].
What is conditional probability?The conditional probability of an event is when the probability of one event depends on the probability of occurrence of the other event.
When two events are mutually exclusive.
Then,
[tex]\rm P(A\cap B)=0[/tex]
The first probability is;
[tex]\rm P(A^C)=1-0.2=0.8[/tex]
Therefore,
The probability that the student answers the question on the first or second try is;
[tex]\rm P(A\cup B)= P(A) +P(B)-P(A \cap B)\\\\ P(A\cup B)= P(A) +P(B|A^C) \times P(A^C)-P(A \cap B)\\\\ P(A\cup B)= 0.2+0.5 \times 0.8 -0\\\\P(A\cup B)=0.2+0.40\\\\ P(A\cup B)=0.60[/tex]
Hence, the probability that the student answers the question on the first or second try is 0.60.
To know more about Conditional probability click the link given below.
https://brainly.com/question/10739947
while watching a football game, Lin Chow decided to list yardage agained as positive integers and yardage lost as negative integers. after this plays, Lin recorded 14, -7, and 9. what was the net gain or lost?
Answers
A car rental costs $50 for the first day. Additional days cost $35 per day, unless the car is rented for 7 days or more, in which case there is a 10% discount on the daily rate. Identify the expression which represents the cost of renting a car if the car has been rented for more than a week.
A.) 45+35x
B.) 45+31.5x
C.) 50+35x
D.) 50+31.5x
Answers
Answer:
Option D [tex]\$50+\$31.5x[/tex]
Step-by-step explanation:
Let
x------> the number of days
y----> the cost of renting a car
we know that
For [tex]x<7\ days[/tex]
[tex]y=\$50+\$35x[/tex]
For [tex]x\geq 7\ days[/tex]
The rate is equal to
[tex]0.90*\$35=\$31.5[/tex]
so
[tex]y=\$50+\$31.5x[/tex]
In this problem. the car has been rented for more than a week
therefore
[tex]x> 7\ days[/tex]
The cost of renting a car is equal to
[tex]y=\$50+\$31.5x[/tex]
QF Q6.) Find the following function for b.
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5(2x - 2)² - 3
First, you do FOIL method of the binomial:
5(4x² - 8x + 4) - 3
Now distribute the 5:
20x² - 40x + 20 - 3
And combine like terms:
20x² - 40x + 17
=g(2x-2)
=5(2x-2)^2-3
=5(4x^2-8x+4)-3
=20x^2-40x+17
k+1=3k-1 please show me the correct steps to solve this problem
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-2k + 1 = -1 |-1
-2k = -2 |:(-2)
k = 1
Can adjacent angles be supplementary complementary or neither
Answers
Answer:
Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees. Supplementary and complementary angles do not have to be adjacent
Step-by-step explanation:
To which sets of numbers does 0.0202002000200002 . . . belong? A. Irrational B.Rational only C.Rational and natural D.Rational and integer
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Please please help i don’t understand this.
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a(n) = a1*r^(n-1)
Where
a(n) = nth term
a1 = first term
r = common ratio
n = 0,1,2,3,4,5, ... n
To establish which graphs agree with this formula, each graph should be tested separately as follows:
Graph A:
a2 = 9
Then
9 = a1*(1/3)^(2-1) =1/3a1 => a1 = 3*9 = 27
Sequence:
a1 = 27
a2 = 9
a3 = 27*(1/3)^(3-1) = 3
a4 = 27*(1/3)^(4-1) = 1
These are the same values shown and thus this graph corresponds to geometric sequence.
Graph B:
a1 = 12
a2 = 12*(1/3)^(2-1) = 4
a3 = 12*(1/3)(3-1) = 4/3
a4 = 12*(1/3)^(4-1) = 4/9
These are the values shown by the graph and thus it corresponds with geometric sequence.
Graph C:
a1 = 3+3/2 = 9/2
a2 = (9/2)*(1/3)^1 = 3/2
a3 = (9/2)*(1/3)^2 = 1/2
a4 = (9/2)*(1/3)^3 = 1/6
a0 = (9/2)*(1/3)^-1 = 13.5 (this is not the case as the graph shows a0 = 12)
Therefore, this graph does not correspond to geometric sequence.
Graph D:
a1 = 4
a2 = 4*(1/3)^1 = 4/3
a3 = 4*(1/3)^2 = 4/9
a4 = 4*(1/3)^3 = 4/27
a0 = 12
This graph seems to agree with values of geometric sequence and thus corresponds to geometric sequence.
Therefore, graphs A, B, and D corresponds with geometric sequence.
What is the domain of the function g(x) = 52x? x > 0 x < 0 all real numbers all positive real numbers
Answers
The domain: all real numbers.
Answer: all real numbers
Step-by-step explanation:
The given function is : [tex]g(x) = 52x[/tex], which is polynomial function with degree one.
The domain of a function is the set of all values for x for which the function must be defined.We know that the domain of a polynomial is the entire set of real numbers because for any real number r the polynomial function exists.
Therefore, the domain of the given function [tex]g(x) = 52x[/tex] is the set of real numbers.
A local am radio station broadcasts at a frequency of 764 khz. calculate the energy of the frequency at which it is broadcasting. energy = kj/photon
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[tex]f=764 kHz = 7.64 \cdot 10^5 Hz[/tex]
The energy of a photon is given by:
[tex]E=hf[/tex]
where h is the Planck constant and f is the photon frequency. Using the frequency given by the problem, we can find the energy of each photon of this radiation:
[tex]E=hf=(6.6 \cdot 10^{-34} Js)(7.64 \cdot 10^5 Hz)=5.04 \cdot 10^{-28} J=5.04 \cdot 10^{-31} kJ[/tex]
Conduct a chi-squared test of independence on the data presented in data set
d. assume equal probabilities of fe for each cell and make sure to report all relevant statistics, including the value of χ2 obtained, the critical value and your decision as to whether to reject the null hypothesis .
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Engineers are analyzing the performance of windshield wiper blades. At the end of one swipe, the tip of a blade is at (−5, 7) when represented graphically. What is the sine value of this function? (2 points) negative 7 square root 74 divided by 74 negative 5 times square root of 74 over 74 7 times square root of 74 over 74 square root 74
Answers
First, we need to get for the "r."r^2 = (−5)^2 + 7^2r^2 = 25 + 49r^2 = 74r = square root of 74
Then, after that, we need to formulate the equation of a sin:sin x = 7 / rsin x = 7 / sqrt(74)sin x = 7 * sqrt (74) / 74
hope this helpsss
Answer:
Option C. [tex]7.\frac{\sqrt{74}}{74}[/tex]
Step-by-step explanation:
At the end of one swipe the tip of one blade is at (-5, 7). We have to find sine value of this function.
As shown in the figure coordinates of the tip of the wiper blade are (-5, 7)
So [tex]sin a = \frac{Height}{Hypotenuse}[/tex]
Here Height of the triangle = 7
and Hypotenuse = x = [tex]\sqrt{(-5)^{2}+7^{2}}=\sqrt{25+49}=\sqrt{74}[/tex]
By putting these values in the expression
[tex]sina=\frac{7}{x}=\frac{7}{\sqrt{74}}=7.\frac{\sqrt{74}}{74}[/tex]
Answer is option C.[tex]7.\frac{\sqrt{74}}{74}[/tex]
find the pair of similar triangles shown . find the length of side h .
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6*h = 21*7
6h = 147
h = 24,5
how is this solved? graph and explanation would be helpful
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The solution space will be above the first line (y > ...) and below the second line (y < ...). As a rule, you indicate the solution space by shading the portion of hte plane that satisfies the inequality.* The solution is the portion of the plane that is in both solution regions (that is, doubly-shaded).
_____
* Sometimes, it may actually work better to shade the portion of the plane that does NOT satisfy the inequality. That way, the remaining unshaded area is the solution space. If you do it that way, make sure the graph is clearly marked indicating that is the case. The usual expectation is that the shaded area is the solution, so you don't want to get your answer marked wrong or misinterpreted.
what are some types of quadrilaterals
Answers
Such as, square, rectangle, trapezoid, and parallelogram
I hope this helped!
seven and thirty twp hundreths plus two and one tenth times two and seven tenths minus 18a
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" 70 [tex] \frac{32}{100} [/tex] +
2[tex] \frac{1}{10} [/tex] * 2[tex] \frac{7}{10[/tex] − 18a " ;
______________________________________________________
or; write as:
______________________________________________________
" 70.32 + (2.1) * (2.7) − 18a " ;
______________________________________________________
To simplify:
______________________________________________________
Using "PEDMAS" (the "order of operations") ;
the "multiplication" comes first;
So: → "(2.1) * (2.7) = 5.67 " .
And rewrite:
______________________________________________________
" 70.32 + 5.67 − 18a " .
Now: " 70.32 + 5.67 = 75.99 " ;
So, we can the final simplified expression as:
______________________________________________________
" 75.99 − 18a " ;
or; write as: " 75[tex] \frac{99}{100} [/tex] − 18a " .
______________________________________________________
N a test population of 1000 people, 210 display hemophilia. you hypothesize that this trait follows mendelian genetics with a 3:1 ratio of non- hemophilia to hemophilia. use the χ2 test to determine whether the data support the hypothesis or not. show your steps and explain your reasoning.
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The chi-square value can be calculated by the formula:
[tex] \chi^{2} = \frac{(O - E)^{2}}{E}[/tex]
where:
O = observed value = 210
E = expected value = 250
Therefore:
χ² = (210 - 250)² / 250
= 6.4
Now, look at a χ² distribution table, in order to find the p-value. In this case, you have only 1 degree of freedom and the closest χ² is 6.6 which corresponds to a p-value of 0.01.
Since p < 0.05, which is the minimum value generally accepted, we can say that the data do not support the hypothesis.
The formula to convert Fahrenheit to Celsius is C=5/9(F-32). Convert 18 degrees C to Fahrenheit. Round to the nearest degree.
Answers
Answer:
Temperature in celcius scale to the nearest degree = 64
Step-by-step explanation:
Temperature in celcius scale = 18° C
We have the formula
[tex]C=\frac{5}{9}(F-32)[/tex]
Substituting value in celcius scale.
[tex]18=\frac{5}{9}(F-32)\\\\F=64.4^OC[/tex]
Temperature in celcius scale to the nearest degree = 64
hat is the sum of the geometric series in which a1 = 3, r = 4, and an = 49,152?
Hint: an = a1(r)n − 1, where a1 is the first term and r is the common ratio.
Sn = −65,535
Sn = 16,383
Sn = 13,120
Sn = 65,535
Answers
To find the sum of the geometric series, we use the formula: Sn = a1 * (r^n - 1) / (r - 1). Substituting the given values and solving, we find that the sum is 16,383.
Explanation:To find the sum of a geometric series, we can use the formula Sn = a1 * (r^n - 1) / (r - 1), where Sn is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.
In this case, a1 = 3, r = 4, and an = 49,152. We can use the formula to find n, which is the exponent.
49,152 = 3 * (4^n - 1) / (4 - 1)
49,152 = 3 * (4^n - 1) / 3
16,384 = 4^n - 1
4^n = 16,385
n = log4(16,385)
n ≈ 7
Now, we can substitute the values into the formula for Sn.
Sn = 3 * (4^7 - 1) / (4 - 1)
Sn = 3 * (16,384 - 1) / 3
Sn = 3 * 16,383 / 3
Sn = 16,383
Therefore, the sum of the geometric series is 16,383. So the correct answer is Sn = 16,383.
The correct answer is [tex]\( S_n = 65,535 \)[/tex].
To find the sum of a geometric series, you can use the formula:
[tex]\[ S_n = a_1 \frac{(r^n - 1)}{r - 1} \][/tex]
Where:
- [tex]\( S_n \)[/tex] is the sum of the series,
- [tex]\( a_1 \)[/tex] is the first term,
- [tex]\( r \)[/tex] is the common ratio,
- [tex]\( n \)[/tex] is the number of terms.
Given [tex]\( a_1 = 3 \), \( r = 4 \), and \( a_n = 49,152 \)[/tex], we need to find [tex]\( n \)[/tex]. The formula for the [tex]\( n^{th} \)[/tex] term in a geometric series is [tex]\( a_n = a_1 \times r^{(n-1)} \)[/tex]. In this case, [tex]\( 49,152 = 3 \times 4^{(n-1)} \)[/tex]
Let's solve for n:
[tex]\[ 4^{(n-1)} = \frac{49,152}{3} \][/tex]
[tex]\[ 4^{(n-1)} = 16,384 \][/tex]
[tex]\[ n-1 = \log_4(16,384) \][/tex]
[tex]\[ n-1 = 7 \][/tex]
[tex]\[ n = 8 \][/tex]
Now that we have [tex]\( n = 8 \)[/tex], we can use it in the sum formula:
[tex]\[ S_n = 3 \frac{(4^8 - 1)}{4 - 1} \][/tex]
[tex]\[ S_n = 3 \frac{(65,536 - 1)}{3} \][/tex]
[tex]\[ S_n = 3 \frac{65,535}{3} \][/tex]
[tex]\[ S_n = 65,535 \][/tex]
Therefore, the correct answer is [tex]\( S_n = 65,535 \)[/tex].
A jar of peanut butter and a jar of jam cost $10.20 in total. the jar of peanut butter costs $10.00 more than the jar of jam. how much does the jar of jam cost
Answers
Julie studied for 3 1 3 hours during the 4 days before her last math test. If she studied for the same amount of time each day, how much time did she spend studying each day?
Answers
Julie studied for 3 1 3 hours during the 4 days before her last math test. If she studied for the same amount of time each day, how much time did she spend studying each day?
Solution:
Julie studied for 3 [tex]\frac{1}{3}[/tex] hrs in 4 days
Let us first find how many minutes Julie studied in 4 days
In 1 hour, there are 60 minutes
Julie studied for 3 complete hours and one-third of the hour.
So, Number of minutes in 3 hours is 3*60=180hrs
and, Number of minutes in one-third of an hour=[tex]\frac{1}{3} *60[/tex]
=[tex]\frac{60}{3}[/tex]=20minutes
So, time spent by Julie in studying in 4 days is 3[tex]\frac{1}{3}[/tex] hours
or, Julie studied for 180+20 minutes in 4 days
Adding 180 and 20
Julie studied for 200 minutes during the 4 days
To find time she spend studying each day, we must divide total time spent in studies by number of days
Time she spend studying each day= [tex]\frac{200}{4}[/tex] minutes
Dividing 200 by 4, we get
Time she spend studying each day=50 minutes
Answer:
time she spend studying each day=50 minutes
Hey can you please help me posted picture of question
Answers
A compound event is one in which there is more than one possible outcome. It is also defined as a probabilistic event with two or more favorable outcomes. For example, when you throw a die (singular for dice), it is called a simple event. On the other hand, when you throw a dice, it is known as a compound event.
Ples help me find slant assemtotes
this one is different because it isn't a rational function
find the slant assemtotes of [tex](y+1)^2=4xy[/tex]
the equation can be rewritten using the quadratic formula as [tex]y=2x-1 \pm \sqrt{x^2-x}[/tex]
ples find slant assemtotes and show all work
thx
Answers
[tex]\displaystyle\lim_{x\to\pm\infty}(f(x)-p(x))=0[/tex]
[tex](y+1)^2=4xy\implies y(x)=2x-1\pm2\sqrt{x^2-x}[/tex]
Since this equation defines a hyperbola, we expect the asymptotes to be lines of the form [tex]p(x)=ax+b[/tex].
Ignore the negative root (we don't need it). If [tex]y=2x-1+2\sqrt{x^2-x}[/tex], then we want to find constants [tex]a,b[/tex] such that
[tex]\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0[/tex]
We have
[tex]\sqrt{x^2-x}=\sqrt{x^2}\sqrt{1-\dfrac1x}[/tex]
[tex]\sqrt{x^2-x}=|x|\sqrt{1-\dfrac1x}[/tex]
[tex]\sqrt{x^2-x}=x\sqrt{1-\dfrac1x}[/tex]
since [tex]x\to\infty[/tex] forces us to have [tex]x>0[/tex]. And as [tex]x\to\infty[/tex], the [tex]\dfrac1x[/tex] term is "negligible", so really [tex]\sqrt{x^2-x}\approx x[/tex]. We can then treat the limand like
[tex]2x-1+2x-ax-b=(4-a)x-(b+1)[/tex]
which tells us that we would choose [tex]a=4[/tex]. You might be tempted to think [tex]b=-1[/tex], but that won't be right, and that has to do with how we wrote off the "negligible" term. To find the actual value of [tex]b[/tex], we have to solve for it in the following limit.
[tex]\displaystyle\lim_{x\to\infty}(2x-1+2\sqrt{x^2-x}-4x-b)=0[/tex]
[tex]\displaystyle\lim_{x\to\infty}(\sqrt{x^2-x}-x)=\frac{b+1}2[/tex]
We write
[tex](\sqrt{x^2-x}-x)\cdot\dfrac{\sqrt{x^2-x}+x}{\sqrt{x^2-x}+x}=\dfrac{(x^2-x)-x^2}{\sqrt{x^2-x}+x}=-\dfrac x{x\sqrt{1-\frac1x}+x}=-\dfrac1{\sqrt{1-\frac1x}+1}[/tex]
Now as [tex]x\to\infty[/tex], we see this expression approaching [tex]-\dfrac12[/tex], so that
[tex]-\dfrac12=\dfrac{b+1}2\implies b=-2[/tex]
So one asymptote of the hyperbola is the line [tex]y=4x-2[/tex].
The other asymptote is obtained similarly by examining the limit as [tex]x\to-\infty[/tex].
[tex]\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-ax-b)=0[/tex]
[tex]\displaystyle\lim_{x\to-\infty}(2x-2x\sqrt{1-\frac1x}-ax-(b+1))=0[/tex]
Reduce the "negligible" term to get
[tex]\displaystyle\lim_{x\to-\infty}(-ax-(b+1))=0[/tex]
Now we take [tex]a=0[/tex], and again we're careful to not pick [tex]b=-1[/tex].
[tex]\displaystyle\lim_{x\to-\infty}(2x-1+2\sqrt{x^2-x}-b)=0[/tex]
[tex]\displaystyle\lim_{x\to-\infty}(x+\sqrt{x^2-x})=\frac{b+1}2[/tex]
[tex](x+\sqrt{x^2-x})\cdot\dfrac{x-\sqrt{x^2-x}}{x-\sqrt{x^2-x}}=\dfrac{x^2-(x^2-x)}{x-\sqrt{x^2-x}}=\dfrac x{x-(-x)\sqrt{1-\frac1x}}=\dfrac1{1+\sqrt{1-\frac1x}}[/tex]
This time the limit is [tex]\dfrac12[/tex], so
[tex]\dfrac12=\dfrac{b+1}2\implies b=0[/tex]
which means the other asymptote is the line [tex]y=0[/tex].
which means the other asymptote is the line .