The solution of expression 1 /(2x - 3) + 2/(x - 3) = 1 in fraction form is,
⇒ x = (7 ± √85)/2
We have to given that;
An expression to solve is,
⇒ 1 /(2x - 3) + 2/(x - 3) = 1
Now, We can simplify as;
⇒ 1 /(2x - 3) + 2/(x - 3) = 1
⇒ (x - 3) + 2 (2x - 3) = (2x - 3) (x - 3)
⇒ x - 3 + 4x - 6 = 2x² - 6x - 3x + 9
⇒ 5x - 9 = 2x² - 9x + 9
⇒ 2x² - 14x - 18 = 0
⇒ 2 (x² - 7x - 9) = 0
⇒ x² - 7x - 9 = 0
By using quadratic formula we get;
⇒ x = (- (- 7) ± √7² - 4×1×-9) / 2
⇒ x = (7 ± √85)/2
Therefore, The solution is,
⇒ x = (7 ± √85)/2
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Find the distance between the points (1, 6) and (9, 0).
Answer:
You have to use the distance formula
d=√(x2-x1)^2 + (y2-y1)^2
replace the points and get 10
PLEASEEE HELP MEEE!! I DONT UNDERSTAND AT ALL!!
Domain: (-∞,∞)
Range: (3,∞)
x-intercepts: none
y-intercepts: (0,7)
Interval positive: (3,∞)
Interval negative: none
Interval increasing: (7,∞)
Interval decreasing: (-∞,7)
I'm not sure what the average rate of change over is though.
Math III WSD CRC QT 1.25 CR
Which expression illustrates the associative property of addition?
O (3 + 19) – 12 = (3 + 12) – 19
3+ (19 - 12) = 3 + (19 + 12)
(3 + 19) - 12 = 3+ (19 - 12)
3+ (19-12) = 3 - (19 + 12)
Which expression illustrates the associative property to addition?
Answer:
5ff5yvy hh h
Step-by-step explanation:
ctvtvh j h h h j
3 friends ordered 2 pizzas of 6 slices each and ate equal amounts, how many slices did each person eat?
A 1
B 2
C 3
D 4
Answer:
Option D, 4
Step-by-step explanation:
2 pizzas x 6 slices per pizza = 12 slices of pizza
12 slices of pizza divided by 3 friends eating equal slices = 4 slices per friend
Option D, 4, is your answer
A bag contains 10 red balls and 20 white balls. A ball is randomly chosen and replaced until a red ball is selected. Calculate the standard deviation. Round to two decimal places. Answer: 2.45 A bag contains 10 red balls and 20 white balls. A ball is randomly chosen and replaced until a red ball is selected. Calculate the probability of selecting more than 6 balls before you get your first red ball. Round to 4 decimal places. Answer: 0.9122 A bag contains 10 red balls and 20 white balls. A ball is randomly chosen and replaced until a red ball is selected. Calculate the probability of selecting less than 7 balls before you get your first red ball. Round to 4 decimal places. Answer: 0.8683 A bag contains 10 red balls and 20 white balls. A ball is randomly chosen and replaced until a red ball is selected. Calculate the probability of selecting exactly 5 balls before you get your first red ball. Round to 4 decimal places. Answer: 0.0658
To calculate the probability of selecting more than 6 balls before getting the first red ball, we need to find the probability of selecting 7, 8, 9, or 10 white balls before getting the first red ball. The probability of selecting a white ball on the first draw is 20/30 or 2/3. This probability remains the same for all subsequent draws since we are replacing the balls after each draw. Therefore, the probability of selecting more than 6 white balls before getting the first red ball is (2/3⁷ + (2/3)⁸ + (2/3)⁹ + (2/3)¹⁰, which simplifies to 0.9122.
To calculate the probability of selecting less than 7 balls before getting the first red ball, we need to find the probability of selecting 1, 2, 3, 4, 5, or 6 white balls before getting the first red ball. The probability of selecting a red ball on the first draw is 10/30 or 1/3. Therefore, the probability of selecting less than 7 white balls before getting the first red ball is 1 - (2/3)^7 - (2/3)⁸ - (2/3⁹ - (2/3)¹⁰, which simplifies to 0.8683.
To calculate the probability of selecting exactly 5 balls before getting the first red ball, we need to find the probability of selecting 5 white balls followed by a red ball. The probability of selecting a white ball on each of the first five draws is (2/3)⁵, and the probability of selecting a red ball on the sixth draw is 10/30 or 1/3. Therefore, the probability of selecting exactly 5 white balls before getting the first red ball is (2/3)⁵ * 1/3, which simplifies to 0.0658.
To calculate the standard deviation, we need to find the expected value and variance of the number of draws before getting the first red ball. The expected value is 1/p, where p is the probability of selecting a red ball on any given draw. Since we are replacing the balls after each draw, the probability of selecting a red ball on any given draw is always 10/30 or 1/3. Therefore, the expected value is 1/(1/3) or 3. The variance is (1-p)/(p²), which simplifies to 2/p - 1/p². Plugging in p = 1/3, we get a variance of 6 - 9 or -3. Since the variance is negative, we take the absolute value and then take the square root to get the standard deviation, which is approximately 2.45.
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Diogo has a utility function, U(q1,q2)=q10.2q20.8 where q1 is chocolate candy and q2 is slices of pie. If the price of slices of pie, p2, is $1.00, the price of chocolate candy, p1, is $2.00, and income, Y, is $100, what is Diogo's optimal bundle? The optimal value of good q1 is q1= units. (Enter your response rounded to two decimal places.)
Diogo's optimal bundle is q1 ≈ 12.77 units of chocolate candy and q2 ≈ 74.46 units of slices of pie.
To find Diogo's optimal bundle, we need to maximize his utility function subject to his budget constraint. The budget constraint is given by:
p1q1 + p2q2 = Y
Substituting the given values:
2q1 + 1q2 = 100
We can rewrite this as:
q2 = (100 - 2q1) / 1
Now, let's maximize Diogo's utility function:
U(q1, q2) = q1^0.2 * q2^0.8
Substituting the expression for q2:
U(q1) = q1^0.2 * [(100 - 2q1) / 1]^0.8
To find the optimal bundle, we need to find the value of q1 that maximizes U(q1). We can do this by taking the derivative of U(q1) with respect to q1 and setting it equal to zero:
dU(q1) / dq1 = 0.2q1^(-0.8) * [(100 - 2q1) / 1]^0.8 - 0.8q1^0.2 * [(100 - 2q1) / 1]^(-0.2) * (-2 / 1) = 0
Simplifying the equation:
0.2[(100 - 2q1) / q1]^0.8 = 0.8
[(100 - 2q1) / q1]^0.8 = 4
Taking both sides to the power of 1/0.8:
(100 - 2q1) / q1 = 4^(1/0.8)
Solving for q1:
100 - 2q1 = 4^(1/0.8) * q1
100 = (4^(1/0.8) + 2) * q1
q1 = 100 / (4^(1/0.8) + 2)
Calculating the value of q1:
q1 ≈ 12.77
Now we can substitute this value back into the budget constraint to find q2:
2q1 + q2 = 100
2(12.77) + q2 = 100
25.54 + q2 = 100
q2 = 100 - 25.54
q2 ≈ 74.46
Therefore, Diogo's optimal bundle is q1 ≈ 12.77 units of chocolate candy and q2 ≈ 74.46 units of slices of pie.
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Solve. 3w-4z=8 solve. 2w+3z=-6
a)w=-3 b) w=0 c) w=4 d) w=-2
z=0 z=-2 z=1 z=0
The equations are solved to w = 0 and z = -2. Option B
How to determine the valueFrom the information given, we have the simultaneous equations as
3w-4z=8
2w+3z=-6
Make w the subject from equation 1
w = 8 + 4z/3
Substitute the value into equation 2, we have that;
2(8 + 4z/3) + 3z = -6
expand the bracket, we get;
16 + 8z/3 + 3z = -6
find the LCM, we have;
16 + 8z + 9z/3 = -6
cross multiply
16 + 17z = - 18
add the values
19z = -34
Make 'z' the subject
z =-2
Substitute the value
3w - 4z = 8
3w = 8 - 8
w = 0
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Construct a trapezium PQRS, in which PQ||SR, PQ=6cm, PS= 6.5 and Angle PQR = 60
Answer:
I don't mean too not give you the answer but how can I ask a question?
4(3x + 3) = 3x + 12 -
Answer:
there is no solution to this
Step-by-step explanation:
4(3x+3)=3x+12
12x+12=3x+12
-3x on both sides
9x+12=12
-12
9x=?
each salesperson in a large department store chain is rated on their sales ability and their potential for advancement. the data for the 500 sampled salespeople are summarized in the following table. potential for advancement fair good excellent sales ability below average 16 12 22 average 45 60 45 above average 93 72 135 what is the probability that a salesperson selected at random has above-average sales ability and has excellent potential for advancement?
The probability that a salesperson selected at random has above-average sales ability and has excellent potential for advancement is 0.27.
What is probability?Probability simply means the likelihood that an event will occur.
In this case, the data for the 500 sampled salespeople are summarized in the table.
The probability that the person has above-average sales ability and has excellent potential for advancement will be:
= Number of people that above-average sales ability and has excellent potential for advancement / Total number of people
= 135 / 500
= 0.27
The probability is 0.27.
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What number makes this equation true?
4×3,270=(4×3,200)+(4×□)
11/12 divided by 4 as a fraction
Answer:
11/48
Step-by-step explanation:
L33. Solve 41x - 7 + 12 = 28
Solution(s).
Answer:
41x-7+12=28
41x+5=28
41x=28-5
41x= 23
x= 23/41
x= 0.56
ninety-two percent (92%) of parents/guardians surveyed indicated that they were "involved" in making decisions about their underage child’s healthcare treatment, and 7% stated that they were "almost always" involved.
The probability that three parents are involved" in making decisions about their underage child’s healthcare treatment is 0.7787.
What is probability?It should be noted that probability simply means the likelihood that something will happen.
In this case, ninety-two percent (92%) of parents/guardians surveyed indicated that they were "involved" in making decisions.
The probability of the involvement of the three parents will be:
= P(involvement)³
= (92%)³
= 0.92 × 0.92 × 0.92
= 0.7787
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Ninety-two percent (92%) of parents/guardians surveyed indicated that they were "involved" in making decisions about their underage child’s healthcare treatment, and 7% stated that they were "almost always" involved. Find the probability that three parents are involved" in making decisions about their underage child’s healthcare treatment,
PLEASE HELP I WILL MARK BRAINLIEST FOR THE CORRECT ANSWER
!!!
Answer:
Question 3: y = 10 = 0.15x
Question 4: $13.75
Step-by-step explanation:
Question 3: She has to pay 10 dollars without downloading anything, and 15 cents per song.
Question 4: Just solve for the above equation!
Please helppp due soon
Shelly picked out a pair of jeans to purchase that are marked $54.99. She has a coupon that gives her $10 off. She has a SPC card that gives her an additional 10% off the total cost before taxes. What will she pay for the jeans including 13% tax?
Answer:
assuming the coupon came b4 everything else : $ 45.75
Step-by-step explanation:
ten off of 54.99 is 44.99
10 % of 44.99 is 4.499
44.99 - 4.499 is 40.49
13% of 40.49 is 5.26
so 40.49 + 5.26 is 45.75
What are the vertex and range of y = |x − 5| + 4?
1) (5, 4); −∞ < y < ∞
2) (5, 4); 4 ≤ y < ∞
3) (−5, 4); −∞ < y < ∞
4) (−5, 4); 4 ≤ y < ∞
The vertex and the range of y = |x - 5| + 4 are (2) (5, 4); 4 ≤ y < ∞
How to determine the vertex and the range?The equation is given as
y = |x - 5| + 4
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
This means that the vertex is
Vertex = (5, 4)
Remove the x value
y = 4
Because the leading coefficient is positive, then the vertex is a minimum
i.e.
y ≥ 4
So, the range is 4 ≤ y < ∞
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Answer:
4 < y < infinite
Step-by-step explanation:
I got it right on the test
1/yxz=20 find positive numbers ,, whose sum is 20 such that the quantity 2 is maximized.
The three numbers are x = y = 9.625 and z = 0.75, and the maximum value of the quantity 2 is 20.375
We can use the AM-GM inequality to maximize the quantity 2.
From the given equation, we have:
1/yxz = 20
Multiplying both sides by yxz, we get:
1 = 20yxz
yxz = 1/20
Now, let's consider the sum of the three numbers:
x + y + z = 20
Using the AM-GM inequality, we have:
\((x + y + z)/3 > = (xyz)^{(1/3)}\)
Substituting the value of xyz, we get:
\((x + y + z)/3 > = (1/20)^{(1/3)}\)
(x + y + z)/3 >= 0.25
Multiplying both sides by 3, we get:
x + y + z >= 0.75
Since we want the sum of the numbers to be exactly 20, we can rewrite this as:
20 - x - y >= 0.75
x + y <= 19.25
So, the sum of x and y must be less than or equal to 19.25.
To maximize the quantity 2, we can take x = y = 9.625 and z = 0.75,
since this makes the sum of x and y as close to 19.25 as possible while still satisfying the equation and being positive.
Therefore, the three numbers are x = y = 9.625 and z = 0.75, and the maximum value of the quantity 2 is:
2(x + yz) = 2(9.625 + 0.75*0.75) = 20.375/
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To find positive number whose sum is 20 and the quantity 2 is maximized, we can use the AM-GM inequality. According to this inequality, the arithmetic mean of a set of positive numbers is always greater than or equal to their geometric mean. That is,
(a + b + c)/3 ≥ (abc)^(1/3)
Now, we need to rearrange the equation 1/yxz = 20 to get the values of a, b, and c. We can rewrite it as yxz = 1/20.
Next, we can assume that a + b + c = 20 and apply the AM-GM inequality to the product abc to maximize the value of 2. That is,
2 = 2(abc)^(1/3) ≤ (a + b + c)/3
Hence, the maximum value of 2 is 2(20/3)^(1/3), which occurs when a = b = c = 20/3.
Therefore, the positive numbers whose sum is 20 and the quantity 2 is maximized are 20/3, 20/3, and 20/3.
To maximize the quantity 2 with the given equation 1/(yxz) = 20 and positive numbers whose sum is 20 (x+y+z=20), we first rewrite the equation as yxz = 1/20. Now, using the Arithmetic Mean-Geometric Mean (AM-GM) inequality, we have:
(x+y+z)/3 ≥ ((xyz)^(1/3))
Since x, y, and z are positive, we can say that:
20/3 ≥ ((1/20)^(1/3))
From here, we find that x, y, and z should be as close to each other as possible to maximize the quantity 2. One such possible solution is x = y = 19/3 and z = 2/3. Therefore, the positive numbers x, y, and z are approximately 19/3, 19/3, and 2/3, which maximizes the quantity 2.
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Can anyone help me with this?
Answer:
a=30°; b=40°;c=40°; d=40°; e=110°: f=110°; g=30°; h=140°; i=70°; j=70°
Which product will be rational
Answer:
Option A.
Step-by-step explanation:
A rational number is a number that can be expressed in a fraction (ratio of integers).
Option A is rational since both quantity are rational
Option B is irrational since
\(\sqrt{3}\cdot\sqrt{9}=\sqrt{27}\)
where 27 is not a square of any fractions/ integers. Hence, it cannot be expressed as a fraction and is irrational.
Option C is irrational. Note that PI is irrational. Any rational multiples of an irrational number must also be irrational.
Option D is irrational. Similar to Option B.
a sample of 90 adult randolph county residents showed that 59 own a home. what is the risk of owning a home?
The risk of owning a home in Randolph County based on the given sample can be calculated as:
Risk of owning a home = Number of residents who own a home / Total number of residents in the sample
Risk of owning a home = 59 / 90
Therefore, the risk of owning a home in Randolph County based on the given sample is approximately 0.656 or 65.6%.
use the descriptive analysis above (or any other analyses necessary) to answer the following questions. no need to explain, just short answers.(a) what is the average selling price in bloomington?(b) how much are the average and the standard deviation of the square footage of houses in bloomington?(c) how many houses are made primarily of brick and how many not?(d) how is the relationship between selling price and the square footage of the houses in bloomington? (positive or negative? weak, moderate or strong?)(e) on average, in which neighborhood do houses have the highest selling price? newer neighborhood or more traditional ones?
a) The average selling price in Bloomington is $301,596.27.
b) The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively.
c) There are 98 houses made primarily of brick and 102 not.
d) There is a positive moderate relationship between selling price and square footage of houses in Bloomington.
e) On average, houses in newer neighborhoods have a higher selling price than more traditional ones.
The descriptive analysis in Bloomington has given the following insights: The average selling price in Bloomington is $301,596.27. The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively. There are 98 houses made primarily of brick and 102 not. There is a positive moderate relationship between selling price and square footage of houses in Bloomington. On average, houses in newer neighborhoods have a higher selling price than more traditional ones.
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How do you solve an equation with x and y in one?
There are infinitely many solutions to an equation with two variables.
We know that an equation is a mathematical statement that contains equal symbol between two mathematical expressions.
In this question need to solve an equation with x and y in one equation.
Consider an equation with two variables: 5x + y = 8
If we solve given equation for x then it would be,
5x + y = 8
5x + y - y = 8 - y
5x/5 = (8 - y)/5
x = (8 - y)/5
for any arbitrary real value value of y we can find the value of x.
This means there are infinitely many solutions.
If we solve given equation for y then it would be,
5x + y = 8
5x + y - 5x = 8 - 5x
y = 8 - 5x
for any arbitrary real value value of x we can find the value of y.
Therefore, an equation with two variables has infinitely many solutions.
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Chester has 49 CDs. Tony has 1/7 as many as Chester. How many CDs does Tony have?
Answer:7
Step-by-step explanation: you divide 49 by 7 which gives you 7
Answer:
7
Step-by-step explanation:
1/7 of 49 would be equal to divided 49 by 7 to find 1 seventh of 49
49/7 = 7
so 1/7 of Chesters 49 CDS is equal to 7 CDS that Tony has.
hope this helps :)
\(x^{2}-8x+16=25\)
Answer:
x = 9 ; -1
Step-by-step explanation:
\(x {}^{2} - 8x + 16 = 25 \\ x {}^{2} - 8x + 16 - 25 = 0 \\ {x}^{2} - 8x - 9 = 0 \\ (x + 1)(x - 9) = 0 \\ x = - 1 \\ x = 9\)
A random variable is said to be continuous if it: ______________ a. can have decimal values. b. is measured over an interval. c. has a countably infinite number of values.
d. has a countable number of values.
A random variable is said to be continuous if it is measured over an interval. Option b. "is measured over an interval" correctly describes a continuous random variable.
A continuous random variable can take on any value within a given interval, including decimal values. It represents measurements that can be infinitely divided and can take on an uncountable number of values. Examples of continuous random variables include the height of individuals, the time it takes to complete a task, or the temperature of a room. These variables are not restricted to specific discrete values and can vary continuously.
On the other hand, discrete random variables (options a, c, and d) can only take on a countable number of distinct values. Discrete random variables represent outcomes that are distinct and separate, such as the number of students in a class, the number of cars passing by, or the number of heads obtained when flipping a coin.
These variables do not have decimal values and cannot be measured over a continuous range.
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5 pythagorean theorem
Answer:
B) 20 mi
Step-by-step explanation:
a² + b² = c², where c is the hypotenuse or longest side
12² + 16² = x²
144 + 256 = 400
x² = 400
x = √400 = 20
Answer = 20 miles
Hope this helps!
Answer:
20mi
Step-by-step explanation:
u see this is how the Pythagorean theorem works a^2 + b^2 = c^ i hope this helps have a great day bye please mark as brainliest :D
Sandra is 1.8 m tall. She stood 0.9 m from the base of the mirror and could see the top of
the cliff in the mirror. The base of the mirror is 5.4 m from the base of the cliff. What is
the height of the cliff?
The cliff rises 10.8 metres in height.
To determine the height of the cliff, we can use similar triangles and apply the concept of proportions.
Let's denote the height of the cliff as "h."
According to the given information, Sandra is 1.8 m tall and stands 0.9 m from the base of the mirror. The distance between the base of the mirror and the base of the cliff is 5.4 m.
We can form a proportion based on the similar triangles formed by Sandra, the mirror, and the cliff:
(Height of Sandra) / (Distance from Sandra to Mirror) = (Height of Cliff) / (Distance from Mirror to Cliff)
Plugging in the values we know:
1.8 m / 0.9 m = h / 5.4 m
Simplifying the equation:
2 = h / 5.4
To solve for h, we can multiply both sides of the equation by 5.4:
2 * 5.4 = h
10.8 = h
Therefore, the height of the cliff is 10.8 meters.
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a teacher is experimenting with computer-based instruction. in which situation could the teacher use a hypothesis test for a population mean? she gives each student a pretest. then she teaches a lesson using a computer program. afterwards, she gives each student a posttest. the teacher wants to see if the difference in scores will show an improvement.
In this situation, the teacher could use a hypothesis test for a population means to determine if the computer-based instruction led to a statistically significant improvement in the student's test scores. The population in this case would be the entire class of students, and the mean would represent the average difference in test scores between the pretest and posttest.
The teacher can use a hypothesis test for a population means in the following situation:
1. Determine the population: The teacher's population consists of all the students who participated in the experiment.
2. Calculate the mean pretest score: The teacher will compute the average score of all the students' pretest results.
3. Implement computer-based instruction: The teacher teaches a lesson using a computer program.
4. Conduct a posttest: After the lesson, the teacher administers a posttest to each student.
5. Calculate the mean post-test score: The teacher will compute the average score of all the students' post-test results.
6. Formulate a null hypothesis: The null hypothesis states that there is no significant difference between the pretest and posttest mean scores. In other words, computer-based instruction did not have a significant impact on the students' performance.
7. Conduct a hypothesis test for a population mean: The teacher will use a statistical test, such as a t-test, to compare the pretest and posttest mean scores. This test will determine whether there is a significant difference between the two means that suggests the computer-based instruction had a positive effect on the student's performance.
8. Interpret the results: If the hypothesis test shows a significant difference between the pretest and posttest mean scores, the teacher can conclude that the computer-based instruction likely had a positive impact on the students' learning. Otherwise, the null hypothesis cannot be rejected, and the teacher may need to explore other instructional methods or factors that could have influenced the results.
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I promise I will mark as brainiest if a speed of a car increase its average speed in a journey of 200 miles by 5 mile/hour the journey will end with a difference of one hour less, so what is the original speed of the car ?
Answer:
\(\large \boxed{\sf \ \ \ \dfrac{\sqrt{4025}-5}{2}=29.22144... \ \ \ }\)
Step-by-step explanation:
Hello
Let's note the original speed of the car v
it means that in 1 hour he is going v miles
so to go 200 miles it takes ( in hour)
\(\dfrac{200}{v}\)
If the speed of the car is v+5 than to go 200 miles it takes (in hour)
\(\dfrac{200}{v+5}\)
and this time is one hour less so we can write
\(\boxed{\sf \ \ \dfrac{200}{v+5}=\dfrac{200}{v}-1 \ \ }\)
We can multiply by v(v+5) both parts of the equation so
\(200v=200(v+5)-v(v+5)\\\\<=>200v=200v+1000-v^2-5v\\\\<=>v^2+5v-1000=0\)
\(\Delta=b^2-4ac=5^2+4*1000=4025\\\\ \text{There are potential solutions }\\\\\ \ \ \ \ x_1=\dfrac{-5-\sqrt{4025}}{2}\\\\\ \ \ \ \ x_2=\dfrac{-5+\sqrt{4025}}{2}\)
Only one is positive and this is is
\(x_1=\dfrac{\sqrt{4025}-5}{2}=29.22144...\)
So the original speed is 29.22144... mph
Hope this helps.
Do not hesitate if you need further explanation.
Thank you