The value of the discriminant for the equation "2x² + 5x + 3" is 1 , and the it has 2 real and rational roots .
The Discriminant of a quadratic equation of the form of ⇒ "ax² + bx + c" is calculated by the expression "b² - 4ac" .
the values of the variables "a", "b" and "c" ; for quadratic equation "2x² + 5x + 3" ,
the value of a is = 2, b is = 5, and c is = 3.
substituting values ;
So , the discriminant is ⇒ b² - 4ac
⇒ 5² - 4×2×3 ;
⇒ 25 - 24
⇒ 1
Since , the discriminant is (1)positive, which means that the equation has 2 real roots. and since, discriminant is a perfect square, that means the roots are rational numbers.
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The given question is incomplete , the complete question is
Find the value of the discriminant for the equation 2x² + 5x + 3 , and then describe the number and type of roots for the equation .
Compare the function g(x) = 4^3√x + 2 -5 to the cube root parent function f(x)=^3√x. How has the function been transformed from the original parent function?
PLEASE SHOW ALL WORK FOR BRAINLIEST!!
The transformations from the parent cube root function to generate function g(x) are given as follows:
Vertical stretch by a factor of 4.Shift left by 2 units.Shift down by 5 units.What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.For this problem, the transformations are given as follows:
Multiplication by 4: vertical stretch by a factor of 4.x -> x + 2: shift left 2 units.y -> y - 5: shift down 5 units.More can be learned about translations at brainly.com/question/28174785
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3^3x=9^9
Find the answer for x in the following equation...............................
Answer:
x= 6
Step-by-step explanation:
3^3x = 9^9
3^3x = 3^(2×9)
3^3x = 3^18
3x = 18
3x/3 = 18/3
x = 6
Solve the following system of equations:
-2x + 3y = 7
y = 3x + 7
(-5, -1)
(-2, 1)
(-1,4)
(1,3)
The solution of the equations 3y - 2x = 7 and y = 3x + 7 will be (-2, 1). Then the correct option is B.
What is the solution to the equation?The possible value of the variables that satisfy the equation which is known as the solution of the equation.
The equations are given below.
-2x + 3y = 7 ...1
y = 3x + 7 ...2
From equations 1 and 2, then we have
- 2x + 3(3x + 7) = 7
- 2x + 9x + 21 = 7
7x = - 14
x = - 2
Then the value of 'y' is given as,
y = 3(-2) + 7
y = - 6 + 7
y = 1
The solution of the equations 3y - 2x = 7 and y = 3x + 7 will be (-2, 1). Then the correct option is B.
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Which statement is true about the end behavior of the
graphed function?
O As the x-values go to positive infinity, the function's
values go to negative infinity.
O As the x-values go to zero, the function's values go to
positive infinity.
O As the x-values go to negative infinity, the function's
values are equal to zero.
O As the x-values go to positive infinity, the function's
values go to positive infinity.
As the x-values go to positive infinity, the function's values go to positive infinity. Then the correct option is D.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The graph of the function is given below.
From the graph, we can conclude that the value of the graph is always positive. So, the function will be an exponential function.
From the graph, as the x-values go to positive infinity, the function's values go to positive infinity. Then the correct option is D.
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Find the value of the X, Triangle Similarity
The value of 'x' in similar triangles is 6.9 units.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know, A line segment parallel to one side of the triangle divides the other two sides in the ratio of their respective lengths.
Therefore, The ratio can be formed as,
13/5 = 18/x.
13x = 90.
x = 6.9 units.
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Are All Fixed Costs Considered Sunk Costs?
No, not all fixed costs are considered sunk costs. Sunk costs are costs that have already been incurred and cannot be recovered, regardless of any future actions.
Fixed costs, on the other hand, are costs that do not vary with changes in output or sales, such as rent or salaries. While some fixed costs may be sunk costs (such as a non-refundable deposit for a lease), other fixed costs may still be recoverable or avoidable with different decisions, and therefore are not considered sunk costs. Sunk costs are only relevant in decision making to the extent that they cannot be recovered and should not be factored into future decisions.
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What's the value x?
The value of x is often used in algebra, meaning a value that isn't known yet. It is called a variable, or unknown
The value x is used often in algebra to specify an unknown variable.
What is Variable?Variables are often alphabets or letters used to represent an unknown number or value.
It is called a variable because it may change it's value according to the value of the others.
x is a variable which is commonly used to solve problems in algebra.
It represents the unknown variable.
We have to do certain operations to find the value of y.
Consider the equation, x + 5 = 13.
Here x is a unknown variable.
We can find the value of x as x = 13 - 5 = 8
Hence x is commonly used to represent an unknown variable.
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Help! Brainliest! Need help with 10, 12, and 13. I really appreciate it!!
The required ST² = TW × RT has been proven for the triangle RST where SW is perpendicular from vertex S to RT.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
Here,
For the triangle RST where SW is perpendicular from vertex S to RT
Rewrite the equation,
ST² = TW × RT
ST/TW = RT/ST
It implies triangle SWT is similar to triangle RST,
Where,
∠S = ∠W and ∠T = ∠T
So triangle SWT is similar to triangle RST, by AA postulate of similarity.
If triangles are similar,
ST/TW = RT/ST [became valid statement]
ST² = TW × RT
Thus, ST² = TW × RT hence proved.
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Write a function where y should vary directly with x, then give a real world example for it.
The function to represent a direct variation relationship between y and x is y = kx.
How to write a function where y should vary directly with x?A direct variation relationship is one where the ratio of two quantities is always constant. In mathematical terms, if y varies directly with x, then there is a constant k such that y = kx.
Below is a function to represent a direct variation relationship between y and x:
y = kx
where k is the constant of proportionality.
A real world example of a direct variation relationship is the relationship between the distance traveled by a vehicle and the time it takes to travel that distance.
If a car travels at a constant speed, then the distance it travels is directly proportional to the time it takes to travel that distance. In mathematical terms, we can write:
distance = rate × time
where the constant of proportionality (rate) is the speed of the car.
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A contact center provides incentives based on the number of sales achieved by its
representatives. Ross made 27 sales in 3 days. His colleague, Mona secured 49 sales in
one week. Who achieved a higher sales target per day? HELPP
Ross achieved a higher sales target.
What is a fraction?A fraction is a number which represents the part of a whole or collection of objects. It is in the from of [tex]\frac{a}{b}[/tex] where a represents the numerator part and the b represents the denominator parts.
A contact center provides incentives based on the number of sales achieved by its representatives.
Ross made 27 sales in 3 days.
Sales per one day =[tex]\frac{27}{3}=9.[/tex]
Mona secured 49 sales in one week
Sales per day =[tex]\frac{49}{7}=7[/tex]
Therefore, in one day sale of Ross is 9 and sale of Mona is 7.
Hence, Ross achieved a higher sales target.
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In figure below, l || m. Find x.
Answer:
70
The top line should add up to 180 and both sides other than x are 55 so since 55+55=110 180-110=70
What does the residual plot tell you about the line of best fit?
The residual plot tell you about the line of best fit, the closer a data point's residual is to 0, the better the fit.
A residual value is a measure of how much a retrogression line vertically misses a data point. Retrogression lines are the stylish fit of a set of data. You can suppose of the lines as pars; a many data points will fit the line and others will miss.
A residual plot has the Residual Values on the perpendicular axis; the vertical axis displays the independent variable.
A residual plot is generally used to find problems with retrogression. Some data sets aren't good campaigners for retrogression, including
Heteroscedastic data( points at extensively varying distances from the line).Data that's non-linearly associated.Data sets with outliers.Learn more about Residual Plot:
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{
x = 10
3x + 5y = 20
What is the solution (x, y)
Answer:
x=10,y= -2).
Step-by-step explanation:
The given system of equations is:
x = 10
3x + 5y = 20
We can use substitution to solve for y. Starting with the first equation:
x = 10
We can substitute the value of x into the second equation:
3x + 5y = 20
3 * 10 + 5y = 20
30 + 5y = 20
5y = 20 - 30
5y = -10
Finally, we can solve for y by dividing both sides of the equation by 5:
y = -10 / 5
y = -2
x=10,y= -2).
pleas answer!!!!!!!!!!
why do i have to put 29 characters in the box
The rate of decrease is 89%.
The function shows exponential decay.
What is exponential decay?An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.
The exponential decay function:
Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.
Given:
An exponential function,
y = 8600(0.11)ˣ.
When we put x = 0,
we get,
y = 8600
And when we put x = 1
we get,
y = 946
So, 1 - r = 0.11
Rate of decrease, r = 0.89
Therefore, the function shows exponential decay.
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2.
(08.02 LC)
Solve nine times two thirds.
Leave your answer as an improper fraction.
A) eleven twenty sevenths
B) eighteen twenty sevenths
C) eleven thirds
D) eighteen thirds
Pls help
The fraction of nine times two thirds is 18/3 (option D)
What is fraction ?
A fraction is a way of representing a part of a whole or a ratio between two numbers. It consists of two numbers written one above the other and separated by a horizontal line called a fraction bar.
The number above the fraction bar is called the numerator, and it represents the part of the whole or the quantity being considered. The number below the fraction bar is called the denominator, and it represents the total number of equal parts into which the whole has been divided.
Given by the question:
Nine times two thirds can be written as:
9 × 2/3 = 18/3=6
Simplifying this fraction, we can divide both the numerator and denominator by their greatest common factor of 3, which gives:
18/3
so the correct option is D.
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suppose that a motorboat is moving at 40ft/s when its motor suddenly quits, and that 10 s later the boat has slowed to 20 ft/s. assume that the resistance it encounters while coasting is proportional to its velocity, so that dv/dtkv. how far will the boat coast in all?
The boat will coast a total distance of approximately 40/ln(0.5)/(-10) ft.
To solve this problem, we can use the concept of exponential decay. If we let v(t) be the velocity of the boat as a function of time t, then we can write the differential equation that describes its motion as:
dv/dt = -kv(t)
where k is the proportionality constant between resistance and velocity. We can separate variables and integrate both sides to get the velocity as a function of time:
∫(dv/dt) = -k∫(v(t))dt
v(t) = Ce^(-kt)
where C is an arbitrary constant of integration. We can use the initial condition v(0) = 40 ft/s to find C:
C = 40
So the velocity of the boat as a function of time is:
v(t) = 40e^(-kt)
We can use the condition v(10) = 20 ft/s to solve for k:
20 = 40e^(-10k)
Taking the natural logarithm of both sides:
ln(0.5) = -10k
k = ln(0.5)/(-10)
Next, we can use the velocity as a function of time to find the distance traveled by the boat:
∫(v(t))dt = ∫(40e^(-kt))dt = 40/k * (1 - e^(-kt))
Let's call the total distance traveled by the boat "D". Then we can write:
D = 40/k * (1 - e^(-kt))
We can plug in the value of k we found earlier and evaluate the expression at t = ∞:
D = 40/ln(0.5)/(-10) * (1 - e^(-∞)) = 40/ln(0.5)/(-10)
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The diameter of a circle is 16 ft. Find its area to the nearest whole number.
Answer:
the area of the circle is approximately
201.06 ft^2
can someone PLEASE help me ASAP! Due today!! I will give brainliest.
Show work please
The surface area of the given figure is 200 yd².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Representing the figure as three dimensional, this consists of two triangular bases and three rectangular faces.
Area of triangle = [tex]\frac{1}{2}[/tex] × base × height
= [tex]\frac{1}{2}[/tex] × 6 × 4
= 12 yards²
Area of two triangular faces = 12 × 2 = 24 yd²
Of the three rectangular faces, two of them have a length of 11 yd and width of 5 yd.
Area of a rectangle = Length × Width
Area of two rectangular faces = 2 × Length × Width
= 2 × 11 × 5
= 110 yd²
Area of the third rectangular face = 11 × 6 = 66 yd²
Total surface area = 24 yd² + 110 yd² + 66 yd²
= 200 yd²
Hence the total surface area is 200 yd².
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write 5x10^3 x 9x10^7in stanadred form
Answer:
Step-by-step explanation:
5 x 10^3 x 9 x 10^7 can be written as follows in standard form:
5 x 10^3 = 5 x 10^3 x 1 = 5 x 10^3
9 x 10^7 = 9 x 10^7 x 1 = 9 x 10^7
So,
5 x 10^3 x 9 x 10^7 = (5 x 10^3) x (9 x 10^7) = 45 x 10^(3 + 7) = 45 x 10^10 = 4.5 x 10^11
In standard form, the coefficient (45) is written as a number between 1 and 10, and the exponent (10) gives the number of places the decimal point must be moved. So, 4.5 x 10^11 is written in standard form as 4.5 x 10^11.
Answer:
Step-by-step explanation:
45*10^10=4.5*10^11
Ex 2: Matt bowled games of 162, 170, and 148. What must he bowl in the next game to
have an average of 155?
Mat must bowl 140 in the next game.
What is Average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Given:
Matt bowled games of 162, 170, and 148.
Average = 155
let the score on fourth game be x.
So, (162 + 170 + 148 + x)/4 = 155
480 + x= 620
x= 140
Thus, he must bowled 140.
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Kirill purchased 20 cows, pigs and chickens for $3,447. If cows cost $750 each, pigs cost $60 each, and chickens cost $3 each, and he bought two more chickens than
pigs, how many of each animal did he buy?
-7 1/7 * (3 2/5)+6 3/5*(-71/7)=x
Answer:
x = -91 8/35
Step-by-step explanation:
Challenging, but lets take it step by step. We have two sets each of complex fractions being multiplied, and then added. As per PEDMAS, do the multiplication first and then add. [I changed the -71/7 as per your note in the comment section.]
[-7 1/7 * (3 2/5)] + [6 3/5*(-7 1/7)] = x
Convert the two numbers into fractions. Eg., 7 1/7 becomes 50/7 and 3 2/5 becomes 17/5. 6 3/5 becomes 33/5 and 7 1/7 becomes 50/7.
[-50/7 * (17/5)] + [33/5*(-50/7)] = x
Now multiply the numerators and denominators.
[-850/35] + [-2343/35] = x
Now we can add the two fractions since they have the same denominator.
-(3193/35) = x
x = -91 8/35
Are 5 2 13 5 and -5 2 13 -5 inverses? Why or why not?
Yes multiplying the matrices shows that it is inverse matrix
How to find if they are inversesThe inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix.
Using multiplication of matrices product is sort as follows
Row 1 column 1
= 5 * - 5 + 2 * 13 = -25 + 26 = 1
Row 1 column 2
= 5 * -2 + 2 * 5 = -10 + 10 = 0
Row 2 column 1
= 13 * -5 + 5 * 13 = -65 + 65 = 0
Row 2 column 2
= 13 * 2 + 5 * -5 = 26 + -25 = 1
The identity matrix is
Row 1 column 1 Row 1 column 2 1 0
Row 2 column 1 Row 2 column 2 0 1
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eric reads an article that says 15 out of 25 adults use their computer everyday. He collects data from a random sample of adults. Out of 1,270 adults, estimate the number of adults who use their computer every day. Please show your work!
we can estimate that 762 adults in Eric's sample use their computer every day.
What is random sample?Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population.
According to question:We can use the proportion from the article to estimate the number of adults who use their computer every day in Eric's sample.
The proportion of adults who use their computer every day from the article is:
15/25 = 0.6
This means that 60% of adults use their computer every day.
To estimate the number of adults who use their computer every day in Eric's sample, we can multiply the proportion by the sample size:
0.6 x 1,270 = 762
So we can estimate that 762 adults in Eric's sample use their computer every day.
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There are 80 people in a choir.
Half of the people in the choir are women
The number of men in he choir is one quarter of the number of women
the number of children in the choir : the number of men in the choir = n:1
Work out the value of n.
You must show how you get your answer.
Answer:
We know that half of the choir members are women, which means:
Number of women = 80/2 = 40
We also know that the number of men is one-quarter of the number of women, which means:
Number of men = 40/4 = 10
Now, we're given that the ratio of children to men in the choir is n:1. Let's call the number of children in the choir "c".
So, we have:
c : 10 = n : 1
We can cross-multiply to get:
c = 10n
Since we know that the total number of people in the choir is 80, we can set up another equation:
40 (women) + 10 (men) + c (children) = 80
Substituting c = 10n, we get:
40 + 10 + 10n = 80
Simplifying the left side, we get:
50 + 10n = 80
Subtracting 50 from both sides, we get:
10n = 30
Dividing both sides by 10, we get:
n = 3
Therefore, the value of n is 3
A museum roomcircular in shape, has 5 equally spaced sensors on its walls. There are no dead or overlapping spots along the perimeter of the roomEach sensor has the same angle of detection What is the detection angle of each sensor ? Enter your answer in the box plsss help asap
Answer: 108 degrees.
Step-by-step explanation:
I think this is how you solve it:
A circle has a total of 360 degrees.
Having 5 equally placed sensors with a certain detection angle means that the sensors form a regular pentagon.
Finding the measure of the interior angles of a regular pentagon can be found using the formula
(180(n-2))/n, with n being the number of vertices of the polygon.
180(5-2)/5 ; 180(3)/5 ; 540/5 = 108
I think this means the detection angle is 108 degrees. Hope this helps!
If you get it wrong I'm terribly sorry T-T
What is change in demand and change in quantity demanded?
Answer:
Step-by-step explanation:
Change in demand refers to a shift in the entire demand curve, either to the right or to the left, resulting in a higher or lower demand for a good or service, respectively. It can be caused by a variety of factors, such as changes in consumer preferences, changes in the price of related goods, changes in income, changes in the population, or changes in consumer expectations.
Change in quantity demanded, on the other hand, refers to a movement along the demand curve, resulting from a change in the price of a good or service, without any change in the underlying demand for the good or service. For example, if the price of a good decreases, the quantity demanded of that good will increase, and vice versa. This relationship between price and quantity demanded is known as the law of demand.
In summary, change in demand represents a shift in the demand curve, while change in quantity demanded represents a movement along the demand curve.
Write (5-√5)² in the form a + b√5, where a and b are intergers
The required expression is 30 - 10√5 which is in the form a + b√5, where a = 30 and b = -10.
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The expression is given in the question, as follows:
(5-√5)²
Expanding the above expression,
(5)² + (√5)² - 2 × 5 × √5
25 + 5 - 10√5
30 - 10√5
Compare the above expression to the form a + b√5, and we get
a = 30 and b = -10
Thus, the required expression is 30 - 10√5.
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Jen’s phone uses a simple algorithm to count the number of strides she takes.
The algorithm looks at the phone’s accelerometer measurements, and counts a
stride each time the acceleration goes from below to above 3 g. Based on the
number of strides counted in the 20-second window shown here, and assuming
that Jen travels 140 cm per stride, what was Jen’s average walking speed, in
meters per second, over the 20-second window? Express your answer as a
decimal to the nearest hundredth.
Using the relationship between speed, distance and time, Jen's average walking speed was approximately 1.75 meters per second over the 20-second window.
What is Jen's average walking speedTo find Jen's average walking speed, we need to first find the total distance that she walked in 20 seconds. We can do this by multiplying the number of strides she took by the distance of each stride, which is given as 140 cm.
From the graph provided, we can see that Jen took 25 strides in the 20-second window. Therefore, the total distance she walked is:
distance = number of strides * distance per stride = 25 * 140 cm = 3500 cm
To convert this to meters, we divide by 100:
distance = 3500 cm / 100 = 35 meters
Finally, we can find Jen's average walking speed by dividing the total distance by the time it took her to walk it, which is 20 seconds:
average speed = distance / time = 35 meters / 20 seconds ≈ 1.75 meters per second
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Answer: 1.33 m/s
Step-by-step explanation:
We need meters per second, not centimeters per second, so convert the stride of 140 cm to meters:
140 cm times 1 m/100 cm = 1.4 meters.
The number of pulses going above the dashed line for the 3 g threshold to
count as strides are 19. Therefore, a total assumed distance of $19 times 1.4 meters is covered in 20 seconds, making the average speed
19 times 1.4/20 = 19 times 0.07 = 1.33m/s.
Jimmy, Jimbo and Jim Bob are all GT Algebra II students. It takes Jimmy 8 minutes to solve a 3-variable substitution problem without a calculator. Together, it takes Jimbo and Jim Bob 6 minutes to solve a 3-variable substitution problem without a calculator. If Jim Bob can solve a problem by himself in 14 minutes, how long would it take Jimbo to solve a problem alone?
It would take Jimbo
Question Blank 1 of 1
type your answer...
minutes to solve a problem alone.
Jimbo approximately 5.09 minutes to solve the problem by himself.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The amount of time it takes Jimbo to solve the problem by himself = x.
The amount of time Jimmy takes to solve the problem.
= 8 minutes
The amount of time it takes Jimmy to solve the problem by himself.
= 1/8
Jimbo and Jim Bob together can solve the problem in 6 minutes, so their combined rate of work is 1/6 of the problem per minute.
The amount of time it takes Jim Bon to solve the problem by himself.
= 1/14
Now,
We can make an equation:
1/8 + 1/x + 1/14 = 1/6
We can solve for x to find the amount of time it would take Jimbo to solve the problem by himself.
1/8 + 1/x + 1/14 = 1/6
Multiply both sides by 168x.
We get,
21x + 168 + 12x = 28x
33x = 168
x = 168/33
x = 5.09
Thus,
Jimbo approximately 5.09 minutes to solve the problem.
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