The runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.
What is the coefficient?
A coefficient is a number multiplied by a variable. Examples of coefficients: In the term 14 c 14c 14c, the coefficient is 14. In the term g, the coefficient is 1.
A) The mechanical energy lost due to friction can be calculated as follows:
Initial kinetic energy of the runner: KE = 0.5 * m * v² = 0.5 * 80 kg * (4.7 m/s)² = 140.29 J
The force of friction acting on the runner is given by:
[tex]friction_{force} = friction_{coefficient} * normal_{force}[/tex]
where,
[tex]friction_{coefficient} = 0.70[/tex]
[tex]and normal_{force} = m * g (g = 9.8 m/s^{2} )[/tex]
The normal force is given by:
[tex]normal_{force} = m * g = 80 kg * 9.8 m/s^{2} = 784 N[/tex]
Therefore, the force of friction acting on the runner is: [tex]friction_{force} = 0.70 * 784 N = 548.8 N[/tex]
The work done by friction is given by:
[tex]W = friction_{force} * distance[/tex]
Since the speed of the runner is reduced to zero, the work done by friction is equal to the change in kinetic energy:
[tex]W = KE_{final} - KE_{initial}[/tex]
= 0 - 140.29 J = -140.29 J
So, the mechanical energy lost due to friction is 140.29 J.
B) The distance the runner slides can be calculated using the work-energy theorem, which states that the work done on an object is equal to its change in kinetic energy.
The work done by friction is given by: W = friction_force * distance
Since the friction force is constant, the work done by friction is equal to the change in kinetic energy:
[tex]W = KE_{final} - KE_{initial}[/tex]
= 0 - 140.29 J = -140.29 J
Rearranging this equation and substituting in the known values, we get:
[tex]distance = -W / friction_{force}[/tex]
= -140.29 J / 548.8 N = 0.255 m or 25.5 cm
Hence, the runner slides a distance of approximately 0.255 meters or 25.5 centimeters, and the mechanical energy lost due to friction is 140.29 J.
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han types the letters a, s, d, f, and then repeats them over and over what is the fith letter diego will type
The fith letter Diego will type is the letter a
How to determine the fith letter diego will typeFrom the question, we have the following parameters that can be used in our computation:
Letters: a, s, d and f
When the letters are repeated, we have
a s d f a s d f a s d f a s d f a s d f......
using the above as a guide, we have the following:
Fifth letter = a
Hence. the fifth letter is a
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What is the conjugate? x-\sqrt(2)
Answer:
[tex]x+\sqrt{2}[/tex]
Step-by-step explanation:
The conjugate of [tex]x-\sqrt{2}[/tex] would simply be [tex]x+\sqrt{2}[/tex]. All you have to do is simply change the sign to its opposite.
Suppose that So, S1, S2,... is a sequence of subsets of N. Which one of the following sets is guaranteed to be different from all sets in the sequence? (a) S = {n | n & Sn²} (b) S = {n | n² & Sn²} (c) S = {n²| n & Sn²} (d) S = {n² | n² & Sn} (e) S = {n² | n & Sn} Explain why your chosen set is guaranteed not to be in the sequence So, S1, S2, ...
Suppose that So, S1, S2,... is a sequence of subsets of N the following sets is guaranteed to be different from all sets in the sequence is S = {n² | n² & Sn}.
Subsets are a part of the mathematical concept of sets. A set is anything that is wrapped in curly braces, such as "a,b,c,d." If set A is a collection of even integers and set B is composed of the numbers 2, 4, and 6, then set A is the superset of set B and set B is said to be a subset of set A. Review Sets Subset and Superset for further details.
Set A is referred to as a subset of Set B if each element of Set A is also present in Set B. In other words, Set B includes Set A.
As an illustration, if set A has the elements X, Y, and set B contains the elements X, Y, and Z, then set A is the subset of set B.
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Complete the sentence below.
The time shown is
15:40
past/to
in the morning/afternoon
Answer:
uajajjahajajaaajjsjaja
The time shown is 15:40, which indicates that it is 20 minutes to 4 o'clock in the afternoon.
How to complete the statementThe time displayed is 15:40, which is consistent with a 24-hour clock. It indicates that there are now 20 minutes left until 6:00.
The time 15:40 is in the afternoon because the afternoon begins at 12:00 and lasts until 18:00.
The 24-hour clock format avoids any doubt regarding AM (morning) or PM (afternoon/evening), it is vital to highlight.
As a result, 15:40 specifies that it is in the afternoon and that there are still 20 minutes until 4 o'clock.
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Question 1(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed.
Question 2(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The table shows the length, in inches, of fish in a pond.
11 19 9 15
7 13 15 28
Determine if the data contains any outliers. If so, list the outliers.
There is an outlier at 28.
There is an outlier at 7.
There are outliers at 7 and 28.
There are no outliers.
Question 3(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 11, with tick marks every one unit up to 25. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 20 on the number line. A line in the box is at 19. The lines outside the box end at 12 and 24.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 12.
The IQR is the best measure of variability, and it equals 12.
The range is the best measure of variability, and it equals 3.
Question 4(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
2 0, 1, 3, 5, 7
3 2, 5, 7, 9
4
5 1
6 5
Key: 2|7 means 27
What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 16.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 16.
Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The table shows the number of goals made by two hockey players.
Player A Player B
2, 3, 1, 3, 2, 2, 1, 3, 6 1, 4, 5, 1, 2, 4, 5, 5, 11
Find the best measure of variability for the data and determine which player was more consistent.
Player B is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with a range of 10.
Player A is the most consistent, with an IQR of 1.5.
Player A is the most consistent, with a range of 5.
Question 6(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the cost of used books in dollars.
A horizontal line starting at 1 with tick marks every one unit up to 9. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There are two dots above 1, 2, 3, 5, and 6. There are four dots above 7.
Which measure of center is most appropriate to represent the data in the graph, and why?
The median is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The mean is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are outliers present.
Question 7(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of center for the data, and what is its value?
The median is the best measure of center, and it equals 6.5.
The mean is the best measure of center, and it equals 7.
The median is the best measure of center, and it equals 7.
The mean is the best measure of center, and it equals 6.5.
The median of 20 is the most accurate to use since the data is skewed.
Option C is the correct answer.
What is a histogram?A histogram is a representation of the distribution of data with intervals.
We have,
The data given shows a histogram that is skewed to the right.
Now,
Since the data is skewed.
The median is a better measure of the center of data than the mean.
Now,
Arrange the data in order:
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
Median = middle value.
Median = 20
Thus,
The median of 20 is the most accurate to use since the data is skewed.
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Answer:
your question is a bit confusing...
Step-by-step explanation:
You are examining the data with a stem-and-leaf plot. Here is the start of the plot. Finish the plot.
The stem-and-leaf plot is finished as follows:
4| 1 3 7.
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
To complete the stem-and-leaf plot, we must obtain the measures above 40 from the table, which are given as follows:
41, 43 and 47.
Considering the format of the plot, the plot is completed as follows:
4| 1 3 7.
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Use the cross products property to solve the proportion.9/10=d/6.4
Using the cross product property, the value of d is 5.76.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s.
If both these ratios are proportional, then we can write it as p : q = r : s or p/q = r/s
Given proportional relation is,
9 / 10=d / 6.4
Doing the cross multiplication,
9 × 6.4 = 10 × d
57.6 = 10d
d = 57.6 / 10
d = 5.76
Hence the solution of the proportion is d = 5.76.
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A wildlife biologist captured and released 34 trouts from two different lakes and measured them to the nearest inch. She captured 17 of the fish from Fralest Lake and 17 of the fish from Lake Reverwalk. She then calculated the following statistical information.
Based on these samples, what generalization can be made?
A. At least half of the trout in Lake Reverwalk measure between 12 and 18 inches.
B. At least half of the trout in both lakes measure between 12 and 18 inches.
C. Not enough information is provided to draw any of these conclusions.
D. At least half of the trout in Fralest Lake measure between 12 and 18 inches.
The requried generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Option B is correct.
What is Statistic?The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
Interquartile range (IQR), The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.
In the given question we have 3 IQR data sets that jointly vary from 10 to 17 by this we can conclude that, at least half of the trout in both lakes measure between 12 and 18 inches.
Thus, the requried generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Option B is correct.
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Rewrite 5^(2 .)5^(4) using a single exponent
Please help due tonight
Answer:
x = 24, y = 12
Step-by-step explanation:
We can use the law of sines to solve for x
The law of sines says the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides (and angles)
In this triangle
the side with length 12√3 is opposite 60°
the side with length x is opposite 90°
Using the law of sines,
[tex]\dfrac{12\sqrt{3}}{\sin60}=\dfrac{x}{\sin 90}\\[/tex]
sin 60 = [tex]\dfrac{\sqrt{3}}{2}[/tex]
sin 90 = 1
[tex]\rightarrow \dfrac{12\sqrt{3}}{\dfrac{\sqrt{3}}{2}}=\dfrac{x}{1}\\\\\\x = 12\sqrt{3} \div \dfrac{\sqrt{3}}{2}}\\\\\textrm{When dividing fractions, flip the divisor and multiply}\\\\\rightarrow 12\sqrt{3} \times \dfrac{2}{\sqrt{3}}\\\\\textrm{$\sqrt{3}$ cancels out from numerator and denominator}:\\\\\\\rightarrow x = 12 \times 2 = \boxed{24}\\\\\\[/tex]
To solve for y we can again use the law of sines
[tex]\dfrac{y}{\sin 30} = \dfrac{x}{\sin 90}\\\\\textrm{again, as before $\sin 90$ is 1}\\\\\rightarrow \dfrac{y}{\sin 30} = x\\\\\rightarrow x = \dfrac{y}{\sin 30}\\\\\rightarrow y = x \sin 30\\\\\sin30 = \dfrac{1}{2}[/tex]
So y = x/2 = 24/ 2 = 12
ans:
x = 24, y = 12
Note
Another way to solve this question is to first recognize the triangle as a 30-60-90 right triangle
In a triangle of this kind, if the longest side side is a, the shortest side is a/2, and the third side is √3/2a
We could have solved this in this manner also
Here longest side = x, shortest side is y
The other side is 12√3 = x √3/2
So x = 12√3 ÷ √3/2 = 24 (as in the first method)
y = x/2 = 12
This approach is ok too, I find it less intuitive and we have to remember the ratios
A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n (*)A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n (*). Observe that, if n=0 or 1 , the Bernoulli equation is linear. For other values of n , the substitution u=y^(1-n) transforms the Bernoulli equation into the linear equation du/dx + (1-n)P(x)u=(1-n)Q(x).Consider the initial value problemxy'+y=3xy^2, y(1)=-3(a) This differential equation can be written in the form (*) withP(x)=?Q(x)=?n=?(b) The substitution u=BLANK will transform it into the linear equation du=dx+ BLANK u=BLANK(c)Using the substitution in part (b), we rewrite the initial condition in terms of x and uu(1)=?(d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c).u(x)=?(e)(e) Finally, solve for yy(x0=?
The solution of the the linear equation is y = 3/(x - 9xlnx)
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
xy' + y = 3xy², y(1) = -3
This is Bernoulli equation: y' + (1/x)y = 3y²;
Let u = y^(1 - 2) = 1/y is new function.
Then u' = - y'/y
or
y' = -u'/u²;
y = 1/u.
Substitute all this in our ODE: - u'/u² +(1/x)/u = 3/u², or u' - (1/x)u = -3.
we get linear, 1st order not homogenies ODE:
integrated factor:
μ = e∫(-1/x)dx = e-lnx = 1/x²
u'·1/x - 1/x2 = -3/x;
(u/x)' = - 3/x; u/x
= ∫(-3/x)dx;
u/x = -3lnx + C;
u = - 3xlnx + Cx;
y =1/u = 1/(- 3xlnx + Cx)
To get C ,use initial conditions:
y(1) = 3;
3 = 1/(-3·1·ln1 + C);
C = 1/3;
y = 3/(x - 9xlnx)
The solution of the the linear equation is y = 3/(x - 9xlnx)
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The solution of the the linear equation is y = 3/(x - 9xlnx)
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
xy' + y = 3xy², y(1) = -3
This is Bernoulli equation: y' + (1/x)y = 3y²;
Let u = y¹⁻² = 1/y is new function.
Then u' = - y'/y
or
y' = -u'/u²;
y = 1/u.
Substitute all this in our ODE: - u'/u² +(1/x)/u = 3/u², or u' - (1/x)u = -3.
we get linear, 1st order not homogenies ODE:
integrated factor:
μ = e∫(-1/x)dx = e-lnx = 1/x²
u'·1/x - 1/x2 = -3/x;
(u/x)' = - 3/x; u/x
= ∫(-3/x)dx;
u/x = -3lnx + C;
u = - 3xlnx + Cx;
y =1/u = 1/(- 3xlnx + Cx)
To get C ,use initial conditions:
y(1) = 3;
3 = 1/(-3·1·ln1 + C);
C = 1/3;
y = 3/(x - 9xlnx)
The solution of the the linear equation is y = 3/(x - 9xlnx)
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prime factorization of 756
The solution is, prime factorization of 756 = 3*2*3*2*3*7
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
756
we know,
756 = 6*6*21
=3*2*3*2*3*7
as, we know, 2,3,7 all are prime.
so, prime factorization of 756 = 3*2*3*2*3*7
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a home with a swimming pool recently sold in the area for 250,000 another home in the same area that does not have a swimming pool but is similar in all other respects sold recently for 230,000 what can you assume from this information.a. All swimming pools cost $20.000b. The aproximate value of pool in that area is $20.000c. No home without a pool in that area will sell for more than $230.000d. Homes without a pool will sell faster in that area than homes with a pool
The correct answer is option b.The approximate value of pool in that area is $20.000c.
What is approximate value?A value that is similar to another value but not exactly equal to it is referred to as an approximation number. When the outcomes of the numerical calculations are unknown, the approximation is applied. They are typically used when greater place value decimal numbers emerge as a result.
Approximate value of a pool in the area = Value of home with a swimming pool in the area - Value of home without a swimming pool in the same area.
Value of home with a swimming pool in the area = $250,000
Value of home without a swimming pool in the same area = $230,000.
The approximate value of pool in the area = 250000 - 230000 = 20000.
Hence, the correct answer is option b. The approximate value of pool in that area is $20.000c.
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Pica is a disorder in which individuals eat substances
People with pica, a type of eating disorder, compulsively consume one or more non-food objects like ice, clay, paper, ash, or soil.
what is eating disorder ?Recurrent episodes of binge eating are the hallmark of a specific type of eating disorder called binge eating disorder. Food addiction and compulsive overeating are both symptoms of this eating disorder. Uncontrollable and quick eating without feeling hungry, as well as negative emotions, depressive symptoms, and guilt over the eating, are prominent symptoms of this illness.
given
People with pica, a type of eating disorder, compulsively consume one or more non-food objects like ice, clay, paper, ash, or soil.
Pica is a kind of pagophagia. It entails consuming ice, snow, or ice water excessively.
Individuals who have pica are not forced to consume ice due to a physical condition like anaemia.
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Rehan proved by mathematical induction that for all the positive integers,
is divisible by 3. Can you find an integer counterexample to show that this statement is not true? Explain.
A counterexample that shows that all the integers are not divisible by 3 is given as follows:
2.
How to obtain the counterexample?The statement for this problem is given as follows:
"All the positive integers are divisible by 3".
The statement is false, as only numbers whose sum of the digits is a multiple of 3 are divisible by 3, hence for example, the number 2 is not divisible by 3.
The counterexample is the statement that proves that a conjecture(another statement) is false, hence the number 2 is the counterexample showing that not all positive statements are divisible by 3.
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College level
Attached photo.
The value of b form the logarithmic equation [tex]log_b}3=0.7925[/tex] is 3.9998688.
What are logarithms?In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
Given that, [tex]log_b}25=2.3219[/tex] and [tex]log_b}3=0.7925[/tex].
Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.
We know that, logₐN=x is written exponential form as aˣ=N
Here, [tex]b^{2.3219}=25[/tex]
b=4.00006709
[tex]b^{0.7925}=3[/tex]
b=3.9998688
Therefore, the value of b is 3.9998688.
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Find the volume of the figure. Express the answer in terms of pi and then round to the nearest whole number.
Answer:
5025π m³
Step-by-step explanation:
the figure consists of two figures;
a cone and phere
volume of a cone=1/3πr²h
volume of hemisphere=2/3πr³
1/3×π×15×15×37=2775π
2/3×π×15×15×15=2250π
sum up the volumes
2775π+2250π
=5025π m³
Translate triangle P by the vector 2
y
P
4
3
No W
2
1
-5 -4 -3 -2 -10
-1
2344
-2
-3
-4
2 3 4 5
Step-by-step explanation:
The translation of triangle P by the vector (2, 3) results in the triangle being moved 2 units to the right and 3 units up. The new coordinates of the triangle are (6, 7), (4, 6), and (3, 5).
Use the method for solving Bernoulli equations to solve the following differential equation. dy dx **=6x?y? Ignoring lost solutions, if any, the general solution is y= (Type an expression using x as the variable.)
The Bernoulli equation for this particular differential equation is [tex]dy/dx = 6x(y-1)[/tex] the final solution is [tex]y = x^3 + 1[/tex].
The Bernoulli equation for this particular differential equation is [tex]dy/dx = 6x(y-1)[/tex]. To solve the equation, we first use the substitution u = y – 1. This substitution simplifies the equation to [tex]dy/dx = 6xu[/tex], which is a first-order linear equation with constant coefficients. Now we can use the method for solving Bernoulli equations to find the solution.
We first find the integrating factor, which is [tex]I(x) = exp(∫6xdx)= exp(3x^2)[/tex]. Then we multiply both sides of the equation by I(x) to get [tex]I(x)dy/dx = 6xI(x)u[/tex]. We can now integrate both sides with respect to x and get the general solution of [tex]y = u + 1 = (1/I(x))∫6xI(x)dx + 1[/tex]. After calculating the integral, the final solution is [tex]y = x^3 + 1[/tex].
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If 12 subtracted from 7 time a number is equal to five times the sum of the number and 2,find the number.
Answer:
7-12=x
5(x+2)
7-12=-5
5(-5+2)
5(-3)
-15Step-by-step explanation:
Simplify the following union and or intersection. [2,3] ∪ (3,∞)
The union of the set elements is [2, ∞)
How to determine the union or the intersectionFrom the question, we have the following parameters that can be used in our computation:
[2,3] ∪ (3,∞)
The above is a union set
The definition of the union set is that we write out all the elements in the set
Using the above as a guide, we have the following:
[2,3] ∪ (3,∞) = [2, ∞)
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Which two integers is /80
[tex] \sqrt{80} [/tex]
between? (A) 9 and 10 B) 7 and 8 8 and 9 D 11 and 12
Find the point slope form of a line with Slope: 6/7 that passes through (-5,4)
The equation of the line with Slope: 6/7 that passes through (-5,4) will be 7y = 6x + 58.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is 6/7. Then the equation is given as,
y = (6/7)x + c
The equation passes through (-5, 4). Then we have
4 = (6/7) (-5) + c
4 = -30/7 + c
c = 58 / 7
Then the equation is given as,
y = (6/7)x + 58/7
7y = 6x + 58
The equation of the line with Slope: 6/7 that passes through (-5,4) will be 7y = 6x + 58.
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Missing value in frequency distribution table
Based on the data, the total number of people would be 350. So the missing value in the table would be 54.
How to find missing value from table?To find the missing value of people in the graph we must do the following procedure. We must add the number of people who are already registered in the graph in the frequency column.
Additionally, we must establish a total number of people, for example 350. In this case we must subtract the result of the people registered in the graph from the total number of people:
350 - 295 = 54.
Then we can establish that the remaining number of people (54) corresponds to the frequency table.
Note: This question is incomplete. The complete information is here:
Total number of people: 350
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If you want to solve the equation by completing the square, then rearrange the equation as x2−6x=11 and add 9 to each side. If you want to solve the equation by using the quadratic formula, rearrange the equation as x2−6x−11=0 and substitute the values of 1, −6 , and −11 into the formula. Round to the nearest hundredth.
Solution of equation x² - 6x = 11 are, x = 7.47 and x = - 1.47
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The equation is,
⇒ x² - 6x = 11
Now, Solve the equation by completing the square as,
⇒ x² - 6x = 11
Add 9 both side, we get;
⇒ x² - 6x + 9 = 11 + 9
⇒ (x - 3)² = 20
⇒ x - 3 = √20
⇒ x - 3 = ± 4.47
This gives two solutions,
⇒ x - 3 = 4.47
⇒ x = 4.47 + 3
⇒ x = 7.47
⇒ x - 3 = - 4.47
⇒ x = - 4.47 + 3
⇒ x = - 1.47
Thus, Solution of equation x² - 6x = 11 are,
⇒ x = 7.47 and x = - 1.47
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Select the correct answer. If f(x)=x^2/x+3, find f(x+h)
The function operation f( x + h ) in the function f(x) = x² / (x + 3 ) is ( x + h )² / (x + h + 3 ).
What is the function operation f(x + h ) in the given function?A function is simply a relationship that maps one input to one output.
Given that;
f(x) = x² / (x + 3 )f( x + h ) = ?To determine f( x + h ), replace all the occurrence of x with (x + h) in the function and simplify.
f(x) = x² / (x + 3 )
f(x + h) = ( x + h )² / (( x + h ) + 3 )
f(x + h) = ( x + h )² / (x + h + 3 )
Therefore, the operation f(x + h) equals ( x + h )² / (x + h + 3 ).
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Which of the following would NOT be an example of a boogie-woogie bass line?
A. F-A-C-D-Eb-D-C-A
B. G-B-D-E-F-E-D-B
C. C-D-E-F-G-F-E-D
D. C-E-G-A-Bb-A-G-E
Answer: Option D, "C-E-G-A-Bb-A-G-E" is not an example of a boogie-woogie bass line. Boogie-woogie is a genre of blues music that is characterized by a repetitive bass pattern that usually consists of 8th notes. The bass line is usually made up of the root note, fifth note, and octave of a chord, and it is played in a swung or shuffle rhythm. The most common boogie-woogie bass line consists of the notes of a I-IV-V chord progression in a 12-bar blues structure. Option D deviates from this typical pattern and therefore would not be considered a boogie-woogie bass line.
Step-by-step explanation:
Express the given quantity as a single logarithm. (Enter your answer using function notation - use In(x) instead of In x.) In(a + b) + In(a - b) – 4 Inc Differentiate the function. (Enter your answer using function notation - use In(x) instead of In x.) f(x) = 5.2 In(4x) - 52 Differentiate the function. (Enter your answer using function notation - use In(x) f(t) = sin(3 In x) Differentiate the function. (Enter your answer using function notation - use In(x) f(x) = ln(4 sin’z)
The given quantity as a single logarithm are as follows:
1. 20.8In(4x)
2. 3cos(3Inx)Inx
3. 4cos'zln'z
What is function?Function ve process of state of instruction that text input papa mississippi start x and output function ladki company it's a programming language allow me the code to create the complex command with simple instruction for example function in the used to it to numbers together a generator and i'm number from san also be combined to create more public sequence are instruction.
Express the given quantity as a single logarithm: In(a + b) + In(a - b) - 4Inx = In[(a+b)(a-b)] - 4Inx
Differentiate the function f(x) = 5.2In(4x) - 52: f'(x) = 20.8In(4x)
Differentiate the function f(t) = sin(3Inx): f'(t) = 3cos(3Inx)Inx
Differentiate the function f(x) = ln(4sin'z): f'(x) = 4cos'zln'z
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100 POINTS HELPWhich column on an accounting worksheet may not balance at the end of an accounting period?
A. The Adjusted Trial Balance
B. The Trial Balance
D. The Adjustments
C. The Income Statement
Answer: C
Step-by-step explanation:
The column on an accounting worksheet that may not balance at the end of an accounting period is the Adjustments column.
The Adjustments column on an accounting worksheet includes all the adjusting entries that are needed to update the accounts before the financial statements are prepared. These adjustments can include accruals, deferrals, depreciation, and other adjustments that need to be made to the accounts to accurately reflect the financial position of the company.
Since the Adjustments column is used to record these adjusting entries, it is possible that this column may not balance at the end of the accounting period, as the adjustments may not perfectly offset each other. However, this is not a problem, as the purpose of the worksheet is to help prepare the financial statements, not to balance each individual column.
Therefore, the correct answer is option D, the Adjustments column.
Answer:
C. The Income Statement
Step-by-step explanation:
The Income Statement column on an accounting worksheet may not balance at the end of an accounting period.
An accounting worksheet is a tool used by accountants to help organize and summarize financial information and to prepare financial statements. The worksheet is typically a multi-column form that includes columns for the unadjusted trial balance, adjustments, adjusted trial balance, income statement, and balance sheet.
The Adjustments column is used to record adjusting entries and to update the account balances to reflect accruals, deferrals, and other accounting adjustments. The Adjusted Trial Balance column is the result of the adjustments made in the Adjustments column and should include all the account balances that will be used to prepare the financial statements.
A credit sale of $2700 is made on July 15, terms 2/10, n/30, on which a return of $300 is granted on July 18. What amount is received as payment in full on July 24?
Answer:
$2,450
Step-by-step explanation:
2/10, n/30 = discounts of 2%
Credit sale = $2,700
Sale return = $200
Net Receivable =$ 2,700 - $ 200 = $2,500
Discount = 2,500 x %2 = 50
Payment Receipt = $2,500 - $50 = $2,450
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