Considering the relation built the presence of point M on line LN, the numerical length of LN is of 9 units.
What is the relation from the presence of point M on the line LN?Point M splits line LN into two parts, LM and MN, hence the total length is given by:
LN = LM + MN.
From the given data, we have that:
LN = 2x - 5.LM = 3.MN = x - 1.Hence we first solve for x.
LN = LM + MN.
2x - 5 = 3 + x - 1
x = 7.
Hence the total length is:
LN = 2x - 5 = 2 x 7 - 5 = 14 - 5 = 9 units.
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give the answer please
The inverse of a function is given as √x - 1
Inverse of a functionTo get the inverse of any function f(x) we need to ensure that it passes the horizontal line test.
Given the following function
f(x) = (x+1)^2
Let y= f(x) to have:
y = (x+1)^2
Replace y with x to have:
x = (y+1)^2
Make y the subject of the formula
√x =y + 1
Subtract 1 from both sides
√x - 1 = y
Swap
y = √x - 1
Hence the inverse of a function is given as √x - 1
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Question 1 of 10
Which expression is the simplest form of - (3x³ + x²) +2 (x³ - 4x²)?
OA.-2³-32²
OB.-2³-92²
O C. 5x³-7x2²
OD. 52³-82²
SUBMIT
Answer:
B. -x³ - 9x².
Step-by-step explanation:
- (3x³ + x²) +2 (x³ - 4x²)
= -3x³ + 2x³ - x² - 8x²
= -x³ - 9x²
Answer: [tex]\Large\boxed{-x^3-9x^2}[/tex]
Hi there! By my calculation, I got the answer above. However, it doesn't fit any one of the answer choices. I am not sure if I am totally correct, but I have been double-checking my answers. Please let me know whether it's the answer choices mistaken or I am wrong so that I could modify my answer if necessary.
Step-by-step explanation:
Given expression
- (3x³ + x²) +2 (x³ - 4x²)
Expand parenthesis by the distributive property
= -3x³ - x² + 2x³ - 8x²
Combine like terms
= -3x³ + 2x³ - x² - 8x²
[tex]\Large\boxed{=-x^3-9x^2}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
i do not know how to get what they are asking me too
The 9th and the 12th term of an arithmetic progression are 50 and 65 respectively. find the common difference
The first term of the arithmetic progression exists at 10 and the common difference is 2.
How to estimate the common difference of an arithmetic progression?
let the nth term be named x, and the value of the term y, then there exists a function y = ax + b this formula exists also utilized for straight lines.
We just require a and b. we already got two data points. we can just plug the known x/y pairs into the formula
The 9th and the 12th term of an arithmetic progression exist at 50 and 65 respectively.
9th term = 50
a + 8d = 50 ...............(1)
12th term = 65
a + 11d = 65 ...............(2)
subtract them, (2) - (1), we get
3d = 15
d = 5
If a + 8d = 50 then substitute the value of d = 5, we get
a + 8 [tex]*[/tex] 5 = 50
a + 40 = 50
a = 50 - 40
a = 10.
Therefore, the first term is 10 and the common difference is 2.
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The sky wheel has 42 glass enclosed gondolas. What is the measure of each central angle between gondola cars, to the nearest hundredth degree?
A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus, the measure of each central angle required in the question is [tex]8.6^{o}[/tex].
A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus each sector has an equal central angle. Since the sum of the internal angles of a circle is [tex]360^{o}[/tex].
From the given question, it has been stated that the sky wheel has 42 glass-enclosed gondolas. This implies that the sky wheel has been divided into 42 equal sectors.
Therefore,
the measure of each central angle = [tex]\frac{360^{o} }{n}[/tex]
where n represents the number of gondolas (42).
Thus,
the measure of each central angle between gondolas cars= [tex]\frac{360}{42}[/tex]
= 8.5714
The measure of each central angle between gondolas cars is approximate [tex]8.6^{o}[/tex].
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Which equations for the line of best fit do not accurately represent the data in the scatter plot? Select all that apply.
The equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A).
What linear equation best fits the scatter plot?
The equation of the line is represented by a polynomial of the form y = m · x + b, where m is the slope of the line and b is the intercept of the line. The slope is equal to the change in the dependent variable (Δy) and in the independent variable (Δx) and the intercept is the vertical distance of the line with the origin when x = 0.
In accordance with the picture, we notice that the scatter plot indice that Δy < 0 and Δx > 0 and therefore, m < 0. Besides, the intercept of the equation of the line must be greater than zero. Thus, the equation for the line of best fit is the linear function y = - 0.4 · x + 70. (Correct choice: A)
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Write an equation that represents the line.
Use exact numbers.
(-2,-1)
(4,6)
Check the picture below.
to get the equation of any straight line, we simply need two points off of it, so let's use those in the picture
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{6 -1}{4 +2} \implies \cfrac{ 5 }{ 6 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{5}{6}}(x-\stackrel{x_1}{(-2)})\implies y-1=\cfrac{5}{6}(x+2) \\\\\\ y-1=\cfrac{5}{6}x+\cfrac{5}{3}\implies y=\cfrac{5}{6}x+\cfrac{5}{3}+1\implies y=\cfrac{5}{6}x+\cfrac{8}{3}[/tex]
please help me with questions 1 and 2 (with explanations and calculation) thank you so much
4/7+3/7 1/5.3/2-4/10
Answer:
3/10
Step-by-step explanation:
=4/7 + 9/70 - 4/10
=l.C.M of 7 , 70 and 10 =70
=4/7 .10/10 +9/70 -4/10 .7/7
=40/70 +9/70 -28/70
=40+9-28/70
=49-28/70
=21/70
=3/10
In a game, a player earns 100 points for each question answered correctly and earns -30 points for each question answered incorrectly. A player answered 14 questions correctly and 6 questions incorrectly.
Part A) Write a numeric expression to represent the total number of points the player earned.
Part B) Determine the total number of points.
The general expression is 130 x - 600 and total points scored by the player is 1220
A) Let the number of correctly answered questions be x.
∴ Number of incorrectly answered questions will be 20 - x.
+ 100 points is awarded for each question answered correctly while -30 points is awarded for each question answered incorrectly.
Thus, the general equation becomes
= 100x - (20 - x)(-30)
= 100x +30x - 600
= 130x - 600
Thus the general expression becomes 130 x - 600
B) The player answers 14 questions correctly, thus x = 14
Substituting the value of x =14 in the general equation we get,
= 130(14) - 600
= 1820 - 600
= 1220.
Thus the total points scored by the player will be 1220
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6 Find the value of x from the following figures.
1)
Given a polynomial function f(x)=2x²+ 7x+6 and an exponential function g(x)=2+ 5, what key features do f(x) and g(x) have in common?
Both f(x) and g(x) increase over the interval of [-4,∞)
Both f(x) and g(x) have the same x-intercepts of (-2, 0) and (-1.5, 0).
Both fox) and gox) have the same y-intercept of (0,6)
Both f(x) and g(x) have the same range of (-00.01]
Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:
Both f(x) and g(x) have the same y-intercept of (0,6)What is the polynomial function about?Polynomial functions are known to be a kind of an expressions that is made up of a set of variables of different extent or degrees, non-zero coefficients, positive exponents (of variables), and also it is made up of constants.
Note that the equation of the functions are stated as:
f(x) = 2x² + 7x + 6
g(x) = 2^x + 5
The right and next thing to do is to plot a graph of both functions (see image attached)
From the graph, we have the fact that Both f(x) and g(x) have the same y-intercept of (0,6)
Therefore, Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:
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A line passes through the point (7, 3. and has a slope of 2. Write an equation for this line.
Answer:
y = 2x - 11.
Step-by-step explanation:
Use the point-slope form of the straight line.
y - y1 = m(x - x1) where m = slope and (x1, y1) is the given point.
Here m = 2 and (x1, y1) = (7,3) so the equation is:
y - 3 = 2(x - 7)
y - 3 = 2x - 14
y = 2x - 11
please help if u cannot skip
The statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
How to determine which statement is true?To determine which statement is true, we need to know the conditions for continuity and differentiablity of a function.
Conditions for continuity and differentiablity of a function.For a function f(x) to be continuous at a point x = a, then both the left hand limit of f(x) and the right hand limit of f(x) as x → a must be equal. That is [tex]\lim_{x \to a^{-} } f(x) = \lim_{x \to a^{+} } f(x)[/tex]. So, [tex]\lim_{x \to a^{} } f(x)[/tex] must exist since [tex]\lim_{x \to a^{-} } f(x) = \lim_{x \to a^{+} } f(x) = \lim_{x \to a^{} } f(x)[/tex]Also, for a function to be differentiable at a point x = a, it must also exist at x = a
So, since f(x) = {x² - 1 if -1 ≤ x ≤ 3 and x²/3 if 3 < x ≤ 8}
From the equality on the first condition,we see that f(x) is exists at x = 3 but is not continuous since f(x) changes to another function when x > 3. So,left hand limit of f(x) and the right hand limit of f(x) as x → 3 are not equal.
That is [tex]\lim_{x \to 3^{-} } f(x) \neq \lim_{x \to 3^{+} } f(x)[/tex] . Thus, the function is discontinuous at x = 3.
For differentiability, both conditions must be met. Since only one condition is met, it is non-differentiable.
So, the function is discontinuous and non-differentiable at x = 3.
So, the statement that is true about the function is D. it is discontinuous and non-differentiable at x = 3.
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A cupcake store has 5 different kinds of cupcakes: chocolate, vanilla, lemon, strawberry, and coffee. Assuming there are at least 12 of each kind of cupcake, how many ways can you choose 12 cupcakes
Assuming there are at least 12 of each kind of cupcake, number of ways can you choose 12 cupcakes is; 1399358844975 ways
How to solve probability combination?We are given the quantity of each type of cupcake as follows;
Number of types of cupcakes = 5
Number of Chocolate Cupcakes = 12
Number of Vanilla Cupcakes = 12
Number of Lemon cupcakes = 12
Number of Strawberry Cupcakes = 12
Number of coffee cupcakes = 12
Thus, total number of cupcakes will be gotten by adding all the quantities given above of the different types of cupcakes and we will get; Total number of cupcakes = 12 + 12 + 12 + 12 + 12
Total number of cupcakes = 60
Now, since there is no order of selection, then the number of ways that you can choose 12 cupcakes will be gotten by using the combination formula which is; nCr = n!/(n!(n - r)!)
Thus, number of ways that you can choose 12 cupcakes =
60C12 = 60!/(12! * (60 - 12)!) = 1399358844975 ways
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What would be the coefficient of determination r2 if the total sum of squares (sst) is 90 and the sum of squares due to error (sse) is 0 (zero)?
The coefficient of determination is 1.
Given
Total Sum of squares (SST) = 90
Sum of squares due to error (SSE) = 0
We have to find coefficient of determination.
The correlation of determination is the ratio of the explained variation to the total variation.
The coefficient of determination is used to analyze how differences in one variable can be explained by a difference in a second variable.
The coefficient of determination is also called r-squared or r-square.
Its the percentage of variation in the y-variable(response) that can be explained by the least squares regression line of y on x.
Coefficient of determination can be found with the following formula:
Formula of coefficient of determination :
[tex]R^{2} = 1 - \frac{SSE}{SST}[/tex]
= 1 - [tex]\frac{0}{90}[/tex]
= 1 - 0
= 1
[tex]R^{2}[/tex] = 1
Therefore,
The coefficient of determination is 1.
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The odds in favor of a horse winning a race are 9:5. find the probability that the horse will win the race.
Answer:
9/14.
Step-by-step explanation:
The probability is given as a fraction or percentage.
9:5 odds in favour of a horse winning means the horse will win 9 races for every 5 it does not win.
So the probability that this horse will win is 9/(9+5)
= 9/14.
Frank went to the playground at 5:20 P.M. He played on the slide for 45 minutes and the swings for 5 minutes, then went home. What time was it when Frank left the playground?
The time it was when Frank left the playground is; 6:10 PM.
How to calculate time difference?We are given;
Time at which Frank went to the playground; 5:20 p.m
Amount of time that frank played on the slide = 45 minutes
Amount of time that frank swings on the play ground = 5 minutes
Now, we are told that after he played on the slide and swung on the playground, that he went home.
Thus, he spent a total time of 45 + 5 = 50 minutes on the playground before going home.
Thus, time he went home = 5:20 p.m + 50 minutes = 6:10 p.m
Thus, we can conclude that the time it was when Frank left the playground is; 6:10 PM.
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Which intervals show f(x) decreasing? Check all that apply.
The intervals which represents those in which case the function, f(x) is reducing are as follows; [–2.5, –2], [–2, –1.5], [1.5, 2], [2, 2.5].
Which intervals naming the answer choices show the function f(x) decreasing?It follows from the complete task content that the x-intervals between which the function value of f(x) is reducing are to be identified from the graph as attached.
On this note, by observation on the graph, it follows that from between the interval; [–2.5, –2], the function f(x) is decreasing.
Also, between the interval; [–2, –1.5], the function f(x) is decreasing.
Also, between the interval; [1.5, 2], the function f(x) is decreasing.
Also, between the interval; [2, 2.5], the function f(x) is decreasing.
Remark: The answer choices are as follows; [–2.5, –2] [–2, –1.5] [–1, 1] [1.5, 2] [2, 2.5) [2.5, 3]
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Gustavo is in a contest where he will win one of four possible prizes. he creates a four-part spinner to represent the four prizes that he has an equal chance of winning: a video game system, a bicycle, a watch, and a gift card. he spins the spinner several times to demonstrate the likelihood of winning a certain prize. what is true about gustavo’s method of data collection and his data on the possible prizes?
Answer:
Gustavo used a simulation where the data is quantitative’
The terminal side of an angle
intersects the unit circle at point
Answer:
[tex] - \frac{ \sqrt{2} }{2} [/tex]
Step-by-step explanation:
The sine of an angle is equal to the y coordinate point where the terminal side of the angle intersects the unit circle.
If the population standard deviation σ=25. What is the required minimum sample size to construct a 95 confidence level for the population mean with an allowable error of ±3?
The required minimum sample size to construct a 95% confidence level for the population mean is 267.
In this question,
In the probability and statistics theory, the confidence interval of the population parameter is the estimated range of values we are sure with a certainty that our parameter will lie within, the range being calculated from the sample obtained. The smaller is the margin of error, the more confidence we have in our results.
The population standard deviation, σ = 25
Confidence level for the population mean = 95%
Margin of error = ±3
Let n be the sample size of the population
The z-score for the confidence level of 95% for the population mean is 1.96.
The formula of margin of error is
[tex]E=\frac{z \sigma}{\sqrt{n} }[/tex]
Now, the sample size of the population can be calculated as
[tex]n=(\frac{z\sigma}{E} )^{2}[/tex]
On substituting the above values,
⇒ [tex]n=(\frac{(1.96)(25)}{3} )^{2}[/tex]
⇒ [tex]n=(\frac{49}{3}) ^{2}[/tex]
⇒ [tex]n=(16.33)^{2}[/tex]
⇒ n = 266.77 ≈ 267
Hence we can conclude that the required minimum sample size to construct a 95% confidence level for the population mean is 267.
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Suppose that a 2 by 10 rectangular grid of seats is filled with people. On the
blow of a whistle, all 20 people get up from their current seat and move to an orthogonally adjacent seat. How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?
688,747,536 ways in which the people can take the seats.
How many ways are there for everyone to do this so that at the end of the move, each seat is taken by exactly one person?There is a 2 by 10 rectangular greed of seats with people. so there are 2 rows of 10 seats.
When the whistle blows, each person needs to change to an orthogonally adjacent seat.
(This means that the person can go to the seat in front, or the seats in the sides).
This means that, unless for the 4 ends that will have only two options, all the other people (the remaining 16) have 3 options to choose where to sit.
Now, if we take the options that each seat has, and we take the product, we will get:
P = (2)^4*(3)^16 = 688,747,536 ways in which the people can take the seats.
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Hey I'm sunny, and i request someone's help (please)
1. Value of b (b - 4.21 = 87.654)
2. Divide: 1.86 and 8.4
3: Compare: 1.92
that's it
Bye! - SunnyBunny <3
The computation shows that the value of b will be 91.864.
How to illustrate the information?From the information given, we are told to find the value of b (b - 4.21 = 87.654). This will be:
b - 4.21 = 87.654
b = 87.654 + 4.21
b = 91.864
Also. dividing 1.86 and 8.4 will be:
= 1.86/8.4
= 0.2213
Therefore, the values are 91.864 and 0.2213.
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triangle ABC is reflected across the y-axis and then dilated by a factor of 1/2 centered at the origin. which statement correctly describes the resulting image
Answer:
Step-by-step explanation:
The reflection preserves the side lengths and angles of triangle ABC. The dilation preserves angles but not side lengths.
Can someone help me find the value of x for the triangle?
Answer:
109°
Step-by-step explanation:
The sum of angles in all triangles is equal to 180. For this given triangle, we can solve for x.
48° + 23° + x° = 180°
180° - 71° = x°
x = 109°
The price of a bus ticket to Saskatoon is $180. This bus has 56 seats. The bus company is considering dropping the bus fare as part of a promotion to increase the ridership on that route. Lately, the busses have only been at half capapcity. The bus company's research shows that for every $5 decrease they will gain 2 more riders.
a) define variables and set up an equation to represent this scenario
b) What is the maximum revenue the bus company can earn and what will be the cost of a ticket when the revenue is at a maximum
If the price of one ticket of bus is $180 and the bus has 56 seats then the maximum revenue that it can earn is $5107.6
Given that the price of a bus ticket to Saskatoon is $180 and the bus has 56 seats.
We are required to find the maximum revenue that the bus company can earn.
Suppose x represents the number of seats, y represents the total amount.
Price=$156
Seats=56
When the bus is of half capacity the bus seats will be 28.
As price decreases th rider gains 2 more.
Revenue equation.
y=(156.5x)(28+2x)-------------1
Expanding the equation.
y=4368-140x+312-10[tex]x^{2}[/tex]
Differentiating with respect to x.
dy/dx=0-140+312-20x
=172-20x
Put dy/dx=0
172-20x=0
x=8.6
Substitute the value of variable x in the equation 1.
y=(156-5x)(28+2x)
=$5107.6
Hence the maximum revenue that the bus company can earn is $5107.6.
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Apply the distributive property to create an equivalent expression. 9(a + 4b + 3c)
[tex] \rm9(a + 4b + 3c) \\ 9(a) + 9(4b) \rm+ 9(3c) \\ \rm 9a + 36b + 27c \\ \therefore \tt9(a + 4b + 3c) = 9a + 36b + 27c[/tex]
Convert 352 base 6 to base 4.
Answer:
(2030)4
Step-by-step explanation:
Base 6 to decimal calculation:
(352)6 = (3 × 62) + (5 × 61) + (2 × 60) = (140)10
Decimal to base 4 calculation:
Divide by the base to get the digits from the remainders:
= (2030)4
Still have any questions?
Do hit me up or contact me
The answer is 2030.
First, convert from base 6 to base 10.
3 × 6² + 5 × 6¹ + 2 × 6⁰108 + 30 + 2140Now, convert from base 10 to base 4.
140 ÷ 4 = 35 ⇒ R = 035 ÷ 4 = 8 ⇒ R = 38 ÷ 4 = 2 ⇒ R = 02 ÷ 4 = 0 ⇒ R = 2Connecting the digits, the answer is : 2030
in the diagram below all angles are given in degrees(°)
find X with 50°,3x,X,X+110
The value of x in the angles of Quadrilateral is 52 degree.
According to the statement
we have given a four angles and we have to find the value of x in these give angles.
From given 4 angles it is clear that the these angles are of a quadrilateral.
And we know that the
A quadrilateral is a four-sided polygon, having four edges and four corners.
And the sum of all angles of a quadrilateral is 360 degree.
so,
50° + 3X + X + (X+110) = 360 degree
50° + 4X + (X+110) = 360 degree
50° + 5X + 110 = 360 degree
160° + 5X = 360
5X = 360-100
5X = 260
X = 52 degree.
So, The value of x in the angles of Quadrilateral is 52 degree.
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