Answer:
y = (-1/3)x + 2/3
Step-by-step explanation:
We can use the slope-intercept form of a linear equation to find the equation of the line passing through the points (5, -1) and (2, 2). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the given points, we have:
slope = (2 - (-1)) / (2 - 5) = -1/3
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We can use the point-slope form of a linear equation to find the y-intercept.
Using the point (5, -1), we have:
-1 = (-1/3)(5) + b
Solving for b, we get:
b = -1 + 5/3 = 2/3
Therefore, the equation of the line passing through the points (5, -1) and (2, 2) is:
y = (-1/3)x + 2/3
A family drives 509 miles to their vacation destination. It takes them 8.6 hours to get there. What was their average velocity in miles per hour?
Answer:
Their average velocity during their trip was 59.19 miles per hour.
Step-by-step explanation:
To calculate the average velocity of the family's trip, we divide the total distance traveled by the time it took to travel that distance:
Average velocity = total distance ÷ time
In this case, the total distance traveled is 509 miles and the time it took to travel that distance is 8.6 hours. So, we can plug these values into the formula:
Average velocity = 509 miles ÷ 8.6 hours
Simplifying this equation, we get:
Average velocity = 59.19 miles per hour (rounded to two decimal places)
Therefore, the family's average velocity during their trip was 59.19 miles per hour.
Factor completely using the GCMF.
10x5 + 8x4 - 4x²
Answer:
To factor completely using the GCMF (Greatest Common Monomial Factor), we first need to identify the common monomial factor of all three terms. In this case, the common monomial factor is 2x²:
10x^5 + 8x^4 - 4x² = 2x²(5x^3 + 4x^2 - 2)
Now, we can see that the expression can be factored further, but it cannot be factored using the GCMF. However, we can use other factoring techniques, such as grouping or factoring by grouping, to factor the remaining expression:
2x²(5x^3 + 4x^2 - 2) = 2x²(5x^3 + 10x^2 - 6x^2 - 2)
= 2x²(5x^2(x + 2) - 2(x + 2))
= 2x²(5x^2 - 2)(x + 2)
Therefore, the expression 10x^5 + 8x^4 - 4x² can be factored completely as 2x²(5x^2 - 2)(x + 2).
Step-by-step explanation:
From a 2-pound bag of flour, Marcella took 1/4 pound to bake bread. Which expression tells the weight of the flour left in the bag?
2-0.25
2-1.4
2-0.14
2-0.025
2.5-2
The expressiοn that tells the weight οf the flοur left in the bag is 2 - 0.25
What is an expressiοn?A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expression or mathematical expression. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression.
Here, we have
Given: From a 2-pound bag of flour, Marcella took 1/4 pound to bake bread.
We have to find the expression that tells the weight of the flour left in the bag.
Marcella took 1/4 pound to bake bread = 0.25
If Marcella took 0.25 pounds from a 2-pound flour bag then she left with 1.75 pounds.
Hence, the expression that tells the weight of the flour left in the bag is 2 - 0.25
To learn more about the expression from given link
https://brainly.com/question/1859113
#SPJ1
I will mark you brainiest!
Given square ERTN, what is the length of NT ?
A) 50
B) 15
C) 25
Answer:
C) 25
Step-by-step explanation:
A square has all four sides equal.
5x = 10x - 25
-5x = -25
x = 5
Now put 5 in for x, and you get the answer is 25
Online Content: Site 1
When calculating simple interest, what must you do if you want to invest for months instead of years?
1. An airplane flies in the path shown by the vector CD on the graph below. What is the magnitude and direction of CD? (1 unit represents 1 mile)
The magnitude of CD is 5 miles and its direction is approximately 53.13°.
option D.
What is the magnitude and direction of the vector?To find the magnitude and direction of CD, we first need to calculate the distance between points C and D, which will give us the magnitude of the vector CD.
The distance formula between two points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)² + (y2 - y1)²)
Plugging in the values for points C and D, we get:
d = √((0 - (-4))² + (1 - 4)²)
= √(16 + 9)
= √(25)
= 5 miles
To find the direction of CD, we can use the arctan function to find the angle that CD makes with the x-axis.
tan(θ) = (y2 - y1) / (x2 - x1)
Plugging in the values for points C and D, we get:
tan(θ) = (1 - 4) / (0 - (-4))
= -3/4
Taking the arctan of both sides, we get:
θ = arctan(-3/4)
≈ -36.87°
However, since CD points in the negative x-direction, we need to add 90 degrees to get the correct direction.
θ = arctan(-3/4) + 90°
≈ 53.13°
Learn more about magnitude of vector here: https://brainly.com/question/3184914
#SPJ1
Use the graph to answer the question. Graph of a polygon ABCD with vertices at 4 comma 4, 12 comma 4, 12 comma 8, 4 comma 8 and a second polygon A prime B prime C prime D prime with vertices at 1 comma 1, 3 comma 1, 3 comma 2, 1 comma 2. Determine the scale factor used to create the image. one half 2 one fourth 2.5
The image was created by translating 5 units down, 5 units up, 1 unit down, and 1 unit up. ABCD and A'B'C'D' are two polygons on the graph.
The first polygon, ABCD, has vertices at (4,4), (12,4), (8,4), and (1,1),). (3,1). The vertices of the second polygon, A'B'C'D', are located at (1,1), (3,1), (3,2), and (1,2). (0.5,.25).
We can establish the translation that was applied to produce the image by comparing the coordinates of the two polygons. The two polygons' initial coordinate is (1,-1) and their second coordinate is (1,-1). (1,-6). The translation is 5 units lower because of the 5-unit difference in the y-coordinate. The second coordinate for the two polygons is (3,-5) and (3,-10). The translation is 5 units lower because of the 5-unit difference in the y-coordinate.
The third coordinate of the second polygon is (7,-5) and (7,-10). The translation is 5 units lower because of the 5-unit difference in the y-coordinate. The fourth coordinate of both polygons is (5,-1). (5,-6). The translation is 5 units lower because of the 5-unit difference in the y-coordinate.
The translation of the image was five units down, five units up, one unit down, and one unit up.
For more questions related to coordinates,
brainly.com/question/13662452
#SPJ1
Answer: C = 1/4
Step-by-step explanation: I got it right on my test
Hope this helps :)
which of the following is a point of tangency on the circle below
The correct option is C. Point B as only the line BC touching the circle at point B is tangent to the circle.
Tangent to a circle theoremThe tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency
We can observe that the line BC touches the circle at point B and the radius of the circle will be perpendicular to the line BC
Therefore, since the radius of the circle is perpendicular to the line BC at point B, then it is tangent to the circle
Know more about tangent to a circle here:https://brainly.com/question/11067500
#SPJ1
Bridge B is 186 feet shorter than Bridge A. The combined length of the two bridges is 9456 feet. Find the length of each bridge.
Answer:
Length of Bridge A = 4821
Length of Bridge B = 4635
Step-by-step explanation:
Let's call the length of Bridge A "x" which is measured in feet. According to the problem, the length of Bridge B is "186 feet shorter than Bridge A." This can be written as the following:
Length of Bridge B = x - 186
The problem also tells us that the "combined length of the two bridges is 9456 feet," which we can write as:
Length of Bridge A + Length of Bridge B = 9456
Now we can substitute the expression we found for the length of Bridge B into this equation. This can be shown as the following:
x + (x - 186) = 9456
Simplifying this equation, we can combine the two x terms and get the following:
2x - 186 = 9456
Now, we can solve for x
2x - 186 + 186 = 9456 + 186
2x = 9642
x = 4821
So the length of Bridge A is 4821 feet. To find the length of Bridge B, we can use the expression we found earlier:
Length of Bridge B = x - 186 = 4821 - 186 = 4635
Therefore, the length of Bridge A is 4821 feet, and the length of Bridge B is 4635 feet.
What is the solution to 4^x = 5^x +^2
The solution to 4^x = 5^x +^2 is
x = -2log 5/( log 5 - log 4)
Option C is correct.
How do we calculate?We will rewrite the equation as:
4^x = 5^x * 5^2
applying the logarithm function to both sides of the equation.
log(4^x) = log(5^x * 5^2)
simplifying the right side of the equation, using the properties of logarithms,
log(4^x) = log(5^x) + log(5^2)
log(4^x) = xlog(4) = x2log(2)
log(5^x) + log(5^2) = xlog(5) + log(25)
Substituting these results back into the original equation, we have:
x2log(2) = x*log(5) + log(25)
x*(2*log(2) - log(5)) = log(25)
Divide both sides by (2*log(2) - log(5)), we get:
x = x = -2log 5/( log 5 - log 4)
Learn more about properties of logarithms, at:
https://brainly.com/question/30759737
#SPJ1
A secretary listed the frequency of calls by a patient to a doctor's office during a year, and the data is displayed in the histogram.
A histogram titled Calls To A Doctor. The x-axis is labeled Number of Calls and has intervals listed for 1 to 25, 26 to 50, 51 to 75, and 76 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every five units up to 60. There is a shaded bar for 1 to 25 that stops at 58, for 26 to 50 that stops at 34, for 51 to 75 that stops at 17, and for 76 to 100 that stops at 12.
Which of the following best describes the spread and distribution of the data?
The data is skewed to the higher values because many patients call the doctor several times a day when they are sick.
The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
The data is bimodal with a narrow spread because many patients call the doctor several times a day when they are sick.
The data is normal and has a wide spread because many patients only call the doctor once or twice a year when they are sick.
The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
Define the terms spread and distribution?Spread and distribution of data are statistical concepts that describe how a set of data is spread out or distributed.
Distribution refers to how the data is distributed or arranged. It is typically described in terms of its shape, center, and spread. Common types of distributions include normal distribution, skewed distribution, and uniform distribution. The distribution can be visualized using various graphs such as histograms, box plots, and scatter plots.
Based on the histogram description, the best answer is:
The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
The histogram shows that the frequency of calls is highest for the 1 to 25 interval, with decreasing frequency for each subsequent interval. The fact that the shaded bars stop at relatively low frequencies for each interval suggests that there are very few patients who call the doctor frequently, skewing the data towards the lower values. The histogram also shows a wide range of values, or spread, with the highest interval going up to 100, but the low frequencies in each interval suggest that the data is not normally distributed.
To know more about set of data, visit:
https://brainly.com/question/27358262
#SPJ1
Answer:its b
Step-by-step explanation:
Answer this question please
The transformation that it could have been is either a rotation or a reflection, over one of the vertices of the figure.
What are transformations on a figure?The possible transformations on a figure are listed as follows:
Translation: Translation left/right or down/up, moving all vertices.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor, hence all vertices are changed.Either a reflection or a rotation can happen over one of the vertices of the graph, which will keep it's coordinates constant, and thus the transformation in the context of this problem is either one of these two.
More can be learned about transformations at https://brainly.com/question/29209050
#SPJ1
Find the values of a and b. Write your answers in simplest form.
The answer of the given question based on finding the values of a and b are 12 and 9, respectively.
What are Triangle?A triangle is geometric shape that consists of the three straight sides and three angles. Triangles are one of basic shapes in geometry and often used in the various mathematical applications.
Since triangles are similar, their corresponding sides are in the proportion. That is:
AB/DE = BC/EF = AC/DF
We can use this proportion to find the values of a and b.
From the diagram, we can see that:
AB = 12 + a
BC = 9 + b
AC = 15
DE = 8
EF = 6
Using the proportion, we get:
AB/DE = BC/EF
(12 + a)/8 = (9 + b)/6
Cross-multiplying, we get:
6(12 + a) = 8(9 + b)
72 + 6a = 72 + 8b
6a = 8b
a/b = 4/3
Similarly, using the other part of the proportion, we get:
AC/DF = 15/DF = (AB + BC)/(DE + EF) = (12 + a + 9 + b)/(8 + 6)
15DF = 21 + a + b
Substituting the value of a/b = 4/3, we get:
15DF = 21 + (4/3)b + b
15DF = 21 + (7/3)b
45DF = 63 + 7b
45DF = 7(b + 9)
Dividing both sides by 7, we get:
DF = (b + 9)
Substituting this value in the previous equation, we get:
45(b + 9) = 63 + 7b
45b + 405 = 63 + 7b
38b = 342
b = 9
Substituting the value of b in the equation a/b = 4/3, we get:
a/9 = 4/3
a = 12
Therefore, the values of a and b are 12 and 9, respectively.
To know more about Proportion visit:
https://brainly.com/question/30241688
#SPJ1
A circle has a circumference of 20 ft. What is the
radius of the circle?
Step-by-step explanation:
The formula to calculate the circumference of a circle is:
Circumference = 2πr
where "r" is the radius of the circle and "π" is the mathematical constant pi, approximately equal to 3.14159.
Given that the circumference of the circle is 20 ft, we can plug in the values into the formula and solve for "r":
20 = 2πr
Divide both sides of the equation by 2π:
r = 20 / (2π)
Simplify the expression by using the approximation of π as 3.14159:
r = 20 / (2 x 3.14159)
r = 3.1831 ft (rounded to four decimal places)
Therefore, the radius of the circle is approximately 3.1831 feet.
There are 88 seats in a theater. The seating in the theater is split into 4 identical sections. Each section has 14 red seats and some blue seats.
write an exspression
Answer:
x = 8
Step-by-step explanation:
Let x be the number of blue seats in each section.
Then the total number of seats in each section is:
14 + x
Since there are 4 identical sections, the total number of seats in the theater is:
4(14 + x) = 56 + 4x
We know that the theater has 88 seats, so:
56 + 4x = 88
Simplifying the equation:
4x = 32
x = 8
Therefore, each section has 14 red seats and 8 blue seats.
The expression for the number of blue seats in each section is x = 8.
Answer:
4(14 + b) = 88---------------------------------
Let b be the number of blue seats.
There are 4 sections, each has 14 red and b blue seats, with the total number of seats being 88.
The equation to reflect this would be:
4(14 + b) = 88Its solution would be:
14 + b = 88/414 + b = 22b = 22 - 14b = 8What is the perimeter of the rectangle in the coordinate plane?
_______________________________
(reporting spams/wrong answers)
(giving brainliest to the correct answer)
_______________________________
Answer:
40 units
Step-by-step explanation:
12+12+8+8=40 units
can you please solve this its urgent
Step-by-step explanation:
Think we can get a better picture, maybe more light? I wouldn't mind helping if you can
A high school drama club is selling tickets for the spring production. One day the president sold 12 adult tickets and 5 child tickets for a total of $169. The next day the president sold 22 adult tickets and 10 child tickets for a total of $314. Let a represent the cost of one adult ticket. Let c represent the cost of one child ticket. Which system of equations will solve for a and c?
12 a + 5 c = 314. 22 a + 10 c = 169.
12 a + 5 c = 169. 22 a + 10 c = 314.
5 a + 12 c = 314. 22 a + 10 c = 169.
22 a + 5 c = 169. 12 a + 10 c = 314.
Mark this and return
The cοst οf οne adult ticket is $12 and the cοst οf οne child ticket is $5.
What is system οf equatiοn?A system οf linear equatiοns can be sοlved graphically, by substitutiοn, by eliminatiοn, and by the use οf matrices.
The cοrrect system οf equatiοns tο sοlve fοr a and c is:
12a + 5c = 169 (equatiοn 1)
22a + 10c = 314 (equatiοn 2)
These equatiοns represent the tοtal ticket sales and revenue οn twο different days.
Tο sοlve this system, we can use the methοd οf eliminatiοn.
-24a - 10c = -338
22a + 10c = 314
-2a = -24
Dividing bοth sides by -2:
a = 12
Nοw we can substitute a = 12 intο equatiοn 1 tο sοlve fοr c:
12(12) + 5c = 169
144 + 5c = 169
5c = 25
c = 5
Therefοre, the cοst οf οne adult ticket is $12 and the cοst οf οne child ticket is $5.
To know more about system of equation visit,
https://brainly.com/question/13729904
#SPJ1
The following question has 2 parts. First, answer part A. Then, answer part B.
Use the image below to answer the questions.
Help fast please!
The fraction that represents the addition model of part A is 5/10, and for part B is 3/100.
What is a fraction?Parts of a whole are defined as fractions. The top and bottom numbers of a fraction are explained in the fundamentals of fractions. The number at the top represents the number of selected pieces of a whole, while the number at the bottom reflects the entire number of components.
According to the given information:
Based on the information provided, a grid A with 10 equal columns is depicted, with 5 shaded in. This will be expressed as a score of 5/10.
A second grid B, same in size, with 100 squares shaded in is also presented. This will be expressed as 3/100.
In this situation, Emma's response is erroneous because he added 5 to 3 and received an 8/100.
To know more about Fraction visit:
brainly.com/question/78672
#SPJ1
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 2 more
than 2 times the number of marbles Mark has, how many does each boy have to sell if the total number
of marbles is 71?
Mark has 23 marbles and Don has 48 marbles.
What is equation?
An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
Mark and Don, are selling their marbles at a garage sale. Don has more marbles than Mark and his number of marbles is equal to "2 more than 2 times the number of marbles Mark has."
Let x be the number of marbles that Mark has. Then, we can represent the number of marbles that Don has as 2x + 2.
Since the total number of marbles is 71, we can set up the equation:
x + (2x + 2) = 71
Simplifying the left side of the equation, we get:
3x + 2 = 71
Subtracting 2 from both sides, we get:
3x = 69
Dividing both sides by 3, we get:
x = 23
So Mark has 23 marbles. To find out how many marbles Don has, we can substitute x = 23 into the expression we derived earlier:
2x + 2 = 2(23) + 2 = 48
Therefore, Don has 48 marbles.
In total, they have 23 + 48 = 71 marbles, as given in the problem statement.
To know more about equation visit:
brainly.com/question/17499155
#SPJ1
The residual plot shows the residuals for a person's age and their vertical jump (in inches). Which statement best
assesses the linearity of the relationship between age and vertical jump if it is known that the scatterplot appears to
be approximately linear?
Although it is given that the scatterplot is approximately linear, because the residual plot has no obvious pattern,
it is appropriate to use the line of best fit to predict vertical jump based on age.
O Although it is given that the scatterplot is reasonably linear, because the residual plot has no obvious pattern, it is
not appropriate to use the line of best fit to predict vertical jump based on age.
O Although it is given that the scatterplot is reasonably linear, because the residual plot has a clear curved pattern,
it is appropriate to use the line of best fit to predict vertical jump based on age.
Although it is given that the scatterplot is reasonably linear, because the residual plot has a clear curved pattern,
it is not appropriate to use the line of best fit to predict vertical jump based on age.
The statement that best assesses the linearity of the relationship between age and vertical jump, given that the scatterplot appears to be approximately linear, is:
Although it is given that the scatterplot is reasonably linear, because the residual plot has no obvious pattern, it is appropriate to use the line of best fit to predict vertical jump based on age.
The second option is correct.
What is a residual plot ?
A residual plot is described as a graphical technique that attempts to show the relationship between a given independent variable and the response variable given that other independent variables are also in the model.
If the residual plot has no obvious pattern, it suggests that the relationship between the variables is linear and that the line of best fit is appropriate for predicting the vertical jump based on age.
Learn more about residual plot at: https://brainly.com/question/16821224
#SPJ1
Answer:
thx to the comments
Step-by-step explanation:
I need help question
Answer:
a= positive
b= When the graph goes up it means it has a positive trend.
c= the direction does not make sense because the measurements for the x and y coordinate do not correlate with each other.
Step-by-step explanation:
The battery life on Marco's cell phone decreases
according to the scatterplot below. What is the longest
amount of time Marco could use his phone without
charging it?
Answer:
The longest amount of time that Marco could use his phone without changing the battery is given as follows:
3.3 hours.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses tbe y-axis.In 5 hours, the battery fell from 50% to 20%, hence the slope is given as follows:
-30/5 = -6% an hour.
The battery is currently at 20%, hence the time that Marco could use the phone without charging it is given as follows:
20/6 = 3.3 hours.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
A cuboid has faces with areas 24, 32, and 48 square centimeters. what are the lengths of its sides?
Answer:
Let's denote the length, width, and
height of the cuboid as "l", "w", and
"h, respectively. Then, we have:
lw= 24 (Area of one face)
Ih 32 (Area of another face)
wh 48 (Area of the third face)
To solve for the dimensions of the
cuboid, we can use a system of
equations. We can start by solving
for one of the variables in terms of
the other two. For example, from the
first equation, we have:
W 24/
Substituting this into the second
equation, we get:
Ih 32
I(24/)h = 32
24h 32
h 32/24
h 4/3
Next, we can substitute the values of
h and w into the third equation to
solve for:
wh = 48
I(24/)(4/3) = 48
I2 72
= sqrt(72)
I= 6sqrt(2)
Finally, we can use the values of I
and w to solve for the remaining
dimension:
lw 24
(6sqrt(2))(24/(6sqrt(2))) = 24
W = 4sqrt(2)
Therefore, the lengths of the sides of
the cuboid are:
Length () = 6v2 cm
Width (w) = 4/2 cm
Height (h) = 4/3 cm
What would (-2, -2) be if it is rotated 90 degrees clockwise?
Answer:
(2, -2)
Step-by-step explanation:
To rotate a point in a coordinate plane 90 degrees clockwise, we need to switch the x and y coordinates and negate the new x coordinate.
So let's apply this formula to the point (-2, -2):
- The new x-coordinate will be the original y-coordinate: -2
- The new y-coordinate will be the negation of the original x-coordinate: -(-2) = 2
Therefore, after rotating (-2, -2) 90 degrees clockwise, we get the point (2, -2).
We can visualize this by plotting both points on a coordinate plane and drawing a line of reflection that represents the rotation:
```
Before rotation:
|
|
|
-------+-------
|
(-2,-2)
After rotation:
|
|
(2,-2)|
-------+-------
|
```
As shown in the diagram above, after rotating (-2,-2) 90 degrees clockwise, it lands at (2,-2).
Which of the following is the same as 8(9+2) ?
8*9+8
8*9+2
8*9+8*2
9(8+2)
2(8+9)
According the question 89+82 expressiοn is the same as 8(9+2).
What is expressiοn?An expressiοn in math is a sentence with a minimum οf twο numbers οr variables and at least οne math οperatiοn. This math οperatiοn can be additiοn, subtractiοn, multiplicatiοn, οr divisiοn.
Algebraic expressiοns are classified οn the basis οf the number οf terms in the expressiοn. The variοus types οf algebraic expressiοns are:
Mοnοmial expressiοnsBinοmial expressiοnsTrinοmial expressiοnsPοlynοmial expressiοnsThe difference between expressiοns and equatiοns is that an expressiοn signifies a cοmbinatiοn οf numbers, variables, and οperatiοn symbοls whereas an equatiοn will always use an equal (=) οperatοr between twο math expressiοns.
The expressiοn 8(9+2) can be simplified using the distributive prοperty οf multiplicatiοn οver additiοn:
8(9+2) = 89 + 82
Therefοre, the answer is: 89+82
To know more about expression visit,
https://brainly.com/question/1859113
#SPJ1
The quotient of a number and negative eight is seven-eighths. Find the number.
The value of the numer is negative seven ( -7 ).
What is the unknown number?Given the statement in the question; the quotient of a number and negative eight is seven-eighths.
Let's translate the given statement into an algebraic equation to solve for the unknown number.
"The quotient of a number and negative eight" means that we are dividing the number by -8.
We can represent this using the division symbol " / ":
Let the number be represented by x.
x / (-8)
"Is" means "equals" " = "
"Seven-eighths" can be written as a fraction:
7/8
Nowm putting it all together, we get:
x / (-8) = 7/8
To solve for x, we can multiply both sides by -8:
x = (-8) × (7/8)
Simplifying the right side, we get:
x = -7
Therefore, the value of x is -7.
Learn to solve more equations here: https://brainly.com/question/9236233
#SPJ1
Find the two linearly independent solutions of the LODE following for x>0, and determine at least the first four leading terms in the second solution y(2). 9x²y" - 6xy' + 2y = 0
Please, I need the solution
Using Cauchy-Euler equation, the solution of the second-order homogeneous differential equation is y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x
What is the solution to the equationThe given LODE is a second-order homogeneous differential equation with constant coefficients. The characteristic equation is given by:
9r^2 - 6r + 2 = 0
Using the quadratic formula, we find the roots to be:
r = (1/3) ± i/sqrt(3)
Thus, the general solution to the differential equation is:
y(x) = c1 * x^(1/3) * cos((1/3)*arccos(sqrt(3)*r)) + c2 * x^(1/3) * sin((1/3)*arccos(sqrt(3)*r))
To find the first solution, we can choose either the cosine or sine term. Let's choose the cosine term for simplicity:
y1(x) = x^(1/3) * cos((1/3)*arccos(sqrt(3)*r))
To find the second solution, we can use the method of reduction of order. Assume that the second solution has the form:
y2(x) = v(x) * y1(x)
Substituting this into the differential equation, we obtain:
9x^2(v''(x)*y1(x) + 2v'(x)*y1'(x) + v(x)*y1''(x)) - 6x(v'(x)*y1(x) + v(x)*y1'(x)) + 2v(x)*y1(x) = 0
Simplifying this equation by dividing by x^2*y1(x), we get:
9v''(x) + (18/r)x*v'(x) + ((2/r^2) - 1)v(x) = 0
where r = sqrt(3)
This is a Cauchy-Euler equation, which can be solved by assuming a solution of the form:
v(x) = x^m
Substituting this into the equation, we obtain:
9m(m-1) + (18/r)m + ((2/r^2) - 1) = 0
Simplifying this equation, we get:
9m^2 + 6m + 1 = 0
Using the quadratic formula, we find the roots to be:
m = (-1/3) or (-1/3)
Thus, the second solution is given by:
y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * ln(x)
To determine the first four leading terms in the second solution, we can use the Taylor series expansion of the natural logarithm:
ln(x) = (x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...
Substituting this into the second solution, we obtain:
y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * [(x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...]
Simplifying this expression, we get:
y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * (x-1) - c4 * x^(1/6) * (1/2)(x-1)^2 + c4 * x^(1/3) * (1/3)(x-1)^3 - ...
Thus, the first four leading terms in the second solution are:
y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x
learn more on Cauchy-Euler equation here;
https://brainly.com/question/15518645
#SPJ1
The city of Pineville held a talent contest. Judges rated the contestants on a scale from 1 to
10. A singer was rated 7.4, while a juggler was rated 7.0. The median rating was 7.9, and the
interquartile range was 0.8. The winner was a magician who was rated 9.7.
Which number best describes a typical rating in the contest?
0.8
7.4
7.9
9.7
The answer of the given question based on the number best describes a typical rating in the contest the answer is 7.9.
What is Median?The median is measure of central tendency in statistics that represents middle value of dataset. It is value that separates highest 50% of values from the lowest 50%.
To find median of a dataset, you first need to sort data in ascending or descending order.
The median rating is 7.9, which means that half of the contestants scored above 7.9 and half scored below. This suggests that 7.9 is a representative value of the ratings overall.
Additionally, the interquartile range (IQR) is a measure of the spread of the middle 50% of the ratings, and it is given as 0.8. This means that the ratings between the 25th and 75th percentile fall within a range of 0.8, which suggests that the ratings are fairly tightly clustered around the median of 7.9.
Therefore, the number that best describes a typical rating in the contest is 7.9.
To know more about Dataset visit:
https://brainly.com/question/30154121
#SPJ1
Given that Z=√3 + √3 i, write Z in Euler form
Answer:
To write Z in Euler form, we first need to find its magnitude and argument.
The magnitude of Z is given by:
|Z| = √(Re(Z)^2 + Im(Z)^2)
where Re(Z) is the real part of Z, and Im(Z) is the imaginary part of Z.
In this case:
Re(Z) = √3
Im(Z) = √3 i
So:
|Z| = √(√3^2 + (√3)^2) = √(3 + 3) = √6
The argument of Z is given by:
arg(Z) = tan^(-1)(Im(Z) / Re(Z))
In this case:
arg(Z) = tan^(-1)((√3) / √3) = tan^(-1)(1) = π/4
Therefore, Z in Euler form is:
Z = |Z| e^(i arg(Z)) = √6 e^(i π/To write Z in Euler form, we first need to find its magnitude and argument.
The magnitude of Z is given by:
|Z| = √(Re(Z)^2 + Im(Z)^2)
where Re(Z) is the real part of Z, and Im(Z) is the imaginary part of Z.
In this case:
Re(Z) = √3
Im(Z) = √3 i
So:
|Z| = √(√3^2 + (√3)^2) = √(3 + 3) = √6
The argument of Z is given by:
arg(Z) = tan^(-1)(Im(Z) / Re(Z))
In this case:
arg(Z) = tan^(-1)((√3) / √3) = tan^(-1)(1) = π/4
Therefore, Z in Euler form is:
Z = |Z| e^(i arg(Z)) = √6 e^(i π/4)