Answer:
1) -10x + 5
2) 5p - 26
3) -5y + 6
Use the data{1,1,1,3,3,5,7,7,9,11,13,14} to create a histogram with 5 bins.
The information needs to be divided into class intervals in order to make a histogram. Following that, make a tally to display the frequency (or relative frequency) of the data within each interval.
How do you make a histogram with data?A frequency histogram or a relative frequency histogram can be used to depict data if there are several data points and we want to examine how they are distributed.A histogram resembles a bar chart in appearance, but it displays numerical data. The data must be divided into class intervals in order to make a histogram. Then make a tally to display the frequency (or relative frequency) of the data within each interval. The frequency in a given class divided by the overall number of observations is the relative frequency. The bars are the same width as the class interval and the same height as the frequency (or relative frequency).Histogram Illustration
Jessica has been self-weighing every Saturday for the past 30 weeks. She was weighed in pounds, as shown in the table below.135 137 136 137 138 139
140 139 137 140 142 146
148 145 139 140 142 143
144 143 141 139 137 138
139 136 133 134 132 132
Her weight should be a histogram.
Answer
Usually, we want histograms to have intervals between 5 and 20. With a class of width 2, which will offer us 9 intervals given that the data ranges from 132 to 148, it is practical to have.131.5-133.5
133.5-135.5
135.5-137.5
137.5-139.5
139.5-141.5
141.5-143.5
143.5-145.5
145.5-147.5
147.5-149.5
To eliminate any doubt about whether the end point belongs to the interval to its left or to its right, we chose the end points to be.5, which is why. The endpoint convention specification is a substitute. The left end point, for instance, is included by Minitab but the right end point is not.To Learn more About histogram refer to:
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an application is using a two-dimensional list defined as follows: write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. write nested loops that get an integer value from the user for each element in the list, example: values
Complete Question :
An application is using a two-dimensional list defined as follows: 1. Write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. 2. Write nested loops that get an integer value from the user for each element in the list, for example: values= [[1, 2, 3], [10, 20, 30], [100, 200, 300],[1000, 2000, 3000]] 3. Write a function named row_values that accepts values as argument and returns the sums of each row and displays the result as a list named row 4. Write a function named column_values that accepts values as arguments and returns the sums of each column and displays the result as a list named column 5. Write a function called sum_values that sums all the elements of the array and displays the result.
Sum of rows : [ 6, 60, 600, 6000 ]
Sum of columns : [ 1111, 2222, 3333]
Sum of all elements : 6666
The nested loops are :
Enter a number at row 0, and column 0 : 1
Enter a number at row 0, and column 1 : 2
Enter a number at row 0, and column 2 : 3
Enter a number at row 1, and column 0 : 10
Enter a number at row 1, and column 1 : 20
Enter a number at row 1, and column 2 : 30
Enter a number at row 2, and column 0 : 100
Enter a number at row 2, and column 1 : 200
Enter a number at row 2, and column 2: 300
Enter a number at row 3, and column 0 : 1000
Enter a number at row 3, and column 1 : 2000
Enter a number at row 3, and column 2 : 3000
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The sampling distribution of the sample mean is formed from random samples of size 16 taken from a population with mean μ = 64 and standard deviation σ = 10. What are the mean and standard deviation of the sampling distribution of ?
mean = 64, standard deviation = 0.625
mean = 8, standard deviation = 2.5
mean = 64, standard deviation = 2.5
The mean and standard deviation of the sampling distribution include the following: C. mean = 64, standard deviation = 2.5.
What is the Central Limit Theorem?In Mathematics and statistics, the Central Limit Theorem states that the sampling distribution of means would always be normally distributed, as long as the sample size is large enough.
This ultimately implies that, the sampling distribution of means would always be normally distributed as the sample size gets larger in accordance with the Central Limit Theorem.
Mathematically, the standard deviation of a sampling distribution can be calculated by using this mathematical expression:
Standard deviation, σy = σ/√n
Where:
σ represents the standard deviation.n represents the sample size or number of items.Substituting the given parameters into the formula, we have;
Standard deviation, σy = 10/√16
Standard deviation, σy = 10/4
Standard deviation, σy = 2.5.
In conclusion, the mean of an original population is expected to be equal to the mean of the sampling distribution of means i.e 64.
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2(x - 6) + 2 = 4x - 4
Answer:
x = - 3
Step-by-step explanation:
2(x - 6) + 2 = 4x - 4 ← distribute parenthesis on left side and simplify
2x - 12 + 2 = 4x - 4
2x - 10 = 4x - 4 ( subtract 4x from both sides )
- 2x - 10 = 4x - 4 ( add 10 to both sides )
- 2x = 6 ( divide both sides by - 2 )
x = - 3
Answer:
SOLUTION
2(X-6)+2=4X-4
open the blanket by multiplication
2x-12+2=4x-4
2x-10=4x-4
collect like term
2x+4x=-4+10
6x=6
divide both side by 6
x=1
a line passes through the point (-6,3) and has a slope of 3/2
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
Define slope intercept form.The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.
Given
A line passes through the point (-6,3)
and has a slope of 3/2
Slope intercept form
y = mx + b
Equation,
y - 3 = 3/2(x - (-6))
y - 3 = 3/2(x+6)
2y - 6 = 3x + 18
2y = 3x + 24
y = 3/2x + 12
The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.
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Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by f(t) = 160e0.03tin thousands of dollars per year. Find the total income from the machines over the first 5 years. (Round your answer to the nearest thousand dollars.)$______
The total income from the machines over the first 5 years is $185.89
How to determine the total income from the machines over the first 5 yearsFrom the question, we have the following parameters that can be used in our computation:
f(t) = 160e0.03t
Where
t = Number of yearsf(t) = thousands of dollars per yearRewrite the function properly
so, we have the following representation
f(t) = 160e⁰.⁰³ⁿ
The above function is an exponential function
So: In the first 5 years, we have the value of t to be 5
This is represented as follows
t = 5
Substitute the known values in the above equation, so, we have the following representation
f(5) = 160e⁰.⁰³ ˣ ⁵
Evaluate the product of the exponents
f(5) = 160e⁰.¹⁵
The products above give
f(5) = 185.89
Hence, the total income is $185.89
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The cost of three pens and one rubber is 2.25 the cost of two pens and two rubbers is 1.90 work out how much one pen costs and how much one rubber costs
Answer:
0.65 pens
2.25 rubber
Step-by-step explanation
You can make two equations with the information given and solve them simultaneously to find x and y. Assume x is pens and y is rubber.
HELP ASAP
3. If the aspect ratio of a tire is 50%, width 10 inches, and the rim diameter is 19 inches, what is the tire diameter?
a. 59in b. 35.8in
d. 49in
4. The standard print paper is 11" by 8.5 in. What is the aspect ratio of a standard print paper?
a. 11:8
c. 8.5
c. 29 in
b. 22:17
d. 11
3) The tire diameter using the aspect ratio is; 29 inches
4) The aspect ratio of a standard print paper is; 22:17
How to solve aspect ratio problems?The aspect ratio is defined as the relationship between the width and height.
Now, in this case, the aspect ratio must be in whole numbers and not decimals and as such we can solve as follows;
3) We are told that the aspect ratio of a tire is 50%.
Thus, the aspect ratio is; 50/100 = 1/2 or 1:2.
Now, we are told that width 10 inches, and the rim diameter is 19 inches, then it means that the tire diameter = 10/2 + 19 + 10/2 = 29 inches
4) The standard print paper is 11" by 8.5. This can also be written as;
11 by 17/2 or 11 * 2 : 17
= 22:17
This then gives us the aspect ratio.
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bella is working two summer jobs, making $10 per hour landscaping and $15 per hour clearing tables. last week bella worked a total of 15 hours and earned a total of $180. graphically solve a system of equations in order to determine the number of hours bella worked landscaping last week, x,x, and the number of hours bella worked clearing tables last week, yy.
The solution of the system of equations by the graphical methods yields x equals 9 and y is 6 i.e, 9 hours of landscaping and 6 hours of waiting tables.
Bella worked x hours working landscaping at $10 per hour.
Total amount earned = 10x
Bella worked y hours working on clearing tables at $ 15 per hour
Amount earned = 15 y
x and y are variables as given
She worked a total of 15 hours and she gets $180 for the combined efforts.
The system of equation can be represented as:
x + y = 15
10x + 15y = 180
Now we will solve the two equations graphically:
So from the attached graph we can see that the point (9,6) is the required solution.
Hence she worked landscaping for 9 hours and clearing tables for 6 hours.
Let us solve by substitution to verify the results:
x + y = 15
or, x = 15 - y
Now 10x + 15y = 180
or, 10 (15-y) + 15y = 180
or, 150 - 10y +15y = 180
or, 5y = 180 - 150
or, y = 6
At y = 6 , x = 15 - 6 = 9
Hence (9,6) is the solution.
System of equations also known as simultaneous equations can also be solved by the elimination method.
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exercise 28 a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
In the given question, a sample of 20 joint specimens of a particular type gave a sample mean proportional limit stress of 8.52 mpa and a sample standard deviation of 0.78 mpa.
We have to calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints.
Sample size: n = 13
Sample mean: x’ = 8.52 mps
Sample standard deviation: s = 0.78 mps
95% lower confidence bound for the true average proportional limit stress of all such joints
Level of Significance (α) = 1-95% = 5% = 0.05
α/2 = 0.025
So the value of t(α/2) = 1.8
The confidence interval = x’± t(α/2)*s/√n
Now putting the value:
The confidence interval = 8.41± (1.8)*(0.78)/√12
The confidence interval = 8.41± (1.8)*(0.226)
The confidence interval = 8.41± 0.4068
The confidence interval = (8.41- 0.4068, 8.41+ 0.4068)
The confidence interval = (8.01, 8.82)
A 95% % lower confidence bound for the true average proportional limit stress of all such joints is 8.01.
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The right question is:
A sample of 12 joint specimens of a particular type gave a sample mean proportional limit stress of 8.41 mpa and a sample standard deviation of 0.78 mpa.
Calculate and interpret a 95% lower confidence bound for the true average proportional limit stress of all such joints. (Round your answer to two decimal places.)
If a loading ramp is placed next to a truck, at a height of 8 feet, and the inclined portion of the ramp is 23 feet long, what angle (in degrees) does the ramp make with the ground?
Answer:
≈20.35°
Step-by-step explanation:
height = 8
hypotenuse =23
angle is x
sin(x) =8/23
[tex]sin^{-1} (\frac{8}{23} )[/tex] ≈20.35°
x is about ≈20.35°
The ramp makes an angle of approximately 20.86 degrees with the ground.
Given that there is a truck with a ramp at a height of 8 feet the size of the ramp is 23 feet,
we need to find the angle ramp make with the ground.
To find the angle that the ramp makes with the ground, we can use the sine function.
The sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle.
In this case, the opposite side is the height of the ramp (8 feet), and the hypotenuse is the length of the inclined portion of the ramp (23 feet).
Let's calculate the angle:
sin(angle) = opposite/hypotenuse
sin(angle) = 8/23
To find the angle, we need to take the inverse sine (or arcsine) of both sides of the equation:
angle = arcsin(8/23)
We can find the approximate value of the angle:
angle ≈ 20.86 degrees
Therefore, the ramp makes an angle of approximately 20.86 degrees with the ground.
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Awnser if this is a function or not yes or no please.
Answer: NO
Step-by-step explanation:
This is not a function, since there are multiple outputs for ONE input.
Answer:
no
Step-by-step explanation:
to be a function, the x's can only have one partner. Here, 7 has two partners (7 goes to 20 and also to 18) and the 11 has two partners also. This relation is not a function.
A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x)=300,000csc(π42x) .
a. The blue line represents g(x) = 250,000csc(π30x).
b. g(5) = 25,000 km. This is the distance of the comet from Earth after 5 days.
c. The minimum distance between the comet and Earth is 250,000 km, which occurs when x = 0. This corresponds to the constant csc(π30x).
d. The equation has a vertical asymptote at x = 30/π.
Write the solution to following questions:a. Graph the value of x on the range [0,35].b. Analyze g(5) and explain the results.c. What is the shortest path the comet must take to reach Earth? When does this take place? What equation constant does this match up to?d. Find any vertical asymptotes and explain their significance.a. Graph g(x):
To graph g(x), we can plot several points on the interval [0,35] and then connect them to form a graph of the function. For example, we can plot the points (0,250,000), (5,50,000), (10,25,000), (15,16,667), (20,12,500), (25,10,000), (30,8,333) and (35,7,143). Connecting these points will give us a graph of the function g(x).
b. Evaluate g(5):
The value of g(5) can be found by plugging in x = 5 into the equation: g(5) = 250,000 csc(π30*5) = 50,000 km. This means that after 5 days, the comet will be 50,000 km away from Earth.
c. Minimum distance between the comet and Earth:
The minimum distance between the comet and Earth can be found by taking the derivative of the equation and setting it to 0.
d. Vertical Asymptotes:
The vertical asymptotes of g(x) occur at x = 0 and x = 30. This means that the comet approaches an infinitely large distance from Earth at x = 0 and x = 30.
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Knowledge Check
Find x
x=
Answer:
x is 44 Hope that helps.
Find the degree to the nearest point
The degree to turn before walking 673 paces is 59 degrees
How to determine the degree to walk?From the question, we have the following parameters that can be used in our computation:
Lengths = 989 paces, 673 paces and 861 paces
These paces can be represented as
x = 989
y = 673
z = 861
The measure of the required angle (angle Z) i.e. the degree to walk can be calculated using the following cosine rule
z² = x² + y² - 2xy * cos(Z)
Substitute the known values in the above equation, so, we have the following representation
861² = 989² + 673² - 2 * 989 * 673 * cos(Z)
Evaluate the exponents, the products and the summation
So, we have the following representation
741321 = 1431050 - 1331194 * cos(Z)
Evaluate the like terms
- 1331194 * cos(Z) = -689729
Divide both sides by - 1331194
cos(Z) = 0.51812808651
Take the arc-cos of both sides
Z = 58.7
Approximate
Z= 59 degrees
Hence, the measure of the angle is 59 degrees
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PLEASE ANSWERE ASAP
If BC = 16.7 ft, what is AY?
The length of segment AY is 16.7 ft if the length of segment BC is 16.7 ft
How to determine the length of the side length AYFrom the question, we have the following parameters that can be used in our computation:
BC = 16.7 ft
The measures of the angles are not given
However, the marks on the side lengths imply that:
The points A, B and C divides the line segments XY, XZ and YZ into equal segmentsThe parallel segments are equal segmentsUsing the above as a guide, we have the following:
AY = BC
This is because these segments are parallel segments
Recall that parallel segments are equal segments
Substitute the known values in the above equation, so, we have the following representation
AY = 16.7
Hence, the length of AY is 16.7 ft
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The table represents a linear relationship. x −2 0 2 4 y −1 0 1 2 Which of the following graphs shows this relationship?
The graph that shows the linear relationship of the table is attached below.
How to Find the Graph that Represent a Linear Relationship?To determine the graph of a linear relationship, do the following:
Find the slope or rate of change = change in y / change in x.Determine the y-intercept which is the value of y when x = 0, and it represents the value on the y-axis where the line intercepts.Given the table which represents a linear relationship above, use two pairs of values, (0, 0) and (2, 1) to find the slope:
Slope = change in y / change in x = (1 - 0) / (2 - 0)
Slope = 1/2.
The y-intercept (b) = 0.
Thus, this means that the graph of the linear relationship will have a slope of 1/2 and crosses the y-axis at 0.
Thus, the graph is shown below.
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LEAST TO GREATEST ( WILL GIVE BRAINIST IF CORRECT )
PLEASE HURYY
Leon Starr purchased 55 shares of stock at
$41.09 per share. His online stockbroker charged him
a $15.99 commission. What is the total amount that he
paid for the stock?
Total amount paid for the stock:
Answer: $2,275.94
Step-by-step explanation: First, we need to find how much he pays for the stocks alone. So, we would use this equation:
41.09(55)
41.09 x 55
That would get us to $2,259.95. Now, we have to add the $15.99, bc he had to pay a fee. So $2,259.95 + 15.99 = $2,275.94. I hope this helped!
A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.
A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.
You will spend an average of $50 a week at this restaurant.
Write the expression \[\frac{4+6a}{5}-\frac{1+3a}{4}\] as a single fraction.
The expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]
What is algebraic expression ?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
According to question
⇒ [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex]
⇒ taking LCM of 4, 5 = 20
now [tex]\[\frac{4(4+6a)-5(1+3a)}{20}[/tex]
⇒ (16 +24a - 5 - 15a)/20
⇒ ((24a - 15a) - (16-5))/20
⇒ (9a - 11)/20
hence, the expression [tex]\[\frac{4+6a}{5}-\frac{1+3a}{4}\][/tex] as a single fraction is [tex]\frac{9a-11}{20}[/tex]
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The Picture and Sound electronics store has hired Brennan to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes. He turns the crank 15 times to lift a box 15 feet. He turns the crank 45 times to lift a box 45 feet.
In this relationship, x represents the number of times Brennan turns the crank to lift a box, and y represents the height the box has been lifted (in feet).
Graph two points for this relationship and the line passing through them.
The graph (created with MS Excel) of the height the box is lifted to the number of times Brennan turns the crank to lift the box which is the graph of the proportional relationship, y = x, is attached.
What is a proportional relationship?A proportional relationship is one in which one variable (the output variable) is a constant multiple of the another variable known as an input variable.
The number of times Brennan turns the crank = x
The height to which the box is lifted = y
The points on the graph are; (15, 15), and (45, 45)
The ratio of the y-values to the x-values is 15/15 = 45/45 = 1, which indicates that the relationship is a proportional relationship
A point on the graph of a proportional relationship is the point (0, 0), therefore, the points on the graph are; (0, 0), (15, 15), and (45, 45)
Please find attached the graph of the proportional relationship between the number of times Brennan turns the crank to the height to which the box is lifted created with MS Excel
The relationship between the variables x and y is; y = x
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what is 309x317/9-4+7/8x3
[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].
Step-by-step explanation:1. Write the expression.[tex]\frac{(\frac{309*317}{9-4+7})}{8x3}[/tex]
3. Solve the main denomonator.[tex]\frac{(\frac{309*317}{9-4+7})}{24}[/tex]
4. Solve the secondary denominator.[tex]\frac{(\frac{309*317}{12})}{24}[/tex]
5. Solve the secondary numerator.[tex]\frac{(\frac{97953}{12})}{24}[/tex]
6. Solve the main numerator.[tex]\frac{(8162.75)}{24}[/tex]
7. Simplify the fraction.[tex]340.11[/tex] or [tex]\frac{32651}{96}[/tex].
Question 1-5
The expression (4c-3d)(3c+d) is equivalent to:
O 12c² 13cd 3d²
O 12c²
O 12c²
O 12c²
O 12c²
13cd3d²
5cd 3d²
5cd +3d²
3d²
The expression (4c − 3d)(3c + d) is equivalent to 12c² - 5cd - 3d²
What is Expression?An expression is combination of variables, numbers and operators.
(4c − 3d)(3c + d) is the given expression.
Four times c minus three times d into three times f c plus d.
In the given expression c and d are variables.
Plus and minus are operators.
We need to find the equivalent expression of (4c − 3d)(3c + d).
(4c − 3d)(3c + d)
4c(3c+d)-3d(3c + d)
Apply the distributive property.
12c² + 4cd - 9cd - 3d²
Add the like terms
12c² - 5cd - 3d²
Hence, 12c² - 5cd - 3d² is the equivalent expression of (4c-3d)(3c+d).
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Solve for the variable.
8 = y - 3
Responses
A -11-11
B 55
C 1111
D 2424
E -5
Answer:
Answer is y = 11
Step-by-step explanation:
8 = y - 3
or, 8 + 3 = y - 3 + 3
or, 11 = y
or, y = 11
Graph the rational function Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X ?
The horizontal and vertical asymptotes for the function f(x) =6/(-2x +1) is equal to y = 0 and x = 1/2 respectively.
Graph is attached.
As given in the question,
Given function is :
f(x) =6 /(- 2x +1)
f(x) = y
Degree of the numerator is zero
Degree of the denominator is 1.
Degree of denominator is greater than the degree of numerator.
Function represent the horizontal asymptotes for y =0
To get the vertical asymptotes equate denominator equals to zero
(- 2x +1) = 0
⇒2x = 1
⇒x = 1/2
Vertical asymptotes is given by x =1/2.
Graph is attached.
Therefore , the horizontal and vertical asymptotes for the given function is equal to y=0 and x =1/2 respectively.
The above question is incomplete, the complete question is:
Graph the rational function. f(x) =6 /(- 2x +1) Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button X.
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Solve the system if we x-3y=0 and 3x-6y=9 by combining the equations.
Step-by-step explanation:
Hope u get it x=3×3
x=9
It didn't include in the photo
A wooden box is in the shape of a regular pentagonal prism. The sides, top, and bottom of the box are 1 centimeter thick. Approximate the volume of wood used to construct the box. Round your answer to the nearest tenth.
The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.
What is a pentagonal prism?A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.
The expression for the volume of a regular pentagon is given as V = 5/2 × abh
Where h is the height and a and b are the length of the sides.
Now, the value of a, b and h as per the question is given as,
a = b = h = 1.
Then, the volume can be calculated as,
V = 5/2 × 1 ×1 × 1
= 2.5
Hence, the volume of the regular pentagonal prism is given as 2.5 cm³.
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Determine the equation of the hyperbola with and vertices (6, 4) and (0, 4) and
asymptotes y = 1/3x + 3 and y = = -1/3x + 5.
The equation of a hyperbola can be written in the form:
(x-h)^2/a^2 - (y-k)^2/b^2 = 1
where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices on the x-axis, and b is the distance from the center to the vertices on the y- axis.
In this case, the vertices of the hyperbola are (6,4) and (0,4), and the center of the hyperbola is at (3,4). The distance from the center to the vertices on the x- axis is 3, and the distance from the center to the vertices on the y- axis is 0.
Plugging these values into the equation for a hyperbola, we get:
(x-3)^2/3^2 - (y-4)^2/0^2 = 1
This equation is not defined, because the value of b is 0. This means that the hyperbola has a horizontal orientation, and its vertices are on the y-axis.
To find the equation of the hyperbola, we need to rewrite the equation in a different form. We can do this by using the fact that the distance between the center of the hyperbola and a point on the hyperbola is given by:
√ ((x-h)^2 + (y-k)^2) = a*√ (1 + (y-k)^2/b^2)
Substituting in the values for h, k, and a, we get:
√ ((x-3)^2 + (y-4)^2) = 3*√ (1 + (y-4)^2/0^2)
This equation can be simplified to:
√ ((x-3)^2 + (y-4)^2) = 3*√((y-4)^2/0^2)
The value of b is still 0, so the equation for the hyperbola is:
(x-3)^2 = 9*(y-4)^2
This is the equation for a horizontal hyperbola with vertices (3,4) and (9,4) and asymptotes y = 1/3x + 3 and y = -1/3x + 5.
What is an equation of the hyperbola?A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces which is known as connected components, that are mirror images of each other and resemble two infinite bows.
Therefore, the correct answer is as given above
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find two polynomials whose difference is 2x^2 + x + 4
The two polynomials whose difference is 2x^2 + x + 4 are
6x² + 3x + 5 and 4x² + 2x + 1.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The difference between the two polynomials is 2x² + x + 4.
The two polynomials are:
6x² + 3x + 5 _____(1)
4x² + 2x + 1 ______(2)
The difference between (1) and (2)
6x² + 3x + 5 - 4x² - 2x - 1
2x² + x + 4
Thus,
The two polynomials are 6x² + 3x + 5 and 4x² + 2x + 1.
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