A point is placed 2 units left and 3 units down from the origin is (-2, -3) and a point is placed 3 units left and 2 units up from the origin is (-3, 2)
How to determine the ordered pairStatement 1:
Given that
A point is placed 2 units left and 3 units down from the origin.
This is represented as
(0 - 2, 0 - 3)
Evaluate
(-2, -3)
Statement 2:
A point is placed 3 units left and 2 units up from the origin.
This is represented as
(0 - 3, 0 + 2)
Evaluate
(-3, 2)
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Which of the following is the equation that represents the graph?
. y equals negative three halves times x minus 3
y equals negative three halves times x minus 2
y equals negative two thirds times x minus 3
y equals negative two thirds times x minus 2
The equation of the line representing the graph is y = - (3/2)x - 3.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
From the given information the line passes through the points
(- 2, 0) and (0, - 3).
Slope(m) = (- 3 - 0)/(0 + 2).
Slope(m) = - 3/2.
Now, - 3 = - (3/2)(0) + b.
b = - 3.
y = - (3/2)x - 3.
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Convert the following quadratic to vertex form:
y = 2(x – 4) (x – 2)
Options:
A. y=2x2–12x+16
B. y=2(x–3)2−2
C. y=2(x–3)2−1
D. y=2(x2–6x+8)
Answer: It's B
Step-by-step explanation: I cheated but it's right ;-;
I need help please :(
Answer:
A
Step-by-step explanation:
z = 1 - i
z³ = z² × z = (1 - i)²×z = (1 - 2i - 1)×(1 - i) =
= (-2i)×(1 - i) = -2i - 2
so, both parameters are -2. therefore, A is correct
What do you put on the X axis of an ogive?
The X-axis (horizontal axis) often represents a "class boundaries" of such an ogive, whereas the Y-axis (vertical axis) typically shows the frequency count.
Explain about the ogive graph?A sort of frequency polygon that displays cumulative frequencies is an ogive, often known as a cumulative frequency polygon.
In other words, the graph adds the cumulative percents from left to right.On an ogive graph, "class boundaries" are shown along the x-axis while cumulative frequency is shown on the y-axis. Comparable to a histogram, an ogive features a single point that indicates in which the top right corner of the rectangular would be located in place of rectangles. This type of graph is typically simpler to make from such a frequency table.Thus, The X-axis (horizontal axis) often represents a class boundaries being measured of such an ogive.
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a full circle has 360° or 2π radians. given this, how many degrees are in 1 radian?
Answer:
1 radian ≈ 57.2958
write a congruence statement for the quadrilateral you created in figure AFEKJB and the image of the quadrilateral in figure MBJKGH
One of the congruence statement can be written as AFEB = MBJH.
What are Quadrilaterals?Quadrilaterals are four sided polygons which also have four vertices and four angles.
Sum of all the interior angles of a quadrilateral is 360 degrees.
Given is a figure.
First we have to draw a line segment to make two quadrilaterals out of this figure.
We can join line EB and JH to form the quadrilaterals AFEB and MBJH.
These two quadrilaterals are congruent to each other as
FA = BM
FE = BJ
EB = JH
AB = MH
Hence the congruence statement can be written as AFEB = MBJH.
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The complete question is :
Figure MBJKGH is the image of figure AFEKJB after being rotated 90 degrees counterclockwise about point K.
Imagine drawing a segment in figure AFEKJB to create a quadrilateral and also the image of the segment when rotated 90 degrees counterclockwise about point K.
Write a congruence statements for the quadrilateral you created in figure AFEKJB and the image of the quadrilateral in figure MBJKGH.
note that the horizontal axis represents time elapased (in minutes) since passing mile marker 291 and the vertical axis represents the disance traveled (in miles) since passing mile marker 291 . how does the distance traveled and time elapsed compare for nicole and justin as they traveled from mile marker 291 to mile marker 298 ?
It is impossible to determine how the distance traveled and time elapsed compare for Nicole and Justin based on the information provided.
The graph only shows the horizontal axis representing time elapsed and the vertical axis representing the distance traveled, but does not provide any data points or information about Nicole and Justin's specific journeys.
The information given in the statement only provides the axes of a graph but does not provide any actual data points or information about Nicole and Justin's journeys. To compare the distance traveled and time elapsed between Nicole and Justin, we would need to know the specific data points or information about their journeys, such as the starting and ending mile markers, and the corresponding time elapsed and distance traveled for each person. Without this information, it is not possible to determine how the distance traveled and time elapsed compare for Nicole and Justin.
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factorise this equation x² - 33²
(x+33)(x-33)
Step-by-step explanation:
a²+b²=(a+b)(a-b) difference of two squares
x²-33²= (x+33)(x-33)
Answer: (x + 33)(x - 33)
What does factorise mean?
In maths, to factorise an expression means to put it in brackets in the max possible multiplication form. It is basically finding what to multiply to get an expression.
If you don't know what expression means: a collection of symbols such as numbers, variables and arithmetic operators that jointly express a quantity.
NOTE: There must be no equal sign in expressions. Equal sign in an expression makes it an equation.
Basic Factorization Formulas: (for your info, " ^ " means, to the power of)
a^2 – b^2 = (a – b)(a + b)(a + b)^2 = a^2 + 2ab + b^2(a – b) 2 = a^2 – 2ab + b^2a^3 – b^3 = (a – b)(a^2 + ab + b^2 )a^3 + b^3 = (a + b)(a^2 – ab + b^2 )(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca(a – b – c)^2 = a^2 + b^2 + c^2 – 2ab + 2bc – 2caNow if you see the formulas; the very first formula seems to match with the expression. If your wondering how,
a^2 - b^2 where , "a" can be replaced by x and, "b" can be replaced by 33 As a result, x^2 - 33^2 can be written in multiplication form as (x - 33)(x + 33)
Hope it helped! If you are still not clear, please get help from a tutor or videos on factorization. Thank you.
b) in a distribution of scores, is it possible for more than half of the scores to have values that are below the mean? why or why not?
It is possible for more than half of the scores to have values below the mean, as the mean is given by the sum of all the values divided by the number of scores, hence a high outlier would cause a mean higher than more than half the scores.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
Suppose a data-set given as follows:
1, 1, 1, 1, 20.
The mean is given as follows:
Mean = (1 + 1 + 1 + 1 + 20)/5
Mean = 4.8.
Which is greater than 4 out of 5 scores, that is, greater than 80% of the data-set, meaning that 80% of the data-set has values below the mean, as the observation 20 is a high outliers.
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8,502,000,000,000
In scientific notation??
A company makes two types of electronic devices: laptops and tablets. Its business
plan says that it must produce from 70 to 130 laptops, and from 50 to 110 tablets,
per day. The total number of devices it must make per day according to the plan
ranges
from 150 to 220. Given that x is the number of laptops made per day, and y
is the number of tablets made, what are the daily constraints that the plan places on
the company? What is the maximum profit
The constraints for the company are -
70<x<130, 50<y<110 and 150<x + y<220
The objective function for maximizing profit is z = 65x + 45y.
What are business constraints?
Constraints can be business or technical in nature and are defined as restrictions or limitations on possible solutions.
Considering that x is the number of laptops and y is the number of tablets.
According to the information provided, there are between 70 and 130 laptops.
Additionally, there are between 50 and 110 tablets.
Specifically, 70<x<130 and 50<y<110.
Between 150 and 220 devices make up the total number of x + y.
This equals 150<x + y<220.
These are all limitations on daily production.
Since each laptop makes $65 in profit and each tablet makes $45.
As a result, the overall profit for laptops is $65x and for tablets it is $45y.
Consequently, the objective function z for calculating total profit is -
z = 65x + 45y
Maximize z = 65x + 45y to make the most profit.
Therefore, the constraints and maximum profit is obtained.
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A company makes two types of electronic devices: laptops and tablets. Its business plan says that it must produce from 70 to 130 laptops, and from 50 to 110 tablets, per day. The total number of devices it must make per day according to the plan ranges from 150 to 220. Given that x is the number of laptops made per day, and y is the number of tablets made, what are the daily constraints that the plan places on the company? The company sells all the electronic devices it makes. Its profit is $65 for every laptop sold and $45 for every tablet sold. What is the objective function for maximizing profit?
Josh multiples the number 6 by another number and the product is more than 6. Which of these could be the number that Josh multiples 6 by?
Josh multiplies 6 with number 2.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation.
Given,
Josh multiples the number 6 by another number and the product is more than 6.
Let the number be x
Equation becomes
6 × x = 6 + 6
6x = 12
x = 12/6
x = 2
Hence, 2 is the number that Josh multiplies 6 by.
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The area of a hexagon is equal to the sum of the areas of its 6 internal triangles.
Using the given measurements, what is the area, in square inches, of the regular hexagon shown above?
The area of the regular hexagon given in the figure is 360 inches²
What is the area of a triangle?The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. To find a triangle's area, use the formula area = 1/2 * base * height.
Given here: A hexagon with six triangles inscribed in it with height 10 inches and base 12 inches.
We know all the triangles must be congruent as we know that all of the sides are of equal length. Therefore, all 6 of the triangles (we get from drawing lines to opposite vertexes) are congruent triangles.
Thus area of the hexagon= 6×area of a triangle
A= 6×1/2×10×12
=360 inches²
Hence, The area of the regular hexagon given in the figure is 360 inches²
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Calculate the rand value of a camera that costs 6 840,45 yuan in China. The exchange rate on the day of the sale was R1 = 0,73 yuan.
Answer: 1000 thats the anwer
The rand value of a camera that costs 6 840,45 yuan is R9,370.47.
What is Exchange rate?A currency's relative value expressed in terms of another currency is called an exchange rate (or group of currencies). The exchange rate is a significant economic variable for nations with active international trade, like Australia.
Given:
The camera that costs 6 840,45 yuan in China.
As, the exchange rate is R1 = 0.73 yuan.
so, the Rand value of Camera
= 6840.45 / 0.73
= R9,370.47
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define a positive integer n to be a factorial tail if there is some positive integer m such that the base-ten representation of m ! ends with exactly n zeros. how many positive integers less than 1992 are not factorial tails?
The number of positive integers which are less than 1992 and not factorial tails are 396.
Positive integer are defined as the all the integers greater then zero.There are positive integers, zero, and negative integers.
Let for some positive integer with exactly n zeros be m
Number at the end of zeros of m! be f(m)
f(m) = ( m /5 ) + ( m /25 ) + ( m /125 ) + ( m /625 ) + ....
Here 'm' is multiple of 5
So ,f(m) = f( m + 1) = f( m + 2) = f( m + 3 ) = f( m + 4 )
And f(m) ≤ ( m /5 ) + ( m /25 ) + ( m /125 ) + ( m /625 ) +...
= m / 4.03
= m / 4
Value of m greater than 7964 such that f(m) = 1991
f( 7975 ) = 1991
Number of distinct positive integer 7975 / 5 = 1595 less than 1992
Number of positive integers less than 1992 and they are not factorial tails are equal to
= 1991 - 1595
= 396.
Therefore, there are 396 positive integers which are less than 1992 and are not factorial tails.
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If working on stairs, which articulated ladder configuration should be used?
An articulated ladder should be utilized in a stepladder design for working on stairs. This structure is especially built for stairway safety and stability, with movable legs that can be placed to different heights to suit uneven stairs and give a level area for standing.
What is area?The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. The area of a planar figure is the space contained by its border. The number of unit squares that cover the surface of a closed form is the figure's area. The area is the region defined by an object's form.
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A family went on a cross-country road trip for their summer vacation. The following table shows the number of days and the total amount of miles their car had driven.
Number of Days 1 3 7 10 15
Miles Driven 380 984 1,986 2,251 3,623
Which of the following graphs is most appropriate to construct for the data given in the table to observe how the miles change over a certain number of days? Explain.
A scatter plot, because it would show how a variable changes over time between each individual data point
A scatter plot, because it would show the association, or relationship, between the two variables
A line graph, because it would show how a variable changes over time between each individual data point
A line graph, because it would show the association, or relationship, between the two variables
Answer:
Based on the information, the most appropriate graph to construct with the data given in the table to observe how miles change over a certain number of days would be a line graph because it would show how a variable changes over time between each individual data point. .
What is the appropriate graph for this data?
To select the appropriate graph for these data we must take into account the following aspects. The data being linked.
In accordance with the above, we want to relate data of days with distance. Therefore, the best option would be the line graph since it allows us to relate two data and in turn contrast the difference with other points.
So the correct answer would be a line graph because it would show how a variable changes over time between each individual data point (option A).
Step-by-step explanation:
The first garden is 4 feet long. Deja is using small bricks, which are 1/3 of a foot long. How many small bricks are neede
Answer: 12
Step-by-step explanation: Divide 4 by 1/3
Answer:
12 bricks
Step-by-step explanation:
This is a division problem.
4 ÷ 1/3 = 4/1 × 3/1 = 12/1 = 12
Answer: 12 bricks
Add. 6/38/45+2/5/9 Enter your answer in the box as a mixed number in simplest form.
Step-by-step explanation:
the correct answer is= 103
what is 2/3-5/6x8 as an simplified fraction
Answer:
-5
Step-by-step explanation:
2/3-5/6x8
8/6 =4/3
2/3 - 5/3*4 =2/3 - 17/3 =-15/3 =-5
on a recent quiz, the class mean was 71 with a standard deviation of 4.2. calculate the z-score (to 4 decimal places) for a person who received score of 73.
The calculated value of z-score for the mean 71 and standard deviation 4.2 with person score 73 is equal to 0.4762( upto to four decimal place)
Mean of the data 'μ' = 71
Standard deviation of the data 'σ ' = 4.2
Score obtained by a person 'X' = 73
Formula for the z-score is equal to :
Z-score = ( X - μ ) / σ
Substitute the value of mean , standard deviation , and person score to get the value of z-score we have,
⇒ Z-score = ( 73 - 71 ) / 4.2
⇒ Z-score = ( 2 ) / 4.2
⇒ Z-score = 0.47619
⇒ Z-score = 0.4762
Therefore, the value of z-score as per the given mean and standard deviation is equal to 0.4762.
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given the fact that both roots can easily be represented with a float, why do you get a couple percent error for one of the roots?
There are several reasons why a couple percent error may occur when calculating roots, even if both roots can easily be represented with a float.
These reasons can include rounding errors, numerical instability, algorithm limitations, machine precision, and incorrect input data or model. To minimize the error, it is important to use a stable and accurate algorithm, and to ensure that the input data and model are correct.
The error in the calculation of one of the roots can be due to several reasons, such as:
Rounding errors: In many cases, when performing calculations with floating-point numbers, intermediate results are rounded to a certain number of decimal places. This can result in a small error that accumulates throughout the calculation and leads to an incorrect answer.
Numerical instability: Some mathematical operations, such as division and square roots, can lead to loss of precision or numerical instability. This can result in an incorrect answer, even if the input numbers can be represented as floating-point numbers.
Algorithm limitations: The algorithm used to calculate the roots may have limitations that result in an error, even if the input numbers can be represented as floating-point numbers. For example, some algorithms may not converge to the correct root, or they may converge very slowly.
Machine precision: The precision of the computer used to perform the calculation can also play a role in the error. For example, if the computer uses single-precision floating-point numbers instead of double-precision floating-point numbers, the error will be larger.
Model or input data error: The error could also be due to incorrect input data or an incorrect model. For example, if the mathematical model used to calculate the roots is not an accurate representation of the underlying system, the error will be larger.
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The value of d in millimeters is
Suppose a spherical astroid has a radius of approximately 8.5 x 10^2 m. Use the formula 4/3 π r^3 to find the approximate volume of the asteroid.
2.57 x 10^9 m^3
1.07 x 10^4 m^3
2.54 x 10^10 m^3
4.51 x 10^10 m^3
A spherical astroid has a radius of approximately 8.5 x 10^2 m. Using the formula 4/3 π r^3 to find the approximate volume of the asteroid, we get volume = 2.57 x 10^9 m^3.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
a spherical astroid has a radius of approximately 8.5 x 10^2 m.
we know,
the volume = 4/3 π r^3
so, by calculating, we get.
volume = 2.57 x 10^9 m^3
Hence, a spherical astroid has a radius of approximately 8.5 x 10^2 m. Using the formula 4/3 π r^3 to find the approximate volume of the asteroid, we get volume = 2.57 x 10^9 m^3.
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On what interval is the graph increasing?
On what interval is the graph decreasing?
Does the graph have a relative maximum or relative minimum? If so, what is it?
Points -
(-3,-2)
(-2,0)
(-1,2)
(0,4)
(1,2)
(2,0)
(3,-2)
The answer is, On the interval (-3,-2) to (0,4), is the graph increasing.
On (0,4) to (3,-2) interval is the graph decreasing.
the graph have a relative maximum at (0,4).
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
from the given graph we get,
On the interval (-3,-2) to (0,4), is the graph increasing.
On (0,4) to (3,-2) interval is the graph decreasing.
the graph have a relative maximum at (0,4).
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pls help! i need helppp!
The given system of equations has no solution.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given system of linear equations are,
5x + y = -2
-5x - y = -1
We solve this by Elimination method.
Adding these two equations,
0 = -3
This means that the system has no solution.
Hence the given system of equations does not have a solution.
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in how many ways can n identical balls be distributed into r bins such that each bin contains at least two balls
Ways can n identical balls be distributed into r bins such that each bin contains at least two balls are 20 ways.
1 ball in each of 3 boxes: 4 ways
3 balls in one box: 4 ways
2 balls in one box and 1 ball in another box: 3*4=12 ways
There are 20 ways to arrange the balls .
In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter. Suppose we have a set of three numbers P, Q and R. Then in how many ways we can select two numbers from each set, is defined by combination.
The combination can also be represented as: –nCr, nCr, C(n,r), Crn
Proof:
nPr = nCr.r!
= [n!/r!(n-r)!].r!
= n!/(n-r)!
Hence the theorem states true.
A permutation is an act of arranging objects or numbers in order. Combinations are the way of selecting objects or numbers from a group of objects or collections, in such a way that the order of the objects does not matter.
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Factors to consider when selecting criteria for decision rules includeI. The decision maker's attitudeII. The nature of the situationI and II
Factors to consider when selecting criteria for decision rules include: III. (I) The decision maker's attitude and (II) The nature of the situation
Both the decision maker's attitude and the nature of the situation must be considered when selecting criteria for decision rules.
When selecting criteria for decision rules, it is important to consider both the decision maker's attitude and the nature of the situation. The decision maker's attitude includes their preferences, goals, and values. The nature of the situation includes the resources available to them, the timeframe, and the costs and benefits associated with the decision. Both of these factors must be taken into account in order to make an informed decision.
Here's the full task:
Factors to consider when selecting criteria for decision rules include:
Choose the right option:
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How many pivot columns must A have if its columns span R5? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. B. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R5" are logically equivalent. C. The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. D. The columns of a 5x7 matrix cannot span R5 because having more columns than rows makes the columns of the matrix dependent.
The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R5. Therefore, the correct answer is C.
A pivot column is a column of the matrix that has a non-zero entry in the pivot position and all entries below the pivot are zero. In row echelon form, every row below a pivot column has a zero in the corresponding position. The pivot columns correspond to the linearly independent columns of the original matrix and the number of pivot columns determines the rank of the matrix.
The rank of a matrix is defined as the number of linearly independent columns or rows in the matrix. If the columns of a matrix span Rn, then the rank of the matrix must be equal to n. This means that the matrix must have n linearly independent columns. To ensure that the columns of A span R5, A must have at least 5 pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have a non-trivial solution, meaning that the columns of A would not be linearly independent and would not span R5.
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Amanda and Hannah like water sports. Amanda is kayaking down the river from a dock in
Fulton County at 9 kilometers per hour. Hannah is jet skiing up the river from the same dock,
going 42 kilometers per hour. How long will it be before the two of them are 16 kilometers
apart on the river?
If necessary, round your answer to the nearest minute.
hours and
minutes
Answer:
Rounding to the nearest minute, the time it will take for Amanda and Hannah to be 16 kilometers apart on the river is 53 minutes.
Step-by-step explanation:
Let's call the time it takes for Amanda and Hannah to be 16 kilometers apart "t" (in hours). During this time, Amanda will have kayaked down the river a distance of 9t kilometers, and Hannah will have jet-skied up the river a distance of 42t kilometers. So, their total separation will be 9t + 42t = 51t kilometers. Setting this equal to 16, we get:
51t = 16
t = 16 / 51
To convert this to hours and minutes, we can multiply by 60 to convert the fraction to minutes:
t = 16 / 51 * 60 = approximately 53.33 minutes