Geometry.
1. Reasoning What is the advantage of using coordinates O(0,0),
E(0, 2b), and F(2a, 0) rather than O(0, 0), E(0, b), and F(a, 0)?
Using coordinates O(0,0), E(0, 2b), and F(2a, 0) rather than O(0, 0), E(0, b), and F(a, 0) has the advantage of allowing the graph to be stretched or shrunk uniformly in both the x- and y-directions by a factor of 2. This can be useful if the scale of the graph needs to be adjusted, or if the graph needs to be compared to another graph with a different scale. It can also make the graph easier to read if the values of the variables being plotted are very large or very small.
By using coordinates that are multiples of the original coordinates, the shape of the graph is preserved, but the scale is changed. This can be useful if the purpose of the graph is to compare the relationships between different variables, rather than to provide an accurate representation of the actual values of the variables.
A cargo ship left port a and is headed across the ocean to shipping port b. After one month, the ship stopped at a refueling station along a path described by a vector with components leftanglebracket 14, 23 rightanglebracket. After another month, on the same path, the ship reached port b, twice the distance from port a as the fueling station. What are the characteristics of the vector representing the path of the ship?.
Answer:
Step-by-step explanation:
The vector representing the path of the ship from port A to the refueling station has components <14, 23>, and the vector representing the path from the refueling station to port B has twice the magnitude as the vector from port A to the refueling station.
To find the characteristics of the vector representing the path of the ship from port A to port B, we can add the two vectors together.
The sum of two vectors <a, b> and <c, d> is given by <a+c, b+d>. Therefore, the vector representing the path of the ship from port A to port B is given by:
<14, 23> + 2*<14, 23> = <14+214, 23+223> = <42, 69>
The vector representing the path of the ship from port A to port B is <42, 69>. This vector has a magnitude of √(42^2 + 69^2) = √(1764 + 4761) = √(6525) = 81 and a direction given by the angle theta, where tan(theta) = 69/42.
I hope this helps! Let me know if you have any other questions.
Answer: D. components:LeftAngleBracket 28, 46 RightAngleBracket, magnitude: 53.85
Step-by-step explanation:
Find an elementary matrix E such that EA = B.A = 2 1 3-2 4 53 1 4B = 2 1 33 1 4-2 4 5
The Elementary Matrix E is [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].
We know that the Matrix
[tex]A = \left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right] , B = \left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right][/tex]
[tex]EA = B[/tex]
⇒ [tex]E = B A^{-1}[/tex]
[tex]A^{-1} = \frac{1}{|A|} \times \left[\begin{array}{ccc}A_{11}&A_{12}&A_{13}\\A_{21}&A_{22}&A_{23}\\A_{31}&A_{32}&A_{33}\end{array}\right][/tex]
[tex]|A| = \left|\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right|[/tex]
[tex]= 2 \times4\times4-2\times5\times1 - 1\times(-2)\times4+1\times5\times3+3\times(-2)\times1 - 3\times4\times3\\= 32 -10+8+15-6-36 = 3[/tex]
[tex]A^{-1} = \frac{1}{3} \left[\begin{array}{ccc}11&-1&-7\\23&-1&-16\\-14&1&10\end{array}\right] \\A^{-1} = \left[\begin{array}{ccc}\frac{11}{3} &\frac{-1}{3}&\frac{-7}{3}\\\frac{23}{3}&\frac{-1}{3}&\frac{-16}{3}\\\frac{-14}{3}&\frac{1}{3}&\frac{10}{3}\end{array}\right][/tex]
[tex]\therefore E =\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right] \times \left[\begin{array}{ccc}\frac{11}{3} &\frac{-1}{3}&\frac{-7}{3}\\\frac{23}{3}&\frac{-1}{3}&\frac{-16}{3}\\\frac{-14}{3}&\frac{1}{3}&\frac{10}{3}\end{array}\right][/tex]
[tex]E = \left[\begin{array}{ccc}\frac{22+23-42}{3}&\frac{2+1-3}{3}&\frac{-14-16+30}{3}\\\frac{33+23-56}{3}&\frac{-3-1+4}{3}&\frac{-21-16+41}{3}\\\frac{-22+92-70}{3}&\frac{2-4+5}{3}&\frac{14-64+50}{3}\end{array}\right][/tex]
[tex]E = \left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]
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The figure shows a loading dock and a side view of an attached ramp, whose run is 12 feet and whose rise is 39 inches. Alex is wondering whether a long rectangular box can be stored underneath the ramp, as suggested by the dotted lines. The box is 2 feet tall and 5 feet long. Answer Alex’s question.
The box with a length 5 feet, and height of 2 feet can be stored underneath the ramp.
How to illustrate the dimension?Dimensions are the measure of the length, width and height of a given object. Yes, a rectangular box of length 5 feet and height 2 feet can be stored underneath the ramp. The measure of the sides of a given object is referred to as its dimensions.
This can be with respect to its length, width, and height.It has been given that the height of the ramp is 39 inches. But,12 inches = 1 feetSo that,39 inches = x feet
make x the subject of the formula to have;
x = [tex]\frac{39}{12}[/tex] = 3.25 feet
x = 3.25 feet
Thus the dimensions of the ramp are ;length = 12 feetheight = 3.25 feet
Therefore, the box with length 5 feet, and height of 2 feet can be stored underneath the ramp.
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Is a length of two sides of an isosceles triangle is 4 cm and 10 cm then the length of the third side?
The length of the third side of an isosceles triangle with sides 4 cm and 10 cm is 10 cm.
We know that in an isosceles triangle, two sides are equal.
One side of the triangle is 4 cm and the other is 10 cm.
Let us consider the third side to be 4 cm,
then 4 cm + 4cm = 8 cm and it is not greater than the third side 10 cm.
Hence, the third side cannot be 4 cm.
Then the third side can be 10 cm,
therefore, 4 cm + 10 cm = 14 cm > 10cm
and 10 cm + 10 cm = 20 cm > 10 cm.
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Can 3 year olds spell?
Simple 3-letter words or alphabets may be spelled verbally by kids as young as 3 years old
What is alphabets?An alphabet is a standardized system of fundamental written graphemes that correspond to the phonemes of certain spoken languages. a group of letters or other symbols used to write one or more languages, especially if they are organized in a regular sequence. a set of symbols or signals used to represent letters.
Simple 3-letter words or alphabets may be spelled verbally by kids as young as 3 years old. Early exposure to the alphabet and the spelling tools it contains, like as songs and reading aloud to them, provides the foundation for their comprehension of how letters combine to form words.
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(6x³ - 15x²)-(2x + 5)
It is 6x^3 - 15x^2 - 2x - 5
Brainly pls have a nice day
What are SAS and RHS congruence criterions?
The SAS states that two triangles that have two pairs of corresponding congruent sides and a pair of corresponding included congruent angles are congruent.
The RHS congruence criterion states that two right triangles that have a congruent pair of hypotenuses and a congruent pair of corresponding sides are congruent.
What is the SAS Congruence Criterion?The SAS congruence criterion is a postulate that shows that if two triangles have two pairs of corresponding congruent sides and a pair of corresponding included congruent angles, then both triangles are equal or congruent to each other.
What is the RHS Congruence Criterion?
The RHS stands for "right angle-hypotenuse-side". This congruence criterion states if two right triangles have congruence hypotenuses and a pair of corresponding congruent sides, then the two right triangles congruent to each other.
In summary, SAS congruence criterion proves that two triangles with two pairs of corresponding congruent sides and a pair of corresponding included congruent angles are congruent, while the RHS congruence criterion proves that two right triangles are congruent if they have equal pair of hypotenuses and a congruent pair of corresponding sides.
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In Fig R5, PT is a tangent to a circle ABCT. Find ATC
an urn contains 5 blue balls and 6 orange balls. in how many ways can we select 1 blue balls and 2 orange balls from the urn? a) 17 b) 75 c) 35 d) 149 e) 30 f) none of the above.
Using the formula of combination and probability theorem , The answer is b) 75.
What do you mean by combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant.
What is the formula of combination?The formula for combination is:
[tex]C(n,r) = \frac {n!}{r!(n-r)!}[/tex]
selecting 1 blue ball from 5 blue balls = C(5,1)
=5
selecting 2 orange balls from 6 balls = C(6,2)
=15
Total ways of selection = 5*15=75
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Convert 190 centimeters into yards.
Round your answer to the nearest
hundredth.
Answer: 190 cm = 2.07787 yards, rounded to the nearest hundredth, 2.08 yards.
Step-by-step explanation:
divide 190 cm by 91.44 to get your answer.
5.) Write a conjecture using the information provided below.
If someone is 18 years old, he or she can vote. Your cousin can vote.
Answer:
Based on the information provided, it can be conjectured that your cousin is 18 years old or older.
Step-by-step explanation:
Based on the information provided, it can be conjectured that your cousin is 18 years old or older.
XYZW is a parallelogram with diagonals XZ and YW that intersect at point A. If XA=3x, ZA=5x-4, and YW = 10x, find the value of x and the length of Wa
Answer:
Step-by-step explanation:
AW=10
Step-by-step explanation:
In a parallelogram opposite sides are congruent meaning XA and AZ are congruent. YA and AW are congruent. So...
Solving for XA and AZ
XA=AZ
3m=5m-4
-2m=-4
m=2
If YW=10m then 10 x 2 = 20
20 divided by 2 = 10
What is the odd integers from 1 to 100?
99
Step-by-step explanation:There are a total of 50 odd numbers between 1 to 100.
1 is the smallest, odd number:
The sum of all the odd numbers from 1 to 100 is 2500.
The average or mean of all odd numbers 1 to 100 is 50.
Soultion:
[tex]\boxed{ 3 + 2 = 5, 5 + 2 = 7, 7 + 2 = 9}[/tex]
The last number in the chart of odd numbers 1 to 100 given below is 99, as, if we add 2 to 99, we will get 101 which is greater than 100. So, 99 is the last odd number in the list of odd numbers from 1 to 100.
Therefore, the odd integers from 1 to 100 is 99
A picture is given below of all the odd numbers of 1 to 100:
For the following images write a triangle congruence statement
Answer:
no images are available here
How do you tell if the inverse of a function is a function?
The process by which we can tell that if the inverse of the function is also a function is the Horizontal Line Test .
The Inverse of the function is defined as a function, which can reverse into another function.
If the graph of the function does not pass the Horizontal Line Test, then the graphed function's inverse will not be a function; and
If all horizontal lines cross at most one spot on the original graph, then the inverse of the function will be a function.
Therefore , the horizontal line test is used to check whether the inverse is a function or not .
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gail was participating in a market research study, and she was given 20 pairs of brands of shampoo and asked to indicate which pair is most similar, which is second most similar, and so forth until all pairs were ranked. which type of indirect measurement technique used to assess gail's evaluative criteria does this represent? perceptual mapping conjoint analysis evaluative mapping regression analysis factor analysis
Perceptual mapping conjoint analysis evaluative mapping regression analysis factor analysis.
Perceptual mapping or market mapping is a diagrammatic technique used by asset marketers that attempts to visually display the perceptions of customers or potential customers.
The positioning of a brand is influenced by customer perceptions rather than by those of businesses. For example, a business may feel it sells upmarket products of high quality, but if customers view the products as low quality, it is their views which will influence sales.
Perceptual maps, also known as market maps, usually have two dimensions but can be multi-dimensional or use multiple colours to add an extra variable.
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Match each radius to the exact area of the circle with the radius
Areas of Circles are for [tex]490.873m^2[/tex] radius 12.5m, [tex]706.858m^2[/tex] for radius 15m, [tex]1256.637m^2[/tex] for radius 20m.
What is area of a circle?The region encircled by a circle with radius r is known as πr² in geometry. Here, the Greek letter stands for the constant proportion of a circle's circumference to its diameter, which is roughly equivalent to 3.14159.
This formula, which was first discovered by Archimedes, can be derived by considering the circle as the boundary of a series of regular polygons. A regular polygon's area is equal to half its perimeter times the distance from its center to its sides. The equivalent formula, [tex]A=\frac{1}{2} *2\pi r*r[/tex] states that the area is equal to half the perimeter times the radius.
The limit for a circle is held by [tex]\pi r^{2}[/tex].
Calculation:Given;
1) r=12.5m
[tex]A=\pi r^2=\pi (12.5)^2=490.873m^2[/tex]
2) r=15m;
[tex]A=\pi r^2=\pi (15)^2=706.858m^2[/tex]
3) r=20m;
[tex]A=\pi r^2=\pi (20)^2=1256.637m^2[/tex]
Areas of Circles are for [tex]490.873m^2[/tex] radius 12.5m, [tex]706.858m^2[/tex] for radius 15m, [tex]1256.637m^2[/tex] for radius 20m.
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Lea wants to make two pillows for her new couch. She needs 314 square yards of fabric for the first pillow and 112 square yards of fabric for the second pillow. Lea wants to know how much fabric she will have to buy for both pillows. Which expression represents the total number of square yards of fabric she needs for both pillows?.
The equation for the total square yards of cloth she needs for both pillows is 314+112=426.
The total number of square yards of fabric Lea needs for both pillows is the sum of the fabric needed for the first pillow and the fabric needed for the second pillow. This can be represented by the expression:
314 square yards + 112 square yards = 426 square yards
Therefore, the expression that represents the total number of square yards of fabric Lea needs for both pillows is:
314 + 112 = 426
This expression would simplify to 426 square yards. This expression uses the addition operator (+) to add the two quantities of fabric that Lea needs for each pillow. The result is the total number of square yards of fabric that she needs for both pillows.
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Do rigid transformations result in congruent figures?
Numbers that undergo rigid transformations are congruent. Congruent can always require precise changes even if you could conceive of them as forms that "appear exactly the same."
What is congruence?
A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.
∠X = ∠Q
And, also
XY = PQ
XZ = RQ
Therefore,
ΔXYZ ≅ ΔPQR
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Which is a valid theorem to show two triangles are congruent?
(Option D.) The Side-Side-Side (SSS) Theorem: If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
Showing Two Triangles are Congruent with the SSS TheoremThe Side-Side-Side (SSS) Theorem is a valid theorem to show that two triangles are congruent. This theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
In other words, if all three of the sides of one triangle are equal in length to all three of the sides of another triangle, then the two triangles are identical in size and shape. This theorem is a fundamental building block of geometry, and is often used to prove the congruence of two triangles in proofs or mathematical arguments.
Since the question is not complete, here's the full task:
Which theorem is not a valid theorem to show that two triangles are congruent?
A. SAS Triangle Congruence TheoremB. SSA Triangle Congruence TheoremC. ASA Triangle Congruence TheoremD. SSS Congruency TheoremLearn more about Triangle Theorem: https://brainly.com/question/343682
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Question Says Graph f(x)-0.5x-3
Picture below please help!
Answer:
Step 1: f(0) = -2
I also attached the graph in the explanation!
Step-by-step explanation:
f(x) = 0.5^x -3
f(0) = 0.5^0 - 3
f(0) = 1 - 3
f(0) = -2
I attached the graph below.
Daniel has a yearly income of $41,300 and claims 4 exemptions. The amount allowed for each exemption is $900. His local tax is4 3/4%. How much local income tax should be withheld from his weekly earnings? (Round your answer to the nearest cent.)
Answer:
$34.37.
Step-by-step explanation:
To calculate Daniel's local income tax withholding, we first need to determine his taxable income. To do this, we subtract the value of his exemptions from his yearly income: $41,300 - (4 x $900) = $37,500.
Next, we need to convert the local tax rate of 4 3/4% to a decimal by dividing it by 100: 4 3/4% = 0.0475.
Finally, we can calculate Daniel's local income tax withholding by multiplying his taxable income by the local tax rate: $37,500 x 0.0475 = $1,793.75.
To find the amount of local income tax that should be withheld from Daniel's weekly earnings, we simply divide his total local income tax by the number of weeks in a year: $1,793.75 / 52 = $34.37. Therefore, Daniel's local income tax withholding from his weekly earnings should be $34.37.
What type of sequence is 8 16 24 and 32?
Given that each term has a common difference, this is an arithmetic sequence. In this instance, the next item in the sequence is obtained by adding the previous term by 8.
What is meant by arithmetic sequence?The difference between consecutive terms in an arithmetic sequence, sometimes referred to as an arithmetic progression, is consistently the same.
What is the general formula to find nth term of arithmetic sequence?To find nth term we will use
[tex]a_{n}=a+(n-1)d[/tex]
where
a=first term
d=common difference
n=number of terms
In 8 16 24 and 32 since common difference d=8 between each successive term so this is a arithmetic sequence.
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if f(x) = 2 cot x and g(x) = sin x/2 what is the slope of the line joining (0.f(0)) and (pi,g(pi))?
wow help
The slope of the line joining (0, f(0)) and (π, g(π)) is given as follows:
Undefined.
How to obtain the slope of a linear function?The slope of a linear function, given two points, is given as the division of the change in y by the change in x.
The numeric values for these functions are given as follows:
f(0) = 2 cot(0) = 2 cos(0)/sin(0) = undefined, as sin(0) = 0, and we cannot divide by 0.g(π) = sin (π/2) = 1. the sine of 90 degrees is of one on the trigonometric circle.Hence the points are given as follows:
(0, undefined) and (π, 1).
The undefined point means that there is a vertical asymptote at x = 0, meaning that the change in y is undefined, and thus the slope of the function is also undefined.
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How do you describe a line on a graph?
A line on a graph is a series of points connected by a straight line. It is used to show continuous change or a relationship between two variables.
A line on a graph is a visual representation of a continuous change or a relationship between two variables. It is made up of a series of points connected by a straight line, making it easy to compare changes in data over a period of time. The points on the line represent the values for the two variables being graphed, with the horizontal axis (x-axis) representing one variable and the vertical axis (y-axis) representing the other. The points on the line can be joined with either a straight line or a curved line, depending on the type of data being graphed. For example, a straight line will be used to show a linear relationship between two variables, while a curved line might be used to show a non-linear relationship. By examining the line, it is possible to determine the rate of change or the correlation between the two variables being graphed.
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How many sides are equal in quadrilateral?
Therefore , for a regular polygon it must have four sides equal to be called as quadrilateral .
What is quadrilateral?A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. It is made up of four linked non-collinear points. The sum of the internal angles of quadrilaterals is always 360 degrees..
Here,
Each of them has four vertices.
Each side has four sides.
360 degrees is the sum of all interior angles.
Two diagonals are present.
There are regular and irregular quadrilaterals.
An ordinary quadrilateral must have four equal sides, four equal angles, and diagonals that cross one another.
Therefore , for a regular polygon it must have four sides equal to be called as quadrilateral .
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C = 5/9(F-32)
Could someone help me with figuring this out?
Josh is talking on the phone to his friend Greg who lives in Europe. Greg is used to describing temperatures in °C, while Josh is used to describing temperatures in °F. Greg can use the formula above to quickly convert the temperatures Josh describes to °C.
How can you rewrite the formula so that Josh can quickly convert the temperatures that Greg describes to °F? Justify your solution method.
Answer:
F = 9/5C +32
Step-by-step explanation:
You want to rearrange C = 5/9(F-32) to make F the subject.
SolutionYou can solve for F the same way you solve any similar 2-step equation:
C = 5/9(F -32) . . . . . . given
9/5C = F -32 . . . . . . . multiply by 9/5 (multiplication property of equality)
9/5C +32 = F . . . . . . add 32 (addition property of equality)
The equation Josh can use to convert to °F is ...
F = 9/5C +32
Miss Meg's salary increases by $450 to $1760. Find her percentage salary increase.
__________________________________________________________
Hello! In this question, we are trying to find the percentage increase in Miss Meg's salary.
__________________________________________________________
Explanation:
From the question, we were provided the following information:
Miss Meg's initial salary was $450Miss Meg's salary increased to $1760With this information, we will be able to find the percentage of increase in her salary.
__________________________________________________________
Solve:
To find Miss Meg's percentage salary increase, let us first calculate the difference between her new and initial salary.
$1760 - $450 = $1310
We now know that Miss Meg's salary increased by $1310
Using this information, we can then get her salary increase amount and divide it by her original salary.
$1310 ÷ $450 = 2.9111
Multiply 2.911 by 100 to get the decimal into percentage form to show us the percentage salary increase.
2.911 × 100 = 291.11%
This means that Miss Meg's percentage salary increase was 291.11%
__________________________________________________________
Answer:
[tex]\boxed{291.11\%}[/tex]
__________________________________________________________
Which is an expression?
A. 4+3<9
B. 2 x 6
C. 2 + 5 = 5 + 2
D. 1 = 3 - 2
Answer:
B. 2 x 6
Step-by-step explanation:
The expression doesn't have an equal sign, so C and D is wrong.
So, the correct answer is B
B is correct answer.
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