draw two lines in the following trapezoid to create three equilateral triangles
Answers
A quadrilateral with at least one pair of parallel sides is called, in American and Canadian English, a trapezoid. In British and other forms of English, a (North American) trapezoid is called a trapezium. The transposition of these two terms was a result of an error in Charles Hutton's mathematical dictionary.
What is a trapezoid?In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases. As opposed to the particular examples below, a scalene trapezoid is a trapezoid without equal sides.
The Greek mathematician Euclid identified five different quadrilateral shapes, of which four had two sets of parallel sides (the square, rectangle, rhombus, and rhomboid in English) and one did not (a trapezia, meaning "a table," which comes from "four" and means "a foot; end, boundary, edge").
In his commentary on the first book of Euclid's Elements, Proclus (412–485) developed two varieties of trapezia: one pair of parallel sides, or a trapezium (v), divided into isosceles (equal legs), and scalene (unequal) Similar to how cuboid and rhomboid both mean "resembles," trapezia with no parallel sides is a trapezoid, trapezoeidé, or literally "trapezium-like."
English followed Proclus's arrangement until the late 18th century, when a prominent mathematical lexicon produced by Charles Hutton in 1795 endorsed a transposition of the terms without providing an explanation. Although this error was fixed in British English around 1875, it remained in American English till the present..
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Related Questions
Need help on question 5 please ASAP I’m going to really appreciate it
Answers
Answer:
x+7
Step-by-step explanation:
to shift the function up, you need to add -4x by 4
and to shift the function to the left you need to add 1 by 6
how might you use the word average in a situation that does not involve math?
Answers
Answer:The mean is commonly referred to as average, but it is not the only kind of average. The mean is often used in research, academics and in sports.
Step-by-step explanation:
There are diffrerent ways to use the word
The average in general is the same as the term average in mathematics.
What is the arithmetic mean or average?Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.
The meaning of average, in general, is quite similar to average in maths.
Suppose If we say the average income of a population is five thousand.
This implies that some portion of the population earns more than five thousand and some portion of the population earns below five thousand.
We can also say that the average rate growth of height of a person per year is 5cm this also means that some years the growth is more than 5cm and some years it is less than 5 cm.
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In a particular college class, 60% of the students are female. Of the female students, 75% have long hair. One student is picked randomly in the class. What is the probability that it is a female with long.
Answers
The probability that it is a female with long hair is 0.75 .
Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability generally refers to the degree to which something is likely to occur. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty. Every event's probability in a sample space is one.
the likelihood of an occurrence, E is
P(E) = The proportion of positive outcomes to all outcomes.
In probability, an event is said to be independent if it is completely unaffected by the occurrence of any other event, and it is considered to be dependent if it is affected by other occurrences.
Using the literature and formulas mentioned above, we have:
Let F stand for the circumstance that the student is a female and L for the circumstance that the student has long hair.
In this illustration, the probability are as follows:
P(F) = 0.60; P(L) = 0.50
P(F AND L) = 0.45 and P(L|F) = 0.75 as a result.
As a result, there is a 0.75 percent chance that a randomly chosen student has long hair.
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What is the quotient of (x³ - 3x² + 5x − 3)÷(x - 1)? x² - 2x - 3
x² + 2x + 7
x² - 3x + 8
x² - 2x + 3
Answers
Which two situations result in a solution of 0?
Responses
On Tuesday morning, the temperature outside is −5∘F. On Tuesday night, the temperature outside is 5∘F. How much does the temperature change from Tuesday morning to Tuesday night?
On Tuesday morning, the temperature outside is − − 5 ∘ ∘ F. On Tuesday night, the temperature outside is 5 ∘ ∘ F. How much does the temperature change from Tuesday morning to Tuesday night?
On Friday morning, a student earns $35 mowing lawns. On Friday night, the student spends the $35 while out with friends. How much of the money that the student earns from mowing lawns is left?
On Friday morning, a student earns $ 35 mowing lawns. On Friday night, the student spends the $ 35 while out with friends. How much of the money that the student earns from mowing lawns is left?
A vacationer goes scuba diving and is at a depth of −30 yards during the dive. Later in the day, the vacationer hikes up to a lookout 30 yards above the ocean. What is the vertical distance between the diving position and the lookout position?
A vacationer goes scuba diving and is at a depth of − − 30 yards during the dive. Later in the day, the vacationer hikes up to a lookout 30 yards above the ocean. What is the vertical distance between the diving position and the lookout position?
A student walks 5 blocks west to school then another 10 blocks west after school. How far is the student from the starting location?
A student walks 5 blocks west to school then another 10 blocks west after school. How far is the student from the starting location?
A student owes a friend $7.50. If the student pays the friend $7.50, how much does the student owe the friend?
A student owes a friend $ 7.50 . If the student pays the friend $ 7.50 , how much does the student owe the friend?
Answers
The two situations which would result in a solution of 0 include the following:
B. On Friday morning, a student earns $35 mowing lawns. On Friday night, the student spends the $35 while out with friends. How much of the money that the student earns from mowing lawns is left?
D. A student owes a friend $7.50. If the student pays the friend $7.50, how much does the student owe the friend?
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
For this exercise, the expression which represents the first situation is given by:
Amount of money left = $35 - $35
Amount of money left = 0
For this exercise, the expression which represents the second situation is given by:
Amount of money owed = $7.50 - $7.50
Amount of money owed = 0.
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show which of the following polygons are similar, write the similar polygons in order of their corresponding vertices and determine the scale factor of similarity
Answers
Answer:
see explanation
Step-by-step explanation:
starting with the polygon on the left at vertex Z ( marked with x ) and going clockwise.
Similarly polygon on right starting with vertex D ( marked with x ) and going clockwise.
ZLXY ≅ DABC
the scale factor of ZLXY → DABC
is the ratio of corresponding sides
scale factor = [tex]\frac{DA}{ZL}[/tex] = [tex]\frac{9}{7.2}[/tex] = [tex]\frac{5}{4}[/tex]
Need answer now!! Pls help! Will give brainliest to the best/correct answer! 40 points
A line is drawn through (-4, 3) and (4, 3). Which describes whether or not the line represents a direct variation?
A. The line represents a direct variation because -4/3 = 4/3.
B. The line represents a direct variation because it is horizontal.
C. The line does not represent a direct variation because it does not go through the origin.
D. The lines does not represent a direct variation because -4 (3) ≠ 4 (3).
Answers
Answer:
Answer: The line does not represent a direct variation because it does not go through the origin.
Needing some help, been working on this for a while now.
Answers
Answer:
x = 15
z = 64
Step-by-step explanation:
Lets make an equation -
(14x - 94) + z = 8x - 4 +z
Both sides are parallel to each other, and therefore the sum is also 180.
Then we solve it -
14x - 8x - 94 + z = -4 + z
Bring the z on the other side to eliminate it.
6x - 94 = - 4
Add 94 on both sides
6x = 90
Divide 6 on both sides and you get x = 15
Substitute x into 8x -4 + z = 180
8*15 - 4 + z = 180
120 - 4 + z = 180
116 + z = 180
Subtract 116 on both sides.
z = 64.
HOPE THIS HELPS!!
CAN U PLSSS HELP ME! I have been stuck on this problem for hours! Pls try to see if u can solve it. This is the problem -
Sean and Emily love making origami. Sean can make a paper crane in 6 minutes, and
Emily can make a paper crane in 8 minutes. One day, they decided to make some paper
cranes together. They started making cranes at the same time, and after a while, they
have 112 total paper cranes. How many of those paper cranes did Sean make?
THANKS A LOT!!
Answer:
Step-by-step explanation:
1. To find the value of x, you'll need to set 14x-94 equal to 8x-4. We do this since the two angels are congruent, and congruent angles are equal to each other:
[tex]14x-94=8x-4[/tex]
You'll then solve for x by isolating the x value.
[tex]14x-8x=94-4[/tex]
[tex]6x=90[/tex]
[tex]x=\frac{90}{6}[/tex]
[tex]x=15[/tex]
2. To find z I would plug in the x value to one of the equations, such as 8x-4, in order to find the measure of that angle:
[tex]8(15)-4\\=116[/tex]
We now know that 14x-94 and 8x-4 are equal to 116. To find z you'll add the angle opposite to it, the blank angle since they are congruent. Now you'll add all the angles together and set the equation equal to 360:
[tex]z+z+116+116=360\\2z+232=360\\2z=(360-232)\\2z=128\\\frac{2z}{2} =\frac{128}{2} \\z=64[/tex]
Your final answers are x=15 and z=64, hope this helps!
Find hcf
a) x³-1, x^4 + x² + 1, x³ + 2x² + 2x + 1
Answers
Answer:
Hope the picture will help you
Lona received a stamp collection from her grandmother. The collection is in a leather book and currently has 120 stamps. Lona joined a stamp club, which sends her 12 new stamps each month. The stamp book holds a maximum of 500 stamps. a. Complete the table at right. b. How many stamps will Lona have in one year from now?zetb c. Write an equation using function notation to represent the total number of stamps that Lona has in her collection after n months. Let the total be represented by t(n). Month Stamps
0, 120
1 ,132
2
3
4
5
Answers
Using a linear function, it is found that:
a. The table is completed as follows: Month 2, Stamps 144; Month 3, Stamps 156; Month 4, Stamps 168; Month 5, Stamps 180.
b. She will have 264 stamps after one year.
c. The function is given by: t(n) = 120 + 12n.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.b is the y-intercept of the function, which is the the value of y when the function crosses the x-axis(x = 0).For the function in this problem, we have that:
The intercept is of 120, as the initial value is of 120 stamps.The slope is of 12, as 12 stamps are added each month to the collection.Hence the function is given by:
t(n) = 120 + 12n.
To complete the table, we find the numeric values are follows:
t = 2, t(2) = 120 + 12(2) = 144.t = 3, t(3) = 120 + 12(3) = 156.t = 4, t(4) = 120 + 12(4) = 168.t = 5, t(5) = 120 + 12(5) = 180.One year from now is 12 months, hence:
t(12) = 120 + 12(12) = 264.
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solve the following equation 2x=12
Answers
2
x
=
12
Step 1: Divide both sides by 2.
2
x
2
=
12
2
x
=
6
Answer:
x
=
6
Evaluate:
Eight to the second power.
Answers
Answer:
[tex] = 8^{2} \\ = 8 \times 8 \\ = 64[/tex]
ATTACHED IS THE SOLUTION
Justin earns $13.9 per hour at the Rite Aid Pharmacy. He regularly works 40 hours per week. He is paid time-and-a-half for each hour of overtime work. Last week he worked 50 hours. What was his gross pay for the week?
Answers
Based on the amount earned by Justin per hour, and the overtime work rate, Justin's gross pay for the week is $764.50
How to find the gross pay?First, find the amount that Justin earns from Rite Aid Pharmacy for his regular work:
= Number of hours in regular week x Pay per week
= 40 x 13.9
= $556
The overtime hours was:
= 50 - 40
= 10 hours
The overtime pay is:
= 10 x 13.9 x 1.5
= $208.50
The total gross pay for the week is:
= 556 + 208.50
= $764.50
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-3b (2y3 +5y) - 6y3b
Answers
Answer:
-15by
Step-by-step explanation:
distribute
rearrange terms
Question
What numbers are a distance of 23 unit from 12 on a number lineQuestion
What numbers are a distance of 23 unit from 12 on a number line
Answers
The number which is at a distance of 23 unit from 12 on a number line is 11.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used to determine the difference between two numbers such as 23 and 12. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
Now, we can determine the distance as follows:
Distance = 23 - 12
Distance = 11.
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Maria used a number line to find 12 ÷ 4.
Explain how she can use the number line to model the division.
Answers
The way she can use the number line to model the division is; Maria should start at 0 and then make “bounces” of 4 to the right until landing at 12. She will make 3 bounces of 4 because 12 divided by 4 is 3.
How to Model a Number Line?She is using a number line to model division, 12 ÷ 4 = 3
To carry out a division operation using a number line, follow the steps below:
Select the origin (point 0) as the starting pointIdentify the dividend and the divisorUse the divisor as the gap between 0 and subsequent consecutive numbersCount the number of gaps between 0 and the dividendFor the division operation 12 ÷ 4, Maria should:
Make 0 as the starting point on the number lineIdentify the dividend (12) and the divisor(4)Make the gap between 0 and subsequent numbers to be 4(the divisor)Therefore, the points on the number line will be 0, 4, 8, and 12
Count the number of gaps between these points
That is, 0 to 4, 4 to 8, and 8 to 12.
Since there are three gaps between 0 and 12 on the number line, using a gap difference of 4, then 12 ÷ 4 = 3
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A physics student walks 100 meters in 80 seconds. The student stops for 30 seconds, and then walks 200 meters farther in 90 seconds. What is the average speed of the entire walk?.
Answers
The average speed of the student for his entire walk is equal to 1.5 m/s. Therefore, option (b) is correct.
What is the average speed?
The average speed of a body is calculated as the total distance traveled in a fixed interval of time. The average speed can be determined by dividing the total distance traveled by a body by the total time.
The average velocity is a single value if the object moves uniformly. Speed is a scalar quantity, it has no specified direction. The average speed has the S.I. unit the same as velocity i.e. m/s.
Given the distance covered by a student in first 80 sec = 100m
After stooping for 30sec again cover a distance of 200m in 90sec.
The total distance traveled by the student = 100 + 200 = 300m
The time taken by student to cover distance = 80 + 30 +90 = 200 sec
The average speed of the student = total distance/ total time taken
= 300/200 = 1.5 m/s
Therefore, the average speed of the student is equal to 1.5m/s.
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Wile-E-Coyote falls from the top of an 45m cliff while chasing the road runner. How long does it take him to strike the ground below?
Answers
Time is considered to be the dimension on which any system evolves.
9.2 seconds will take for him to strike the ground.
How long does it take Wile to strike the ground?Time can be thought of as the dimension in which the evolution of every system occurs.
It can be calculated using the following units: seconds, minutes, hours, days, weeks, months, and years.
Given,
h = 45m
g = -9.8m/s
Solution:
Vi = 0
h = Vi t + 1/2gt^2
Since Vi is 0
2h = gt^2
t^2 = 2h/g
t = [tex]\sqrt{2h/g}[/tex]
[tex]t =\sqrt{2 * -45/-9.8}[/tex]
t = 9.183s
9.2 seconds will take for him to strike the ground.
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Algebraic Expression
a is 7 times less than b.
Answers
[tex]7a = b[/tex]
THIS SIMPLY MEANS THAT TO ATTAIN b we have to multiply a by 7.
Which equation represents the line that passes through
the points (2, 0) and (0, 7)?
Answers
Answer: [tex]y=-\frac{7}{2}x+7[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{7-0}{0-2}=-\frac{7}{2}[/tex].
So, since the y-intercept is 7, the equation is [tex]y=-\frac{7}{2}x+7[/tex].
75 + 25x = 300 ......................................................................................
Answers
The answer is : X = 9
Answer:
9
Step-by-step explanation:
75 + 25x = 300
subtract 75 from both sides:
75 + 25x - 75 = 300 - 75
25x = 225
divide both sides by 25:
25x/25 = 225/25
x = 9
Select the correct answer.
What is the effect on the graph of f(x)
The au
=
when the function is changed to g(x) = |(x - 1)|?
Answers
Function transformation: Function transformation is the process of changing one function into another.
The f(x) graph will be shifted 1 unit down in the vertical direction.
How to do this function sum?Function transformation: Function transformation is the process of changing one function into another.
changing a function's form from one to another
Transformational rule
The function will move 'a' units higher when f(x)->f(x)+a is used.
f(x)-> f(x)-a The action is going to be 'a' units down.
The function will be relocated 'a' units left if f(x)->f(x+a).
The function will be relocated 'a' units right if f(x)->f(x-a).
The fundamental job is [tex]f(x)=\frac{1}{x}[/tex]
F(x)-1 is used in place of f(x).
It indicates that the graph of f(x) will shift down by one unit.
A unit down will be added to the vertical translation of the f(x) graph.
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Refer to the figure below if m<2 = (a+15)
, and m<3=(a+35) find the value of a that :-P hi
Answers
The value of a that makes ∠2 and ∠3 perpendicular is 20.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.
From the image, HL is perpendicular to HJ, hence:
m∠2 + m∠3 = 90° (Definition of perpendicular)
Substituting gives:
(a + 15) + (a + 35) = 90
2a + 50 = 90
a = 20
value of a = 20
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Rachel is making premade 3-inch by 5-inch tile rectangles for her driveway. If it takes her 6 minutes to position each rectangle, how many hours will it take her to create a 2-foot by 4-foot pattern drive? Write your answer as a decimal.
Answers
Answer:
Tile a rectangle with unit squares. It is 8 unit squares long and 7 unit squares wide. Each unit square represents one square inch.
Step-by-step explanation:
The time taken to create a 2-foot by 4-foot pattern drive is 38.4 minutes.
What is a unit rate?A unit rate means a rate for one of something.
It is written as a ratio with a denominator of one.
We have,
A rectangle tile area = 3-inch by 5-inch
Area = 15 inches
Time taken to position 15 inches tile = 6 minutes.
We can write as,
15 inches = 6 minutes _____(1)
We have a 2-foot by 4-foot pattern drive.
Area = 8 feet
We know that,
1 foot = 12 inches
Multiply both sides by 8.
8 feet = 8 x 12 inches
8 feet = 96 inches _______(2)
Now,
From (1) and (2) we get,
15 inches = 6 minutes
Multiply 96/15 on both sides we get,
96/15 x 15 inches = 96/15 x 6 minutes
96 inches = 38.4 minutes
Thus the time taken to create a 2-foot by 4-foot pattern drive is 38.4 minutes.
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c(x) = 0.08x + 9.75
please answer
Answers
Step-by-step explanation:
I hope this will be helpful for you.
If f(x) = 1/x which equation describes the graphed function? Apex ...
Answers
1) horizontal translation 2 units left (x+2)
2) vertical translation 1 unit down (-1)
The equation that describes the graphed function [tex]f(x) = \frac{1}{x}[/tex] is option A:[tex]y = (x + 2) - 1.[/tex] This is shown in the graph given below, and transformation is translation.
To mathematically derive this equation, start with the original function [tex]f(x) = \frac{1}{x}[/tex].
The given function [tex]f(x) = \frac{1}{x}[/tex] has a reciprocal relationship between x and y.
To perform a horizontal translation 2 units left, substitute (x + 2) for x. This gives:[tex]f(x + 2) = \frac{1}{x + 2}[/tex].
Next, to achieve a vertical translation 1 unit down, subtract 1 from the function.
Thus, [tex]f(x + 2) - 1 = \frac{1}{x + 2}- 1[/tex].
Simplifying further, combine the terms gives:
[tex]y = (x + 2) - 1.[/tex]
This equation represents the original function :
[tex]f(x) = \frac{1}{x}[/tex]
After a horizontal translation of 2 units left and a vertical translation of 1 unit down.
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Kareem caught a 4 3/4 pound fish. How much did it weigh in ounces?
Answers
Answer:
76 ounces as ( 1 lb = 16 oz ) 4 3/4 * 16 = 76
Step-by-step explanation:
4 3/4 pounds = 76 ounces or 4 3/4 pounds = 2.15456376 kilograms
help me I can't solve this question
Answers
The constant of proportionality of the given function of the graph would be 3 / 4.
What is the constant of proportionality?The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.
Let the equation below which is shown in the graph:
y = kx ....(i)
where k is the constant of proportionality.
As per the given graph, take a point x = 4, and y = 3
Substitute the values x = 4, and y = 3 in the equation (i)
3 = k × (4)
4k = 3
k = 3 / 4
Thus, the constant of proportionality of the given function of the graph would be 3 / 4.
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a new test has been developed to determine whether a given student is overstressed. this test is 95% accurate if the student is not overstressed, but only 85% accurate if the student is in fact overstressed. it is known that 99.5%
Answers
0.030844 is the probability that the test results are correct, and that this student is not overstressed.
What is a probability math example?
Probability is the measurement of how likely something is to happen. As an example, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head. We write P(heads) = 12 here. The four most popular approaches to probability are axiomatic, classical, empirical, and subjective.Given that a particular students test negative for stress negative for stress then probability that the test result are correct and this student is not over stressed.
= 0.5% × 95% / ( 99.5% × 15% ) + ( 0.5% × 95% )
= 0.030844
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The complete question is -
A new test has been developed to determine whether a given student is overstressed. This test is 95% accurate if the student is not overstressed, but only 85% accurate if the student is in fact overstressed. It is known that 99.5% of all students are overstressed. Given that a particular student tests negative for stress, what is the probability that the test results are correct, and that this student is not overstressed?
Question content area top
Part 1
Write the absolute value function as a piecewise-defined function with linear parts.
f(x)=4x+5
Answers
The absolute function f(x) = 4x+5 as a piecewise-defined function is:
f(x) = { -4x-5 , x<-5/4
4x+5 , x ≥-5/4 }
Given, the absolute function f(x) = 4x+5
The fundamental tenet of piecewise linear regression is that we should construct the regression function in "pieces" if the data exhibit various linear trends over various parts of the data. The components may or may not be joined.
when 4x+5 < 0
4x < -5
x < -5/4
f(x) = -(4x+5) = -4x-5
when 4x+5 ≥ 0
4x ≥ -5
x ≥ -5/4
f(x) = 4x+5
so f(x) = { -4x-5 , x<-5/4
4x+5 , x ≥-5/4 }
since, I x I = { -x , x<0
x , x ≥0}
Therefore, we get the required piecewise-defined function with linear parts.
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