Select all the true statements for the figures shown.
A. If m∠D + m∠E = 90, then m∠F = 90. The triangles are congruent by HL.
B. If m∠D = 37, then m∠A = 37. The triangles are congruent by AAS.
C. If ∠E ≅ ∠B, then the triangles are congruent by SAS.
D. If ∠F is a right angle, then the triangles are congruent by HL.
E. If m∠D + m∠E = 90, then m∠F = 90. The triangles are congruent by SSA.
Answer:
i just had this lol its a and d
Step-by-step explanation:
Question 1
What is their rate of change (speed) in Section A? Remember to include units.
Question 2
What is the rate of change of (speed) in section B? Remember to included units
Question 3
What is their rate of change of (speed) in section D (hours 7-10)? Remember to include units
Question 4
During which section was the person moving at the highest speed? What was their speed? Defend your answer
Question 5
During which section did the person travel the farthest? How did they travel?
Question 6
BONUS: write a short (paragraph) scenario that tells the story about where on the graph came from. You can be as creative as you want!
Please only comment if you will give me all these answers thank you!
Answer:
On attached woksheet
Step-by-step explanation:
The graph has units of time (sec) on the x axis and distance (meters) on the y. The lines in the graph represent a change in distance from the origin as a function of time. The slopes of these lines represent the speed, in m/sec., for that line. Since they are straight lines, the speed is not changing for that time period. A flat, horizonal, line represent a stationary object. Distance does not change with time. Steeper lines represnt faster speeds - the distance changes more quickly for the same time period.
See attached worksheet.
tan(-x)cos(-x) simplify
The trigonometric equation be tan(-x)cos(-x) then we get -sin (x).
What is meant by trigonometric functions?A function of an angle is a trigonometric function. They are utilized to connect the triangle's angles and sides' lengths.
Trigonometry is the study of angles and the angular connections between figures in two and three dimensions. The trigonometric functions that make up trigonometry are cosecant, cosine, cotangent, secant, sine, and tangent. These are also known as the circle functions.
Trigonometry is used to define directions such as the north, south, east, and west. It also tells you the direction to point the compass in order to travel straight forward. It helps to locate a certain location during navigation. The shore's separation from a certain place in the sea can likewise be determined using this method.
Let the given function be tan (-x) cos (-x)
Use the negative angle identity: tan (-x) = -tan (x)
= cos (x) (-tan (x))
Remove parentheses: (-a)= -a
= -cos (x) tan (x)
Express with sin, cos
= -sin (x)
Therefore, simplifying the equation, tan(-x)cos(-x) we get -sin (x).
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tan(-x).cos(-x) = -sin(x)
What are trigonometric ratios?
Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.are therefore assessed in relation to sides and angles.
We know that, tan(x) = sin(x)/cos(x)
Now, calculating tan(-x).cos(-x)
⇒ [tex]\frac{sin (-x).cos (-x)}{cos (-x)}[/tex]
⇒ sin(-x)
Since, sin function is an odd function, it can be expressed as below.
sin(-x) = -sin(x)
Thus, tan(-x).cos(-x) = -sin(x)
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For the following diagrams find the measure for all the Missing angles
The missing measures of the named angles are:
w = 62°
z = 57°
y = 57°
x = 61°
b = 24°
a = 132°
c = 156°
d = 156°
e = 132°
f = 24°
g = 24°
h = 156°
i = 156°
How to Find the Measure of Missing Angles in a Triangle?To find the measures of each of the named angles in the figure above, note the following:
Angles on a straight line = 180 degrees.Base angles of any isosceles triangle are congruent.Vertical angles are congruent.Sum of triangle = 180 degrees.Therefore:
w = 62° [alternate interior angles are congruent]
z = 180 - 123 = 57° [angles on a straight line]
y = 180 - 62 = 57° [angles on a straight line]
x = 180 - 62 - 57 = 61° [triangle sum theorem]
b = 24° [base angles of isosceles triangle]
a = 180 - 2(24) = 132°
c = 180 - 24 = 156°
d = 180 - 24 = 156°
e = a = 132°
f = g = 1/2(180 - e)
Plug in the value of e:
f = g = 1/2(180 - 132)
f = g = 24°
h = i = 180 - 24 = 156°
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among the 20 first-class passengers on the flight, there were four businessmen from the middle east. two of them were the two passengers selected to be searched. they complained of profiling, but the airline claims that the selection was random. what do you think? support your conclusion with a simulation.
Therefore the probability that all person are chosen at random for security screening is P=0.0315 Thus, the search was random and passengers should not be suspicious for the search
What is probability ?The likelihood of an event happening is determined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us. In these situations, we state that there is a likelihood that the event will occur or not.
Here,
The probability that all person are chosen at random for security screening is
Where four businessmen from the middle east= [tex]C^{4} _{2}[/tex]
and remaining 16 are not searched =[tex]{C^{16} _{0}[/tex]
Thus, for selection of 2 people at random from 4 businessman
P = [tex]\frac{C^{16} _{0} * C^{4} _{2}}{ C^{20} _{2}}[/tex]
P=1*6/190
P=6/190
P=0.0315
Therefore the probability that all person are chosen at random for security screening is P=0.0315 Thus, the search was random and passengers should not be suspicious for the search.
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How do you write 82 in scientific notation?
How you write it is...
m x 10n
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 9 cubic feet and the volume of each large box is 17
cubic feet. There were twice as many large boxes shipped as small
boxes shipped and the total volume of all boxes was 258 cubic feet.
Determine the number of small boxes shipped and the number of large
boxes shipped.
There were __?_
small boxes shipped and __?_
large boxes shipped.
Answer:
9 small boxes and 15 large boxes
Step-by-step explanation:
x = small box
y = large box
x + y = 24
9x + 24y = 441
-9x - 9y = -216
15y = 225
y = 15
x + 15 = 24
x = 9
Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form.
3,4+i
The conventional form of the polynomial is f(x)=x 28x+17. If polynomial function f has rational coefficients and a leading factor of 1, then it has the lowest degree.
How can you recognize a polynomial?A polynomial function is a function in an equation, such as the quadratic equation, cubic equation, etc., that only uses quasi integer powers or only positive integer coefficients of a variable. A polynomial with an exponent of 1 is, for instance, 2x+5.
As conjugate pairs make up complex zeros, we can infer that 4-i4-i is also a zero from the fact that 4+i4+i is also a zero.
A polynomial function's factor x-axa is one of the factors if aa is its zero. Consequently, the polynomial function is
f(x)=a[x-(4+i)] [x-(4-i)]
f(x)=a[x−(4+i)]
[x−(4−i)]
Expand:\sf(x)=a[x^2-(4-i)
x-(4+i)x+(4+i)(4-i)]
F(x) = a [x 2 (4i)x(4+i)x+(4+i)(4i)]
f(x)=a[x^2-4x+ix-4x-ix+
(16-i^2)]
F(x) = a [x 2 4x+ix4x+ix+(16i 2)]
f(x)=a[x^2-8x +(16-(-1))]
f(x)=a[x 2 −8x+(16−(−1))]
f(x)=a(x^2-8x +17)
f(x)=a(x 2 −8x+17)
Considering that a=1a=1 is the leading coefficient, this means:
color="#c34632" f(x)="x2-8x +17"
f(x)=x 2 −8x+17
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consider the inequality x 36>x4 1. which value of x is a solution to the inequality?
Using the laws of inequality, the inequality x-36>4x can be solved as x>-12.
What is inequality?In mathematics, the term "inequality" refers to a relationship between two expressions or values that is not equal to each other. The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. Both mathematical phrases, equations and inequalities, are created by connecting two expressions. The equal sign (=) indicates that two expressions in an equation are deemed to be equal. The symbols >,,, or indicate that the two expressions in an inequality are not necessarily equal.
Here,
x-36>4x
3x<-36
-3x>36
x>-12
The solution for the inequality x-36>4x is x>-12 using properties of inequality.
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The area of a rectangle is 215.1 m². If the length is 18 m, what is the perimeter of the
rectangle?
Answer: 59.9 m
Step-by-step explanation:
Area of rectangle = Length times Width
We already know the length is 18m
So take 215.1 divided by 18= 11.95m
To find the perimeter of the Rectangle we use the formula
p= 2(18+ 11.95) = 59.9 m
So the perimeter is 59.9 m
The length of a picture frame is 8 inches more than the width. For what values of x is the perimeter of the picture frame greater than 160 inches?
What year was math invented?
Answer:
Around 3000 BC
Answer:
It is difficult to pinpoint a specific year or time period in which math was "invented," as math is a fundamental aspect of human thought and has likely been present in some form since ancient times.
The study of mathematics has a long and rich history, dating back to ancient civilizations in Mesopotamia, Egypt, Greece, and India. These early societies developed mathematical concepts and techniques to aid in practical tasks such as measuring land, calculating the volume of objects, and tracking the movement of celestial bodies.
As human civilizations developed and advanced, so too did the study of mathematics. Over time, new mathematical concepts and techniques were developed and refined, leading to the development of more advanced branches of mathematics such as algebra, geometry, trigonometry, and calculus.
In summary, math has a long and complex history, and it is difficult to pinpoint a specific year or time period in which it was "invented." It has likely been present in some form since ancient times and has evolved and developed over the course of human history.
Step-by-step explanation:
SELF EXPLANATORY
the advantage of using the work sampling approach during a training needs assessment is that the assessor:
The advantage of using the work sampling approach during a training needs assessment is that the assessor : sees the work actually being done , the correct option is (d) .
In the question ,
it is asked about the advantage of using the work sampling approach during the training .
we know that Assessing need special skills and experience to be competent.
Generally, evaluators or assessors need to have interpersonal skills and communicates effectively with students.
So , During the training if the work sampling approach is used then assessor will see the work actually being done before hand .
Therefore , the advantage is that the will see the work actually being done .
The given question is incomplete , the complete question is
The advantage of using the work sampling approach during a training needs assessment is that the assessor:
(a) sees the results of each person doing the work
(b) does not get heavily involved with any job
(c) actually does each job
(d) sees the work actually being done
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Question The most common graphical presentation Of quantitative data is a...... a)histogram b)bar graph c)relative frequency d)pie chart
A bar graph is the most popular visual representation of quantitative data.
Define bar graph.Another name for them is bar charts. One tool used in statistics for data processing is the bar graph. Using a bar diagram, it is simple and quick to compare sets of data among several groupings. On one axis of the graph are discrete numbers, while on the other are categories. The purpose is to illustrate how the two axes are related. Bar charts can also show significant alterations in data over time.
Given,
A bar graph is the most popular visual representation of quantitative data.
b) Bar graph
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How do you simplify 2/(3/11) ?
The simplified form of the expression [tex]\frac{2}{\frac{3}{11}}[/tex] is [tex]\frac{22}{3}[/tex].
To simplify the expression [tex]\frac{2}{\frac{3}{11}}[/tex], you can start by performing the division in the parentheses first:
[tex]\frac{2}{\frac{3}{11}}[/tex] = [tex]\frac{2}{\frac{3}{11}}[/tex] × [tex]\frac{11}{11}[/tex]
= 2 × [tex]\frac{11}{3}[/tex]
Then, you can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor:
2 × [tex]\frac{11}{3}[/tex] = [tex]\frac{(2 * 11)}{(3 * 1)}[/tex]
= [tex]\frac{22}{3}[/tex]
So the simplified form of the expression [tex]\frac{2}{\frac{3}{11}}[/tex] is [tex]\frac{22}{3}[/tex].
Simplification is a process of making something simpler or easier to understand by reducing the amount of complexity or detail. This can be done by removing or combining elements, or by reorganizing the structure. Simplification can be used in problem-solving, decision-making, or other tasks to make it easier to understand, interpret, or use the information.
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how many groups of five can be chosen that contain at most three women? a group of five that contains at most three women can contain no women, one woman, two women, or three women. so, the number of groups of five that contain at most three women is
The no. of groups of five can be chosen that contain at most three women is 60.
The method we use to solve this is combination method.
What is combination in mathematics?Mathematical combinatorics is a division that deals with counting.
Combinatorics can assist us in counting the possible sequences in which something can occur.
Numerous applications of combinatorics can be found in other branches of mathematics, such as graph theory, coding and cryptography, and probability.
In mathematics, you can also have combinations, such as linear combinations or combinations of functions.
solutionTo solve this we use combination method of mathematics
The no. of groups of five can be chosen is
⁵C₃ * ⁴C₂
⇒ (5 * 4 * 3! / 3! * 2!) * (4 * 3 * 2! / 2! * 2!)
⇒ (5 * 4 / 2 * 1) * (4 * 3 / 2 * 1)
⇒ 5 * 2 * 2 * 3
⇒ 60
The no. of groups of five can be chosen that contain at most three women is 60.
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Last year, 160 new houses were built in a neighborhood. So far this year, 3/8 of them have been sold. How many new houses have been sold this year?
Write your answer in simplest form.
Answer:
The answer is 60
Step-by-step explanation:
160 × 3/8 = 480/8 = 60
Thus, 60 new houses have been sold this year.
A cookie jar contains six chocolate chip cookies, four peanut butter cookies and five oatmeal cookies Two cookies are chosen from the jar What are the odds against both chosen cookies being chocolate chip cookies? Write your ratio in lowest terms. (ex: 3.2)
The odds that the chosen cookies being chocolate chip cookies is 1/7
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
We are given that
A cookie jar contains six chocolate chip cookies, four peanut butter cookies and five oatmeal cookies
Hence the total number of cookies are 15
Two cookies are selected from the jar
This can be done in 15c2 ways that is 105
Now we have six Choco chip cookies in the same jar
Number of ways in which we can select 2 cookies is 6c2
That is 15
Hence the odds are 15/105
That is 1/7.
The odds that the chosen cookies being chocolate chip cookies is 1/7.
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Reflect the traingle ABC Whose vestices areA(3,1), B(-2,5) & C(5,2) in x-axis on the graphpaper. Shade the reflected image & Write theCo-ordinates.
Answer:
A' (3,-1)
B' (-2,-5)
C' (5, -2)
Step-by-step explanation:
Notice how the x values stay the same and the y values become the opposite of the original points.
Please help
Select the correct answer.
For which quotient is = 7 an excluded value?
On solving the provided question, we can say that the root of the equation [tex](x^2 - 10x+21)(x+7)=0[/tex]are x= -7,+7,3
What is equation?An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
A quadratic equation is a second-order polynomial equation in one variable that goes like this: x ax2 + bx + c=0, where a 0. Given that it is a second-order polynomial equation, the algebraic basic theorem ensures that it has at least one solution. Real or complicated solutions are both possible.
Set the denominator to 0
[tex](x^2 - 10x+21)(x+7)=0\\(x^2-7x-3x+21)(x+7)=0\\(x(x-7)-3(x-7))(x+7)=0\\(x-7)(x+7)(x-3)=0\\ (x-3)(x^2 - 7^2)=0\\x= -7,+7,3[/tex]
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It can sometimes get colder than 3 degrees in the north. Select all the
possible temperatures for the north.
A) -2 degrees
B) 0 degrees
C) 2 degrees
D) 4 degrees
E) 6 degrees
The possible temperatures for the north will be 4 degrees and 6 degrees. The correct option is D and E.
How to calculate the temperature?Mathematical statements with at least two terms connected by an operator and containing either numbers, variables, or both are referred to as expressions.
The direction that heat energy will spontaneously flow depends on temperature. Temperature is the degree to which a body is hot or cold. because it was mentioned that the north can occasionally experience temperatures below 3 degrees. D and E are the appropriate choices
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the length of the sides of a square are initially 0 cm and increase at a constant rate of 7 cm per second. suppose the function f determines the area of the square (in cm2) given a number of seconds, t , since the square started growing. write a function formula for f .
The function of the area of the square is A(t) = 49t².
A function is a relation between the input abd output values.
The length of a square's side starts from 0 cm and increases at a constant rate of 7 cm per second.
Let us assume that the function 'f' determines the area of the square (in cm²)
Also Lets the length of side of square is x
rate of change of length with respect to time can be denoted as (dx/dt) = 7 cm/sec
⇒ x = 7*t
Area of square = ( length of side )²
{as the length of side is 7t} {varies by time}
Area of square A(t) = ( 7*t )²
Therefore, The function of the area of the square is A(t) = 49t².
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Find the missing side of the triangle
Round your answer to the nearest tenth
The length of missing side of triangle is 11cm.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The given triangle is a right angled triangle.
In the triangle hypotenuse is 12cm, opposite side is 4.8cm.
We need to find the adjacent side which is represented by x.
By pythagoras theorem we find the missing side
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides
12²=4.8²+x²
144=23.04+x²
subtract 23.04 on both sides
120.96=x²
Take square root on both sides
x=10.99
x=11
Hence, the length of missing side of triangle is 11cm.
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Susan has a collection of 60 nickels and dimes. If the number of nickels is five times the number of dimes, how many nickels and how many dimes does she have?
There are 10 dimes and 50 nickels.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Susan has a collection of 60 nickels and dimes.
And, The number of nickels is five times the number of dimes.
Now,
Let number of dimes = x
Then, The number of nickels = 5x
Since, Susan has a collection of 60 nickels and dimes.
Hence, We get;
⇒ x + 5x = 60
⇒ 6x = 60
⇒ x = 10
Thus, The number of dimes = x
= 10
Then, The number of nickels = 5x
= 5 × 10
= 50
Therefore, There are 10 dimes and 50 nickels.
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find the volume of the given solid. bounded by the coordinate planes and the plane 7x + 9y + z = 63
The volume of the given solid, with the boundaries, is given as follows:
661.5 cubic units.
How to obtain the volume of the solid?The volume of the solid is obtained using a double integral.
The equation for the solid is given as follows:
7x + 9y + z = 63.
z = 63 - 7x - 9y.
The coordinate planes bound the plane, hence:
y varies between 0 and 7 - 7x/9.x varies between 0 and 9.Hence the double integral that is used to obtain the volume of the solid is given as follows:
[tex]V = \int_{0}^{9}\int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dydx[/tex]
The inner integral is given as follows:
[tex]I = \int_{0}^{7 - \frac{7x}{9}} 63 - 7x - 9y dy[/tex]
Which, applying the Fundamental Theorem of Calculus, has the result given as follows:
[tex]I = -98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441[/tex]
Then the volume of the solid is given by the outer integral as follows:
[tex]V = \int_{0}^{9} \left(-98x + \frac{49x^2}{9} - \frac{(7x + 63)^2}{18} + 441\right) dx[/tex]
Which has a numeric value of:
661.5 cubic units.
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would the following side lengths make a right triangle:20,20 square root of 800
No, The side lengths does not make a right triangle.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The sides of the triangle are;
⇒ 20, 20 and √800
Now,
Since, The sides of the triangle are;
⇒ 20, 20 and √800
Hence, We can apply the Pythagoras theorem as;
⇒ (√800) ² = √ 20² + 20²
⇒ 800 ≠ √800
Thus, The side lengths does not make a right triangle.
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a shipment contains 10,000 switches. of these, 1000 are bad. an inspector draws 2 switches at random, one after the other.
The probability that both switches are defective is 1%.
What is a probability answer?
Mathematics' branch of probability, where probability is the likelihood that any event will occur, deals with the occurrence of random events.
Probability values range from 0 to 1, with 1 being the most likely value.
Given that a shipment contains 10,000 switches, and of these, 1000 are bad, and an inspector draws 2 switches at random, one after the other, to find the probability that both switches are defective the following calculation must be performed:
1000/10000 = 1/10
1/10 x 1/10 = X
0.1 x 0.1 = X
0.01 = X
0.01 x 100 = 1
Therefore, the probability that both switches are defective is 1%.
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The complete question is -
Inspecting switches A shipment contains 10,000 switches. Of these, 1000 are bad. An inspector draws 2 switches at random, one after the other.A) Draw a tree diagram that shows the sample space of this chance process.B) Find the probability that both switches are defective.
Your friend thinks that the triangles shown below are congruent by SAS. Is your friend correct? Explain.
Choose the correct answer below.
A.
Yes, the figure indicates that two corresponding angles and their included side are all congruent.
B.
No, the congruent sides are not the included sides.
C.
No, the congruent angles are not the included angles.
D.
Yes, the figure indicates that three corresponding sides are congruent.
E.
No, the figure only indicates that two corresponding sides are congruent, not three as required by the SAS Postulate.
F.
Yes, the figure indicates that two corresponding sides and their included angle are all congruent.
Yes, the figure indicates that two corresponding angles and their included side are all congruent. Option A
What is the congruency?We know that the term congruency can be used to refer to the triangles that are equivalent. For the triangles that are equivalent, we can see that there are some kind of relationship that binds the triangles together.
The kinds of congruency of the triangles that we may have are the following;
Angle Angle side
Side angle side
Side side side
Angle Side angle
If we look at the triangles that we have in the two images that have been conspicuously attached to the question that we are trying to attend to, it is clear that two triangles have similar sides and a similar included angle hence they are congruent by the theorem of SAS.
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The variables x and y vary directly. Use the values to find the constant of proportionality, k. Then write an equation that relates x and y. Write any fractions in simplest form.
y=20; x=12
Step-by-step explanation:
x =ky
x=12,y=20
12 =20k
divide both sides by 20
k=12/20
= 6/5
X=6/5y
What big problem does Power Query solve? a. Creating interactive visuals b.Cleaning messy data
c.Making PivotTable more user friendly d.Allowing users to share data
Power Query solve the problem b) Cleaning messy data
Power Query is a Microsoft Excel feature that is designed to help users extract, transform, and load data from a variety of sources. It is particularly useful for solving the problem of cleaning messy data.
Cleaning messy data is a common challenge that many people face when working with large or complex datasets. Data can be messy for a variety of reasons, such as being in an inconsistent format, having errors or typos, or containing duplicates or missing values. Cleaning up this data can be time-consuming and error-prone, especially if it is done manually.
Power Query provides a set of tools and features that make it easier to clean and transform data in Excel. It allows users to easily extract data from various sources, remove unwanted columns or rows, split or merge columns, apply filters and transformations, and more. This helps users save time and effort when working with large or complex datasets, and ensures that their data is clean and ready for analysis.
In summary, Power Query helps users solve the problem of cleaning messy data by providing a set of tools and features that make it easier to extract, transform, and load data in Excel.
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