Answer:
∠ ABC ≈ 78°
Step-by-step explanation:
using the Cosine rule in Δ ABC
cos ABC = [tex]\frac{a^2+c^2-b^2}{2ac}[/tex]
where a is the side opposite ∠ A , b is the side opposite ∠ B and c the side opposite ∠ C
here a = BC = 6 , b = AC = 7 and c = AB = 5 , then
cos ABC = [tex]\frac{6^2+5^2-7^2}{2(6)(5)}[/tex] = [tex]\frac{36+25-49}{60}[/tex] = [tex]\frac{12}{60}[/tex] , then
∠ ABC = [tex]cos^{-1}[/tex] ( [tex]\frac{12}{60}[/tex] ) ≈ 78° ( to the nearest degree )
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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In the given figure, write the relation between AB and CD as well as AB and AE.
Answer:
A point and C point are correspondingC and D point are parallel linesI'm not really sure about this one but I think A and E point are also parallel as there is a straight lineHope this Helps!!!
Please help! Thank you!
Answer: I believe f(-1) will be -1
Step-by-step explanation:
You'll notice that f(x) is increasing by 7, so instead of adding 7 subtract 7.
Extend the table to the left having the (x) go down
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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a summer camp that offers one-week programs faces the challenges of long queues as parents try to check in their children each saturday morning. if they were to add more staff to assist with the check-in process, then which of the following will occur? the average time parents wait decreases. the maximum time the parents wait decreases. the average number of parents waiting to check in their child decreases.
If they were to add more staff to assist with the check-in process, then the average time parents wait decreases, the maximum time the parents wait decreases and average number of parents waiting to check in their child decreases. So, the correct answer is (i), (ii), (iii).
Parents and students standing in line for check-in and actually checking in. Parents and children are the customers here, and the staff who support parents and students are the servers. A limited number of servers and many clients will increase the queue length. In other words, as more parents enter the queue, the wait time for each parent increases, increasing the average wait time. Additionally, the longer the queue, the longer the maximum wait time.
Therefore, adding check-in staff will increase the number of customers to serve the same number of patients. Queues are split across multiple servers, so you get all three benefits.
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Solve this and I give you brain crown and points please quickly
Answer:
one solution
Step-by-step explanation:
because it has diffrent slopes
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
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.
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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Which of the following is not a congruence criteria a SSA B SAS C AAS D RHS?
The congruency of a triangle is not determined by SSA. As a result, choice C is the right response.
What is a triangle and the response?
Triangles are a particular kind of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here.
Three-sided polygons include triangles. Three triangle angles added together equal 180 degrees.
The sides (S) and angles (A) of two triangles are said to be congruent if they are equal.
The triangle must meet the SAS, ASA, SSS, and RHS criteria in order to be congruent.
The congruency of a triangle is not determined by SSA. As a result, choice C is the right response.
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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
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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Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour. How many pages can Shawn type in one hour? A. B. C. D.
Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.
What is typing speed?
How many words a person can correctly type in one minute. He types at a 60 wpm rate.
Given:
Shawn is typing a paper for class. He can type 1 2/7 pages in 1/3 of an hour.
We have to find how many paged he can type in one hour.
First to convert improper fraction 1 2/7 into a fraction.
⇒ [tex]1\frac{2}{7} = \frac{7*1+2}{7} = \frac{9}{7}[/tex]
So, Shawn can type 9/7 pages in 1/3 of an hours.
i hour = 3/3
So, Shawn can type
9/7 x 3/3 = 27/21 = [tex]1\frac{6}{21}[/tex] pages in one hour.
Hence, Shawn can type [tex]1\frac{6}{21}[/tex] pages in an one hour.
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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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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.
Is a origin on a graph proportional relationship?
Answer: Yes
Step-by-step explanation:
Most of the time, if a graph passes through the origin it is a proportional relationship!
Amelia left her house at time zero and drove to the store, which is 4 blocks away, at a speed of 2 blocks per minute. Then she stopped and went into the store for 2 minutes. From there, she drove in the same direction at a speed of 7 blocks per minute until she got to the bank, which is 14 blocks away from the store. She stopped at the bank for 3 minutes. Then she drove home at a speed of 6 blocks every minute. Make a graph of showing the number of blocks away from home that Amelia is x minutes after she leaves her house, until she gets back home.
The distance time Graph of Amelia as she gets back home is attached below
What is a distance-time graph?
How far an item has come in a certain amount of time is displayed on a distance-time graph. The graph that shows the result of the distance vs time analysis is a straight-line graph.
The Y-axis represents the distance.
The X-axis is used to plot time.
On a graph of distance vs time, curved lines denote a changing speed.
When analyzing the motion of bodies, we work with the distance-time graph. A distance-time graph related to a body's motion may be created if we measure a body's motion's distance and time and display the resulting data on a rectangle graph.
let us take Amelia at (0,0) when she is at her home she went to the store which is 4 blocks away with a speed of 2 blocks per min which means she will reach the store after 2 min,i.e. now her location is (2,4) she went into the store for 2 min which means she doesn't move from that location for 2 min so the time is now 6 min from the moment she started. So, now here location is (4,4)From there, she drove in the same direction at a speed of 7 blocks per minute until she got to the bank, which is 14 blocks away from the store. which means she is at (6,18) because it took he 2 min to reach the bank as she was travelling with a speed of 7 blocks per minShe stopped at the bank for 3 minutes which means she is at the same location but the time is now 9 min so she is at (9,18)Then she drove home at a speed of 6 blocks every minute and she need to travel 18 blocks with the speed of 6 blocks per min so, she will reach her home after 3 min and now the is at her home which is at (12,0)Learn more about the Distance time graph from the link below
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Which expression is equivalent to (m^-2n^-3)^-4
By using some exponent properties, we will find the equivalent expression:
(m⁻²*n⁻³)⁻⁴ = m⁸*n¹²
How to find an equivalent expression?Here are some exponent properties that we need to use:
(aⁿ)ˣ = aⁿ*ˣ
(a⁻ⁿ) = (1/a)ⁿ
Here we have the expression:
(m⁻²*n⁻³)⁻⁴
The exponents can be distributed under multiplication, then:
(m⁻²)⁻⁴*(n⁻³)⁻⁴
Now we can use the first property so we get:
(m⁻²)⁻⁴*(n⁻³)⁻⁴ = m⁽⁻²*⁻⁴⁾*n⁽⁻³*⁻⁴⁾
m⁽⁻²*⁻⁴⁾*n⁽⁻³*⁻⁴⁾ = m⁸*n¹²
That is the equivalent expression.
(m⁻²*n⁻³)⁻⁴ = m⁸*n¹²
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The value of x is the equation X + 5 = 12 is
Answer:
x+5=12
or,x=12-5
or,x=7
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 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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If point R is the greatest integer smaller than √51 on a number line, what is the value of point R?
The value of R is 7 , we can find answer using concept of greatest integer and square root .
What is square root of a number ?
Square root , in mathematics , a factor of a number that , when multiplied by itself , returns the original number.
e.g. Square root of 9 are both 3 and -3.
Symbol = " √ "
In given que, we need to find greatest integer smaller than √51.
Root of 51 will not give exact integer value.
As we know root of 49 is 7 and root of 64 is 8.
And 51 lie between 49 and 64,
So, Square root of 51 will also lie between 7 and 8.
So, the greatest integer smaller than √51 will be 7.
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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.
Find each of these values. a) (19² mod 41) mod 9 b) (32³ mod 13)² mod 11 c) (7³ mod 23)² mod 31 d) (21² mod 15)³ mod 22
The remainder will be 33, 9, 7, and 14 for options a, b, c, and d respectively.
The Remainder is the extra part of a number that restricts the number to be divided completely.
a)
(19² mod 41) mod 9
Let us determine 361 mod 41
a=361 = 328+33= 8*41+33 =8d+33
The remainder is the constant in the final expression: 361 mod 41=33
33 mod 9 = 6 (since a=33= 27+6=3*9+6=3d+6)
b)
(32³ mod 13)² mod 11
Let us determine 32 mod 13
a=32=26+6=2*13+6+2d+6
The remainder is the constant in the final expression: 32 mod 13=6
[tex](6^{3} mod13)^{2} mod 11\\(216mod13)^{2} mod 11[/tex]
Let us determine 216 mod 13
a= 216= 208+8=16*13+8 = 16d+8
The remainder is the constant in the final expression: 216 mod 13=8
[tex]8^{2} mod 11\\64 mod 11[/tex] = 9 (since, 64= 55+9= 11*5+6= 11d+6)
c)
(7³ mod 23)² mod 31
[tex](343mod23)^{2} mod 31\\[/tex]
Let us determine 343 mod 23
a=343=322+21=14*23+21=14d+21
The remainder is the constant in the final expression: 343 mod 23= 21
[tex]21^{2} mod 31 = 441 mod 31=7[/tex] (since a = 441=434+7=14*31+7=14d+7)
d)
(21² mod 15)³ mod 22
[tex](441mod15)^{3} mod 22[/tex]
Let us determine 441 mod 15
a=441 = 435+6= 29*15+6= 29d+6
The remainder is the constant in the final expression: 441 mod 15= 6
[tex]6^{2} mod 22=36mod22= 14[/tex] (since a = 36= 22+14= 1*22+14= d+14)
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THREE HOLIDAY ASSIGNMENT -mati 1. A husband earns sh 2450 more than his wife. If the wife earns sh 9470. Find their total earnings.
Answer:
husband = wife earn + 2450
wife = 9 470
Husband earnings:
9 470 + 2 450 = sh 11 920
husband + wife
11 920 + 9 470 = sh 21 390
Therefore their total earnings is sh 21 390Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-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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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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determine if the following statements are true or false, and explain your reasoning. (a) describe the strength of the relationship in the data, and whether or not fitting a linear model would be reasonable: weak relationship moderate, linear model is reasonable strong, linear model is reasonable strong, but linear model is not reasonable moderate, but linear model is not reasonable (b) describe the strength of the relationship in the data, and whether or not fitting a linear model would be reasonable: strong, linear model is reasonable moderate, but linear model is not reasonable moderate, linear model is reasonable strong, but linear model is not reasonable weak relationship (c) describe the strength of the relationship in the data, and whether or not fitting a linear model would be reasonable: moderate, linear model is reasonable strong, but linear model is not reasonable strong, linear model is reasonable moderate, but linear model is not reasonable weak relationship (d) describe the strength of the relationship in the data, and whether or not fitting a linear model would be reasonable:
Part-A: linear model is not reasonable which is strong
Part-B : Strong, but linear model is not reasonable
Part-C : Strong, linear model is reasonable
Part-D : moderate, linear model is not reasonable
Given that,
We have to find explain the strength of the relationship in the data and whether or not it would be appropriate to fit a linear model.
We know that,
There are 4 options that are:
weak relationship
moderate, linear model is reasonable
strong, linear model is reasonable
strong, but linear model is not reasonable
moderate, but linear model is not reasonable
Therefore,
Part-A: linear model is not reasonable which is strong
Part-B : Strong, but linear model is not reasonable
Part-C : Strong, linear model is reasonable
Part-D : moderate, linear model is not reasonable
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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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How can you distinguish between a linear and exponential function?
Answer:
A linear function is a function whose graph is a straight line. An exponential function is a function in which the variable appears in an exponent. A linear function has a constant rate of change, meaning that the rate of change between two points on the line is the same. An exponential function has a variable rate of change, meaning that the rate of change between two points on the line is not constant.
Explanation: A linear function, has y-values with equal differences. An exponential function has y-values with equal ratios.
