I really need help with thisAvailable Choices:Acute TriangleEquiangular TriangleObtuse TriangleRight TriangleScalene TriangleIsosceles TriangleEquilateral Triangle
Answers
Observe the given figure carefully.
Consider the triangle ABE.
Since the angle formed at vertex A is a square angle, that is 90 degrees. So ABE must be a right triangle. Also, it is clearly visible that the side AE and AB are unequal. Also, we know that hypotenuse is the largest side of a right triangle, so it cannot be equal to either of the other two sides. So it can also be claimed that ABE is a scalene triangle.
Consider the triangle BEC.
Since all the angles formed by the sides of the triangle at vertices are less than 90 degrees, it can be claimed that BEC is an acute triangle. Also, note that,
[tex]\begin{gathered} ED=EF=5 \\ EC=EF+FC=5+2=7 \\ BE=7 \end{gathered}[/tex]So we see that the sides BE and EC of the triangle are equal, therefore, BEC will be an isosceles triangle.
Consider the triangle DEF.
From the diagram, it is clearly seen that,
[tex]DE=DF=EF[/tex]Since all three sides of the triangle measure equal, so DEF must be an equilateral triangle. Also, note that the angles formed by the sides at the vertices of the triangle are all 60 degrees that is less than 90 degrees. So DEF can also be designated as Acute Triangle.
Consider the triangle CDF.
In the triangle, the side DF measures 5 units, side CF measures 2 units. Also, it can be observed that the angle CFD is greater than 90 degrees. So CDF must be an obtuse triangle.
We just saw that side CF and DF are unequal. The side CD being opposite to the obtuse angle, is the largest side of the triangle, so it cannot be equal to either CF or DF. Therefore, triangle CDF must be a Scalene Triangle.
Thus, it is obtained that,
Triangle ABE is a right triangle and scalene triangle.
Triangle BEC is an acute triangle and isosceles triangle.
Triangle DEF is an acute triangle and an equilateral triangle.
Triangle CDF is an obtuse triangle and a scalene triangle.
Related Questions
Find the equation of the line that passes through (27,186) and (67,205) in slope intercept form
Answers
The equation of a line passing through points (x₁, y₁) and (x₂, y₂) is given by:
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]In this problem, we have:
x₁ = 27
y₁ = 186
x₂ = 67
y₂ = 205
So, we can use those values in the above formula to find the equation of the line:
[tex]\begin{gathered} \frac{y-186}{x-27}=\frac{205-186}{67-27} \\ \\ \frac{y-186}{x-27}=\frac{19}{40} \end{gathered}[/tex]Now, we can multiply both sides of the equation by the factor (x - 27):
[tex]\begin{gathered} \frac{y-186}{x-27}(x-27)=\frac{19}{40}(x-27) \\ \\ y-186=\frac{19}{40}x-\frac{513}{40} \end{gathered}[/tex]Finally, the equation in slope-intercept form requires y to be isolated on one side of the equation. So, we need to add 186 to both sides to put the equation in this form:
[tex]\begin{gathered} y-186+186=\frac{19}{40}x-\frac{513}{40}+186 \\ \\ y=\frac{19}{40}x+\frac{-513+186\cdot40}{40} \\ \\ y=\frac{19}{40}x+\frac{7440-513}{40} \\ \\ y=\frac{19}{40}x+\frac{6927}{40} \\ \\ y=0.475x+173.175 \end{gathered}[/tex]Notice you can write the slope and the intercept of the equation using fractions or decimal form.
The slope is the number multiplying x (0.475), while the y-intercept is the constant 173.175.
Therefore, the equation of the line that passes through (27,186) and (67,205) in slope-intercept form is
[tex]y=0.475x+173.175[/tex]what is the simplified form of [tex] {0.2}^{5} [/tex]
Answers
You have the following expression:
(0.2)⁵
in order to simplify it, you take into account that 0.2 can be written as 2/10, that is, 0.2=2/10=1/5. Furthermore, you take into account that for a fraction number, exponentiated to some n intenger, you have:
(a/b)ⁿ = aⁿ/bⁿ
Then, you have for (0.2)⁵:
(0.2)⁵ = (2/10)⁵ = (1/5)⁵ = 1⁵/5⁵
1⁵ = 1x1x1x1x1 = 1
5⁵ = 5x5x5x5x5 = 3125
Hence: (0.2)⁵ = 1⁵/5⁵ = 1/3125
In the formula A = ½b(h1 + h2)…What does A stand for?What does b stand for?What does h1 stand for?What does h2 stand for?
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The given formula is
[tex]A=\frac{1}{2}b(h_1+h_2)[/tex]Where the variables are
• A stands for Area.
,• b stands for base.
,• h_1 stands for height 1.
,• h_2 stands for height 2.
We can deduct the meaning of these variables because they are about the area of a geometric figure.
I'm stuck on this hw question. This has two parts:Part A: What postulate can you use to justify the similarity of the two triangles?Part B: Find the height of the flagpole
Answers
is your question complete?
Bre is shopping with her mom.She picks out a pair of jeans thatcost $60 and some t-shirts thatcost $12 each. If Bre's mom gavehe a budget of $130, what is themaximum number of t-shirtsshe can buy?
Answers
Given:
The total number of jeans is, j = 2.
The cost of jeans is, c (j) = $60.
The cos of t shirts is, c (t) = $12.
The total budjet of the purchase is, T = $130.
The objective is to find the maximum number of t-shirts that can be buy.
Explanaion:
Consider the number of t-shirts as t.
Then, the equation of cost can be written as,
[tex]\begin{gathered} j(c(j))+t(c(t))=T \\ 2($60$)+t(12)\le130\text{ . . . .(1)} \end{gathered}[/tex]To find t :
On solving the equation for t,
[tex]\begin{gathered} 120+12t=130 \\ 12t=130-120 \\ 12t=10 \\ t=\frac{10}{12} \\ t=0.83333\ldots. \end{gathered}[/tex]Since the value of t-shirt is less than 1, the person cannot buy any t-shirt.
Hence, the maximum number of t-shirts that can be buy with a budjet of $130 is zero.
In a recent survey of 230 voters, 62% of them in the upcoming election. which of the following is closest to the margin of error for this statistic
Answers
The sample size 230 here.
Among them 62% is them in the upcoming election.
Hence they are
[tex]\frac{62}{100}\times230=142[/tex]in number.
now we have to find the population standard deviation with the sample size 230.
It is given by
[tex]\frac{142}{230}=0.62[/tex]Hence the margin of error is given
[tex]0.62\times10=6.2[/tex]Hence the closest margin value is 6.4%
I need help on the last 3 columns on the right hand side and on the bottom as well.
Answers
EXPLANATION:
Given;
We are given a table of x and y values in order to calculate the correlation coefficient.
Required;
We are required to calculate and populate the tables for the values;
[tex]\begin{gathered} (i)\frac{X-\bar{X}\text{ }}{S_x} \\ (ii)\frac{Y-\bar{Y}}{S_y} \\ (iii)\frac{(X-\bar{X})(Y-\bar{Y})\text{ }}{S_xS_y} \end{gathered}[/tex]The variables here are;
[tex]\begin{gathered} \bar{X}=mean\text{ }value\text{ }of\text{ }x \\ \bar{Y}=mean\text{ }value\text{ }of\text{ }y \\ S_x=standard\text{ }deviation\text{ }of\text{ }x \\ S_y=standard\text{ }deviation\text{ }of\text{ }y \end{gathered}[/tex]With the use of a calculator the mean and standrd deeviations are as follows;
[tex]\begin{gathered} \bar{X}=31 \\ \bar{Y}=10.77 \\ S_x=10.68 \\ S_{y=2.17} \end{gathered}[/tex]The values that goes in the column;
[tex]\begin{gathered} \frac{X-\bar{X}}{S_x} \\ (i)\frac{18-31}{10.68}=-1.2172 \\ (ii)\frac{20-31}{10.68}=-1.0299 \\ (iii)\frac{22-31}{10.68}=-0.8427 \\ (iv)\frac{25-31}{10.68}=-0.5618 \\ (v)\frac{31-31}{10.68}=0 \end{gathered}[/tex]For the next column;
[tex]\begin{gathered} \frac{Y-\bar{Y}}{S_y} \\ \\ (i)\frac{14-10.77}{2.17}=1.4885 \\ \\ (ii)\frac{14-10.77}{2.17}=1.4855 \\ \\ (iii)\frac{12-10.77}{2.17}=0.5668 \\ \\ (iv)\frac{11-10.77}{2.17}=0.1059 \\ \\ (iv)\frac{10-10.77}{2.17}=-0.3548 \end{gathered}[/tex]For the last column;
[tex]\begin{gathered} \frac{(X-\bar{X})(Y-\bar{Y})}{S_xS_y} \\ \\ (i)\frac{(-1.2127)(1.4885)}{(10.68)(2.17)}=-0.0779 \\ \\ (ii)\frac{(-1.0299)(1.4885)}{(10.68)(2.17)}=-0.0661 \\ \\ (iii)\frac{(-0.8427)(0.5668)}{(10.68)(2.17)}=-0.0206 \\ \\ (iv)\frac{(-0.5618)(0.1059)}{(10.68)(2.17)}=-0.0026 \\ \\ (v)\frac{(0)(-0.3548)}{(10.68)(2.17)}=0 \end{gathered}[/tex]I need help with table of square of root function
Answers
To summarize the table.
what is the measures of each angle in a triangle that is equiangular and eguilateral
Answers
A Triangle is defined as a polygon that has three sides and three vertices. The sum of its interior angles is 180 degrees.
An Equilateral triangle is a triangle whose three sides have equal length.
If a polygon is equiangular, then all its interior angles have the same measure.
Based on the explained above, if a triangle is equiangular and equilateral, then its interior angles have equal measure and its three sides have equal length.
Since its three angles have equal measure, and you know that the interior angles of a triangle add up to 180 degrees, you can calculate the measure of each angle of a triangle that is equiangular and equilateral, as following:
[tex]\frac{180\degree}{3}=60\degree[/tex]Therefore, the answer is:
[tex]60\degree[/tex]The graph below represents which of the following functions? ਜਾ ST 25 जए TT 3 3 G 3 3 7 O A. y = -3 cos2x+ ---3008/21 O -(-4) O C. y = 3 sin(2[x = 1) / B. y = 3 cos 2 * = 2 +
Answers
Notice that two of the intersections of the function with the x-axis are x=-pi/3 and x=2pi/3.
Therefore, in the case of each of the options,
[tex]\begin{gathered} A)-3\cos (2(-\frac{\pi}{3})+\frac{\pi}{3})=-3\cos (-\frac{\pi}{3})\ne0 \\ B)3\cos (2(-\frac{\pi}{3}-\frac{\pi}{3})=3\cos (-\frac{4}{3}\pi)\ne0 \\ C)3\sin (2(-\frac{\pi}{3}+\frac{\pi}{3}))=3\sin (0)=0 \end{gathered}[/tex]Thus, the answer is option C.
Solve the quadratic equation x2 - 6x + 8 = 0 by the graphing method.
Answers
The given quadratic equation is
x^2 - 6x + 8 = 0
It can be written as
y = x^2 - 6x + 8
We would substitute values of x into the equation and find corresponding values of y. We have
For x = - 1, y = -1^2 - 6(-1) + 8 = 15
For x = 0, y = 0^2 - 6(0) + 8 = 8
For x = 1, y = -1^2 - 6(11) + 8 = 3
The graph is shown below
The solutions are the values of x where the curve touches the x axis.
The solutions are
x = 2
x = 4
The given diagram shows a construction completed using a straightedge and a compass.
Answers
SOLUTION
The diagram simple shows the construction for copying angle ABC, this is because the width of a compass was opened to measure angle ABC and then used to construct angle FDE.
Hence the answer is
for copying angle ABC
If angle ABC is 24 degress, angle FDE must be 24 degrees too
Hence the answer is 24 degrees
Triangle XYZ is dilated by a scale factor of 3 to form trianle TUV
Answers
Since triangle XYZ is dilated by a scale factor 3 to form the triangle TUV
That means each side of triangle TUV is 3 times the corresponding side in triangle XYZ
TU = 3(XY)
UV = 3(YZ)
Since UV = 39
39 = 3(YZ)
Divide both sides by 3
39/3 = YZ
13 = YZ
The length of YZ is 13
The answer is A
ada bought 80 feet of wire for 16.80. she need 20 more feet. if the unit price is the same, how much would she pay for the extra 20 feet of wire
Answers
The unit price is obtained as follows:
[tex]\frac{16.80\text{ \$}}{80\text{ ft of wire}}=0.21\frac{\text{ \$}}{\text{ ft of wire}}[/tex]Then, 20 ft of wire cost:
[tex]20\text{ ft of wire}\cdot0.21\frac{\text{ \$}}{\text{ ft of wire}}=4.2\text{ \$}[/tex]She would pay $4.2 for the extra 20 feet of wire
Use the appropriate form of the percentage formula.60% of what number is 30?B=
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Let the required number be x.
According to the given condition,
[tex]\begin{gathered} 60\text{ \% of x = 30} \\ \frac{60}{100}\times x^{\text{ }}\text{ = 30} \\ 60x\text{ = 3000} \end{gathered}[/tex]Simplifying further,
[tex]\begin{gathered} x\text{ = }\frac{3000}{60} \\ x\text{ = 50} \end{gathered}[/tex]Thus the required number is 50.
Out of 740 children, 400 children have an iron deficiency. What is the population?
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the population is 740 children
and out of the 740 400 have iron deficiency
Please help me answer this question! :D It will be greatly appreciatedQuestion:Find the total surface area of the square pyramid.A.80 IN2B.105 IN2C.185 IN2D.25 IN2
Answers
The surface area of the pyramid is the sum of the areas of the 4 triangles and the square
The area of the square is found this way
[tex]\begin{gathered} As=l^2 \\ As=5^2=25 \end{gathered}[/tex]The area of each triangle is found this way
[tex]\begin{gathered} At=\frac{b\cdot h}{2} \\ At=\frac{5\cdot8}{2} \\ At=20 \end{gathered}[/tex]The total surface area is
[tex]\text{Apyr}=20+20+20+20+25=105[/tex]The area is 105 in^2. The correct option is B
I don't quite understand this scatter plot and I know it is not b or c because they are negative
Answers
The linear equation that is a good fit for the data is
[tex]y\text{ = }\frac{1}{2}x\text{ + 1}[/tex]This corresponds to option D
Reason:
The best fit line cuts the y-axis where y = 1 and has a slope of 0.5
Each letter of the word "supercalifragilisticexpialidocious" is placed into a bag and drawn at 3 times, replacing the letter after each draw. Find the probability that the letter "i" is drawn at least once. Round your answer to two decimal places.
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Given the graph, find the coordinates of the vertices of each figure after the transformation.
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Solution
Step 1
Write the coordinates of the triangle.
H(0, 3), I(-2, 1) and (-4, 2)
Step 2
[tex]\begin{gathered} (x\text{ , y\rparen }\rightarrow\text{ \lparen x + 3, y - 3\rparen} \\ \\ H\left(0,3\right),I\left(-2,1\right)and\text{ G\lparen}-4,2)_ \\ \\ (x\text{, y}\operatorname{\rparen}\operatorname{\rightarrow}\operatorname{\lparen}\text{x+3, y-3}\operatorname{\rparen} \\ \\ H(0_+3,\text{ 3-3}),I(-2+3,1-3)and\text{ }G\operatorname{\lparen}-4+3,2-3) \\ \\ H(3,\text{ 0\rparen, I \lparen1, -2\rparen. G\lparen-1, -1\rparen} \end{gathered}[/tex]Final answer
H'(3, 0), I'(1, -2), G'(-1, -1)
Find the intercepts and domain and perform the symmetry test on each of the following hyperbol (a) 9x?- 16y? = 144 (c) 25x2 - 4y? = 100 (g) -9x2 + 16y= 144 (e) x² + y² = 1 (b) 9x² - y² = 9 (d) 25x - 36 = 900 (0) -25x + 4y = 100 (h) -x + 4y = 16 mantiene foci endnoints of the conine fundamental rectangle an
Answers
We are asked to find the intercepts and symmetry test on the following hyperbola:
- x^2 + y^2 = 1
Recall the formulas for vertical transverse axis hyperbolas given in the following image:
This type of hyperbolas have a POSITIVE term in ÿ", and a NEGATIVE term in x.
The image represents the type of graph you get with a hyperbola of this type. And it gives you how to find intercepts if any on each coordinate axis.
As we can see, the a and b parameters are 1 for both in our case, since y^2 is not accompanied by any factor but "1" (one), and the same for the x variable.
Therefore: We don't expect any x intercept (the branches of the hyperbola would NOT cross the x axis.
We expect y-intercepts at the values y=1 and y = -1.
The Domain is all the real axis. The graph of one branch is symmetric to the other branch around the x-axis.
The vertices of the hyperbolas branches are : (0, 1) and (0, -1)
The foci are located on the vertical y axis at the values given by :
[tex]\begin{gathered} (0,\sqrt[]{1^2+1^2})=(0,\sqrt[]{2}) \\ \text{and} \\ \\ (0,-\sqrt[]{1^2+1^2})=(0,-\sqrt[]{2}) \end{gathered}[/tex]And here the actual graph of the given conic equation is shown below:
Notice that for the hyperbolas that follow problem e) seem to be of this same type (where the x term in the hyperbola's equation is NEGATIVE, and the y term is POSITIVE)
A new car valued at $20000, depreciates at 8% per year. What is the value of the car one year after purchase?
Answers
The value of the car one year after purchase if the initial value is $20000 and depreciates at 8% is $18400.
What is depreciation?Depreciation refers to the term used to defined the lost in value of an article over a period of time.
To calculate the value of the car after one year, we use the formula below.
Formula:
A' = A-Ad/100........ Equation 1Where:
A = Original value of the carA' = value of the car after one yeard = Percentage of depreciation per annum.From the question,
Given:
A = $20000d = 8%Substitute these values into equation 1
A' = 20000-(20000×8/100)A' = 20000-1600A' = $18400Hence, the value of the car after one year is $18400.
Learn more about depreciation here: https://brainly.com/question/25806993
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The following are distances (in miles) traveled to the workplace by 15 employees of a certain hospital.
Answers
Given:
We're given a list of distances traveled to the workplace by 15 employees of a certain hospital.
To find:
We need to find 25 and 70 percentile of the given data.
Step-by-step solution:
We will firstly arrange the given data in ascending format:
5,6,7,9,11,13,14,15,18,18,20,31,34,36,37
We will now calculate the value of the 25th percentile:
L = k/100 × n
n = number of values = 15
k = percentile in question = 25
L = 25/100 × 15
L = 3.75
In case L is not an integer, The kth percentile is Lth value, where L has been rounded to next integer.
Thus 4th value is equal to 25th percentile.
The 25th percentile = 9 miles
We will now calculate the value of the 70th percentile:
L = k/100 × n
n = number of values = 15
k = percentile in question = 70
L = 70/100 × 15
L = 10.5
In case L is not an integer, The kth percentile is Lth value, where L has been rounded to the next integer.
Thus 11th value is equal to 70th percentile.
The 70th percentile = 20 miles
Final answer:
The 25th percentile = 9 miles
The 70th percentile = 20 miles
Instructions: For the following piecewise functions, evaluate forthe given value of a.f(x) =-x-4, x<-42, -4≤ x ≤ 1-x+1, x>1Evaluate the function when x = -4.f(-4)=Evaluate the function when x = 3.f(3) =DO ESTHEDFi
Answers
SOLUTION
Given the question on the question tab;
[tex]Obeying\text{ the given conditions:}[/tex][tex]\begin{gathered} When\text{ x=-4} \\ \Rightarrow-4\leq x\leq1\text{ \lparen suitable condition\rparen} \\ \therefore f(-4)=2 \end{gathered}[/tex][tex]\begin{gathered} When\text{ x=3} \\ \Rightarrow x>1\text{ \lparen suitable condition\rparen} \\ \therefore f(3)=-x+1=-3+1=-2 \\ f(3)=-2 \end{gathered}[/tex]
Final answer:
[tex]\begin{gathered} f(-4)=2 \\ f(3)=-2 \end{gathered}[/tex]Select the equation of the line that passes through the point (5,7) and is perpendicular to the line x=4A) y=4B) x=5C) y=7D) x=7
Answers
Answer: C) y = 7
Explanation
Perpendicular lines are those that form a 90º angle. Additionally, x = 4, is a vertical line, thus, we have to find the corresponding horizontal line that passes through a point (5, 7).
As the coordinate is (x, y), and we need a horizontal line (y = a), then:
[tex]y=7[/tex]All odd numbers greater than 7 can be expressed as the sum of three prime numbers. Which three prime numbers have a sum of 43? Justify your answer.
Answers
31,7, 5
1) Considering that we can write the following listing the three prime numbers
43 = 31 +7+5
2) This statement:" All odd numbers greater than 7 can be expressed as the sum of three prime numbers." is a consequence of the Goldbach Conjecture:
"Every number greater than 5 is the sum of 3 prime numbers."
3) Hence, 43 can be the sum of these three prime numbers:
31,7, 5
what is kruskal's algorithm and how do i use it?
Answers
Kruskal's Algorithm used to discover the shortest path between two points in a connected weighted graph.
Given,
What is Kruskal's algorithm and how do I use it?
Now,
What is Kruskal's algorithm?
Kruskal's algorithm is the concept that is introduced in the graph theory of discrete mathematics. It is used to discover the shortest path between two points in a connected weighted graph. This algorithm converts a given graph into the forest, considering each node as a separate tree.
Why does Kruskal's algorithm work?
Kruskal's algorithm uses the greedy approach for finding a minimum spanning tree. Kruskal's algorithm treats every node as an independent tree and connects one with another only if it has the lowest cost compared to all other options available.
Hence, Kruskal's Algorithm used to discover the shortest path between two points in a connected weighted graph.
Learn more about Kruskal's Algorithm at:
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-3, -6, -12, -24 common difference/Ratior = 2d = -6d = -3r = -3
Answers
hello
we simply need to check if the sequence given has a common ratio or a common difference and what is the value
[tex]-3,-6,-12,-24[/tex]let's check if the sequence has a common ratio
to do this, let's pick two consecutive terms and check if the value corresponds
[tex]\begin{gathered} d=\frac{-6}{-3}=22 \\ d=\frac{-12}{-6}=2 \\ d=\frac{-24}{-12}=2 \end{gathered}[/tex]from the calculation above, the value of the common ratio is 2 and this corresponds to the first option
nineteen nickels and dimes are inside the bank for a total of $1.30 how many nickels are there
Answers
Given data:
The total numbers of nickel and dimes are n+d=19.
The expression for the total cost is 0.05n+0.1d=1.3.
The first equation can be written as,
[tex]n=19-d[/tex]Substitute above exprression in second equation.
[tex]\begin{gathered} \text{0}.05(19-d)+0.1d=1.3 \\ 0.95-0.05d+0.1d=1.3 \\ \text{0}.05d=0.35 \\ d=7 \end{gathered}[/tex]The numbers of nickels are,
[tex]\begin{gathered} n=19-7 \\ =12 \end{gathered}[/tex]Thus, the numbers of nickels are 12, and numbers of dimes are 7.
4 megabytes to 19 megabytes, the ratio is?
Answers
The form of the ratio of 2 numbers is a: b, where
a is the first number and b is the second number
Since the first number is 4 megabytes
Since the second number is 19 megabytes, then
a = 4 and b = 19, then
The ratio is 4: 19 = 4/19
