in triangle ABC, bisectors of angle A and angle C cross each other in point M. find angle ABC if it is half of AMC. (no shape given)
Answers
Answer:
[tex]\angle ABC=60[/tex]
Step-by-step explanation:
[tex][Kindly\ refer\ the\ image\ attachment.]\\We\ are\ given\ that,\\AM\ is\ the\ Angle\ Bisector\ of\ \angle BAC.\\Hence,\\\angle BAM= \angle MAC\\CM\ is\ the\ Angle\ Bisector\ of\ \angle BCA.\\Hence,\\\angle BCM= \angle MCA.\\Also,\\\angle AMC=2 \angle ABC[/tex]
[tex]Now,\\As\ we\ can\ observe\ that,\\\angle BCM + \angle MCA= \angle BCA\\\angle MCA+ \angle MCA= \angle BCA\ [\angle BCM = \angle MCA]\\Hence,\\2 \angle MCA= \angle BCA\\Or, \\\angle MCA=\frac{\angle BCA}{2} \\\\Similarly,\\\angle BAM + \angle MAC= \angle BAC\\\angle MAC + \angle MAC= \angle BAC\\2 \angle MAC = \angle BAC\\Or,\\\angle MAC=\frac{\angle BAC}{2}[/tex]
[tex]Through\ the\ Angle\ Sum\ Property\ of\ a\ Triangle,\ we\ know\ that:\\'The\ Sum\ of\ all\ interior\ angles\ of\ a\ triangle\ is\ 180.'\\Hence,\\In\ \triangle BAC,\\\angle ABC + \angle BCA + \angle CAB=180\\In\ \triangle MAC,\\\angle MAC+ \angle ACM + \angle AMC=180[/tex]
[tex]Hence,\\As\ \angle AMC= 2 \angle ABC, \angle MCA=\frac{\angle BCA}{2}, \angle MAC=\frac{\angle BAC}{2},\\2 \angle ABC+\frac{\angle BCA}{2}+\frac{\angle BAC}{2}=180\\By\ resolving\ the\ denominators,\\\frac{4 \angle ABC+\angle BCA+\angle BAC}{2}=180\\\\By\ comparing\ the\ Sum\ of\ angles\ in\ both\ the\ triangles,\\We\ find\ that\ the\ RHS\ of\ both\ the\ equations\ are\ equal\ i.e.180,\\The\ LHS\ of\ the\ equations\ are\ equal\ too.\\[/tex]
[tex]Hence,\\\angle ABC+ \angle BCA + \angle BAC=\frac{4 \angle ABC+\angle BCA+\angle BAC}{2}\\Hence,\\2(\angle ABC+ \angle BCA + \angle BAC)=4 \angle ABC+\angle BCA+\angle BAC\\Hence,\\2 \angle ABC+ 2 \angle BCA + 2 \angle BAC=4 \angle ABC+\angle BCA+\angle BAC\\Hence,\\2 \angle BCA + 2 \angle BAC-\angle BCA- \angle BAC=4 \angle ABC- 2 \angle ABC\\Hence,\\\angle BCA+\angle BAC= 2\angle ABC[/tex]
[tex]Lets\ get\ back\ to\ the\ Angle\ Sum\ of\ \triangle ABC,\\\angle ABC + \angle BAC + \angle ACB=180\\Hence,\\As\ \angle BCA + \angle BAC= 2 \angle ABC,\\\angle ABC + 2 \angle ABC=180\\Hence,\\3 \angle ABC=180\\\angle ABC=\frac{180}{3}=60[/tex]
Related Questions
If 5 1/3= x/3 then x=
Answers
Answer:
x=16
Step-by-step explanation:
Please mark BRAINLEST
whats slope intercept form for 2x- 5y=10
Answers
Answer:
y=-2/5x-2
Step-by-step explanation:
First, you put x to the other side of the equation so you get y alone, getting the equation of -5y=-2x+10. In order to just have y on one side, you need to divide the whole equation by -5. This leads to the final answer of y=-2/5x-2.
What is the distance between the points R(5, 7) and S(-2, 3)?
Answers
Answer:
Step-by-step explanation:
D
The distance between points is √65.
What is distance?The length of the line that connects two points is the distance between them. The distance can be determined by subtracting the coordinates that are not the same if the two points are on the same horizontal or vertical line.
The distance formula is used in analytic geometry to determine the distance between two lines, the sum of the lengths of all sides of a polygon, the perimeter of polygons on a coordinate plane, the area of polygons, and a variety of other measurements.
Given coordinates
R(5, 7) and S(-2, 3)
to find the distance between
the formula of distance for coordinates is
d = [tex]\sqrt{(y_{2} - y_{1} )^{2} + (x_{2} - x_{1} )^{2} }[/tex]
here y₂ = 3, y₁ = 7
x₂ = -2, x₁ = 5
substitute value in equation we get
d = [tex]\sqrt{({3 - 7 )^{2} + (-2 - 5 )^{2} }[/tex]
d = [tex]\sqrt{({-4 )^{2} + (-7 )^{2} }[/tex]
d = √(16 + 49)
d = √65
Hence the distance is √65.
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can someone help me asap please
Answers
Answer:
Here you go. It is really easy. All you have to do is translate the points. If it says translate 3 units up, you'd pick a point, and move it up 3 units. Then do it with all the others and BOOM! You did it! Try one of the problems yourself to make sure you understand what to do next time.
Have a nice day!
Which unit rate corresponds to the proportional relationship shown in the graph?
Drag and drop the answer into the box to match the graph with its unit rate.
•1/3 cm/s
•1/2 cm/s
•2/3 cm/s
•3/2 cm/s
Answers
Answer:
•3/2 cm/s
Step-by-step explanation:
from (0, 0) to (6, 9). The graphed function rose 9 units (went up) and ran 6 units (shifted right). In slopes, we use this equation:
[tex] \frac{rise}{run} [/tex]
to find slopes. So ⁹⁄₆ is what we get. But ⁹⁄₆ simplified is ³⁄₂, so that's the answer.
19) Find the acros F(x) = x4 + 8x? -
Answers
Answer:
F'(x)=4x3+16x
Step-by-step explanation:
Which of the following is not a function?
a. (1,1),(2,2), (3,3), (4,4)
b. (2,3), (2,4), (3,3), (3,4)
c (2,4),(4,8).(10,12). (4,10)
d. (2,4), (3,4), (5,4), (6,4)
Answers
Number on the left: x-value
Number on the right: y-value
If there are 2 y-values for one x-value it is NOT considered a function.
For instance in the answer:
(2,3), (2,4), (3,3), (3,4)
You can clearly see that the x-values (2 & 3) repeat more than once; therefore, it is NOT a function.
On the other hand if you have 2 DIFFERENT x-values for the same y-value it IS A FUNCTION.
For ex D: (2,4), (3,4), (5,4), (6,4)
As you can see there are 4 DIFFERENT x-values with same y-value; therefore it is A FUNCTION
To make it easier:
If x-values appear more than once = NOT A FUNCTION
If x-values appear only ONCE = FUNCTION
Remember: y-values are ALLOWED to repeat
I hope this helps. If you have any questions please let me know in the comments.
Find ghe solution to the system. Write your solution as an ordered pair (x,y) with no spaces,no solution,or infinitely many.y=4x and 3x+2y=55
Answers
Answer:
The solution of the system is (5, 20).
Step-by-step explanation:
y = 4x and 3x + 2y = 55 are simultaneous equations. To find the unknowns, we have to solve these equations simultaneously.
The first can be rewritten as
4x – y = 0.
Therefore, we have:
4x – y = 0
3x + 2y = 55
Multiplying the first equation by 2 all through, we have
8x – 2y = 0.
So we can now combine the second equation with the first multiplied by 2.
8x – 2y = 0
3x + 2y = 55
Adding these equations we have:
11x = 55
Divide both sides by 11 and we have
x = 5
Substitute x = 5 in equation 1, we have
4(5) – y = 0
y = 20.
Therefore, x = 5 and y = 20.
The solution of the system is (5, 20).
Can someone find the slopes of these two please?
Answers
Answer:
you put the points into the slope formula and solve : (y2-y1)/(x2-x1)
1. (4 -1) / (-2 -3)
3 / -5
2. (-1 -(-2)) / (5 - 0)
(-1 +2) / 5
1/ 5
Step-by-step explanation:
i hope this helped :)
Answer:
the first slope is 3/-5
the second one is 3/5
Step-by-step explanation:
I'm so confused. Helpppp.
Answers
What is the midpoint of the segment shown below?
10
(-1,5)
O A. (-3.3)
B. (-7,3)
. 10
10
(-6, -2)
O C. (-7, )
O D. (
-3)
10
SUBMIT
Answers
Answer: D. (-7/2,3/2)
Step-by-step explanation: (apx)
The midpoint of the segment shown below is option D. (-7/2, 3/2).
What are the Coordinates?Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.
Given a line segment with the given coordinates for the end points.
Midpoint of a segment with end points (x, y) and (x', y') is,
Midpoint = ((x + x') / 2, (y + y') / 2)
Here the end points of the segment are (-6, -2) and (-1, 5).
Midpoint of the segment = ((-6 - 1) / 2, (-2 + 5) / 2)
= (-7/2, 3/2)
Hence the mid point of the segment is (-7/2, 3/2).
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A number plus 17 is 25 algebraic expression
Answers
Answer:
x + 17 = 25
Step-by-step explanation:
x is "a number" and you just add it to 17. (Also the answer would be 8 if you need to solve it too)
The algebraic expression is x + 17 = 25 and the number is 8 if the number plus 17 is 25.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have:
A number plus 17 is 25 algebraic expressions:
Let x be the number:
x + 17 = 25
After solving:
x = 25 - 17
x = 8
Thus, the algebraic expression is x + 17 = 25 and the number is 8 if the number plus 17 is 25.
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Step-by-step explanation:
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y=-4/3x
Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer
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Answer:
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Step-by-step explanation:
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+
+
+
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Answers
Answer:
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Step-by-step explanation:
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A) 10
B) 23
C) 40
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Answers
Answer:
c.40
Step-by-step explanation:
the answer is 40 your welcome
The table compares actual lengths in a room to lengths in a blueprint of the room.
Blueprint length (in.)
3
6
9
12
15
18
Actual length (ft)
5
10
15
20
25
30
Complete the equation for the relationship, where y is the actual length in feet, and x is the blueprint length in inches. y =
The length of a wall on the blueprint is 10 inches. Find the actual length of the wall.
The actual wall is
feet long.
A window in the room has an actual width of
2.5 feet.
Find the width of the window in the blueprint.
The width of the window in the blueprint is
in.
Answers
Answer:
The actual wall- 30
The width of the window blueprint- 1.5
Step-by-step explanation:
The actual wall- its the last answer you get for length
I just know the answer
The width of the window in the blueprint will be 2.7 inch.
What is the equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
From the given table choose;
⇒ (x₁ , y₁ ) = (3, 5) & (x₂, y₂ ) = (3, 5)
Since, We know that equation of line is,
⇒ y – y₁ = ((y₂ – y₁)/(x₂ – x₁ )) (x – x₁)
⇒ (y - 3) = ((10-5)/(6-3))(x - 3)
⇒ 3(y - 3) = 5(x - 3)
⇒ 3y = 5x -15+9
⇒ 5x- 3y = 6 ….(i)
This is the required equation.
Given that; the length of wall on blue print = 10 inch
Then, put x = 10 in equation (i) we get;
⇒ 5x10 – 3y = 6
⇒ -3y = 6 - 50
⇒ y = 14.6 ft
The actual length be = 14.6 ft
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Then put y = 2.5 in equation (i) we get
⇒ 5x – 7.5 = 6
⇒ 5x = 13.5
⇒ x = 2.7 inch
Thus, The width of the window in the blueprint is 2.7 inch.
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21=21
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X= 7
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Answer:
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Step-by-step explanation:
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Answer:acute
Step-by-step explanation:
Each of the 20 employees in an office took a 60 point test on office safety. The test scores are listed in the table below. Which histogram best represents the data in the table
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Answer:
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Step-by-step explanation:
But to construct a histogram, we use frequence on the y-axis and class boundaries on the x-axis
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Examples
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Answer:
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Step-by-step explanation:
2+4=6
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Answer:
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Step-by-step explanation:
Elsa is decorating for a wedding. She has 79 flowers and some vases. if she puts 8 flowers in each vase, how many flowers will she have left over.
Answers
Answer:
She will have 7 flowers left.
Step-by-step explanation:
I drew out clumps of 8 dots and counted them up to 79. The last clump only had 7 flowers left. Hope this helps :)