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
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!
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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19) Find the acros F(x) = x4 + 8x? -
Answers
Answer:
F'(x)=4x3+16x
Step-by-step explanation:
Solve for x]. The polygons in each pair are similar.
Answers
21=21
3x/3 = 21/3
X= 7
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).
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.
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
And, Also given that actual width of window = 2.5 feet
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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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
Answers
Answer:
There is no table
Step-by-step explanation:
But to construct a histogram, we use frequence on the y-axis and class boundaries on the x-axis
PLEASE HELP, is this graph parallel, perpendicular or neither?
Answers
Answer:
Step-by-step exp perpendicular becaus it makes a 90 degree angle
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 :)
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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1. Albert bought a bicycle for $27 500. He sold it for $35 500.
a) What was the amount of his profit?
b) What was his percentage profit?
Answers
35,500-27,500= 8000 meaning $8,000 is the profit and the percentage is %35
Which statement about the dilation of these triangles is true?
The scale factor is
The scale factor is 2
The scale factor is 3.
The scale factor is 4.
Answers
Answer
when 2 triangle scales are similar the ration reduces and become a scale factor
Answer:
The scale factor is 2
Step-by-step explanation:
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.
Please help me with this question!!
Answers
Answer:acute
Step-by-step explanation:
will give brilintest if u answer correctly plz
Answers
Answer:
D. (3, 4, 5)
Step-by-step explanation:
[tex]5 = \sqrt{ {(3)}^{2} + {(4)}^{2} } \\ 5 = \sqrt{9 + 16} \\ 5 = \sqrt{25 } \\ 5 = 5[/tex]
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.
A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function?
y = –negative StartFraction 4 Over 3 EndFraction equals StartFraction 4 Over 3 EndFractionx
y = –k equals negative StartFraction 3 Over 4 EndFraction x.x
y = k equals StartFraction 3 Over 4 EndFraction x.x
y = k equals StartFraction 4 Over 3 EndFraction x.x
Answers
Answer:
y=-4/3x
Step-by-step explanation:
Solve the proportion 20/3 = ?/6.
Choose the correct option.
A) 10
B) 23
C) 40
D) 120
Answers
Answer:
c.40
Step-by-step explanation:
the answer is 40 your welcome
Looking at the problem what’s the difference between the two highlighted please I’m Russian and don’t understand English every well
Answers
Answer: Разница между ними восемь
Step-by-step explanation:
What’s the commutative property of addition ?
Answers
Answer:
Its when you just swthc your thingy
Step-by-step explanation:
2+4=6
turns into
4+2=6
Answer:
When it is opposite
Step-by-step explanation:
Water forms______
when it is cold.
Answers
Answer:
As a Solid
Step-by-step explanation:
Examples
river icesea icehail2.50+0.50=21 help meeeeeeeeeee
Answers
Answer:
You are missing some of the equation my dude
Step-by-step explanation:
I'm so confused. Helpppp.
Answers
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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If 5 1/3= x/3 then x=
Answers
Answer:
x=16
Step-by-step explanation:
Please mark BRAINLEST
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:
this my last question for the day
Answers
Answer:
x=72
Step-by-step explanation:
Which is better deal and why:) help ASAP plz!?
Answers
Answer:
$36.00 is better because you get 54 apples
Step-by-step explanation:
36÷9= 4*12=48
Tell whether the expressions modeled below are equivalent. Explain how you know.
+
+
+
2(x-3)
2x-3
Answers
Answer:
they're not
Step-by-step explanation:
when you distribute the 2 into (x-3) you get 2x-6
and thats not equivalent to 2x-3