Point D is the in center of triangle ABC. Write an expression for the length x in terms of the three side lengths AB, AC, BC.
Hint: Use areas of triangles...A=1/2bh
Answers
Answer :
[tex] \underline{ \boxed{x = \frac{2(A_T) }{(AB) + (AC) + (BC)} }}[/tex]
Explanation :
[tex]i \: figured \: it \: out \to \: notice \: that \\ there \: are \:( thre e\: trianges) \: in \: triangle \: ( ABC) \\ and \: they \: all \: have \: the \: same \: height \: = x \\ first \: triangle \: is \: \to \: triangle \: (ABD) \\ second\: triangle \: is \: \to \: triangle \: (ACD) \\ third \: triangle \: is \: \to \: triangle \: (BCD) \\ if \: the \: area \: of \: a \: triangle \: is \: = \frac{1}{2} bh : then \to \\ the \: area \: of \: triangle \: (ABD) = \frac{1}{2} (AB)x \\ the \: area \: of \: triangle \: (ACD) = \frac{1}{2} (AC)x \\ the \: area \: of \: triangle \: (BCD) = \frac{1}{2} (BC)x \\ let \: the \: total \: area \:(A_T) \: be \to \: \frac{1}{2} (AB)x + \frac{1}{2} (AC)x + \frac{1}{2} (BC)x \\ if \to\\ (A_T) = \frac{1}{2} (AB)x + \frac{1}{2} (AC)x + \frac{1}{2} (BC)x \\ then \to \\ (A_T) = \frac{1}{2} \{(AB)x + (AC)x + (BC)x \} \\ x \{(AB) + (AC) + (BC) \} = 2(A_T) \\ x = \frac{2(A_T) }{(AB) + (AC) + (BC)} [/tex]
Expression representing the length 'x' will be, [tex]x=\frac{(AB)(AC)}{AC+BC+AB}[/tex].
In-center of a triangle,In-center of a triangle defines the center of a circle inscribed in the triangles (touching all sides),Perpendicular drawn from in-center to the sides of the are equal in measures (radii of the inscribed circle).Use the hint → Area of the large triangle = sum of the small triangles inside the larger triangle
Area of ΔABC = [tex]\frac{1}{2}(AB)(AC)[/tex]
Area of ΔADC = [tex]\frac{1}{2}(AC)(x)[/tex]
Area of ΔBDC = [tex]\frac{1}{2}(BC)(x)[/tex]
Area of ΔADB = [tex]\frac{1}{2}(AB)(x)[/tex]
Since, Area of ΔABC = Area of ΔADC + Area of ΔBDC + Area of ΔADB
[tex]\frac{1}{2}(AB)(AC)=\frac{1}{2}(AC)(x)+\frac{1}{2}(BC)(x)+\frac{1}{2}(AB)(x)[/tex]
[tex](AB)(AC)=[(AC)+(BC)+(AB)](x)[/tex]
[tex]x=\frac{(AB)(AC)}{AC+BC+AB}[/tex]
Therefore, expression representing the length 'x' will be [tex]x=\frac{(AB)(AC)}{AC+BC+AB}[/tex].
Learn more about the in-center of a triangle here,
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Related Questions
Work out angle BXC.
Give a reason for each angle you work out.
Answers
Answer:
∠ BXC = 70°
Step-by-step explanation:
∠ XBC and ∠ AXY are corresponding angles and are congruent, then
∠ XBC = 55°
Since XB = XC , then Δ XBC is isosceles and the 2 base angles are congruent.
∠ BXC = 180° - (55 + 55)° ← angle sum of triangle
∠ BXC = 180° - 110° = 70°
The measure of angle BXC is 70°
What s transversal?"It is a line that passes through two lines in the same plane at two different points."
What are parallel lines?"These are the lines in the same plane that are at equal distance from each other and never meet."
What are isosceles triangle?"It is a triangle having any two sides equal in length."
For given example,
We can observe that XY and BD are parallel lines and AB is the transversal.
Here,
∠AXY = ∠XBC ..............(Corresponding angles)
⇒ ∠XBC = 55°
In figure, for ΔXBC the sides XB and XC are equal.
So, ΔXBC is an isosceles triangle.
We know, for isosceles triangle, angles opposite to equal sides are equal in measure.
⇒ ∠XBC = ∠XCB
⇒ ∠XCB = 55°
We know, the sum of all angles of the triangle is 180°.
⇒ ∠XBC + ∠XCB + ∠BXC = 180°
⇒ 55° + 55° + ∠BXC = 180°
⇒ 110° + ∠BXC = 180°
⇒ ∠BXC = 70°
Therefore, the measure of angle BXC is 70°
Learn more about the angles formed by parallel line and transversal here:
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Write an equation of the line with a slope of
-
and y-intercept of -6.
y
Answers
Answer:
Y = mX+C
Y =mX-6
Y =m(0)-6
Y = -6
the line passes through origin so
X=0
(0,6)
If x and y vary directly, and x = 12 when
y = 4, what is the value of x when y = 1 ?
Answers
Answer:
3
Step-by-step explanation:
Answer: x = 3
Step-by-step explanation:
y for x
4 for 12
1 for ?
Cross multiply
4? = 12 x 1
4? = 12
Divide both sides by 4
? = 3
When y = 1, x = 3.
Hope that helped!
3/4x-4=-19
Whats is the solution to the equation?
Answers
Answer:
x=-20
Step-by-step explanation:
what is the radical of 508.0015677?
Answers
Answer:
I have the same question and I need it answeeed
Step-by-step explanation:
Answer:
22.538890116862454
Step-by-step explanation:
......
Please please help please please ASAP
Answers
Answer:
a
Step-by-step explanation:
tan is the opposite divided by the adjecent. The opposite of x is 24 and the adjecent of x is 18, so you would get 24/18 but you have to simplify which simplified is equal to 4/3
Find the length of side a.
Answers
Answer:
Answer B) 5
Step-by-step explanation:
Set [tex]a^{2}=c^{2}-b^{2}[/tex]
[tex]a^{2}=13^{2}-12^{2}[/tex]
Before getting to school, Jason has a few errands to run. Jason has to walk 10 blocks to the theater, and 12 blocks to the gallery, before walking the final 6 blocks to arrive at school. If Jason has already walked 7 blocks, how many more blocks must he walk before arriving at school?
Answers
Answer:
11
Step-by-step explanation:
simplify. e^(in x)=, e^(in 5)=, e^(in 3x)=
Answers
Answer:
Step-by-step explanation:
e^ lnx = x
e^ ln5 = 5
e^ ln 3x = 3x
I think you get the idea... e is an inverse operation to ln :o
Answer:
Simplify.
ln e =
✔ 1
ln e2x =
✔ 2x
ln 1 =
✔ 0
Simplify.
eln x =
✔ x
e ln 5 =
✔ 5
e ln 3x =
✔ 3x
Step-by-step explanation:
Find the measure of each numbered angle
Answers
2:109 Degree
3&4:90 Degrees
Answer:
1. 71 degrees 2. 109 degrees 3. 90 degrees 4. 90 degrees
Step-by-step explanation:
109 + 71 = 180 (straight line)
so the other side (under) of 109 degrees is 71 degrees. That angle is the same angle as 1 because that same line (transversal) runs through both parallel lines.
The angle diagonal from 2 is 109 because it mirrors the same measurements as the one on the left. Angle 2 is the same angle as 109 degrees because it's a vertical angle. All vertical angles are equal.
Because the same line on the bottom runs through the parallel lines then the same angles apply to both on the bottom. The right one is a 90 degree angle
which makes both 3 and 4 90 degrees because 90 + 90 equals a straight line 180 degrees.
can someone help me im looking for the the x
Answers
Answer:
x = 4√5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightEquality Properties
Trigonometry
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is one legb is another legc is hypotenuseStep-by-step explanation:
Step 1: Identify Variables
a = 19
b = x
c = 21
Step 2: Solve for x
Substitute [PT]: 19² + x² = 21²Isolate x term: x² = 21² - 19²Exponents: x² = 441 - 361Subtract: x² = 80Isolate x: x = √80Simplify: x = 4√5What does 5/12 - 1/3 equal?
Answers
Answer: 1/12
Step-by-step explanation:
5/12 - 1/3
1/3 = 4/12
5/12 - 4/12 = 1/12
PLEASE HELP !!! ASAPPPP Select the statement that describes this expression: 10 + fraction 1 over 4x (5 + 3) − 3.
O 10 more than fraction 1 over 4 of the sum of 5 and 3, then subtract 3 fraction.
O 1 over 4 of 10 times the sum of 5 and 3, minus 3
O 3 more than 3 plus 5 multiplied by fraction 1 over 4, then add 10
O 10 times fraction 1 over 4 plus 3 and 5, minus 3
Answers
Answer:
I think its the first one...
Step-by-step explanation:
Answer:
First one
Step-by-step explanation:
A number pattern was created by dividing the previous term by 3. If the starting value for the pattern was 135, which of the following shows the resulting pattern?
A.
135, 45, 30, 5...
B.
135, 45, 15, 5...
C.
135, 45, 15, 2...
D.
135, 45, 30, 25...
Answers
Answer:
B. 135, 45, 15, 5...
Step-by-step explanation:
I'll go in order from 135 using the pattern shown (tᵇ/3)
135 / 3
135 = 120 + 15
135/3 = (120/3) + (15/3)
135/3 = 40 + 5
135/3 = 45
All four answer choices show this, so no elimination yet.
45 / 3
45 = 30 + 15
45/3 = (30/3) + (15/3)
45/3 = 10 + 5
45/3 = 15
A and D show 30 as term 3, so they are out.
15 / 3
15/3 = 5
C shows 2 as term 4, so that is also out.
This leaves B as the correct answer.
I WILL GIVE YOU BRAINLY PLSS
Which of the following is in the solution set (would appear in the shaded region of
the graph) for the inequality + 7 > 9?
A. 6
B. -6
C. -4
D. 2
SHOW YOUR WORK PLSS
Answers
Answer:
the answer Is D.2
Step-by-step explanation:
9 is greater than 7 by 2
Picture attached below
Answers
Answer:
it's answer is B. 4/5
Step-by-step explanation:
perpendicular (p) = 8
hypotenuse (h) = 10
sin < A
= p/h
= 8/ 10
= 4/ 5
Hope it will help :)
4(x-5)=10(x-10)
solve for x
Answers
Answer:
40/3
Step-by-step explanation:
4x -20 = 10x -100 (Distributive Property)
4x -10x = -100 +20 (I swith the numbers so all of them are similar)
-6x= -80 (Divide -6 on both sides)
And you will get 40/3 or 13.3333..
Answer:
x = 40/3
Step-by-step explanation:
4(x-5)=10(x-10)
=> 4x - 20 = 10x - 100
=> 4x - 10x = - 100 + 20
=> -6x = -80
=> x = 80/6
=> x = 40/3
(4x^2y)^2 · 2(7(3))^4
Answers
Judith received the following amounts of money for doing chores: $5, $7, $3.50, $5, and $8. Give the mean, median, mode, and
range for her earnings.
Answers
Answer:
Step-by-step explanation:
2) divide 54kg in the ratio 1:5=
Answers
Answer:
9:45
Step-by-step explanation:
1:5= 6 parts
54/6=9
9*1=9
9*5=45
9:45
Answer:
9kg and 45kg
Step-by-step explanation:
In fraction from 1:5 is equivalent to 1/(1+5) = 1/6 and 5/(1+5) = 5/6.
So the answer is 54 * 1/6 and 54 * 5/6.
= 9 and 45.
Find the area of a circle with radius,
r
= 7.46m.
Give your answer rounded to 2 DP.
Answers
Answer:
174.74m²
Step-by-step explanation:
♪＼(*＾▽＾*)／＼(*＾▽＾*)／
give the answer of this question by using prime factorization in exponential form 486×768
Answers
Answer:
its 373248
Step-by-step explanation:
I got this by 2squared 9 and 3squared 6
If x = -1, then which of the following inequalities makes a true statement?
A. -4x + 9 > 20
B. -4x – 5 < -15
C. -3x + 15 ≤ 18
D. -5x – 15 ≤ -22
Answers
Answer:
It is C
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
(b) The perimeter of a rectangular window is 298 cm.
If the length of the window is 81 cm, what is its width?
Width of the window: cm
Answers
Answer:
68
Step-by-step explanation:
81 +81 is 162
298-162=136
136/2=68
Solve for x
Solve for BCF
Solve for CFE
Solve for CFG
Answers
Answer:
13x+23x=180[co interior angle♧
36x=180
x=5°
then,
<BCF=13X=13×5=65°
<CFE=23X=23×5=115
<CFG=<BCF[alternating angles]
<CFG=65°
Answer:
13x+23x=180[co interior angle♧
36x=180
x=5°
Step-by-step explanation:
6(x+4)+1= pleaseee help
Answers
Write in slope intercept: slope=2/3 y-intercept =-1
Answers
Answer:
y=2/3-1.
Step-by-step explanation:
Slope intercept is the easiest out of the forms because you just plug in what is given. Here you are given 2/3 for the slope and the y-int Is -1.
The formula for slope intercept is y=mx+b
m= slope
b= y-int
And you just plug it in.
so the answer would be: y=2/3-1. Hope this helps!
will Mark brainliest if correct.
Answers
Answer:
SF = 7/3
Step-by-step explanation:
Like the problem hint says, you want to put the new coordinate over the old one to find the scale factor. We'll use both x and y.
-7/-3 = 7/3
14/6 = 7/3
Therefore, the scale factor is 7/3.
Solve this please question
Answers
Answer:
the speed will be 3 meters
Step-by-step explanation:
Answer:
speed is 3m
Step-by-step explanation:
cause i did count the 3 lines so i did have the 3m and it say their is 1m per 1 line and count the line and you have 3m hope it help!!
A line with a slope of 1/3 passes through (-5,r) and (4,1).
To make this work correctly, the value of r=
Answers
Answer: Add the 1/3 to look for the r