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
Mrs. Carter has 4 boxes of colored chalk. There are 30 pieces of chalk in each box.
How many total pieces of chalk does Mrs. Carter have?
Answers
Answer:
120
Step-by-step explanation:
30 x 4 = 120
I need help pleaseee
Answers
7p+79=-2p-10
9p=-89
p=-9.89
This question has two parts. Use the information to answer Part A and Part B.
Two angles are supplementary. The measure of one angle is 3 times the measure of the other angle.
Part A
Which equation can be used to find x, the measure of the smaller angle in degrees?
A. 3x - x=90
o
B. 3x + x = 90
o
C. 3x - x = 180
D. 3x + x = 180
Part B
What is the measure of each angle? Enter the answers in the boxes.
The smaller angle measures
and the larger angle measures
Answers
Answer:
Part A: D. [tex]3x+x=180[/tex]
Part B: Smaller angle [tex]=45^{\circ}[/tex], larger angle [tex]=135^{\circ}[/tex]
Explanation:
The term supplementary is used when the sum of two angles add to [tex]180^{\circ}[/tex].
Part A:
From the information given that the "angles are supplementary" and the "measure of one angle is 3 times the measure of the other", the equation to find for x can be written as:
[tex]3x+x=180[/tex]
Part B:
To find the measure of each angle, we can first find the measure of the smaller angle [tex]x[/tex]:
[tex]3x+x=180[/tex]
[tex]4x=180[/tex]
[tex]x=45^{\circ}[/tex]
[tex]\therefore[/tex] The smaller angle is [tex]45^{\circ}[/tex]
Since the measure of the larger angle is [tex]3[/tex] times the measure of the smaller angle:
Larger angle [tex]=3x[/tex]
[tex]=3(45)[/tex]
[tex]=135^{\circ}[/tex]
[tex]\therefore[/tex] The measure of the larger angle is [tex]135^{\circ}[/tex]
Hope this helps :)
Write each of these ratios in their
simplest form.
A) 3:9 B) 12:36 C) 13:39 D) 71:213 E) 142:213 F) 38:57 G) 33:44 H) 31:42
Answers
Answer:
A) 3:9 => 1:3
B) 12:36 => 1:3
C) 13:39 => 1:3
D) 71:213 => 1:3
E) 142:213 => 2:3
F) 38:57 => 2:3
G) 33:44 => 3:4
H) 31:42 => 31:42 or 21:42 => 1:2
Step-by-step explanation:
The simplest form of the ratios are as follows:
A) 3:9
Dividing the ratio by 3
1:3
B) 12:36
Dividing the ratio by 12
1:3
C)13:39
Dividing the ratio by 13
1:3
D) 71:213
Dividing the ratio by 71
1:3
E) 142:213
Dividing the ratio by 71
2:3
F) 38:57
Dividing the ratio by 19
2:3
G) 33:44
Dividing the ratio by 11
3:4
H) 31:42
The ratio is already in simplest form as 31 and 42 don't have a common multiple.
Or it might be mistakenly typed 31 instead of 21
Then the simplest form will be:
21:42
1:2
Hence,
A) 3:9 => 1:2
B) 12:36 => 1:3
C) 13:39 => 1:3
D) 71:213 => 1:3
E) 142:213 => 2:3
F) 38:57 => 2:3
G) 33:44 => 3:4
H) 31:42 => 31:42 or 21:42 => 1:2
A company rents out 16 food booths and 23 game booths at the county fair. The fee for a food booth is $100 plus $9 per day. The fee for a game booth is $95 plus $5 per dat. The fair lasts for d days, and all the booths are rented for the entire time. What is the simplified expression for the amount, in dollars, that the company is paid.
Answers
Answer:
3785 + 259d
Step-by-step explanation:
cost of food booths = 16 * (100 + 9d) = 1600 + 144d
cost of game booths = 23 * (95 + 5d) = 2185 + 115d
total = 1600 + 2185 + 144d + 115d = 3785 + 259d
A plane took 3h 33 min to finish a journey. If the distance of the journey was 2840 miles, at what average speed did the plane travel?
____ mph
Answers
Answer:
The average speed of the plain was 800 miles/h
Step-by-step explanation:
= 2840/ 3h 33mins
= 2840 / 213
= 13.3
Therefore the speed of the plane is 13.3 mph
If a beetle crawls at a constant rate of 3 feet per minute, how long, in minutes, will it take the beetle to travel 75 feet?
A. 25 min.
B. 72 min.
C.78 min.
D. 225 min.
Answers
3/1=75/x
x=25
Answer:
A. 25 minutes
Step-by-step explanation:
3ft/min = 75ft/?min
75ft ÷ 3ft = 25min
it will take the beetle 25 minutes to travel 75 feet.
What is the measure of angle F in degrees?
Answers
Find the perimeter??
Answers
Answer:
13 in
Step-by-step explanation:
just add all the numbers lol
Answer:
the perimeter of the triangle is 13[tex]in^{2}[/tex]
Step-by-step explanation:
All you have to do is add up all the sides together, but first we need to find a common denominator, and it can be 12
[tex]3\frac{1}{3}[/tex] = [tex]\frac{10}{3} = \frac{40}{12}[/tex] ( i multiplied them by 4 (numerator and denominator))
[tex]4\frac{1}{6} = \frac{25}{6} = \frac{50}{12}[/tex] ( i multiplied them by 2 (numerator and denominator))
[tex]5\frac{1}{2} = \frac{11}{2} = \frac{66}{12}[/tex] ( i multiplied them by 6 (numerator and denominator))
Now that you have a common denominator for all 3 fractions, you can now add them all up
[tex]\frac{40}{12} + \frac{50}{12} + \frac{66}{12}[/tex]
Now to add, the denominator has to stay the same (12), and add up all the numerators
[tex]\frac{40}{12} + \frac{50}{12} = \frac{90}{12} + \frac{66}{12} = \frac{156}{12} = 13 (simplified)[/tex]
Hope this helped!
3x + 9 = x + 5 Two sided equations
Answers
Answer:
x=-2
Step-by-step explanation:
Let's solve your equation step-by-step.
3x+9=x+5
Step 1: Subtract x from both sides.
3x+9−x=x+5−x
2x+9=5
Step 2: Subtract 9 from both sides.
2x+9−9=5−9
2x=−4
Step 3: Divide both sides by 2.
2x /2=-4/2
x=−2
10. (02.03)
Find the solution of 3 to the square root of x+6=-12 , and determine if it is an extraneous solution. (1 point)
x= -3; extraneous
x = -3; not extraneous
x= 10; extraneous
x= 10; not extraneous
Answers
Answer:
x= 10; extraneous
Step-by-step explanation:
Given the expression:
3√x+6 = -12
We are to find the value of x
Divide both sides by 3
3√x+6/3 = -12/3
√x+6 = -4
Square both sides
(√x+6)² = (-4)²
x + 6 = 16
x = 16-6
x = 10
Hence the solution is x =10 and it is extraneous solution
Find XY. (help pleaseee)
Answers
Answer:
XY = 15Step-by-step explanation:
Its in the image.
I used Pythagoras theorem in solving for the unknown side.
Sorry for the rough working
What are the missing numbers in the sequence?
Answers
And 0 at the end
Answer:
-37, -30, -23, -16, -9, -2
Step-by-step explanation:
The rule is subtracting -7 each time
Hope I was able to help! :)
Antonio tried to evaluate an expression. Here is his work: (57–8+5)÷9(17–14) = (49+5)÷93 Step 1 = (49+5)÷27 Step 2 = 54÷27 Step 3 = 2 Step 4 Is Antonio's work correct?
Answers
Answer:
Antonio's work is correct but his method is not
Step-by-step explanation:
(57–8+5)÷9(17–14) = (49+5)÷9
Antonio work:
Step 1 = (49+5)÷27
Step 2 = 54÷27
Step 3 = 2
Correct working:
Step 1:
Addition first
-8 + 5 = -3
= (57 - 3) ÷ 9(3)
Step 2:
= 54 ÷ 27
Step 3:
= 2
Antonio's work is correct but his method is not
He subtracted first when he is supposed to add first according to the rule of BODMAS
B - bracket
O - off
D - division
M - multiplication
A - Addition
S - subtraction
Find the missing angle
Answers
Hey there!
31 is the answer
You simply do 96 - 65 = 31
Hope it helps and have a great day!
HELP I NEED HELP ASAP ILL GIVE U BRAINILEST!
Answers
(a).
36 players = 100%
? = 10%
(36×10) / 100%
= 3.6 gloves for left hand players.
Explanation :- Object needs to be in full form whereas 3.6 would be written as only 3 gloves in full.
Ans: Yes. Total gloves were enough.
(b).
36player gloves = 100%
7 lefties = ?
=700/36 = 19.4%
=19.4444444 as recurring would be,
19 % (nearest to whole percent) DONE ✅.
hi, this is an ad. are you good at math? :D do you have nothing to do? :D do you like helping people? :D. if you answered yes to the very first question...help, please...I need it..... :D... :)...T n T ( also just click on my pfp and see if you can answer any of my recent math questions uh if not its fine )
Answers
Answer:
ok and ty oof
Step-by-step explanation:
HELP ME PLEASE!!!!!!!!!!!!!!!! You have to figure out whether its undefined or zero
Answers
Answer:
It's an undefined slope
What is a simpler form of the following expressions?
(7m2 - 5)(7m2 + 5)
(This is a rushed one so pls help?)
Answers
Answer:
49m^4 - 25
Step-by-step explanation:
The simpler expression can simply be found by expanding
The kind of expansion we have here is the difference of two squares
(a + b)(a-b) = a^2 - b^2
Thus, we have it that;
(7m^2-5)(7m^2 + 5)
=
49m^4 - 25
solve for x it is a parallelogram please help
Answers
Answer:
UW = EW+UE=2×EW because, EW=UE
7x-2=2×6= 12
7x=14
x=14/7
x=2
2 is the right answer.What is the Pythagorean Theorem? Provide the equation and an explanation as to what it means.
Answers
Answer:
The Pythagorean Theorem is a squared + b squared = c squared. It is used to find out a side of a triangle if you already know the two others. C is always the H=hypotenuse, while the other two sides are a and b.
Answer: a^2+b^2 (factored) = c^2
Step-by-step explanation:
This only helps if you are solving for the hypotenuse.
Which of the following is not a rate?
I WILL GIVE BRAINLIEST IF YOUR ANSWER IS RIGHT
Answers
Answer:
540 feet 5 feet
Step-by-step explanation:
they're both feet, it cant be a rate.
Help ill mark u brainliest pls
Answers
Answer:
a = 151
Step-by-step explanation:
Both angles make a supplementary angle meaning their angles will add up to 180°.
a + 29 = 180
a = 151
We have to fill in all the boxes in order for me to submit. PLEASE HELP!!
Answers
Answer:
2 and 3 maybe?
Step-by-step explanation:
The measures of the angles of a triangle are shown in the figure below. Solve for x.
(5x-3)°
(x+9)°
Answers
Answer:
14
Step-by-step explanation:
5x-3+ x+9 + 90= 180
6x+ 96=180
6x=180-96
6x=84
x=84/6
x=14
Factor: -12n - 20 they are asking for an expression
Answers
Answer:
-4(3n+5)
Step-by-step explanation:
Factored -4 out of -12n-20. Let me know if this answers the question!
i need help on this plz
a. b. c. d. ???
Answers
Answer:
I'm pretty sure the answer is B
Put the following list of numbers in order from smallest to largest.
1. first 28.3
2. second 28.15
3. third 27.068
4. fourth 29.94
5. fifth 28.08
Answers
27.068
28.08
28.15
28.30
29.94
i need to identify the slope and the y-intercept of the line with a given equation, the given equation is y = 1/2x +5 . i need to graph it aswell.
Answers
Answer:
y-intercept: 5
slope: 1/2
Step-by-step explanation:
The equation y=1/2x+5 is an example of y-intercept form(y=mx+b). This is where b represents the y-intercept and m represents the slope. I will not graph this for you but can explain it.
First plot the y-intercept on the graph. (0.5). Then use the slope to find the next point off of the y-intercept. So for example, the next point would be (2,6).
I have a three in the ones place. I am greater than 14 but less than 31.
What number am I?
Answers
Answer:
Youre the number 23
Answer:
23
Step-by-step explanation:
