Answer:
18x - 36
Step-by-step explanation:
In an equilateral triangle the 3 sides are congruent, then
perimeter = 6x - 12 + 6x - 12 + 6x - 12 ← collect like terms
= 18x - 36
The required expression would be 18x - 36 for the perimeter of the triangle in simplest form.
What is the perimeter of a triangle?The perimeter of a triangle is defined as the addition of the lengths of the triangle's three sides.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operations is called the arithmetic operator.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
As we know in an equilateral triangle the 3 sides are congruent.
The perimeter of the triangle = 6x - 12 + 6x - 12 + 6x - 12
Combine the likewise terms and we get
The perimeter of the triangle = 18x - 36
Therefore, the required expression would be 18x - 36 for the perimeter of the triangle in simplest form.
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If G is the incenter of triangle ABC, find each measure
Answer:
m∠ABG = 20 degrees
m∠BCA = 22 degrees
m∠BAC = 118 degrees
m∠BAG = 59 degrees
DG = 4
BE = 12.4
BG = 11.7
GC = 20.4
Step-by-step explanation:
The given parameters are;
m∠CBG = 20°, m∠BCG = 11°
The incenter of a triangle is the point where the three bisectors of ΔABC meets
m∠ABG = m∠CBG = 20° by definition of angle bisector
m∠ABG = 20°
m∠ACG = m∠BCG = 11° by definition of angle bisector
m∠BCA = m∠ACG + m∠BCG = 11° + 11° = 22°
m∠ABC = m∠ABG + m∠CBG = 20° + 20° = 40°
m∠BAC = 180° - (m∠BCA+m∠ABC) = 180° - (40° + 22°) = 118°
m∠BAG = m∠CAG by definition of angle bisector
m∠BAC = 118° = m∠BAG + m∠CAG = m∠BAG + m∠BAG = 2 × m∠BAG
2 × mBAG = 118°
m∠BAG = 118°/2 = 59°
m∠BAG = 59°
Given that "G" is the incenter of the triangle ABC, we have;
GF = GE = DG = The radius of the incircle of the triangle = 4
Therefore, by Pythagoras' theorem, we have;
BG = √(11² + 4²) = √137 ≈ 11.7
BE = √((BG)² + 4²) = √(137 + 4²) = √153 ≈ 12.4
GC = √(20² + 4²) = √416= 4·√26 ≈ 20.4
Applying the definition of the incenter of a triangle, the measures in triangle ABC where G is the incenter are:
[tex]\mathbf{m \angle ABG = 20^{\circ}}[/tex][tex]\mathbf{m \angle BCA = 22^{\circ}}[/tex][tex]\mathbf{m \angle BAC = 118^{\circ}}[/tex][tex]\mathbf{m \angle BAG = 59^{\circ}}[/tex]DG = 4BE = 10.99BG = 11.7GC = 20.4Recall the following facts about the incenter of a triangle:
The incenter of a triangle is the point where the three angle bisectors that divides each angle vertex into two intersect each other.
The incenter also, is a point equidistant to all three sides of the triangle at right angle.
Applying the properties above, the measures in the image can be calculated as shown below.
Given:
[tex]m \angle EBG = 20^{\circ}\\\\m \angle ECG = 11^{\circ}\\\\CF = 20\\\\EG = 4\\\\BD = 11[/tex]
Find [tex]m \angle ABG[/tex]:
[tex]m \angle ABG = m \angle EBG[/tex] (angle bisector definition)
Substitute[tex]\mathbf{m \angle ABG = 20^{\circ}}[/tex]
Find [tex]m \angle BCA[/tex]:
[tex]m \angle BCA = 2(m \angle ECG)[/tex] (angle bisector definition)
Substitute[tex]m \angle BCA = 2(11)\\\\\mathbf{m \angle BCA = 22^{\circ}}[/tex]
Find [tex]m \angle BAC[/tex]:
[tex]m \angle BAC = 180 - (m \angle CBA + m \angle BCA)[/tex] (sum of triangle definition)
Substitute[tex]m \angle BAC = 180 - (40 + 22)\\\\\mathbf{m \angle BAC = 118^{\circ}}[/tex]
Find [tex]m \angle BAG[/tex]:
[tex]m \angle BAG = \frac{1}{2} (m \angle BAC)[/tex] (angle bisector definition)
Substitute[tex]m \angle BAG = \frac{1}{2} (118)\\\\\mathbf{m \angle BAG = 59^{\circ}}[/tex]
Find DG:
[tex]DG = EG[/tex] (Perpendicular bisectors of the sides of a the triangle are equal in length from the incenter of a triangle)
Substitute[tex]\mathbf{DG = 4}[/tex]
Find BG:
[tex]BG = \sqrt{BD^2 + DG^2}[/tex] (Pythagorean Theorem)
Substitute[tex]BG = \sqrt{11^2 + 4^2} \\\\BG = \sqrt{137} \\\\\mathbf{BG = 11.7}[/tex]
Find BE:
[tex]BE = \sqrt{BG^2 - EG^2}[/tex] (Pythagorean Theorem)
Substitute[tex]BE = \sqrt{11.7^2 - 4^2} \\\\BE = \sqrt{120.89} \\\\\mathbf{BE = 10.99}[/tex]
Find GC:
[tex]GC = \sqrt{CF^2 + FG^2}[/tex] (Pythagorean Theorem)
Substitute[tex]GC = \sqrt{20^2 + 4^2} \\\\GC = \sqrt{416} \\\\\mathbf{GC = 20.4}[/tex]
In summary, applying the definition of the incenter of a triangle, the measures in triangle ABC where G is the incenter are:
[tex]\mathbf{m \angle ABG = 20^{\circ}}[/tex][tex]\mathbf{m \angle BCA = 22^{\circ}}[/tex][tex]\mathbf{m \angle BAC = 118^{\circ}}[/tex][tex]\mathbf{m \angle BAG = 59^{\circ}}[/tex]DG = 4BE = 10.99BG = 11.7GC = 20.4Learn more here:
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HELP ASAP ASAP ASAP PLS PLS PLS LOL
Which one? Btw please don’t just pick randomly just for points this is important.
Answer:
I think it is (-4,-5) I am not sure
Answer:
Step-by-step explanation:
(4,-5)
You reflect the point and the numbers which are positive become negative and the negative numbers become positive!
answer=(4,-5)
Solve the system using the
elimination method
-2x + 4y = -20
3x + 8y = -12
Help me pleaseeeeeeeeeeeeeeeeeeeeee
Answer:
11
Step-by-step explanation:
90-35=55
55=5x
x=11
good luck
Johnny has 30 marbles. Mark has m marbles. If Johnny has 10 times as many marbles as Mark, write an equation that shows how many marbles Mark has.
Answer: 3
Step-by-step explanation:
From the question, we are informed that Johnny has 30 marbles while Mark has m marbles.
Since Johnny has 10 times as many marbles as Mark, it means that Johnny has: = 10 × m = 10m
Therefore, 10m = 30
m = 30/10
m = 3
Mark has 3 marbles
Find the measure to angle A
Answer:
45
Step-by-step explanation:
HELP IN MATH PLEASE. NEED DONE ASAP
help please and fast bc it’s timed :)
Answer:
x value
Step-by-step explanation:
brainly if you can help me
Answer:
(1, 6)
Step-by-step explanation:
Use elimination or substitution (elimination is easier)
Please help, quick math, and a short explanation on how you got the answer! Thank you!!
Answer:
this is an iscoceles triangle.
I know this because 2 of the sides are equal in length
Therefore,
AB=AC
3x-5=-2x+15
x-5=15
x=20
if x=20 then BC=2(20)
BC=40
Step-by-step explanation:
NEED ASAP CORRECT ANSWER GETS BRAINLIESt
Answer:
QS = 8x - 2
Step-by-step explanation:
QS = QR + RS
QS = 6x - 11 + 2x + 9
QS = 8x - 2
Find the slope and y-intercept value in 7x – 2y = -16.
In the following figure, m || QR. Then, the measure of ∠QPR is
Given:
m || QR
To find:
The measure of ∠QPR.
Solution:
Since m || QR and a transversal line intersect them, therefore the alternate interior angles are equal.
Let points S and T lie on the line m. S is on the right and T is on the left side of point P.
[tex]m\angle RPS=m\angle PRQ[/tex]
[tex]m\angle RPS=45^\circ[/tex]
Now, angles TPQ, QPR and RPS lie on the one side of a straight line. It means, their sum is 180 degrees.
[tex]m\angle TPQ+m\angle QPR+m\angle RPS=180^\circ[/tex]
[tex]50^\circ+m\angle QPR+45^\circ=180^\circ[/tex]
[tex]m\angle QPR+95^\circ=180^\circ[/tex]
[tex]m\angle QPR=180^\circ-95^\circ[/tex]
[tex]m\angle QPR=85^\circ[/tex]
Therefore, the measure of angle QPR is 85 degrees.
answer correctly and i’ll mark brainliest, pls help
Answer:
22.5% increase.
Step-by-step explanation:
Because her collection grows by 9, that means it increases by 9/40 total. As a decimal, this would be 0.225. Then, as a percent you multiply that by 100 to get 22.5%. Pilar's collection increased by 22.5%
Answer:
hahaha is
easy hmm..........
What is the solution to this system of linear equations?
x-3y=-2
x+3y=16
1.(7,3)
2.(3,7)
3.(-2,-3)
4.(-3,-2)
Square WXYZ has coordinates W (2, 4), X (-2, 4), Y (-2,-2), Z (2,-2). What are the coordinates of its
image after the dilation Below?
Answer:
(-8*6)
Step-by-step explanation:
hope I helped
A group of 45 students went to the space museum. Tickets cost $11 for each
student. What was the total cost for all of the tickets?
$56
))
$90
1)) $490
1)
$495
Done
8th Grade Science
your answer is 495 dollars. as 45 times 11 equals 495 being the 45 is students and 11 is price
you can answer 5 math problems in 4 mins how many math problems can you complete in 12 minutes? i need help!!
Answer:
your answer,
you can answer 15 math problems in 12 minutes
Do I have this right this my last question I need help
Answer:
Yes, it is
Step-by-step explanation:
For the first part is 10 per people = y = 10x
And the second part is 2 per people = y = 2x
So the two equations are
y = 10x
and
y = 2x
Hope this helped!
Have a supercalifragilisticexpialidocious day!
the product of a number and 7 as an expression
Answer:
If I'm understanding your question right, the correct response would be something along the lines of 7n = a, where n is the number and a is the product.
Step-by-step explanation:
Help please I will give brainlest
The HCF of 60 and 108 is 12. write their LCM
Answer:
What is the LCM of 60 and 108? The LCM of 60 and 108 is 540.
Step-by-step explanation:
What is the LCM of 60 and 108? The LCM of 60 and 108 is 540.
The HCF of 60 and 108 is 540.
What is HCF?It is the greatest factor present in between given two or more numbers.To find the HCF of numbers: - express each number as product of prime numbers. - find the product of the least powers of common prime number.What is LCM?It is the least number which is exactly divisible by two or more numbers. To find the least common multiple, - express each number as a product of prime numbers. - find the product highest power of the prime numbersFor given question,
We have been given the HCF of 60 and 108 is 12.
We know, the product of LCM and HCF of numbers is equivalent to the product of the given numbers.
⇒ LCM × 12 = 60 × 108
⇒ LCM = 540
Therefore, the HCF of 60 and 108 is 540.
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Calculate the slope represented by the table. Please help me...18points
Answer:
The slope is 1/2
Step-by-step explanation:
Slope Formula: m = y2 – y1
x2 – x1
(-3 , -2) (5 , 2)
m = 2 – (-2) = 4 = 1
5 – (-3) = 8 = 2
Angela purchased a storage cube with a volume of 10 cubic feet. She wants to put it on a shelf that is 24 inches tall.
A.
Yes, because the height of the cube is approximately 4.93 inches.
B.
Yes, because the height of the cube is approximately 2.15 inches.
C.
No, because the height of the cube is approximately 25.85 inches.
D.
No, because the height of the cube is approximately 39.96 inches.
Answer:
B
Step-by-step explanation:
Find the value of x
A. X=16
B. X=7
C. X=56
D. X=4
Answer:
I think answer is
D. X=4
:-))
last one pls help for brainlest
Answer:
24/30-5/30=19/30
this is the answer
Answer:
It's 24/30 and 5/30 and it's 19/30
Step-by-step explanation:
Heather designed some artwork that she plans to sell. She spent $22 on supplies
and will price the artwork at 80% markup. What will be her selling price?
Answer: She should sell her artwork for $39.60 or almost $40.
Step-by-step explanation:
First you need to find out what 80% of 22 is, which is 17.6, then you add that price to the price of her supplies.
22+17.6=$39.60
if 1 pound of candy is 3.50 how much candy can you get with one dollar?
Answer:
Step-by-step explanation:
16 divided by $3.50 = 4.5
Answer:
0.286 pounds
Step-by-step explanation:
one pound=$3.50
x pounds=$1.00
then
1/3.5=0.286 pounds
check:
0.285 pounds per dollar x $3.50=1 pound
An elected official surveyed residents of a town to assess their satisfaction with city services. The survey includes
both those who own and those who rent their homes.
Level of Satisfaction
EEEE
High
Medium
Low
Total
Owners
26
34
18
78
Renters
15
12
5
22
Total
41
46
23
110
What proportion of those surveyed have low satisfaction with city services?
O 0.2091
O 0.2308
0.2644
O 0.3727
Save and Exit
Next
Submit
Answer:
A
Step-by-step explanation:
Not much of a reason but thats what i g ot
Answer:
a
Step-by-step explanation: