A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
The statements that are always true regarding the diagram are:
i. m∠5 + m∠6 =180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
Exterior and interior angles of a triangle.A triangle is a 2 dimensional plane figure which is formed by three straight lines and has three interior angles. It has both interior and exterior angles. Some examples of a triangle are; isosceles, equilateral, scalene, right angled etc.
The interior angles of a triangle are the measure of the three internal angles of the triangle, while exterior angles are external to the interior angles of the triangle.
Note that; the exterior angle of a triangle is equal to the sum of the two adjacent interior angles.
Therefore considering the given diagram, the required statements that are always true regarding the diagram are:
i. m∠5 + m∠6 =180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
A sketch of the diagram is herewith attached to this answer for clarity.
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Related Questions
Please complete the square, show your work.
x^2 - 19x +c
Answers
Answer:
Step-by-step explanation:
We need to transform the given x^2 - 19x + c into the form
(x - a)^2 + d
by completing the square:
1. Take half of the coefficient (-19) of x, obtaining -19/2.
2. Square this result, obtaining 361/4.
3. Add this to x^2 - 19x, and then immediately subtract it:
x^2 - 19x + c becomes x^2 - 19x + 361/4 - 361/4+ c
4. Replace the first three terms with (x - 19/2)^2:
x^2 - 19x + 361/4 - 361/4+ c => (x - 19/2)^2 - 361/4 + c
5. Put this into final form: (x - 19/2)^2 - (361/4 - c)
a)
b)
2
Complete the prime factor trees for 24 and 84:
24
2
||||
6
2
84
7
2
3
What is the Lowest Common Multiple of 24 and 84?
4
6
Answers
The prime factor trees for 24 and 84 are attached in the image below. The Lowest Common Multiple of 24 and 84 is 168.
What are prime factors?A natural number other than 1 whose only factors are 1 and itself is said to be a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth. The lowest of two or more natural numbers' common multiples is referred to as the Lowest Common Multiple (LCM). A prime factor is a natural integer, other than 1, whose sole factors are itself and 1. Actually, 2, 3, 5, 7, 11, and so forth are the first few prime numbers. The term "Lowest Common Multiple" refers to the common multiple of two or more natural integers that is the lowest (LCM).
The prime factors of 24 are: 2,2,2 and 3.
The prime factors of 84 are: 2,2,3 and 7.
Now, The Lowest Common Multiple (LCM) of 24 and 84 is calculated using the prime factors of both the numbers.
LCM= 2*2*2*3*7= 168
Hence, The Lowest Common Multiple of 24 and 84 is 168.
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Marla is four years less than twice as old as Darla. If the sum of their ages is 47, how old is Marla?
Answers
Marla is 30 years old.
Let marla age be x and Darla age be y
Given : Marla is four years less than twice as old as Darla
What is equation ?
In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
Marla is four years less than twice as old as Darla can be represented as : 2y - x = 4
sum of their ages is 47 can be represented as : x + y = 47
Solving both the equation using addition we got ,
3y = 51
y = 17
Substituting the value of y in x + y =47 , we get
x + 17 = 47
x = 47 -17
x = 30
Hence , Marla is 30 years old.
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Need the answer plsss!
Answers
By solving, we see that the product of the polynomials 4 - a and a3 + 7a - 18 is a3 + 3a2 + 46a + 72.
what is polynomial ?The location on the y-axis where the slope of the line passes is known as the intersection point in mathematics. a point on a line or curve where the y-axis crosses. The equation for the straight line is given as Y = mx+c, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercept form (y=mx+b) are m and b, respectively. There are several equations that can be rewritten to look like slope intercepts. The slope and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0, for example.
given
(4 - a) * ( a3 + 7a - 18 )
= 4a3 + 28a - 72 - a4 + 7a2 + 18 a
= a3 + 3a2 + 46a + 72
By solving, we see that the product of the polynomials 4 - a and a3 + 7a - 18 is a3 + 3a2 + 46a + 72.
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How do you find the endpoint and midpoint?
Answers
To find the endpoint we have to calculate the distance between the known midpoint to the known endpoint. To calculate the midpoint we add two points and divide them by 2.
The formula for midpoint = (x1 + x2)/2, (y1 + y2)/2.
Substituting in the two x-coordinates and two y-coordinates from the endpoints.
Putting it together,
The endpoint formula is:
(x a ,ya)= ((2xm−xb),(2ym−yb))
( x a , y a ) = ( ( 2 x m − x b ) , ( 2 y m − y b ) ).
The end of a line at a point that is equally distant from both ends, a time interval between an event's beginning and end.
The point on a graph or figure where the figure stops might be referred to as the endpoint. It can be the point joining the sides of a polygon (the vertex), the common endpoint of two rays making an angle, the two extreme points of a line segment, the one end of a ray.
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Please don't steal, actually try your best and do it fast if you can.
Answers
Answer:
7. B. 0.08
8. C. 0.60
9. D. 0.44
Let Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).
(a) Using the distribution method, find the pdf of U = Z 2. (We proved this in class by using the MGF method. )
(b) Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution. Write down the corresponding parameters for each
Answers
On using the distribution method the value could be [tex]e ^ {t^{2}[/tex]/ 2
What is the Gamma Distribution ?
A distribution which is described as two parameters – shape parameter and inverse scale parameter, having continuous probability distributions.
Given,
Z be a standard normal random variable: i. E. , Z ∼ N(0, 1).
Using the distribution method, find the pdf of U = Z 2.
And Using result from previous part, show that pdf of U follows a special case of Gamma distribution and also of χ 2 distribution.
Suppose e Z ∼ N (0, 1), then
mZ (t) = 1√2πetxe−x2/2dx
= et2/21/√2π
[tex]e ^ {-(x-t)^{2} /2[/tex] dx
= [tex]e ^ {t^{2}[/tex]/ 2
hence, on using the distribution method the value could be [tex]e ^ {t^{2}[/tex]/ 2
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need help on khan NOW! question is on picture. will report link and mark brainliest if right
Answers
Explanation: no matter how you do it you still get 1 bc its x divided by y which is 1
PLZ HELP!!!! The school bus travels at an average speed of 30 miles an hour in the morning because of the traffic. Diego's Home is 3 miles away from the school. If he got picked up by the bus at his house at 7:12am, what time did he arrive at the school?
Answers
Answer:
he arrived at school at 7:18
Step-by-step explanation:
Time = distance/speed = 3mi/30mph
= 3/30
= 0.1 hour
= 6 minutes
= 00:06:00
Find the values of x and y 2x+2y=x+13
Answers
sum of two positive number is always
Answers
what is the equation of the line that is perpendicular to the line y=3/5x+10 and passes through the point (15,-5)?
Answers
Answer:
y = -5/3x + 20
Step-by-step explanation:
y = -5/3x + b
-5 = -5/3(15) + b
-5 = -25 + b
20 = b
y = -5/3x + 20
Answer:
In other words.. The fourth option D.
Step-by-step explanation:
EDGE2022
i like your cut g
Evaluate the expression 5(x – 6 + 3x)2 – 6 where x = 2.
Answers:
1: 974
2: 14
3: -16
4: 26
Answers
So the expression evaluates to 14 when x = 2.
To evaluate the expression, we first substitute x = 2 into the expression:
5(2 - 6 + 3*2)^2 - 6
There are two methods for solving simultaneous linear equations: graphical methods and algebraic methods. The algebraic technique includes the substitution method as one of its categories.
The value of one variable from one equation is substituted in the second equation using the substitution method. In this manner, a pair of linear equations is reduced into a single linear equation with only one variable, which can then be solved quickly.
Next, we simplify the expression inside the parentheses:
=5(2 - 6 + 6)^2 - 6
=5(2)^2 - 6
=5*4 - 6
=20 - 6
=14
So the expression evaluates to 14 when x = 2.
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Alice, Bob, Charles and Darwin are sharing an orange. Bob got twice as many slices as Charles,
Charles got 5 times less slices than Darwin, and Darwin got 8 slices more than Charles. Find the
number of slices in the orange given that Alice got only the peel.
(A) 10 (B) 12 (C) 14 (D) 15 (E) 16
Answers
Answer:
E
Step-by-step explanation:
Let
A = # of slices Alice got
B = # of slices Bob got
C = # of slices Charles got
D = # of slices Darwin got
First, write equations based on given information:
A = 0
B = 2C
5C = D
D = C + 8
5C = D -> D = 5C
Now that we have two equations for D, we can set them equal to each other:
5C = C + 8
4C = 8
C = 2
Now just plug in the rest:
A = 0
B = 2(2) = 4
C = 2
D = 2 + 8 = 10
Add all solutions together to get (E) 16 slices
What does 4 more than mean?
Answers
Answer:
+4
Step-by-step explanation:
if x is your number, then x+4 is four more than
Answer:
Answer Below
Step-by-step explanation:
The phrase "4 more than" means 4 has been added onto a number. Eg:"Sue has 4 more sweets than Ann, means that however many sweets Ann has, Sue's number is bigger by 4.
Find the volume of the cylinder to the nearest tenth, if necessary. Use 3.14 for pi.
Answers
Answer:
62.9 inches cubed
Step-by-step explanation:
V=πr²h
Have a good day :)
Answer:
62.83 or 62.9( if you want simplified )
Step-by-step explanation:
V = π r2 h
Let h(x)=[tex]\sqrt{x+3}[/tex] and k(x)=2x+7
Find the value of h(k(3))
Answers
Which expression is undefined?
Answers
Answer:c
Step-by-step explanation:
Anything divided by 0 is undefined
The first leg of a bike race is 6 km due east. For the second leg of the race, the riders turn northwest and ride 9 km. The final leg of the race runs at a 40° angle back to the second leg and brings the racers back to the starting point. To the nearest tenth, at what angle measure does the third leg of the race meet the first leg? Enter only a number.
Answers
hi quick whats 18 x 1.25
step by step !!
Answers
Answer:
22.5
Step-by-step explanation:
125
x 18
---------
1. first set up your problem
2 4
125
x 18
------
1000
2. next multiply the 8 by 5 getting 40, drop the 0 anf move the 4 to the top above 2.
3. multiply 8 by 2 getting 16, then add the 4 you have ontop of the 2 to the 16 getting 20. Drop the 0 and bring the 2 over and place it above the one.
4. multiply 8 by 1 getting 8 then add the 2 above the 1 to 8 getting 10. Then put the ten infront of the tw zeros. 1000
125
x 18
--------
1000
0
Next add a 0 as a place filler under the 0 at the end.
125
x 18
-------
1000
1250
Then multiply the 1 by 5, then 1 by 2, then finnaly 1 by 1, getting you 1250.
1000
+1250
add together
getting 2250
then move 2 decimal places over to get 22.5
The graph of a function is line that passes through the points (1,4) (3,8) and (6,y) what is the value of y?
Answers
Step-by-step explanation:
First, find the slope from the first 2 points, then use the value of the slope and either one of the first 2 points to find y in the 3rd point.
m = (8 - 4)/(3 - 1) = 4/2 = 2
2 = (y - 4)/(6 - 1)
Rochelle deposits $5,000 in an IRA. What will be the value (in dollars) of her investment in 15 years if the investment is earning 7% per year and is compounded continuously? (Simplify your answer completely. Round your answer to the nearest cent.)
Answers
Answer:
$80.438.11
Step-by-step explanation:
the formula for calculating future value when there is continuous compounding is : A x e^r x N A= amount e = 2.7182818 N = number of years r = interest rate
$5,000 x (2.7182818 ^0.07) x 15 = $80.438.11
Use the correct order of operations to solve the problem below.
14 - 8 + 6 - 10 ÷ 2
Answers
Answer: 7
Step-by-step explanation:
How do you find the slope of a line example?
Answers
The easiest way to find the slope of a line is converting the line equation into the slope-intercept form.
There are 3 forms of line equations:
- slope intercept form, the equation is given by:
y = mx + b
Where:
m = slope
- point slope form, the equation is given by:
y − y₁ = m (x - x₁)
Where:
m = slope
- standard form: Ax + By = C
The easiest way to find the slope of a line is to convert it into a slope-intercept form.
Example:
Line equation in standard form:
2x + 4y = 6
We will convert it into slope-intercept form.
4y = -2x + 6
y = (-2/4) x + 6
y = (-1/2) x + 6
Hence, the slope is (-1/2)
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Ashleyspent 64 minutes studying for her reading test. She spent 5/8 of that time studying flashcards. How much time did ashley spend studying flash cards
Answers
Answer:
40 miniutes studying flash cards because 5/8 of 64 miniutes
Step-by-step explanation:
PLZ give me brainliest.
What is the length of JL, nearest tenth
Answers
Answer:
I believe the answer is 45.
Step-by-step explanation:
a 90 degree angle is represented by a square on the corner.
So half of 90 is:
90 ÷ 2 = 45
the angle next to the letter M is 90 degreess, so the other side of the line is also 90 degrees.
45 + 90 = 135
and 180 - 135 = 45
(You subtract 135 from 180 since " the sum of angles of a triangle equals the straight angle", which is 180 degrees.
So, the length of JL is equal to 45 degrees.
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Hope it helps!
Find the total surface area of this cuboid.
5 cm
4 cm
6 cm
Answers
Answer: 15cm2
Step-by-step explanation:
5cm+4cm+6cm=15cm2
1 Total surface area = units?
Answers
Answer:
The answer is Thirty Six (36)
Answer:
36 g
Step-by-step explanation:
How to multiply 20x67?
Answers
Answer:
do 20 times 67 and it will equal 1,340
Step-by-step explanation:
1
20
x 67
1 , 3 4 0
Answer:
Your answer is 1340
Step-by-step explanation:
2 0
× 6 7
--------------------------------------
+ 1 4 0 First you do 7 * 20
+ 1 2 0 0 Then you do 60 * 20
--------------------------------------
= 1 3 4 0 Then you add them together.
Work out the length of x.
Give your answer rounded to 1 decimal place.
9 m
14.5 m
The diagram is not drawn accurately
Please help
Answers
Answer:
Calculate the value of x. Give your answer ... Hyp. 5.8 m. Opp. 1. Adi. Diagram NOT accurately drawn. POR is a triangle. Angle Q = 90° ... the value of x. Give your answer correct to 1 decimal place. ... a. Diagram NOT accumtely drawn. 9,6 cm. 6.4 cm. A. Hyp. To. Aaj. LMN is a right-angled triangle. MN = 9.6 cm. ... x = ton-14.5.
Step-by-step explanation:
please be right