Answers
Answer:
The correct options are;
1. Definition of supplementary angles
2. m∠1 + m∠2 = m∠1 + m∠3
3. m∠2 = m∠3
4. Definition of congruent angles
Step-by-step explanation:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. ∠1 and ∠2 are supplementary [tex]{}[/tex] Given
∠1 and ∠3 are supplementary [tex]{}[/tex]
2. m∠1 + m∠2 = 180° [tex]{}[/tex] (1) Definition of supplementary angles
m∠1 + m∠3 = 180°
3. (2) m∠1 + m∠2 = m∠1 + m∠3 [tex]{}[/tex] Transitive Property
4. (3) m∠2 = m∠3 [tex]{}[/tex] Subtraction property of equality
5. ∠2 ≅ ∠3 [tex]{}[/tex] (4) Definition of congruent angles
Given that angles ∠1 and ∠2 are supplementary, we have, ∠1 + ∠2 = 180°
Given that angles ∠1 and ∠3 are also supplementary, we also have, ∠1 + ∠3 = 180°
∴ ∠1 + ∠2 = 180° = ∠1 + ∠3
∠1 + ∠2 = ∠1 + ∠3
∠1 + ∠2 - ∠1 = ∠1 + ∠3 - ∠1
∴ ∠2 = ∠3
∴ ∠2 ≅ ∠3, by definition of congruent angles.
Related Questions
The city of Austin has a bridge that is famous for housing the largest urban bat colony in the
world. It is home to 2 million bats. It has been determined that the bats eat a total of 10 tons
of insects a night. If the population of the bats increases to 2.5 million, about how many
insects would they consume?
Answer:
tons
Answers
Answer:
12.5 tons
Step-by-Step Explanation
There are 2 million bats and they eat 10 tons so 1 million bats would eat 5 tons half of 5 is 2.5 so if there where 2.5 million bats then you would increase the number of insects by half of a half or 2.5 because the number increased by half a million and 1 million bats eat 5 tons. Hope this was helpful :D
what is. the value of x in the equation 2.5(6x-4)=10+4(1.5+0.5x)?
Answers
Answer:
x=2
Step-by-step explanation:
We first distribute this. So we have 15x-10 = 10 + 6 +2x.
Then we move the variable to one side and have 13x= 10+10+6
Simplify to get 13x = 26.
x=2
Diego cut 7 smaller boards of equal length from a board that is 9 and one-third feet long. How long is each of the 7 smaller boards?
Answers
Answer:
1 1/3 feet long
Step-by-step explanation:
Answer:
Each of the seven smaller boards will be 1.3 feet long
Step-by-step explanation:
We must divide 9 1/3 by 7
9 1/3 / 7 = 1.333286
We now have to round to the nearest tenth which would give us:
1.3
So our final answer would be 1.3
4. write the following in standard form
four hundred, thirty - two thousand, six hundred eight
Answers
please help it is due today
Answers
A
Step-by-step explanation:
because i did this and i pass this
Answer:
45= p x 60, 0.75
Step-by-step explanation:
To solve the equation, you just do 45/60 this will give you 0.75.
if the slope is -2/5 and the y-intercept is 5/2 the slope-intercept form is y=5/2x-2/5 true or false
Answers
Answer:
is false
explanation
just trust me
20z-8 please helpppp
Answers
Answer: 4(5z−2)
Step-by-step explanation: Brainliest pls
nya wants to buy a sweater that had an original price of 55. the sweater is now discounted 20% and the sales tax rate is 5.5%. how much will nya pay for the swearter
Answers
Answer:
Step-by-step explanation:
55 - 20% = 44
5.5% of 44 = 2.42
2.42 + 44 = 46.42
hope this helps. :]
A three-and-a-half foot stick is cut into two pieces. One piece is
1.65 ft long. How long is the other piece?
Answers
Answer:
1.4
Step-by-step explanation:
3.05 is the length of the stick and 1.65 is one part if the stick si we subtract 1.65 from 3.05 to find the length of the other piece
Random variation in a process indicates __________; whereas non-random variation indicates process __________.
Answers
Answer: b. Stability/instability
Step-by-step explanation:
Random variation in a process indicates stability; whereas non-random variation indicates process instability.
When there is random variation in a process, it means that the process is stable and under control such that the only variations are those expected to be in the process.
When the variation is non-random however, it points to instability in process because this variation is special and not inherent in the process.
a line passes through (3, -2) and (6, 2).
a. Write an equation for the line in point slope-form
b. rewrite the equation in standard form using integers
Answers
9514 1404 393
Answer:
a) y +2 = (4/3)(x -3)
b) 4x -3y = 18
Step-by-step explanation:
a) The slope formula gives part of what is needed for point-slope form:
m = (y2 -y1)/(x2 -x1)
m = (2 -(-2))/(6 -3) = 4/3
Point-slope form is ...
y -k = m(x -h) . . . . . . for slope m and point (h, k)
Using the first point, we get ...
y +2 = 4/3(x -3)
__
b) Multiplying by 3 and eliminating parentheses, we get ...
3(y +2) = 4(x -3)
3y +6 = 4x -12
Adding 12 -3y to both sides gives ...
18 = 4x -3y
Putting this in the usual form, we have ...
4x -3y = 18
The points (10, 8) and (19, 17) fall on a particular line. What is its equation in slope-intercept
form?
Answers
Answer:
Step-by-step explanation:
First, find the slope using the two given points and the slope equation.
[tex]m=\frac{y2-y1}{x2-x1}=\frac{17-8}{19-10}=\frac{9}{9}=1[/tex]
We can enter [tex]m[/tex] into our slope-intercept form now.
[tex]y=mx+b\\y=1x+b\\y=x+b[/tex]
Now, plug in one of the given points to solve for b.
[tex]8=10+b\\b=-2[/tex]
So our final form is:
[tex]y=x-2[/tex]
Hope this helps!
The equation of the line passing through the points (10, 8) and (19, 17) is y = x - 2.
What is the general equation of a straight line?The general equation or the slope - intercept form of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a line such that points (10, 8) and (19, 17) lie on this line.
The given coordinates are (10, 8) and (19, 17).
First, we will find the slope of the line as follows -
m = (17 - 8)/(19 - 10)
m = 9/9
m = 1
So, the equation of the line will be -
y = x + c
Now, we will find the y - intercept. As the line pass through the point
(10, 8), we can write -
8 = 10 + c
c = 8 - 10
c = -2
So, the equation of the line will be y = x - 2.
Therefore, the equation of the line passing through the points (10, 8) and (19, 17) is y = x - 2.
To solve more questions on straight line, visit the link below-
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HELP ME 50 POINTS RN
Answers
Answer:
A
Step-by-step explanation:
Because it can only lift 2,200 pounds and that means it can lift 2,200 - 0 Pounds
Can someone answer this for me ill give brainliest asap
Answers
The regular price is $8.45 more than the sale price. The regular price
is $24.95. What is the sale price? _____
Answers
Answer:
33.04
Step-by-step explanation:
just add lolz :P
Answer:
$33.40
Step-by-step explanation:
1 1 1
24.95
+ 8.45
__________
33.40
5+5 is 10 so bring a 1 to the top and put a 0 for the bottom
1+9+4 is 14 so put the 4 down and put the 1 on top.
1+4+8 is 13 so put the 3 down and put the 1 on top.
1+2 is 3 so put the 3 down
then you get 33.40
A= 12.8m
B=13.9m
C=12m
D= 7m
Answers
Answer:
C: 12m
Step-by-step explanation:
We can solve this by using the Pythagorean Theorem [tex]a^{2} + b^{2} = c^{2}[/tex]
For this triangle
a= x b= 5 c= 13
We now have the equation
[tex]x^{2} + 5^{2} =13^{2}[/tex]
If we simplify this we get
[tex]x^{2} + 25 = 169[/tex]
Next, we subtract 25 from both sides
[tex]x^{2} = 144[/tex]
Finally, if we take the square root of both sides of the equation, we find that
x= 12
Solve the equation sin^2x=3Cos^2X.
I would love to graduate...so thanks in advance!
Answers
Answer:
240°
Step-by-step explanation:
[tex]sin^2x=3cos^2x \\ \\ sin^2x=3(1 - sin^2x )\\ \\ sin^2x=3 - 3sin^2x \\ \\ sin^2x + 3sin^2x=3 \\ \\ 4sin^2x=3 \\ \\ sin^2x= \frac{3}{4} \\ \\ sinx= \sqrt{ \frac{3}{4} } \\ \\ sinx= \frac{ \sqrt{3} }{2} \\ \\ sinx= sin \: 60 \degree \\ \\ in \: the \: second \: quadrant \\ sinx= sin \: (180 \degree - 60 \degree ) = sin \: 120 \degree \\ \\ in \: the \: third \: quadrant \\ sin x= sin \: (180 \degree + 60) \degree = sin \: 240 \degree[/tex]
Hakim Ellison wants to buy a 4 door sport utility vehicle 4 wheel drive hybrid. There is an 8% sales tax on the purchase price of the SUV in his state. If he pays the full sticker price for the SUV, how much is the total?
Answers
Answer: $60401.16
Step-by-step explanation:
From the attached image, the total price for the vehicle = $55,927.
If he were to pay the full sticker price for the SUV, the total would sum up to
= $55,927 + 8% sales tax
= $55,927 + 8/100( $55,927)
= $55,927 + 0.08($55,927)
= $55,927 + $4474.16
= $60401.16
The total would sum up to $60401.16
If the perimeter of the triangle is 40 cm, find the area of the triangle.
The area of the triangle is, ? cm2.
Answers
Answer:
102 cm²Step-by-step explanation:
Perimeter is:
P = 40 cmand P = 2x - 4 + 5x - 13 + x + 9 = 8x - 8Comparing the value:
8x - 8 = 40 8x = 48x = 8 cmAre formula:
A = 1/2ahReplacing values:
A = 1/2(x + 9)(2x - 4)A = 1/2(8 + 9)(2*8 - 4) = 1/2*17*12 = 102 cm²Answer:
60cm²
Step-by-step explanation:
To find :-
The Area of the triangle .We know that Perimeter is the sum of sides of a triangle. Here the perimeter is 40cm .
→ 2x - 4 +5x - 13 + x + 9 = 40cm .
→ 8x - 8 = 40cm
→ 8x = 40+8 cm
→ 8x = 48 cm
→ x = 6cm .
We know that the area of the triangle is half the product of base and height .
Base = x + 9 = 15cm Height = 2x -4 = 8cm .→ A = 1/2 × b × h
→ A = 1/2 × 8cm × 15cm
→ A = 60cm²
If an arithmetic sequence
begins with a 6 and the constant term is 2, what would be the
fourth term of the sequence?
plsssss help
Answers
Answer:
a₄ = 12
Step-by-step explanation:
To obtain the terms in the sequence add 2 to the previous term, that is
a₂ = a₁ + 2 = 6 + 2 = 8
a₃ = a₂ + 2 = 8 + 2 = 10
a₄ = a₃ + 2 = 10 + 2 = 12
Giving brainless! Don’t answer if you don’t know I’ll flag you.
Answers
Answer:
The sales tax is $0.40
Step-by-step explanation:
10 x 0.04 = 0.4
0.04 is 40% when multiplying
What is the answer to 0.5x(y - z) in distributive Property?
Answers
Please help me please!
Answers
Answer:
(2) 19
Step-by-step explanation:
[tex]2(3^x)+1[/tex][tex]2(3^2)+1[/tex][tex]2(9)+1[/tex][tex]18+1[/tex][tex]19[/tex]
Find the equation of the line that is perpendicular to y = –3x + 1 and passes though the point (6, 3).
A) y =
1
3
x + 1
B) y = –
1
3
x + 1
C) y = 3x – 5
D) y = –3x – 5
Answers
Answer:
A. y=1/3x+1
Step-by-step explanation:
When finding a line that is perpendicular to another line, all you have to do is find the "opposite reciprocal" of the slope. In this case that means writing the slope as the fraction -3/1, and then flipping the fraction over (1/-3) and taking away the negative sign which gets you 1/3 for the slope of your new line. Now, all you have of your new equation is the slope. You need to take your new equation (y=1/3x+b) and plug in the x and y coordinates to that equation, and then solve for the last variable which is b. That solving process goes as follows:
3=1/3*6+b
3=2+b
1=b
now you can replace the b with 1 in your equation to get your final answer of y=1/3x+1
Eeeeeeeeeeeeeeeeeeeeeee
Answers
Which of the following expressions is in simplified form?
9 j - 3 - j
4 w - 5
1 1/2 n + 2.9 n
-2 + 1.4 m + 0.5
Answers
Answer:
The answer is 4w-5 its in its simplest form
Demons answer this for me.
Answers
Answer:
Step-by-step explanation:
if you have negative numbers of x (this means negative meters) then the equation transform them into negative yards.
then replace y by 40yd in the equation like
40 = 1.09x
x = 40/1.09 = 36.7 meters
so in a 40yd race, there are 36.7 meters.
Given the parallelogram below, find the value of angle 1
Answers
Pleaseee I need help
Answers
Answer:
32
Step-by-step explanation:
2x-16 + 4x+4 =180
6x=180+12
6x=192
x=32
I hope this helps, have a good day
A bricklayer can build a wall of a certain size in 5 hours. Another bricklayer can do the same job in 4 hours. If the bricklayers work together, how long would it take to do the job?
a. 9h
b. 2(2/9)h
c. 20h
d. 4(1/2)h
Answers
Answer:
b
Step-by-step explanation:
It will take [tex]\frac{20}{9}[/tex] hours as per linear equation to complete the wall.
What is a linear equation?A linear equation is an equation where the variable of the equation has the highest power of degree one.
Given, the 1st bricklayer build a complete wall of certain size in 5 hours.
Therefore, that bricklayer build [tex]\frac{1}{5}[/tex]th of the complete wall in 1 hour.
Similarly, the 2nd bricklayer build a complete wall of certain size in 4 hours.
Therefore, that bricklayer build [tex]\frac{1}{4}[/tex]th of the complete wall in 1 hour.
If they work together, in 1 hour they build a total of ([tex]\frac{1}{5}[/tex]+[tex]\frac{1}{4}[/tex])th = [tex]\frac{9}{20}[/tex] of the complete wall.
Hence, they will complete the wall in (1÷[tex]\frac{9}{20}[/tex]) hours = [tex]\frac{20}{9}[/tex] hours.
Learn more about a linear equation here: https://brainly.com/question/13738061
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