Given: angle 1 and angle 2 form a linear pair; angle 2 is congruent to angle 4 Prove: angle 1 and angle 3 are supplementary
Answers
Answer:
Step-by-step explanation:
1. ∠1 and ∠2 are a linear pair 1. Given
2. ∠1 and ∠2 are supplementary 2. Linear Pair Postulate
3. m∠1 + m∠2 = 180° 3. Definition of Supplementary Angles
4. ∠1 and ∠3 are vertical angles 4. Given
5. ∠1 ≅ ∠3 5. Vertical angles are congruent.
6. m∠1 = m∠3 6. Congruent angles have equal measure.
7. m∠3 + m∠2 = 180º 7. Substitution into step 3.
8. ∴∠2 and ∠3 are supplementary 8. Definition of Supplementary Angles
Supplementary angles are two or more angles that add up to [tex]180^{o}[/tex]. Thus < 1 and < 3 are supplementary due to the supplementary angles addition theorem.
When two or more angles add up to form [tex]180^{o}[/tex], then they are supplementary. So that applying the required angles postulates or theorems, the following reasons can be deduced:
Statements Reasons
1. ∠1 and ∠2 are a linear pair Given
2. ∠1 and ∠2 are supplementary Linear Pair Postulate
3. m∠1 + m∠2 = 180° Definition of Supplementary Angles
4. ∠2 = ∠4 Given
5. ∠3 = ∠4 Vertical opposite angle Postulate
6. ∠2 = ∠3 Corresponding angle theorem
7. m∠2 = m∠3 Corresponding angles are congruent
8. m∠1 + m∠3 = [tex]180^{o}[/tex] Supplementary angle Postulate
9. <1 and <3 are Supplementary Supplementary angles addition theorem
Therefore <1 and <3 are supplementary angles because they add up to [tex]180^{o}[/tex].
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Related Questions
Parallel lines s and t are cut by a tranversal r. Which angles are alternate interior angles? <3 and <5 <1 and <7 <3 and <7 <4 and <5
Answers
Answer:
it Would be easier to answer with a picture but since these Question are normaly the same picture but it is Angle 3 and 7
Step-by-step explanation:
#NO ADDS
Are the equations – 2x = 10 and -5x = 25 equivalent?
Answers
Answer: [tex]Yes[/tex]
Q: How are they the same answer?
A: You divide both of them by the number with x.
Divide both sides by -2
[tex]-2x/-2=10/-2\\x=-5[/tex]
Divide both sides by -5
[tex]-5x/-5=25/-5\\x=-5[/tex]
That's how both of them are equivalent to each other.
[tex]\text{Hey there!}[/tex]
[tex]\text{Are the equations -2x = 10 \& -5x = 25 equivalent?}[/tex]
[tex]\text{-2x = 10}[/tex]
[tex]\text{DIVIDE both sides by -2}[/tex]
[tex]\bf{\dfrac{-2x}{-2} = \dfrac{10}{-2}}[/tex]
[tex]\text{Cancel out \dfrac[-2x}{-2} because it gives 1}[/tex][tex]\text{Cancel out:}\ \bf\dfrac{-2x}{-2} \text{ because it gives you 1}[/tex]
[tex]\text{Keep:} \bf{\dfrac{10}{-2}}\text{ because it gives you the result of x}[/tex]
[tex]\bf{\dfrac{10}{-2} = -10\div2 \rightarrow -5}[/tex]
[tex]\boxed{\underline{\text{\bf{x = -5}}}}\checkmark[/tex]
[tex]\text{-5x = 25}[/tex]
[tex]\text{DIVIDE both sides by -5}[/tex]
[tex]\bf{\dfrac{-5x}{-5}= \dfrac{25}{-5}}[/tex]
[tex]\text{Cancel out:}\ \bf{\dfrac{-5x}{-5}}\text{ because it gives you 1}[/tex]
[tex]\text{Keep:}\ \bf{\dfrac{25}{-5}}\ \text{ because it gives you the result of x }[/tex]
[tex]\bf{\dfrac{-25}{5} = -25 \div 5 \rightarrow -5 }[/tex]
[tex]\boxed{\underline{\bf{x = -5}}}\checkmark[/tex]
[tex]\boxed{\text{To answer your question: \boxed{\bf{YES}} because both x's equal to -5}}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
who can solve these!!!
Answers
Answer:
1. 5 months2. 147 pagesStep-by-step explanation:
1....................................
Company A
75 + 20xCompany B
35xTime required:
75 + 20x = 35x15x = 75x = 5 months2....................................
Set up fee = $15
Additional fee= $0.17 per page
Max amount= $40
0.17x + 15 < 400.17x < 25x < 25/0.17x < 147Max number of pages is 147
Step-by-step explanation:
the solution is attached
have a good day
the cost of a camp is $300 for the first week and $125 for each week beyond the first. the total cost can be modeled by the expression 300+125(x-l). what does (x-l) repreasent
Answers
Answer: hopefully this helps
D. The number of weeks after the first week
Step-by-step explanation:
A movie club charges a one-time fee membership fee of $25. This allows members to purchase movies for $7 each. Lincoln is a member of the movie club and has spent a total of $60. How many movies has Lincoln purchased
Answers
Answer:
he purchased 5 movies bro
Step-by-step explanation:
25
Highest Temp(°F)
What is the
difference
in the low
and high
temp?
0
Lowest Temp °F)
-25
Answers
Answer:
there both the same number its just that one is on top and the other is on bottom
If EF=6 and EG=23 find the value of FG
Answers
Answer:
FG = 17
Step-by-step explanation:
EF=6 and EG=23
find the value of FG
6
E-------------F-----------------------------------G
|<-----------------------23---------------------->|
EF + FG = 23
6 + FG = 23
FG = 23 - 6
FG = 17
A rectangular prisms base has an area of 40cm2.the prisms height is 5cm .what is the volume of the prism?
Answers
Answer:
5
Step-by-step explanation:
5679
If y is directly proportional to x and y = 6 when x = 2, what is the proportion equation?
Answers
Answer:
y = 3x
Step-by-step explanation:
Direct proportion equation is
y = kx
6 = k*2
Divide each side by 2
6/2 = 2k/2
3 =k
The equation is y = 3x
Formula for direct proportion: y = kx
Solution:
6 = 2k
~Divide 2 to both sides
3 = k
Best of Luck!
What is the best first step for solving the equation 5 = 3x - 4? a. Add 4 to both sides of the equation. b. Subtract 4 from both sides of the equation. c. Multiply both sides of the equation by 3 d. Divide both sides of the equation by 3.
Answers
Answer:
A. Add 4 to both sides of the equation.
Step-by-step explanation:
Isolate your variable by using inverse operations.
Amy buy 5 pounds potatoes for $2.50. How much does 1 pound of potatoes weight? (What is the unit rate?)
Answers
Answer:
$0.50
Step-by-step explanation:
If there are 5 pounds of potatoes for $2.50, you must divide to find the unit rate.
$2.50 / 5 = $0.50
1 pound of potatoes costs $0.50
Answer:
0.5 $/pound
Step-by-step explanation:
[tex]5[/tex] pounds ⇒ [tex]2.50$[/tex]$to khow much dollars one 1 pound costs, we must divide the price of 5 pounds by 5
[tex]\frac{2.50}{5} = 0.5[/tex] $/ pound2.5 is in dollars and 5 is in pounds so the rate unit is $/pound
Find the reciprocal of 5.
Answers
Answer:
0.2 is the answer
Step-by-step explanation:
Answer:
0.2
Step-by-step explanation:
5^-1=0.2
Can v11 be classified as a rational
Answers
Answer:
yes it should
Step-by-step explanation:
factorise 9(a+b)^2 + (a+b) -8
Answers
Answer:
[tex](9a+9b-8)(a+b+1)[/tex]
Step-by-step explanation:
[tex]9(a+b)^2 + (a+b)-8[/tex]
Expand [tex](a+b)^2[/tex]
[tex]9(a^2+2ab+b^2)+a+b-8[/tex]
[tex]9a^2+18ab+9b^2+a+b-8[/tex]
Now it is time to think.
Once
[tex]9a^2=9a \cdot a[/tex]
[tex]9b^2=9b \cdot b[/tex]
[tex]18ab=9ab+9ab[/tex]
[tex]-8=-8 \cdot 1[/tex]
We can get something in the format
[tex](9a+9b-8)(\text{some expression here})[/tex]
From the conclusions above,
[tex](9a+9b-8)(a+b+1)[/tex]
What is the answer for 4x+3=36
Answers
[tex]4x + 3 = 36\\4x = 36 - 3\\4x = 33\\x = \frac{33}{4}[/tex]
[tex]x = 8[/tex]I need help solving this.
Answers
Answer:
2
Step-by-step explanation:
x³ = 8
∛8 = 2
found by 2 • 2 • 2 = 4 • 2 = 8
can someone help me with this geometry question?
Answers
Answer:
(-1,4.5)
Step-by-step explanation:
You would have to use the formula for midpoint. 5+-3/2= -1
3+6/2= 4.5 which would be -1 for x and 4.5 for y.
For a given recipe, 10 cups of flour are mixed with 20 cups of sugar. How many cups of flour should be used if 4 cups of sugar are used? Assuming a constant ratio, fill out the table of equivalent ratios until you have found the value of x.
Answers
Answer:
2
Step-by-step explanation:
If 20 cups are used on the first recipe then 4 are used on the second, the way to find the answer is to divide 20 by 4. 20 divided by 4 will get 5. Now we have to divide the 10 cups of flour by 5 which in the end will get 2.
What is 3.000 in standard notation?
Answers
Answer:
3 x 10(to the 3rd power)
Step-by-step explanation:
❗️URGERNT❗️
I will give brainliest if your response comes with an explanation.
During a heavy rainstorm, a city in Florida received
12 1/4 inches of rain in 25 1/2 hours. What is the approximate rainfall rate in inches per hour?
Answers
Answer: 0.48 in
Step-by-step explanation:
The problem asks for unit rate. To solve, let's convert the fractions to decimals.
[tex]12\frac{1}{4} =\frac{49}{4} =12.25[/tex]
[tex]25\frac{1}{2}=\frac{51}{2}=25.5[/tex]
Now that they are in decimals, we can set up a proportion.
[tex]\frac{12.25 in}{25.5 hrs} =\frac{x}{1 hr}[/tex] [cross multiply]
[tex]12.25=25.5x[/tex] [divide both sides by 25.5]
[tex]x=0.48[/tex]
Now, we know that there was approximately 0.48 in of rainfall per hour.
4a−2(3a+8)=6 what is the answer
Answers
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{a = - 11}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{4a - 2(3a + 8) = 6}[/tex]
Distribute 2 through the parentheses
[tex] \longrightarrow{ \sf{4a - 6a - 16 = 6}}[/tex]
Collect like terms
[tex] \longrightarrow{ \sf{ - 2a - 16 = 6}}[/tex]
Move 16 to right hand side and change it's sign
[tex] \longrightarrow{ \sf{ - 2a = 6 + 16}}[/tex]
Add the numbers: 6 and 16
[tex] \longrightarrow{ \sf{ - 2a = 22}}[/tex]
Divide both sides by 2
[tex] \longrightarrow{ \sf{ \frac{ - 2a}{ - 2} = \frac{22}{ - 2}}} [/tex]
Calculate
[tex] \longrightarrow{ \sf{a = - 11}}[/tex]
Hope I helped !
Best regards! :D
The measure of two vertical angles are given by the expressions (x+3) and (2x-7). Find the value of x.
Answers
Answer:
61.3
Step-by-step explanation:
two vertical angles add up to 180°
so (x+3)+(2x+7)=180°
open brackets & collect like terms
x+3+2x-7=180°
3x+-4=180°
3x=184°
x=61.3 after dividing by 3 on both sides
Use the Distributive Property to simplify. s 5 a solution to 2t - 1 = 11?
Answers
Answer:
5 is NOT a solution to the equation.
t = 6
Step-by-step explanation:
Step 1: Write out equation
2t - 1 = 11
Step 2: Add 1 to both sides
2t = 12
Step 3: Divide both sides by 2
t = 6
Find the value of the expression -1/3-(-5/12).
Answers
Answer:
1/12
Step-by-step explanation:
what is 125.2 X 3 3/4=?
Answers
Answer: 31.3x33
Step-by-step explanation:
Did the test :)
A text font fits 12 characters per inch. Using the same font, how many characters can be expected per yard of text? There are 12 inches in a foot, and 3 feet in a yard. 36 characters 144 characters 360 characters 432 characters
Answers
432 characters can be expected to fit per yard of text. Therefore, option D is the correct answer.
Given that, a text font fits 12 characters per inch.
We need to find how many characters can be expected per yard of text.
How to convert yards to inches?To convert a yard measurement to an inch measurement, multiply the length by the conversion ratio. The length in inches is equal to the yards multiplied by 36.
Let x be the number of characters to be used in a yard.
12 characters / in = x/ 36 in
(12 characters * 36 in) / in = x
x = 432 characters
Therefore, option D is the correct answer.
To learn more about yards visit:
https://brainly.com/question/14516546.
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the answer is 432 characters
16) Evaluate the expression with its given values.
hi idk if it’s right but could anyone help at least if so ty
Answers
HELPP!!! Which of the following is a negative externality of a parent taking afternoon and
evening classes at a local college?
A potential career change and income decrease
A tighter schedule limiting time with children
The list of assignments due for each semester
The number of future job postings
Answers
Euclid relied on five basic axioms to build the propositions in his book Elements. The first axiom states, “Things that are equal to the same thing are also equal to one another.” Which modern mathematical statement is equivalent to this axiom? Will give brainiest Asap If a = b, then b = a. If a = b and b = c, then a = c. If a ≠ b, then b ≠ a. If a = b, then a + c = b + c.
Answers
Answer: B
Step-by-step explanation:
Answer:
B. If a = b and b = c, then a = c.
Step-by-step explanation:
I just did it.
ASAP!!!!! A square pyramid and its net are shown below. What is the surface area of the pyramid?
Answers
Answer:
800
Step-by-step explanation:
16x16=256
17x16=272
272/2=136
136x4=544
544+256=800
