Given: y || z
Prove: mZ5+ m2 2 + m26 = 180°
Angles Lines Statements Reasons
21
23
25
26
m21
m23
m25
m26
L
A
M
1
2
3
y
Statements
Reasons
4
5
6
7
z
Assemble the proof by dragging tiles to
the Statements and Reasons columns
Intro
D
Answers
Using the above statements and reasons can be used to prove the triangle sum theorem, which is: ∠5 + ∠2 + ∠6 = 180°
What is the Triangle Sum Theorem?The triangle sum theorem states that, when we add the all three interior angles of a triangle together, it will give us a sum of 180°.
Given that y || z:
∠1 ≅ ∠5 and ∠3 ≅ ∠6 based on the interior angles theorem. This implies that:
∠1 = ∠5 and ∠3 = ∠6 (Eqn. 1)
m∠LAM = 180° (def. of straight line angle)
Thus, using the angles addition theorem, we have:
∠1 + ∠2 + ∠3 = m∠LAM
∠1 + ∠2 + ∠3 = 180° (eqn. 2).
Using eqn. 1 and eqn. 2, substitute ∠1 = ∠5 and ∠3 = ∠6 into eqn. 2.
∠5 + ∠2 + ∠6 = 180° (substitution).
Therefore, using the above statements and reasons can be used to prove the triangle sum theorem, which is: ∠5 + ∠2 + ∠6 = 180°
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The proof for the triangle sum theorem, which is: ∠5 + ∠2 + ∠6 = 180°
What is Angle Sum Property?According to the triangle sum theorem, if we total up a triangle's three internal angles, we receive a value of 180°.
We have, y || z.
So, ∠1 ≅ ∠5 and ∠3 ≅ ∠6 (Alternate Interior Angle)
Using Linear Pair
∠1 + ∠2 + ∠3 = m ∠LAM
∠1 + ∠2 + ∠3 = 180°
Now, substitute ∠1 = ∠5 and ∠3 = ∠6 in above equation
∠5 + ∠2 + ∠6 = 180° .
Thus, using the above statements can be used to prove the triangle sum theorem, which is: ∠5 + ∠2 + ∠6 = 180°
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Related Questions
How would I find the lower left interior angle of a triangle whose lower right interior angle is 60 and the exterior angle is x?
Answers
How would I find the lower left interior angle of a triangle whose lower right interior angle is 60 and the exterior angle is x?
simplify if y<0.
[tex]-\sqrt{9y^{2} }[/tex]
Answers
Answer:
-3y
Step-by-step explanation:
Whether y is smaller than 0 or not, the square root of y^2 is y, a positive quantity.
Thus, -√(9y²) = -3y
Answer
It's actually 3y instead of -3y.
BTW, anybody from RSM
Help me solve this-> g(x) = 2x + 3
g(7) =
Answers
Answer:
17
Step-by-step explanation:
it's sufficient to set x=7
g(7)=2×7+3=14+3=17
Answer:
g(7)=2.7+3=17
does anyone know this i need it fast
Answers
HOW MUCH IT’S ( 4/2 - 1/2 ) + 3/4 I need the answer because I’m stay in test
Answers
Answer:
= 7.25
Conversion a mixed number 4 3/
4
to a improper fraction: 4 3/4 = 4 3/
4
= 4 · 4 + 3/
4
= 16 + 3/
4
= 19/
4
To find a new numerator:
a) Multiply the whole number 4 by the denominator 4. Whole number 4 equally 4 * 4/
4
= 16/
4
b) Add the answer from previous step 16 to the numerator 3. New numerator is 16 + 3 = 19
c) Write a previous answer (new numerator 19) over the denominator 4.
Four and three quarters is nineteen quarters
Conversion a mixed number 2 1/
2
to a improper fraction: 2 1/2 = 2 1/
2
= 2 · 2 + 1/
2
= 4 + 1/
2
= 5/
2
To find a new numerator:
a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/
2
= 4/
2
b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
c) Write a previous answer (new numerator 5) over the denominator 2.
Two and one half is five halfs
Add: 19/
4
+ 5/
2
= 19/
4
+ 5 · 2/
2 · 2
= 19/
4
+ 10/
4
= 19 + 10/
4
= 29/
4
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(4, 2) = 4. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 2 = 8. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - nineteen quarters plus five halfs = twenty-nine quarters.
Step-by-step explanation:
Answer:
you can write it in exact form which is 9/4 or decimal form which is 2.25 or mixed number form 2 1/4
Step-by-step explanation:
Kolby decided he wanted to go to the amusement park. The amusement park charges $8.00 for entry and $1.40 for each ride.
Part A Write an expression to represent this scenario where r represents the number of rides.
Part B Create and solve an equation to determine how many possible rides Deniss can ride if his parents gave him $26.00
Show your work.
Answers
Part A: y=mx+b where m is the slope and b is the constant. $8 for entry is the constant, at is wont change during our equation. $1.4 is our slope as its the cost per ride. r is going to be our x. So our equation will be 1.40r + 8
Part B: Now that we know the amount of money, we can place the $26 for y. So lets solve now with our new equation of:
26 = 1.4r + 8
26 - 8 = 1.4r
18 = 1.4r
18 / 1.4 = r
12.85 = r
Obviously he cant ride 12.85 rides. Typically we round up, but to say he rides 13 rides means he has to have $26.2, which we know he does not have. Therefore, we say that he can ride 12 rides.
Quick math check:
1.4(12) + 8 = $24.8 which is less then $26.
I hope this helps! :)
the product of two irrational numbers is _____ rational
1.always
2.never
3.sometimes
Answers
Answer:
3. sometimes
Step-by-step explanation:
The product of two irrational numbers is sometimes rational. It depends on the two given numbers.
The following machine doubles each input, subtracts 3, and then squares the result. (check photo) For example, if we input 5, then double 5 to get 10, subtract 3 to get 7, and finally square 7 to get 49.
-Write the expression that comes out of the machine if the input is 4.
Use ^ to express exponents. For example. 3² = 3^2
-If 121 is the output, what was the input?
Answers
Answer:
Step-by-step explanation:
Find the value of x in the triangle shown below.
102
48
Answers
Answer:
The sum of the angles of a triangle is always 180, so the answer is
180-102-48=30
Step-by-step explanation:
1) A covered hot cup of coffee will cool to the temperature of the room as governed by a physics principle known as Newton's Law of Cooling. The data from an experiment is shown in the table. If the room temperature is 73 degrees Fahrenheit, which statement is correct?A) The relationship could be linear with c ≈ 83oF.B) The relationship could be linear with c ≈ 63oF.C) The relationship could be exponential with c ≈ 83oF.D) The relationship could be exponential with c ≈ 63oF.
Answers
Answer:
f(t) = 80 + 120 e^(-0.08 t)
Step-by step explanation:
The exponent is negative, so this is an example of exponential decay. As t increases, the exponent becomes more and more negative. So e^(-0.08 t) gets closer and closer to 0. Meaning f(t) gets closer and closer to 80.
need help plssss!!!!
Answers
should I call 911 !!!!!!!!!!!!!!
Can you answer the question and explain it to me simply im just in 5th grade and i dont get it
Answers
Answer:
13/20
Step-by-step explanation:
12/20-4/20+5/20=
8/20+5/20=
13/20
Answer:
[tex] \frac{13}{20} [/tex]
Step-by-step explanation:
Before we can do anything with the fractions, we need to find a common denominator.
To do that, we will first divide 10 by 2 to get a denominator of 5, and whatever we do to the bottom we must do to the top as well. So we will also divide 6 by 2 to get 3.
So 6/10 has now been simplified to 3/5.
Next we can subtract 1/5 from 3/5 since they both share a common denominator of 5, now we have 2/5.
Now in order to find the common denominator of 2/5 and 1/4, we will simply cross multiply the two fractions together like so: (2 × 4 = 8 and 5 × 1 = 5), to get 8/20 and 5/20. So now we can add 8 and 5 normally, since they both share a common denominator now. That's how you get 13/20.
Hope it helps :)
I tried to keep it simple for you.
What is the nth term rule of the quadratic sequence below?
8
,
16
,
26
,
38
,
52
,
68
,
86
,
.
.
.
Answers
The [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex] .
What is quadratic sequence ?Quadratic sequences are sequences that include [tex]nth[/tex] term. They can be identified by the fact that the differences between the terms are not equal, but the second differences between terms are equal.
Quadratic sequence [tex]=an^2+bn+c[/tex]
Here [tex]a,b,c[/tex] are constant and [tex]n[/tex] is the position of term.
First difference [tex]= 3a+b[/tex]
Second difference [tex]=2a[/tex]
We have,
Quadratic sequence [tex]8,16,26,38,52,68,86,....[/tex]
Quadratic sequence [tex]=an^2+bn+c[/tex]
so,
For [tex]n=1[/tex];
[tex]8=an^2+bn+c[/tex]
[tex]8=a+b+c[/tex] [tex]........(i)[/tex]
For [tex]n=2[/tex];
[tex]16=4a+2b+c[/tex] [tex]........(ii)[/tex]
For [tex]n=3[/tex];
[tex]26=9a+3b+c[/tex] [tex]........(iii)[/tex]
Now,
Subtract equation [tex](i)[/tex] from [tex](ii)[/tex]
we get,
[tex]8=3a+b[/tex] [tex]........(iv)[/tex]
Subtract equation [tex](ii)[/tex] from [tex](iii)[/tex] we get,
[tex]10=5a+b[/tex] [tex]........(v)[/tex]
Subtract equation [tex](iv)[/tex] from [tex](v)[/tex] we get,
[tex]2=2a[/tex] (This is second difference mentioned above)
[tex]a=1[/tex]
Putting [tex]a=1[/tex] in [tex](iv)[/tex]
⇒[tex]b=5[/tex]
Now putting values of [tex]a[/tex] and [tex]b[/tex] in equation [tex](i)[/tex]
[tex]8=1+5+c[/tex]
[tex]c=2[/tex]
Now, putting values of [tex]a[/tex] , [tex]b[/tex] and [tex]c[/tex] in,
Quadratic sequence [tex]=an^2+bn+c[/tex]
we get,
[tex]nth[/tex] term rule [tex]=n^2+5n+2[/tex]
Hence, we can say that the [tex]nth[/tex] term rule of the quadratic sequence will be [tex]n^2+5n+2[/tex].
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Alan and Pedro eat today at the same Taqueria, but Alan attends every 20 days and Pedro every 38 when will they meet again?
Answers
Answer:
380 days
Step-by-step explanation:
38 × 1 = 38 38 × 6 = 228
38 × 2 = 76 38 × 7 = 266
38 × 3 = 114 38 × 8 = 304
38 × 4 = 152 38 × 9 = 342
38 × 5 = 190 38 × 10 = 380
20 × 1 = 20 20 × 6 = 120
20 × 2 = 40 20 × 7 = 140
20 × 3 = 60 20 × 8 = 160
20 × 4 = 80 20 × 9 = 180
20 × 5 = 100 20 × 10 = 200
20 x 10 = 200 20 x 20 = 400
so 20 x 19 = 380
First common number in both times table is 380
Please help quickly
Answers
Answer:
the answer is n=17
Step-by-step explanation:
1/5= 8-5/n-2
How do you find the quotient in the equation 8÷304
Answers
Answer:
304 divided by 8 in decimal = 38
304 divided by 8 in fraction = 304/8
304 divided by 8 in percentage = 3800%
Step-by-step explanation: You just simply divide.
Please help and please no links..thanks ¯\_(ツ)_/¯
Answers
Answer:
[tex]\frac{c}{4} +5 = 7[/tex]
Step-by-step explanation:
The wording, "the quotient of a number and 4," can be displayed as c/4. C would be our variable for the number because the question asks specifically for it. 5 more would demonstrate that we're adding 5 more to our equation. Which would result in c/4 + 5. However, since it equals 7, just add that portion to create the following equation:
[tex]\frac{c}{4} +5 = 7[/tex]
Answer:
c / 4 + 5 = 7
Hope this helps!
Step-by-step explanation:
5 + ( more ) than the quotient ( division ) of a number and ( + ) 4 is ( = ) 7
5 + c / 4 = 7
c / 4 + 5 = 7
Answer the questions below, no links.
Answers
Answer:
[Graph] See attached
[Question] A, C, & E
Step-by-step explanation:
[Graph] 0.4 -> 2/5
() It will go through the origin (0, 0) because we have no b, or y-intercept
() From (0, 0) it will go 2 up and 5 over, 2 up and 5 over, etc etc
() See attached
[Question]
() A, C, E
() It is proportional (one to one as it is a straight line) so A is correct
() The slope in y = mx + b is m, and our m is 0.4 so it is the slope
() 3 * 0.4 = 1.2, so E is correct
verizon wireless charges $85 for a 5 person plan and $65 for a 3 person plan.
Answers
Answer:
so whats the question. ...........
what is 32623y32t76237uy23762376etyedw7ed87fe=46y73e78se2w782wsey67edty
Answers
CALCULATE
(32/40×100%) =??
NO SPAM PLEASE ,ಠ_ʖಠ
I WILL MAKE BRAINLIEST WHO WILL ANSWER CORRECT ( ╹▽╹ )
Answers
Answer:
[tex] \frac{32}{40} \times 100[/tex]
[tex] \frac{32}{4} \times 10[/tex]
[tex]8 \times 10[/tex]
[tex]80[/tex]
80 is the answer
Answer:
(32/40×100%)= x
(32/ 40 ) × 100 = x
0.8 × 100 = x
x = 80
(32/40×100%)= 80
Find x and y.
Answers
[tex]\\ \sf\longmapsto 2x+11=3x-9[/tex]
[tex]\\ \sf\longmapsto x=11+9[/tex]
[tex]\\ \sf\longmapsto x=20[/tex]
And
[tex]\\ \sf\longmapsto y+10=2y-40[/tex]
[tex]\\ \sf\longmapsto 2y-y=10+40[/tex]
[tex]\\ \sf\longmapsto y=50[/tex]
Step-by-step explanation:
x2x + 11 = 3x - 9
2x - 3x = -9 - 11
x = -20
[tex] \: [/tex]
yy + 10 = 2y - 40
y - 2y = -40 - 10
-y = -50
y = 50
What is the zero of the function represented by this graph?
Answers
Answer:
Step-by-step explanation:
The easiest way to answer your question is to graph it. I've enclosed a graph for you. The answer to the question as it is asked is y ≥ 2.
The answer to your question (which is a much more interesting question) is that there is no 0. A zero of a function must touch or intersect the x axis.
Given f(x) = 8 — x/6 evaluate f(66). Leave your answer in fraction form.
Answers
Answer:
f(66) = -3
Step-by-step explanation:
f(x) = 8 - x/6 Substitute 66 for the vale of x and solve
f(66) = 8 - 66/6
f(66) = 8 - 11
f(66) = -3
8. The area of a rectangular fence is 500 square feet. If the length of the
fence is 25 feet, then find its width.
Answers
Answer:
20 square feet
Step-by-step explanation:
500/25 = 20
20x25 = 500
what is 5000000000000 divided by 11
Answers
45.454.545,45454545
Answer:
45.454
Step-by-step explanation:
guys pa help po thank you
Answers
Answer: Should be 90
Step-by-step explanation:
Find an irrational number between 6 and 28
Answers
Answer:
Step-by-step explanation:
All the whole numbers or integers between 6 and 28 are rational numbers because they can be expressed as improper fractions as for example 7 = 7/1 but the square root of 7 is an irrational number because it can't be expressed as a fraction.
Answer:
√101 (square root of 101)
Step-by-step explanation:
Irrational numbers are numbers that can't be written as fractions.
The square root of 101 is irrational because it is not a perfect square which means that it has an infinite amount of numbers after the decimal point. Because of this the square root of 101 cannot be expressed as a fraction.
Using the formula find the slope of a line with the points (10,20) and (30,50).
Answers
Answer:
m = 2/3
Step-by-step explanation:
Slope is defined as the ratio rise/run.
As we move from (10, 20) to (30, 50), the run is 30 - 10, or 20, and the rise is 50 - 20, or 30. Thus, the slope of the line is m = 30/20, or 2/3.
Which expression is equivalent to 4(6 - 2x) ?
Answers
Answer:
Option A
Step-by-step explanation:
[tex]4(6-2x)\\\rule{150}{0.5}\\\rightarrow ((6 * 4) ( -2x*4)) \leftarrow \text{Distribute the '4' into the content in the parenthesis.}\\\\\\\\\rightarrow 6 * 4 = 24\\\\\rightarrow -2x * 4 = -8x\\\\\\\\\rightarrow 4(6-2x) = \boxed{24 - 8x}[/tex]
Hope this helps.