Please help! I’m this figure, which angles are congruent? Find the measure of all the angles if m< 2= 76 degrees
Answers
Problem 1.
Yes it is true that vertical angles are congruent, but that's not what your teacher is asking. Instead, your teacher is asking basically how the term "congruent" is defined.
Two segments are congruent if they are the same length. Two angles are congruent if they are the same measure. Two triangles are congruent if they have the same angles and sides.
So in short, "congruent" just means "same". You can think of having mirror copies.
==========================================
Problem 2.
Angles 2 and 4 are one pair of vertical angles. They are opposite one another in this X shape formed by the two lines. The other pair of vertical angles are angle 1 and angle 3.
Angle 2 is given to be 76 degrees, so this means angle 4 is this measure as well.
Angle 1 = 180 - (angle 2) = 180 - 76 = 104, which is also the measure of angle 3 as well. I'm using the idea that the adjacent angles form a straight angle. This is known as a linear pair (ie the angles form a straight line).
==========================================
Problem 3.
If all three angles are the same (all 60 degrees), then we have an equilateral triangle. We could say it's equiangular, but it's also equilateral as well meaning all 3 sides are the same length. "equi" means "equal", "angular" means what you'd expect, and "lateral" means "side".
If only two angles are equal with the third one different, then we have an isosceles triangle. An isosceles triangle is one where only two sides are the same length.
If none of the angles are the same, then we have a scalene triangle. As you probably expect, none of the sides are the same length with a scalene triangle.
----
If all three angles are less than 90 degrees, then the triangle is acute
If one angle is 90 degrees, then we have a right triangle
If one angle is over 90 degrees (but less than 180), then the triangle is obtuse
---
Often you'll see the terms of the previous two sections combined. For instance, we could have an isosceles right triangle. Or we might have an obtuse scalene triangle. Any equilateral triangle is acute (as all three angles are less than 90).
To solve this problem we have to understand what congruent angles are and then find the angles that are congruent to one other in this given question.
What are Congruent Angles?Congruent angles are angles that are equal to one another and in the given question, we were given m<2 = 76 degrees.
Data;
m<2 = 76 degreesIf we look critically at the angles, we can use opposite angle theorem here to predict angles that are congruent to another here.
angles 2 and angle 4 are congruent to one another while angle 1 and angle 3 are congruent to one another.
This implies that
m<2 = 76°m<4 = 76°Let's solve for other angles.
But the some of angles at a point is equal to 360°
Applying that theorem here,
[tex]m > 1=x\\m > 2 = 72^0\\m > 3 = x\\m > 4 = 72^0[/tex]
Let's substitute the values and solve.
[tex]x+ x + 72+72 = 360\\2x + 144 = 360\\2x = 360 - 144\\2x = 216\\x = \frac{216}{2} \\x = 108^0[/tex]
This can be further summarized as
m<1 = 108°m<2 = 72°m<3 = 108°m<4 = 72°Learn more on corresponding angles here;
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Related Questions
Please answer the question in the image below ASAP
Answers
Answer:
c
Step-by-step explanation:
diameter will be 36, radius 18 and the height is 6
The Ruiz family is exchanging euros for US dollars. The exchange rate is 1 euro equals 1.35261 USD. Since the Ruiz family knows that USD are stated to the nearest hundredth of a dollar, they used the conversion ratio. Will this give the Ruiz family the correct exchange?
Answers
Answer:
It will depend on how many euros they intend to convert. If they were only converting one euro they would get $1.35 whichever rate they used, but imagine it was a thousand euros - at the correct rate they would get $1352.61, at the proposed rate they would only get $1350.
Step-by-step explanation:
No, by rounding the conversion ratio, the Ruiz family will not be getting the most accurate answer. Using the more accurate conversion ratio will give an answer with more than 2 decimal places so the answer can accurately be rounded after the conversion.
Answer:
No, by rounding the conversion ratio, the Ruiz family will not be getting the most accurate answer. Using the more accurate conversion ratio will give an answer with more than 2 decimal places so the answer can accurately be rounded after the conversion.
Step-by-step explanation:
just copy/paste
A dolphin is swimming with her friend. The dolphin jumps to a height of 4.5 meters above the surface of the water as her friend swims 9.8 meters directly below her.
Answers
Answer:
-5.3 meters
The dolphin's friend is 5.3 meters below the water surface
Step-by-step explanation:
Complete question below:
A dolphin is swimming with her friend. The dolphin jumps to a height of 4.54 meters above the surface of the water as her friend swims 9.8 meters directly below her. What is the position of the dolphin's friend relative to the surface of the water?
Solution
The dolphin jumps to a height of 4.5 meters above the surface of the water
Her friend swims directly 9.8 meters below her
The position of the dolphin's friend relative to the surface of the water= dolphins position above the surface of the water - her friend's position below her
=4.5 meters - 9.8 meters
= -5.3 meters
-5.3 meters means below the water surfaces
This means, the dolphin's friend is 5.3 meters below the water surface
25 POINTS! FIRST TO ANSWER ****CORRECTLY**** GETS BRAINLIEST!
What number should be placed in the box to help complete the division calculation?
Numerical Answers Expected!
Answers
Answer:
The answer to your question is given below.
Step-by-step explanation:
To divide 2635 by 17 using long division method, we simply do the following:
2635 ÷ 17
17 can not go into 2. Therefore, we try 17 into 26, keeping 35 constant.
26 ÷ 17 = 1
Put the 1 on top.
Multiply 17 by 1
17 x 1 = 17
Subtract 17 from 26
26 – 17 = 9
Put the 9 in from of 35 to become 935
Next:
935 ÷ 17
17 can not go into 9. Therefore, we try 17 inot 93 keeping 5 constant.
93 ÷ 17 = 5
Put the 5 on top together with the 1 to become 15.
Multiply 17 by 5
17 x 5 = 85
Subtract 85 from 93
93 – 85 = 8
Put the 8 in front of 5 to become 85
Next:
85 ÷ 17
17 can not go into 8. Therefore, we try 85
85 ÷ 17 = 5
Put the 5 on top together with 15 to become 155
Multiply 17 by 5
17 x 5 = 85
Subtract 85 from 85
85 – 85 = 0
Since no number is remaining, we shall stop here.
Therefore,
2635 ÷ 17 = 155
Please attached photo for further details.
Esmereldas family went out to dinner paying 20% tip at the end of the meal. Their credit card was charged $51.00. What was the amount on the bill without the tip
Answers
Answer:
42.50
Step-by-step explanation:
bill + tip = total bill
The tip is based on the bill
tip = bill * 20%
tip = bill * .20
Replace in the original equation
bill + .20 bill = total bill
Combine like terms
1.20 bill = total bill
The total bill was 51 dollars
1.20 bill = 51
Divide each side by 1.20
1.20 bill / 1.2 = 51/ 1.2
bill =42.50
Answer:
$42.50
Step-by-step explanation:
If the total was $51 with the tip, and you know the tip was 20%, you can set up an equation and solve:
0.2x+x=51
1.2x=51
x=42.5
Therefore, the bill (w/o tip) was $42.50
p.s.Please give me brainliest. Thank you! :)
find a rational number that is between 5.2 and 5.5. explain why it is rational.
Answers
Answer:
5.3
Step-by-step explanation:
A rational number is a number that can be written as the quotient of two integers.
5.2 and 5.5 are both rational since they can be written as quotients of integers as shown below.
5.2 = 52/10
5.5 = 55/10
5.3 is a number between 5.2 and 5.5, and since 5.3 can be written as 53/10, it is rational.
Answer: 5.3
Answer:
Step-by-step explanation:
rational numbers can be written in form a/b where b≠0
5.2 and 5.5
52/10 and 55/10
so some rational numbers could be
53/10, 54/10
irrational numbers most likely the square root numbers
square them
5.2^2=27.04
5.5^2=30.25
5.2<?<5.5
square everybody
27.04<?²<30.25
so pick a number between 27.04 and 30.25
29 or 30 are 2 numbers
I'll pick 29
?²= 29
square root
?=√29
the irrational number can be √29
it is 5.39 to the hundredth
Can you help me find all the seventh roots of unity? what do they look like graphed?
Answers
Answer:
There are seven seventh roots of unity, e2πki7 , all on the unit circle, r=1 above.
The first one is at θ=2π7=360∘7=5137 ∘ , and there are others at 4π7,6π7,8π7,10π7,12π7 and of course at 0 radians, i.e. unity itself.
How to find?
There are 4 fourth roots of unity and they are 1, i,−1 and−i
Each of the roots of unity can be found by changing the value of k k k in the expression e 2 k π i / n e^{2k\pi i/n} e2kπi/n. By Euler's formula, e 2 π i = cos ( 2 π ) + i sin ( 2 π ) = 1.
The size of a television screen is given as 95 cm, correct to the nearest 5 cm.
Write down the upper bound of the size of the television screen.
Answers
Answer:
The upper bound is 97.5 cm
Step-by-step explanation:
The upper bound is given as the value that is larger than or equal to all values in a data set, for example, in the data set, {3, 6, 16, 23, 25}, an upper bound is 25, however, where the accuracy of the data is given, the upper bound can be found by the following relation
Where the number is given to the nearest 100, add and subtract half of hundred to obtain the upper bound and lower bound respectively
For the question, given that the size of the television is given as 95 cm, correct to the nearest 5 cm, we add add half of 5 cm to get the upper bound as follows;
Upper bound = 95 cm + 5/2 cm = 97.5 cm
The upper bound = 97.5 cm.
This diagram is a straightedge and compass construction. A is the center of one circle,
and B is the center of the other. Explain how we know triangle ABC is equilateral.
Answers
ABC is a equilateral triangle .
Proof :-
Let's assume both circles as C1 and C2 [ as shown in the figure ]
AB is the radius of circle C1 AB is the radius of Circle C2AC is the radius of circle C1.
BC is the radius of circle C2 .
AB and AC both are radius of circle C1 so both are equal ie AB = AC .
AB and BC both are radius of circle C 2 so both are equal ie AB = BC .
Hence we conclude that .
AB = BC = AC.
So the triangle is equilateral triangle.
-when finding data as well as plotting data, you can find relationships within the data
displayed in charts or graphs, noticing the relationships can help build a solution a lot
easier.
this is what they wrote.
just type anything if u want the points.
Answers
Answer:
I came up with the answer check my questions to see it
Step-by-step explanation:
(−2a+5−b)⋅(−5) <- does this equal to 10a−25+5b?
Answers
Answer:
Yes!
Step-by-step explanation:
SOS...Complete the following proof. 25 POINTS!!!
Answers
Answer:
See below
Step-by-step explanation:
Given:
AC ≅ CE
To Prove:
ΔABC ≅ ΔEDC
Proof:
Statements | Reasons
ΔABC ⇔ ΔEDC |
AC ≅ CE | Given
∠ACB ≅ ∠ECD | Vertical Angles are congruent
∠BAE ≅ ∠DAE | Alternate Interior Angles are Congruent
ΔABC ≅ ΔEDC | S. A . A Postulate
[Hence Proved]
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
6) C
7) A
8) D
9) B
Step-by-step explanation:
when the sign is < or > then the point is clear point(white)
when the sign is ≤ or ≥ then the point is solid ( black)
6) 4y+3≤y+6
4y-y≤6-3
3y≤3
y≤3/3
y≤1 (C)
7) -2y>2 ( wen sign is negative you flip the sign from> to <)
y<-2/2
y<-1 (A)
---------------------------------------------------------------------------------------
8) y/3<-1 ⇒ y<-3 the sign is < means it is clear and on -3 (D)
--------------------------------------------------------------------------------------
9) 3y≤2y+3
3y-2y≤3
y≤3 ( B)
ignore pls sorry
HELP idk what the slope is
Answers
Answer:
the slope is -3
Step-by-step explanation:
Answer:
the slope is 3
Step-by-step explanation:
if a white birch tree and a pin oak tree each now have a diameter of 111 foot, which of the following will be closest to the difference, in inches, of their diameters 101010 years from now? (1(1(, 1 foot = 12=12equals, 12 inches))
Answers
Answer:
Can you solve #18 from practice test 5 calculator section? ... years old and a pin oak tree with a diameter of 12 inches is ... because on the test you would have figured these mechanics out on ... Now, note that the concept of a “growth factor” as provided in the table ... That's a difference of about 1.3 inches.
Step-by-step explanation:
I NEED HELP PLEASE ! I GIVE 5 STARS !
Answers
Answer:
2
Step-by-step explanation:
Remember, a radical is the same thing as an exponent, but as a fraction. Therefore, instead of taking the 12th of the root, you can put [tex]8^4[/tex] to the 12th power like this: [tex](8^4)^{\frac{1}{12} }[/tex]
The two exponents can multiply together, so now it'll be [tex]8^{\frac{4}{12} }[/tex] which is [tex]8^{\frac{1}{3} }[/tex] when reduced
[tex]8^{\frac{1}{3} }[/tex] is the same thing as [tex]\sqrt[3]{8}[/tex]
Now, think about which number, when multiplied by itself 3 times is equal to 8... that number is 2--your answer
Answer:
2
Step-by-step explanation:
make it simple.. use a scientific calculator.
= ¹²√8⁴
= ¹²√4096
= 2
PLEASE HELP WILL MARK BRAINLIEST
Answers
Answer:
18 m
Step-by-step explanation:
Answer:
18m
Step-by-step explanation:
You pack sandwiches for a hike with your friends. Each sandwich takes 2 slices of bread, and each hiker eats one sandwich.
How many slices of bread are used for n hikers?
Answers
Given that:-
→ 1 sandwich = 2 slices of bread.
→ 1 hiker = 1 sandwich.
→ Then we have to find number of bread slices for n hikers .
→ Number of bread slices for 1 hiker = 2
→ Number of bread slices for 2 hikers = 2 × 2
→ For 3 hikers = 3 × 2
So in similar way
→ Number of bread slices for n hikers = 2×n → 2n
So 2n is the answer.
4n-6 (n - 2) = -24 + 7n
O No Solutions
O All Real Numbers
O n = 4
O n = 2.9
Answers
4n-6 (n-2) = -24 + 7n
You first multiply the six with the equation in the parentheses making it:
4n-6n + 12= -24 + 7n
You then subtract 4n from -6n changing it to:
-2n + 12 = -24 + 7n after that you switch the 12 and 7n so that the equation can be
-2n -7n = -24 - 12
After that combine the numbers together:
-9n = -36
Then divide both sides by -9 making
n= 4
Water flows through a pipe at a rate of 4 quarts per day. Express this rate of flow in liters per week. Round your answer to the nearest tenth.
Answers
Answer:
26.5 liters
Step-by-step explanation:
We know that 1 gallon is 4 quarts, and 1 gallon is approx. 3.78 liters. There's 7 days in a week, so 7 gallons of water is being flowed through. Multiplying 3.78 by 7, we get 26.46 liters per week. Rounding to the nearest tenth, and we get 26.5 liters.
A prisoner is trapped in a cell containing 3 doors. The first door leads to a tunnelthat returns him to his cell after 2 days’ travel. The second leads to a tunnel thatreturns him to his cell after 4 day’s travel. The third door leads to freedom after 1day of travel. If it is assumed that the prisoner will always select doors 1,2,and 3with respective probabilities 0.5,0.3, and 0.2, what is the expected number of daysuntil the prisoner reaches freedom?
Answers
Answer:
2 days
Step-by-step explanation:
Expected number of days until prisoner reaches freedom=E(x)=?
E(x)=x*p(x)
Where x is the number of days and p(x) is the probability associated with them.
X 1 2 3
P(x) 0.5 0.3 0.2
E(x)=1*0.5+2*0.3+3*0.2
E(x)=0.5+0.6+0.6
E(x)=1.7.
Thus, the expected number of days until prisoner reaches freedom are 2 days.
Which graph represents a function?
Answers
Answer:
The first Answer:
Step-by-step explanation:
The x-values are not the same on one line:
Image
The line connecting isn't perfect but see what I mean?
A boom seller sold 50 books for $ 890.00 and earned a profit of $ 90.00. Find the cost price of 50 books.
Answers
Answer:
$ 800
Step-by-step explanation:
number of books sold = 50
money earned = $ 890.00
profit = $ 90.00
Then the price of 50 books will be (money earned) - (profit)
= 890 - 90
= 800
So, the cost of 50 books is $ 800
HOPE IT HELPS :)
PLEASE MARK IT THE BRAINLIEST!
Which of these expressions is equivalent to 3x(x-1)-5(x-1)? Select all that apply.
3x^2-8x+5
x-1(3x-5)
(3x-5)(x-1)
(x-1)(3x+5)
Answers
Answer:
3x(x-1)-5(x-1)
=3x²-3x-5x+5 (we can count it one by one)
=3x²-8x+5 (we can calculate the same variable)
#i'm from indonesia
hope it helps.
Answer:
[tex]\boxed{3x^2 -8x+5}[/tex]
[tex]\boxed{(3x-5)(x-1)}[/tex]
Step-by-step explanation:
[tex]3x(x-1)-5(x-1)[/tex]
Expand brackets.
[tex]3x(x)+3x(-1)-5(x)-5(-1)[/tex]
[tex]3x^2 -3x-5x+5[/tex]
Combine like terms.
[tex]3x^2 -8x+5[/tex]
[tex]3x(x-1)-5(x-1)[/tex]
Take x-1 as a common factor.
[tex](3x-5)(x-1)[/tex]
How many of the positive integer factors of 15552 are perfect squares? (WILL MARK BRAINLIEST IF CORRECT)
Answers
Answer:
The positive integer factors of 15552 that are perfect squares are;
1, 4, 9, 16, 36, 64, 91, 144, 324, 576, 1296, 5184
Step-by-step explanation:
The positive integer factors of 15552 are;
1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 432, 486, 576, 648, 864, 972, 1296, 1728, 1944, 2592, 3888, 5184, 7776, 15552
The perfect square integers are;
1 = 1 × 1
4 = 2 × 2
9 = 3 × 3
16 = 4 × 4
36 = 6 × 6
64 = 8 × 8
91 = 9 × 9
144 = 12 × 12
324 = 18 × 18
576 = 24 × 24
1296 = 36 × 36
5184 = 72 × 72
Therefore, the positive integer factors of 15552 that are perfect squares are;
1, 4, 9, 16, 36, 64, 91, 144, 324, 576, 1296, 5184.
[tex]12 \times \frac{5}{6} - 14x + \frac{1}{6} x[/tex]
can anyone help me solve this !
Answers
Answer:
x = 60/83
Step-by-step explanation:
Solve for x:
10 - (83 x)/6 = 0
Put each term in 10 - (83 x)/6 over the common denominator 6: 10 - (83 x)/6 = 60/6 - (83 x)/6:
60/6 - (83 x)/6 = 0
60/6 - (83 x)/6 = (60 - 83 x)/6:
(60 - 83 x)/6 = 0
Multiply both sides of (60 - 83 x)/6 = 0 by 6:
(6 (60 - 83 x))/6 = 6×0
(6 (60 - 83 x))/6 = 6/6×(60 - 83 x) = 60 - 83 x:
60 - 83 x = 6×0
0×6 = 0:
60 - 83 x = 0
Subtract 60 from both sides:
(60 - 60) - 83 x = -60
60 - 60 = 0:
-83 x = -60
Divide both sides of -83 x = -60 by -83:
(-83 x)/(-83) = (-60)/(-83)
(-83)/(-83) = 1:
x = (-60)/(-83)
Multiply numerator and denominator of (-60)/(-83) by -1:
Answer: x = 60/83
Kate travels for 1 1/3hour to visit a friend
who lives 4 1/2 miles away. Martin travels 4 1/4
miles to visit his friend, and it takes him 1 1/5
hours. Who travels more miles per hour?
Answers
Answer:
Martin
Step-by-step explanation:
Calculate their speeds with the formula s = d/t (speed = distance/time)
Calculate Kate's speed:
s = d/t
s = 4.5/1.33
s = 3.375 mph
Calculate Martin's speed:
s = d/t
s = 4.25/1.2
s = 3.541 mph
So, Martin travels more miles per hour
Solve for X in the diagram below
PLS HELP BRAINLIST AND A THANK YOU WILL BE REWARDED :)
Answers
The 3 angles need to equal 180
The middle angle is given as 100.
180 -100 = 80
There is an x on each side so you have 2x
2x = 80
X = 80/2
X = 40 degrees
after allowing 5 percent discount on the marked price of a radio 10 percent vat is charged on it , then its price became rs 1672 .how much amount was given in the discount
Answers
Answer:
Marked price= RS 1600
Discount= RS 80
Step-by-step explanation:
Let
x= the marked price
Discount= 5%
Discount = 5% of x
=0.05x
Cost after discount = x-0.05x
= 0.95x
Vat=10%
=0.1
Cost of the radio including vat=0.95x + 0.1(0.95x)
=0.95x + 0.095x
=1.045x
Price became rs 1672
Therefore,
1.045x=1672
Divide both sides by 1.045
x= RS 1600
Discount=5% of 1600
=0.05 * 1600
=rs 80
What is the volume of this rectangular prism?
2 cm
7/3 cm
2 cm
Answers
9.3
Explanation
I got it right
Answer:
28\3
Step-by-step explanation:
