Answers
The sum of the interior angles of a triangle is 180° is proved below.
We are given that;
To prove angle sum property of triangle
Now,
There are different ways to prove that the sum of the interior angles of a triangle is 180°. Here are three common proofs:
Proof : Using parallel lines and alternate interior angles
Since the line PQ is parallel to the side BC, and AB and AC are transversals, we can use the property that alternate interior angles are congruent.
Therefore, we have:
∠QAC = ∠ACB
∠PAB = ∠ABC
Adding these equations, we get:
∠QAC + ∠PAB = ∠ACB + ∠ABC
But ∠QAC + ∠PAB is a straight angle, which measures 180°. So, we have:
180° = ∠ACB + ∠ABC
Adding ∠CAB to both sides, we get:
180° + ∠CAB = ∠ACB + ∠ABC + ∠CAB
Simplifying, we get:
180° = ∠ACB + ∠ABC + ∠CAB
Hence, by the triangles the answer will be given above.
Learn more about the triangles;
https://brainly.com/question/2773823
#SPJ4
Related Questions
log16^*+log4^*+log2^*=7
Answers
Answer:
[tex]x = 16[/tex]
Step-by-step explanation:
Given
[tex]log_{16}(x) + log_4(x) + log_2(x) = 7[/tex]
Required
Solve for x
[tex]log_{16}(x) + log_4(x) + log_2(x) = 7[/tex]
Change base of 16 and base of 4 to base 2
[tex]\frac{log_2(x)}{log_2(16)} + \frac{log_2(x)}{log_2(4)} + log_2(x) = 7[/tex]
Express 16 and 4 as 2^4 and 2^2 respectively
[tex]\frac{log_2(x)}{log_2(2^4)} + \frac{log_2(x)}{log_2(2^2)} + log_2(x) = 7[/tex]
The above can be rewritten as:
[tex]\frac{log_2(x)}{4log_22} + \frac{log_2(x)}{2log_22} + log_2(x) = 7[/tex]
[tex]log_22 = 1[/tex]
So, we have:
[tex]\frac{log_2(x)}{4*1} + \frac{log_2(x)}{2*1} + log_2(x) = 7[/tex]
[tex]\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x) = 7[/tex]
Multiply through by 4
[tex]4(\frac{1}{4}log_2(x) + \frac{1}{2}log_2(x) + log_2(x)) = 7 * 4[/tex]
[tex]log_2(x) + 2}log_2(x) + 4log_2(x) = 28[/tex]
[tex]7log_2(x) = 28[/tex]
Divide through by 7
[tex]\frac{7log_2(x)}{7} = \frac{28}{7}[/tex]
[tex]log_2(x) = 4[/tex]
Apply the following law of logarithm:
If [tex]log_ab = c[/tex] Then [tex]b = a^c[/tex]
So, we have:
[tex]x = 2^4[/tex]
[tex]x = 16[/tex]
Gia has 80 tiles each tile is white or blue she arranges the tiles in 8 equal rows each row has an equal number of with and blue tiles. how many blue tiles are in each row?
Answers
Answer:
5
Step-by-step explanation:
80 divided by 8 = 10 divided by 2 = 5
In a small private liberal arts college, 40 percent of the students receive financial aid, and 30 percent of the students that receive financial aid also are first generation college students. In addition, 25 percent of the students in the college own a hybrid car. What is the probability that a randomly selected student receives financial aid and is first generation college student
Answers
Answer:
P(A∩B) = 0.12
Step-by-step explanation:
Given:
Students receive financial aid P(A) = 40% = 0.4
Students receive financial aid and first generation P(B/A) = 30% = 0.3
Find:
Probability [Selected student receives financial aid and is first generation college student] P(A∩B)
Computation:
P(A∩B) = P(A) x P(B/A)
P(A∩B) = 0.4 x 0.3
P(A∩B) = 0.12
Based on the table, what is the unit rate for one gallon of gasoline?
Answers
Answer:
a.3.30
Step-by-step explanation:
Answer:
3.30
Step-by-step explanation:
Because I did le Quiz
Determine whether the triangles are congruent using sas sas asa aas HL
Answers
Answer:
They are congruent bc they are the same size and shape
Answer:
Congruent by SAS
Step-by-step explanation:
As given by the diagram, we have two congruent sides already. From the set of parallel lines, we see that two angles are congruent because they are corresponding. Luckily, this angle falls between the two congruent sides, which gives you the proof of SAS.
Three concert tickets cost $27. At this rate, what is the cost per ticket?
Answers
Hello.
To find this, divide the cost per amount.
In this case, the cost of the tickets is $27, and the amount is 3.
Divide 27 by 3.
27 / 3 = 9
Each ticket costs $9.
Answer:
$9 per ticket
Step-by-step explanation:
all you do is divide 27 by 3 and get 9
Thank you so very much will give branliest
Answers
Answer:
Slope = 7
Y intercept = 23
Step-by-step explanation:
(can I get brainliest now)
Please help ASAP
What are the equations of the asymptotes of the hyperbola?
(y-1)^2/9-(x-2)^2/100=1
Answers
y-1= ±3/10(x-2)
Im not sure how to get this answer but my teacher gave it to me so i hope this helps!
The equation of the asymptote of the given hyperbola is; y - 1 = ±(3/10)(x - 2)
We are given the equation of the hyperbola as;
[(y - 1)²/9] - [(x - 2)²/100] = 1
We can rewrite this equation as;
[(y - 1)²/3²] - [(x - 2)²/10²] = 1
The general equation form of hyperbola is;
[(y - k)²/a²] - [(x - h)²/b²] = 1
Comparing this general form to our given equation we can see that;
k = 1
h = 2
a = 3
b = 10
Now the equation of the asymptote of a hyperbola follows the general formula;
y = ±[a(x - h)/b] + k
Plugging in the relevant values gives us;
y = ±(3/10)(x - 2) + 1
y - 1 = ±(3/10)(x - 2)
Read more about hyperbola asymptotes at;https://brainly.com/question/12919612
CAN SOMEONE PLEASE HELP ME!! THANK YOU
Answers
Answer:
C
Step-by-step explanation:
I'm pretty sure it's C
Answer:
not sure but b or c because it says less than
Step-by-step explanation:
the pie chart shows about voters in an election. 2800 more women vote than men. work out the total number of voters.
Answers
Answer:
Can you show the pie chart please.
Step-by-step explanation:
Answer:
show pie chart
Step-by-step explanation:
find the value of x. A. 35 B. 40 C. 45 D. 50
Answers
Answer:
D
Step-by-step explanation:
Answer:
scalene trangle
Step-by-step explanation:
which of these mappings is a function
Answers
Answer:
x
Step-by-step explit can only be a function if every input has its own output
What is the difference of the fractions? Use the number line to help find the answer.
-
T0
Answers
Answer:
-7/10
Step-by-step explanation:
Answer:
you got you must be so Mad rn that I'm not helping you with your question Jiggle what you going to do with that big old behind
Step-by-step explanation:
−2 1/6 divided by 1 1/4
100 points
Answers
Answer:
-1 11/15Step-by-step explanation:
−2 1/6 divided by 1 1/4:
-2 1/6 ÷ 1 1/4 = - 13/6 ÷ 5/4 = - 13/6 × 4/5 = - 26/15 =-1 11/151) to divide that mixed number we'll need to turn it into an improper fraction:
[tex] - 2\frac{1}{6} = - ( \frac{6 \times 2 + 1}{6} ) = - \frac{13}{6} \\ 1 \frac{1}{4} = \frac{4 \times 1 + 1}{4} = \frac{5}{4} [/tex]
2) now let's divide it, reciprocating 1 1/4 and multiplying both fractions one by another:
[tex] - \frac{13}{6} \times \frac{4}{5} = - \frac{52}{30} = - \frac{26}{15} [/tex]
3) Hence the answer is -26/15
9^x-6=729^3(x+2) solve the equation
Answers
Answer:
x= -730/363
Step-by-step explanation:
9x-6=729×3(x+2) multiply
9x-6=2187(x+2) remove the paranthesis
9x-6=2187x+4374 move the terms
9x-2187x=4374+6 collect like terms calculate
-2178x=4380 divide both sides
Find an equation for the line below
Answers
Rise/run
What value(s) of b will cause 3x2 + bx + 3 = 0 to have one real solution? Select all that apply.
b = –6
B.b = –9
C.b = 6
D.b = 9
Answers
Answer: -6 and 6
Step-by-step explanation:
Possible factors that could produce 3x² + 6x +3 are (x + 1)(3x + 3)
the solution for values of x: x+1=0, x= -1 3x+3=0, 3x= -3 . x= -1 . Same.
Possible factors that could produce 3x² - 6x +3 are (x - 1)(3x - 3)
the solution for values of x: x-1=0, x= 1 3x-3=0, 3x= 3 . x= 1 . Same.
From the attached graph of the possible equations, you can see that 9 and -9 won't produce ONE real solution. They each have "zeros" at two points on the x-axis. That is two solutions that would make x = 0.
The equations with -6 and +6 each touch the x-axis at only one point each.
what is the sum of the first five terms of the geometric sequence in which a1=5 and r=1/5
express your answer as an improper fraction.
Answers
Answer:
Sum of the first five terms of the geometric sequence in which a1=5 and r=1/5 is [tex]\mathbf{S_n=\frac{781}{125} }[/tex]
Step-by-step explanation:
We need to find sum of the first five terms of the geometric sequence in which a1=5 and r=1/5
The formula used to find sum of the geometric sequence is: [tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
Where a is the first term, r is the common ratio and n is the number of terms
Now finding sum of the first five terms of the geometric sequence
We have a=5, r=1/5 and n=5
Putting values in the formula:
[tex]S_n=\frac{a(r^n-1)}{r-1}\\S_n=\frac{5((\frac{1}{5}) ^5-1)}{\frac{1}{5}-1}\\S_n=\frac{5(\frac{1}{3125}-1)}{\frac{1-5}{5}}\\S_n=\frac{5(\frac{1-3125}{3125})}{\frac{-4}{5}}\\S_n=\frac{5(\frac{-3124}{3125})}{\frac{-4}{5}}\\S_n=5(\frac{-3124}{3125})}\times{\frac{-5}{4}}\\S_n=\frac{781}{125}[/tex]
So, sum of the first five terms of the geometric sequence in which a1=5 and r=1/5 is [tex]\mathbf{S_n=\frac{781}{125} }[/tex]
Jamie borrows $2,000 to purchase a new living room furniture set. She will pay an 8% interest rate over 18 months. How much will Jamie pay in interest?
Answers
Answer: 2800 dollars in intrest
Step-by-step explanation:
Fill in the missing numbers to complete the pattern:
1.31, 1.81, _____ ,2.81, _____ ,3.81
Answers
Answer:
2.31 and 3.31
Step-by-step explanation:
since .81 is repeating, we can assume .31 does too
Lisa, a researcher at the Centers for Disease Control and Prevention, is studying the growth of a bacteria. She starts her experiment with 77 bacteria that grow at a rate of 21% per hour. She will check on the bacteria every 11 hours. How many bacteria will she find in 11 hours? Round your answer to the nearest whole number.
Answers
Answer:
776
Step-by-step explanation:
PLEASE HELP!!!
John and Chuck are building a new house. When finished, the house will cost $190,750. The price of the house is 9% higher than the price when the original plans were made. What was the price of the house when the original plans were made?
Answers
Answer:
190,750 decreased by 9% is 173,582.5
Step-by-step explanation:
Dennis has less than 70 min. to spend on some homework questions. He spent 10 min. on the first two questions. The rest of the questions will take 52 min. each.
Which statement describes the solution to this inequality?
Drag and drop the answer into the box.
Answers
Answer:
A. Dennis can complete less than 24 questions.
Step-by-step explanation:
Let x represent the remaining number of questions to be completed. He can complete each of them in 5/2 minutes each; this gives us the expression 5/2x.
He has already spent 10 minutes; this gives us 5/2x+10.
He has less than 70 minutes to spend; this gives us the inequality
5/2x+10<70
Subtract 10 from each side:
5/2x+10-10 < 70-10
5/2x < 60
Divide both sides by 5/2:
5/2x÷5/2 < 60÷5/2
x < 60/1 ÷ 5/2
To divide fractions, flip the second one and multiply:
x < 60/1 × 2/5
x < 120/5
x < 24
Answer:
Dennis can complete fewer than 24 questions.
Step-by-step explanation:
what is the GCF of 16s^3t, 40s^5, and 68t^2
Answers
Answer The Greatest Common Factor of 16, 40, 68 is 4. But the GCF of 16s^3t, 40s^5 and 68t^2 is 1, as there are no common terms for these given alphanumeric terms.
Step-by-step explanation:
Which equation could have been used to create this graph?
Answers
Explanation: Slope means rise/run. You can use the points (0,0) and (1,4) to find the answer to the question. Rise basically is how much the distance is between the two points going vertical (up). And when you do that, you should get 4 units. Now, you're at (0,4) since you moved the point up 4 and you want to find how many spaces away is (0,4) from (1,4) horizontally, which is 1 unit. The rise/run is 4/1, which is the slope.
What number has the prime factorization 2^2*3*5^2 * 7? Show how you
found the number.
Answers
Answer:
3 • 74509
I this is right
plssss i need help it’s due rn if u don’t know the answers pls don’t write random stuff plsssss
Answers
Answer:
1. y=3x+2
2. slope=3 It represents the rate of which the panda gained weight over the course of 4 weeks
3. 2 It represents the weight of the panda at the first week
Step-by-step explanation:
Write an equation for the n th term of the arithmetic sequence 56, 48, 40, 32, ....
Answers
Answer:
-8n+64
Step-by-step explanation:
Write 14/9
as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Answers
Answer:
1.5 repeating
Step-by-step explanation:
Which of the following is an example of a culture maintaining traditional ways?
Answers
Answer:
Amish driving buggies and using horses and mules instead of tractors
Step-by-step explanation: