Points A,B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ABC is 180 degrees
Answers
Answer:
Step-by-step explanation:
Statements Reasons
1). Points A, B and C form the triangle 1). Given
2). Let DE be a line passing through 2). Definition of parallel lines
B and parallel to AC
3). ∠3 ≅ ∠5 and ∠1 ≅ ∠4 3). Theorem of Alternate
interior angles
4). m∠1 = m∠4 and m∠3 = m∠5 4). Definition of alternate angles
5). m∠4 + m∠2+ m∠5 = 180° 5). Angle addition and definition
of straight lines
6). m∠1 + m∠2+ m∠3 = 180° 6). Substitution
Related Questions
brainliest to first answer again :)
Answers
Answer:
20
Step-by-step explanation:
you just ÷ 12 and 3/5 and the simplified answer is 20
Is the sequence geometric? If so, identify the common ratio.
2, -4, 8, 16, ...
Answers
No its not.
The real form is, -4,2,8,16
Answer:
No its not because I know my maths and that incorrect
A road is inclined at an angle of 3°. After driving 5330 feet along this road, find the drivers increase in altitude
Answers
it takes jackie 2 hours to make 9 bracelets how many bracelets can she make in 8 hour's?
Answers
Answer:
8b = 96
Step-by-step explanation:
Help pls someone can someone help me pls pls
Answers
Answer:
Mo is correct because when you divide 66.25 from both sides it is 12.
Step-by-step explanation:
Which is the most reasonable measure for the capacity of a bathtub?
O 5 liters
O 159 liters
O 159 milliliters
O 1000 milliliters
Answers
what time is it from where y’all live ?
Answers
Answer:
1 Pm
Step-by-step explanation:
Answer:
3:18 Pm
Step-by-step explanation:
Nice picture of mute button
100 points to who ever can answer this the best
Answers
a. n =17
b. n =23
c. n = 9
d. n = 15
Answer:
(a) n = 17
(b) n = 23
(c) n = 9
(d) n = 15
Step-by-step explanation:
Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac{n}{2}(a+a_n)}[/tex]
where:
a is the first term.aₙ is the nth term.Part (a)[tex]\displaystyle \sum^n_{i=1}(3i+5)=544[/tex]
To find a substitute i = 1 into the equation:
[tex]\implies a=3(1)+5=8[/tex]
To find aₙ substitute i = n into the equation:
[tex]\implies a_n=3n+5[/tex]
Substitute the values of a, aₙ and Sₙ into the arithmetic series formula and solve for n:
[tex]\begin{aligned}S_n & =\dfrac{n}{2}(a+a_n)\\ \implies 544&=\dfrac{n}{2}(8+3n+5)\\1088&=n(3n+13)\\1088&=3n^2+13n\\3n^2+13n-1088&=0\\3n^2-51n+64n-1088&=0\\3n(n-17)+64(n-17)&=0\\(n-17)(3n+64)&=0\\\\n-17&=0 \implies n=17\\3n+64&=0 \implies n=-\dfrac{64}{3} \end{aligned}[/tex]
As n is positive, n = 17.
Part (b)[tex]\displaystyle \sum^n_{i=1}(-4i-1)=-1127[/tex]
To find a substitute i = 1 into the equation:
[tex]\implies a=-4(1)-1=-5[/tex]
To find aₙ substitute i = n into the equation:
[tex]\implies a_n=-4n-1[/tex]
Substitute the values of a, aₙ and Sₙ into the arithmetic series formula and solve for n:
[tex]\begin{aligned}S_n & =\dfrac{n}{2}(a+a_n)\\ \implies -1127&=\dfrac{n}{2}(-5-4n-1)\\-2254&=n(-4n-6)\\-2254&=-4n^2-6n\\4n^2+6n-2254&=0\\2n^2+3n-1127&=0\\2n^2-46n+49n-1127&=0\\2n(n-23)+49(n-23)&=0\\(2n+49)(n-23)&=0\\\\2n+49&=0 \implies n=-\dfrac{49}{2}\\n-23&=0 \implies n=23 \end{aligned}[/tex]
As n is positive, n = 23.
Part (c)[tex]\displaystyle \sum^n_{i=5}(7+12i)=455[/tex]
[tex]\boxed{\displaystyle \sum _{i=m}^n\:=\:\sum _{i=1}^n\:-\:\sum _{i=1}^{m-1}}[/tex]
Therefore:
[tex]\displaystyle \sum^n_{i=1}(7+12i)-\sum^{4}_{i=1}(7+12i)=455[/tex]
To find a substitute i = 1 into the equation:
[tex]\implies a=7+12(1)=19[/tex]
To find aₙ substitute i = n into the equation:
[tex]\implies a_n=7+12n[/tex]
To find a₄ substitute i = 4 into the equation:
[tex]\implies a=7+12(4)=55[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \sum^n_{i=1}(7+12i)-\sum^{4}_{i=1}(7+12i)&=455\\\dfrac{n}{2}(19+7+12n)-\dfrac{4}{2}(19+55)&=455\\\dfrac{n}{2}(12n+26)-148&=455\\ \dfrac{n}{2}(12n+26)&=603\\6n^2+13n&=603\\6n^2+13n-603&=0\\ 6n^2-54n+67n-603&=0\\6n(n-9)+67(n-9)&=0\\(6n+67)(n-9)&=0\\\\6n+67&=0 \implies n=-\dfrac{67}{6}\\n-9&=0 \implies n=9\end{aligned}[/tex]
As n is positive, n = 9.
Part (d)[tex]\displaystyle \sum^n_{i=3}(-3-4i)=-507[/tex]
[tex]\boxed{\displaystyle \sum _{i=m}^n\:=\:\sum _{i=1}^n\:-\:\sum _{i=1}^{m-1}}[/tex]
Therefore:
[tex]\displaystyle \sum^n_{i=1}(-3-4i)-\sum^{2}_{i=1}(-3-4i)=-507[/tex]
To find a substitute i = 1 into the equation:
[tex]\implies a=-3-4(1)=-7[/tex]
To find aₙ substitute i = n into the equation:
[tex]\implies a_n=-3-4n[/tex]
To find a₂ substitute i = 2 into the equation:
[tex]\implies a=-3-4(2)=-11[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \sum^n_{i=1}(-3-4i)-\sum^{2}_{i=1}(-3-4i)&=-507\\\dfrac{n}{2}(-7-3-4n)-\dfrac{2}{2}(-7-11)&=-507\\\dfrac{n}{2}(-4n-10)+18&=-507\\-2n^2-5n&=-525\\2n^2+5n-525&=0\\ 2n^2-30n+35n-525&=0\\2n(n-15)+35(n-15)&=0\\(2n+35)(n-15)&=0\\\\2n+35&=0 \implies n=-\dfrac{35}{2}\\n-15&=0 \implies n=15 \end{aligned}[/tex]
As n is positive, n = 15.
For any positive numbers a, b, and d, with b + 1, logo
= d.logy a.
A. da
B. ad. logo ad
оооо
c. logo a + logo d
+
D. ad
Answers
For any positive numbers a, b, and d, with b ≠ 1, [tex]d*log_ba=lob_ba^d[/tex]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given:
[tex]d*log_ba\\\\Using\ law\ of\ logarithms:\\\\d*log_ba=lob_ba^d[/tex]
For any positive numbers a, b, and d, with b ≠ 1, [tex]d*log_ba=lob_ba^d[/tex]
Find out more on equation at: https://brainly.com/question/2972832
For a parallelogram with a long side that is 4 times the length of its short side find the area if the height from the long side is 23 and the perimeter is 125.
a. 2,875
b. ~ 514.3
c. 1,150
d. 2,200
Answers
9514 1404 393
Answer:
c. 1150 square units
Step-by-step explanation:
The sum of the two side lengths is half the perimeter, so is 125/2 = 62.5 units. The long side is 4/5 of that, so is 50 units.
The area is the product of the long side and the height to the long side:
A = bh
A = (50 units)(23 units) = 1150 units²
__
Additional comment
This geometry is impossible, because the height from the long side cannot be more than the length of the short side. Here, the short side is 12.5 units, so it is not possible for the height to be 23 units.
If the height is measured from the short side, then the area is 287.5 square units.
what number shoild come next 100,96,88,72
Answers
Answer - 40
----------
100 - 4
96 - 8
88 - 16
72 - 32
FM whdi3zldkejrht info
Answers
[tex]9\frac{x}{y} -10-\sqrt{x} 5[/tex]
Answers
Possible asks from the question?!
3/4 of Stella's garden is flowers. She grows 6 types of flowers spaced equally. What fraction of her garden is dedicated to each type of flower?
Answers
Answer: 1/8 of her garden
1/8 of her garden is dedicated to each type of flower.
What is a fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Given
part of stella's garden has flowers = 3/4
types of flowers = 6
fraction of her garden is dedicated to each type of flower = 3/4 / 6 = 3/4 *1/6 = 3/24 = 1/8.
To learn more about fractions refer to:
https://brainly.com/question/78672
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Josie has a standard number cube and a fair coin. What is the probability that Josie will roll a 3 and flip a tail?
A) 1/4
B) 1/6
C) 1/8
D) 1/12
Answers
Mr. Halsey leans a ladder against an 11.5 foot wall the bottom the of the ladder is 3.5 ft from the base of the wall as shown what is the approximate length of the ladder
Answers
Explanation :(x)^2=(11.5)^2+(3.5)^2
X^2=132.25+12.25
X^2=144.5 then square root it
X=12 feet
Hence, the approximate length of the ladder is [tex]12ft[/tex].
What is the approximation value?
An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding.
A calculation can be approximated by rounding the values within it before performing the operations.
Here given that,
[tex](x)^2=(11.5)^2+(3.5)^2\\X^2=132.25+12.25\\X^2=144.5 \\X=\sqrt{144.5}\\X=12 feet[/tex]
Hence, the approximate length of the ladder is [tex]12ft[/tex].
To know more about the approximation value
https://brainly.com/question/29580932
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find K if 4 x square - 2 X square + kx + 5 leaves a remainder -10 when divided by 2x+1
Answers
Answer:
[tex]k = 31[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 4x^2 - 2x^2 + kx + 5[/tex]
[tex]r = -10[/tex] --- remainder
[tex]d = 2x + 1[/tex] --- divisor
Required
Find k
We have:
[tex]d = 2x + 1[/tex] --- divisor
Equate to 0
[tex]2x + 1 = 0[/tex]
Solve for x
[tex]2x = -1[/tex]
[tex]x =-0.5[/tex]
This means that:
[tex]f(-0.5)=-10[/tex]
So, we have:
[tex]4*(-0.5)^2 - 2*(-0.5)^2 + k*-0.5 + 5 =-10[/tex]
[tex]0.5 -0.5k + 5 =-10[/tex]
Collect like terms
[tex]-0.5k=-10-5-0.5[/tex]
[tex]-0.5k=-15.5[/tex]
Solve for k
[tex]k = -15.5/-0.5[/tex]
[tex]k = 31[/tex]
Which of the following resulted from the Euclidean postulate below?
Through a given point not on a given line, there is exactly one line parallel to
the given line.
A. The discovery of hyperbolic geometry
B. The discovery of perpendicular lines
C. The discovery of non-Euclidean geometry
D. The discovery of the complex coordinate plane
Answers
Answer:
C
Step-by-step explanation:
The discovery of non euclidean
Which fraction is equivalent to
1/3
Answers
Answer:
there's many! three examples of equivalent fractions to 1/3 are: 3/9 9/27. and 27/81
Hope that helps!
What is the length of YZ?
Answers
Answer:
28.6 units
Step-by-step explanation:
44/36=35/YZ
44 YZ = 35*36
44 YZ = 1260
YZ = 28.6 units
determine the most appropriate hypothesis test to use for the following scenario: the august 2008 edition of academy of management journal featured an investigation of the performance and tiing of corporate acquisitions. the investigations discovered that in random sample of 2778 firms, 748 annouced one or more acquisitions during the year 2000. does the sample provide suffcient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 30%
Answers
Answer:
Since the calculated z =-3.5357 falls in the critical region z ≥ 1.645 we reject H0 and conclude that the sample provides sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is ≥ 30%
Step-by-step explanation:
Testing hypothesis about a population proportion when sample size is large.
If the sample size is large then the variable
z= p^-p / sqrt [pq/n]
is approximately standard normal.
Formulate the hypotheses as
H0 : p < 30% against the claim Ha: p ≥ 30%
Choose the significance level ∝= 0.05
the critical region is z ≥ 1.645 because the alternative hypothesis is stated on a greater than or equal to basis.
Computing
Z= 748-(2778*0.3)/ √2778*30/100*70/100
z= 748-833.4/√583.38
z= -85.4/24.153
z=-3.5357
Since the calculated z =-3.5357 falls in the critical region z ≥ 1.645 we reject H0 and conclude that the sample provides sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is ≥ 30%
The p- value is 0.0002
Express y-4[y-3(y-2)] -5 in simplest form
Answers
Answer:
y^3 - 9y^2 + 26y - 29
Step-by-step explanation:
y - 4[y - 3(y - 2)] - 5
I'm going to separate it into parts
(y - 3)(y - 2)
y^2 - 5y + 6
(y - 4)(y^2 - 5y + 6)
y^3 - 5y^2 + 6y - 4y^2 + 20y - 24
y^3 - 9y^2 + 26y - 24
y^3 - 9y^2 + 26y - 24 - 5
y^3 - 9y^2 + 26y - 29
n manufacturing a product, 85% of the units that are produced are not defective. Of the products inspected, 10% of the good ones (i.e., not defective) are falsely seen as defective and not shipped whereas only 5% of the defective products end up approved and shipped. If a product is shipped, what is the probability that it is defective?
Answers
Answer:
0.0097 = 0.97% probability that it is defective
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Product is shipped.
Event B: It is defective.
Probability of the product being shipped:
100 - 10 = 90% of 85%(not defective).
5% of 100 - 85 = 15%(defective). So
[tex]P(A) = 0.9*0.85 + 0.05*0.15 = 0.7725[/tex]
Probability of being shipped and being defective:
5% of 15%. So
[tex]P(A \cap B) = 0.05*0.15 = 0.0075[/tex]
What is the probability that it is defective?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0075}{0.7725} = 0.0097[/tex]
0.0097 = 0.97% probability that it is defective
Which is less: an angle showing a turn 1/3 of a circle or an angle showing a turn through1/4 of a circle ?
Answers
Answer:
1/4 of a circle is less
Step-by-step explanation:
1/4=90°
1/3=120°
The sales tax in your city is 8.8\%8.8%8, point, 8, percent, and an item costs \$63$63dollar sign, 63 before tax.
How much tax would you pay on that item?
Answers
9514 1404 393
Answer:
$5.54
Step-by-step explanation:
8.8% of $63 is ...
0.088×$63 = $5.544
The tax is rounded to the nearest cent, so you would pay $5.54 in tax.
Answer: 5.54
Step-by-step explanation: khan said it was correct
Please help me fast i need help
First question: less or greater
Second question: decrease or increase
Third question: would or would not
fourth question: correct or incorrect
You have to choose the answer's
Ok
Answers
Answer:
Look at the image.
Step-by-step explanation:
The Smiths painted their house blue. The complete predicate of this sentence is _____.
Smiths
the Smiths
Answers
Cole knows that r/s = t for integers r, s, and Based on what Cole knows which of the following equations is NOT true?
A. -r/-s =t
B. -r/s =-t
C. -r/-s =-t
D.r/-s =-t
Answers
c because -t=-r/-s equals -t=r/s
If the radius of the circle x² + y2 - 4x - 6y - k = 0 is
4 units, find the value of k.
Answers
Answer: 3
Step-by-step explanation:
Given
The equation of the circle is [tex]x^2+y^2-4x-6y-k=0[/tex]
Using completing the square method
[tex]\Rightarrow x^2+y^2-4x-6y+4-4+9-9-k=0\\\Rightarrow \left( x^2-4x+4\right)+\left( y^2-6y+9\right)-\left( k+4+9\right)=0\\\Rightarrow \left( x-2\right)^2+\left( y-3\right)^2=\left( k+13\right)[/tex]
on comparing with standard form, [tex]r^2=k+13[/tex]
Insert the value of r
[tex]\Rightarrow 4^2=k+13\\\Rightarrow k=16-13\\\Rightarrow k=3[/tex]
Patrica buys a total of 5 party hats and 5 balloons for the children at a party. Each party hat costs $0.50. Patrica spends a total of $7.50 for the party hats and the balloons. Enter an equation that models the situation with b, the cost of 1 balloon.
Answers
Answer:
b=2.5-7.50
Step-by-step explanation: so 5 party hats cost 50 cents, so times that by 5 to get 2.50, and then use the 7.50 and minus it.