Supplementary angles are two angles whose combined angle is 180 degrees. As shown below, the table of the proof that (1) is an addition to (3) can be completed.
What are Supplementary angles?Supplementary angles are two angles whose combined angle is 180 degrees. When a straight line crosses another line, two angles are created on either side of the initially imagined straight line. Two sets of additional angles make up those two-two angles. This implies that a straight line will be formed by the outside sides of any extra angles that are positioned next to one another.
For the demonstration that 1 is an addition to 3, the preceding table can be completed as shown below.
1) Line m in is parallel to line n;
2) ∠1 = ∠2 → Corresponding angles
3) m∠1 = m∠2 → Definition of Congruent angles
4) ∠2 and ∠3 for a linear pair → Adjacent angles on a straight line
5) ∠2 is supplementary to ∠3 → Definition of linear pair
6) m∠2 + m∠3 = 180° → Definition of supplementary angles
7) m∠1 + m∠3 = 180° → Substitution Property
8) ∠1 is supplementary to ∠3
As a result, the table containing the proof that item 1 is an addition to item 3 can be completed as displayed above.
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f(x) = -9x+14 g (x) = -3x^2
Answer: Graphed: f(x)=-9x+14gx Answer: =-3x2
Use the given functions to set up and simplify .
Exact Form: x=0,-1/3
Decimal Form: x=0,-0.3
Step-by-step explanation:
how to we convince other people that geometric claim is true?
you might want to write an essay on, but it's your choice.
A tree is currently 8 feet tall and grows 3 feet per year
a. Model this scenario with an arithmetic sequence in explicit form
b. Rewrite the explicit form of the sequence using function notation
c. How tall will the tree be in 12 years?
Answer:
You have to multiple to get you answer
Step-by-step explanation:
f f(x)=tan(2x), what is the absolute difference between f(5.4) and T2(5.4), if the second degree Taylor polynomial is centered at x = 5?
Round your answer to 3 places.
The absolute difference rounded to three decimal places is 2.674.
What is polynomial?
An expression that consists of variables, constants, and exponents and is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given: f(x) = tan(2x)
Then f(5.4) = tan(2 x 5.4) = tan(10.8) = tan(54/5)
The second degree Taylor polynomial centered at x = 5 is given by,
T2(x) = Σ(n = 0, 2) f^n(5)/5!(x - 5)^n
Now,
f°(x) = f(x) = tan(2x)
f(5) = tan(2 x 5) = tan(10)
f'(x) = d/dx(tan(2x))
f'(x) = 2 sec^2x = 2( 1 + tan^2(x))
f'(5) = 2(1 + tan^2(10))
f"(x) = d/dx[2(1 + tan^2(2x)]
f"(x) = 0 + 2(2tan(2x)(2sec^2(2x))
f"(x) = 8 tan(2x)(1 + tan^2(2x))
f"(5) = 8 tan(10)(1 + tan^2(10)
Then
[tex]T_2(x) = \frac{tan(10)}{0!}(x - 5)^0 + \frac{2 + 2tan^210}{1!}(x - 5)^1 + \frac{8(tan(10)(1+tan^2(10)}{2!}(x - 5)^2 \\T_2(5.4) = tan(10) + 2(1 + tan^2(10)) (5.4 - 9) +4tan(10)(1 + tan^2(10)(5.4 - 5)^2\\T_2(5.4) = \frac{16}{25} tan^310 + \frac{4}{5}tan^2(10) + \frac{41}{25} tan(10) + \frac{4}{5}[/tex]
The absolute difference is,
[tex]|f(5.4) - T_2(5.4)| = 2.673745[/tex]
|f(5.4) - T2(5.4)| ≈ 2.674
Hence, the absolute difference rounded to three decimal places is 2.674.
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in an isosceles triangle the perimeter is 8 more than two times one of the legs if the perimeter is 28 find the length of the base
Answer:
base = 8
Step-by-step explanation:
In an isosceles triangle, the legs are equal.
P = 28 = 2L + 8
2L + 8 = 28
2L = 20
L = 20/2 = 10 (length of each leg)
P = 2L + b (sum of the lengths of the 2 legs and the base)
28 = 2(10) + b
b = 28 - 20 = 8
Country X had a population of 12 million in 2010. With a population of 15 million in 2022, calculate the country's growth rate.
Round your answer to four decimal places
Use A = Pert
[tex]A=Pe^{rt} \\ \\ 15000000=10000000e^{12r} \\ \\ 1.5=e^{12r} \\ \\ \ln(1.5)=12r \\ \\ r=\frac{\ln(1.5)}{12} \\ \\ r \approx \boxed{0.0338}[/tex]
The exponential growth rate of the population of the country is given by the relation r = 1.8595 %
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the initial population of the country in 2010 be = 12 million
Let the final population of the country in 2022 = 15 million
Now , let the growth rate be represented as r
And , growth rate r = [ ln( final population - ln (initial population ) / no of years ] x 100
Growth Rate = (ln(15 ) - ln(12 )) / (2022 - 2010)
r = (2.70805 - 2.48491) / 12
r = 0.018595
r = 1.8595 %
Hence , the growth rate r = 1.8595 %
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For 8 Bonus Points, find all the missing angles! You just get them all correct to receive credit. Good Luck!
All angles are:
a = 37
b = 143
c = 37
d = 58
e = 37
f = 53
g = 48
h = 94
k = 96
m = 26
p = 69
r = 111
s = 69
What is sum of angles of a triangle?
A triangle's total angles equal the straight angle (180 degrees, radians, two right angles, or a half-turn) in a Euclidean space. Three angles, one at each vertex and bounded by two neighbouring sides, make up a triangle.
For a very long period, it was unknown if there were any alternative geometries for which the total is different. During the 19th century, this issue had a particularly significant impact on mathematics. Ultimately, it was determined that the response was correct: in other geometries, this total can be higher or smaller, but it must then depend on the triangle. Its deviation from 180° represents an instance of an angular defect and is a crucial distinction for geometric systems.
From the fig.
we know,
e=37
b= 143 (vertically opposite angle)
143 + a = 180 (Linear pair)
a = 180 - 143
a = 37
e = 37
So, c = 37 (Vertically opposite angle)
c + d + 85 = 180 (Sum of angles on straight line)
37 + d + 85 = 180
d = 180 - 122
d = 58
e + 90 + f = 180 (Sum of all angles of a triangle)
37 + 90 + f = 180
f = 180 - 127
f = 53
g = 48 (if two sides are equal , then the two angles opposite to the equal
sides will also be equal.)
48 + 48 + h = 180 (Sum of angles of a triangle)
h = 180 - 96
h = 94
h+ k = 180 (Linear pair)
94 + k = 180
k = 180 - 94
k = 96
d + k + m = 180 (Sum of angles of a triangle)
58 + 96 + m = 180
m = 180 - 154
m = 26
26 + 85 + p = 180 (Sum of angles of a triangle)
p = 180 - 111
p = 69
p + r = 180 (Linear pair)
r = 180 - 69
r = 111
p = s (corresponding angles)
s = 69
Hence all angles are:
a = 37
b = 143
c = 37
d = 58
e = 37
f = 53
g = 48
h = 94
k = 96
m = 26
p = 69
r = 111
s = 69
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...............................................................
Answer:
a) 53.33 miles per hour
b) 1.7 pages per minute
c)2.25 $ per avocado
Step-by-step explanation:
a) 320/6 = 53.33333
b) 68/40 = 1.7
c) 27 /12 = 2.25
A sample was done, collecting the data below. Calculate the standard deviation, to one decimal place.
x
13
2
16
18
19
Standard deviation of given data corrected to one decimal place is 6.9(rounding off)
What is standard deviation and mean?The average degree of variability in your datasets is represented by the standard deviation. It reveals the average deviation of each statistic from the mean.
In general, values with a large standard deviation are spread out from the mean, and those with a low standard deviation are grouped together near to the mean.
Given: Data values = 13,2,16,18,19
Mean of data is given as m,
[tex]=\frac{13+2+16+18+19}{5} \\=\frac{68}{5}\\ =13.6[/tex]
Standard deviation, σ
[tex]=\sqrt{\frac{(m-x)^{2} }{n-1} } \\=\sqrt{\frac{(13.6-13)^{2} +(13.6-2)^{2}+(13.6-16)^{2} +(13.6-18)^{2} +(13.6-19)^{2} }{4} }\\ =\sqrt{\frac{0.36+134.56+5.76+19.36+29.16}{4} }\\ =\sqrt{\frac{189.2}{4} }\\ =6.87[/tex]
Hence, standard deviation of given data is 6.9(rounding off)
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Question #8
Cameron read that his favorite NBA team won their game last night by a score of 142 to 124.
Which is true about the digit 2 in each number?
The true statement is that 2 in 142 represents a greater value than 2 in 124 because 142 > 124.
How to identify the place value of a digit in a number?The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol. The place values on the left ofthe decimal point start as ones, tens, hundreds, and so on.
The place value on the right of the decimal point starts from a point and goes to right as tenths, hundredths, and so on.
We are given that encore or points for an NBA Team are usually as whole numbers.
For example, 1, 2, 3, 4, e.t.c. points of an NBA Team are not in decimals or fractions.
The withiner of points awarded for an NBA match is called Discrete because that can be counted with a given amount of time.
Hence, 2 in 142 represents a greater value than 2 in 124 because 142 > 124.
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p+ 1.4 ≤ 0.5; p = 0.1
The inequality expression p + 1.4 ≤ 0.5 is false for p = 0.1
How to determine if the expression is trueFrom the question, we have the following parameters that can be used in our computation:
p + 1.4 ≤ 0.5;
p = 0.1
Substitute p = 0.1 in p+ 1.4 ≤ 0.5;
So, we have the following representation
0.1 + 1.4 ≤ 0.5;
Evaluate the like terms
This gives
1.5 ≤ 0.5;
The above inequality is false
This is because 1.5 is greater than 0.5
Hence, p + 1.4 ≤ 0.5; p = 0.1 is false
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How do I rewrite “y = -9x² + 18x +0” into vertex form?
Please help asap!!!!!!
By SAS congruence triangle MLN and triangle OLN are congruent.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, LM≅LO, ∠MLN≅∠OLN.
LM≅LO (Given)
∠MLN≅∠OLN (Given)
LN≅LN (Reflexive property of congruence)
ΔMLN≅ΔOLN (SAS congruence)
∠M≅∠O (CPTC)
MN≅ON (CPTC)
Therefore, by SAS congruence triangle MLN and triangle OLN are congruent.
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Give the equation of the line passing through the points (-3,-15/2} and(1,-3/2).
The equation of the line passing through the points (-3,-15/2) and(1,-3/2) is 3x - 2y - 6 = 0.
What is the equation of a line?
An algebraic way to represent a collection of points that together make a line in a coordinate system is called the equation of a line. An algebraic equation, commonly known as the equation of a line, can be created using the various points that together make up a line in the coordinate axis as a collection of variables (x, y). It is possible to determine whether a specific point lies on a line by utilising the equation of a line.
The equation of a line passing through two points [tex](x_{1} ,y_{1} )[/tex] & [tex](x_{2},y_{2})[/tex] is given by
[tex]\frac{y-y_{1} }{x-x_{1} } = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Given, two points are (-3,-15/2) and(1,-3/2).
[tex](x_{1} ,y_{1} )[/tex] = (-3,-15/2) and [tex](x_{2},y_{2})[/tex] = (1,-3/2).
So, The equation of line passing through (-3,-15/2) and (1,-3/2) is given by
or, [tex]\frac{y+\frac{15}{2} }{x+3 } = \frac{-\frac{3}{2} +\frac{15}{2} }{1 +3 }[/tex]
or, [tex]\frac{y+\frac{15}{2} }{x+3 } = \frac{6}{4 } =\frac{3}{2}[/tex]
or, 2(y+7.5) = 3(x+3)
or, 2y + 15 = 3x + 9
or, 3x - 2y - 6 = 0
Hence, the required equation of the line is 3x - 2y - 6 = 0.
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Give a bijective proof that the number of partitions of n using distinct parts equals the number of partitions of n using only odd parts.
k(n) is also the number of partitions of n into distinct, odd parts. We begin with the generating function P(x) = ∑p(n) x_n which counts all partitions of all numbers n, with weight x_n for a partition of n.
How do you explain partitioning numbers?
By breaking huge numbers into smaller parts, partitioning helps to simplify the solution of arithmetic issues involving large numbers. 782, for instance, may be divided into: 700 + 80 + 2. It aids children in understanding the real value of each digit. They will perceive 782 as 700, 80, and 2, rather than as a terrifying number.
The numbers of partitions of 10 with number of parts {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} are respectively {1, 5, 8, 9, 7, 5, 3, 2, 1, 1}. (There are 20 partitions of 10 into an odd number of parts and 22 partitions of 10 into an even number of parts.)
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The mean amount of time it takes a kidney stone to pass is 14 days and the standard
deviation is 6 days. Suppose that one individual is randomly chosen. Let X=time to pass
the kidney stone. Round all answers to two decimal places.
The probability that an individual will take far longer than 21 days to complete it is 0.12.
What is standard deviation?In the descriptive analysis, the standard deviation is the amount of scatter or dispersal of the pieces of data in relation to their mean. It provides information on the distribution of values within the sample data and serves as a gauge for how widely apart the measured values are from the mean.
As per the information available in the question,
Meantime, μ = 14 days
Standard deviation, ρ = 6 days
Assume the time to pass the kidney stone be x.
The probability that it will take someone more time than 21 days to complete it.
Let's find out the Z-score first,
Z-score = (x - μ)/ρ
Substitute values in above equation,
= (21 - 14)/6
Z-score = 1.166.
The probability that it will take someone more time than 21 days to complete it :
P(x > Z) = P(x > 1.16) = 0.12
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Eloise practiced piano for 25 of an hour. Sarah practiced piano for 34 of an hour.
Answer:im assuming you need to know the difference and its nine
Step-by-step explanation: 34-25=9
$2, 900 is invested in an account earning 6.1% interest (APR), compounded quarterly. Write a function showing the value of the account after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
Answer: The value of the account after t years can be found using the formula:
Value = 2900 * (1 + 0.0061/4)^(4t)
The annual growth rate, or APR, is 6.1%. When this rate is compounded quarterly, the effective annual growth rate, or APY, is 6.17%, which is the nearest hundredth of a percent.
Therefore, the function showing the value of the account after t years is:
Value = 2900 * (1 + 0.0061/4)^(4t)
And the annual growth rate, or APY, is 6.17%.
Ann is 11 more than two times older than Stacy. If Ann is 59 years old,
solve an equation to determine Stacy's age
The age of Stacy is 24 years old provided the age of Ann is 59 years old.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, Ann is 11 more than two times older than Stacy.
Let the age of Stacy and Ann be s and a respectively, then:
a = 11 + 2s
Substitute a = 59 into the above equation:
59 = 11 + 2s
2s = 59 -11
s = 24
Hence, the age of Stacy is 24 years old provided the age of Ann is 59 years old.
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Noble Crown Books sells books including those
from the Bestseller List for substantially lower
prices than most book stores. To buy from them
however, one must have a membership which costs
$25. The average book cost turns out to be only
$12.47. The equation b= 12.47a+ 25 represents
the amount of money b a member will have spent
after buying a number of books. If Alex intends
to spend no more than $110 on books this year.
how many books can he buy from Noble Crown
Books during the year?
A. 6 books
C. 9 books
B. 8 books
D. 10 books
John entered a cross-country ski race. The first part of the race was 14 km long, and he completed it in 1 hour. The second part was 18 km long, and he completed this part in an hour and a half. What was John's average speed for the whole race?
A.
12.8 kilometers per hour
B.
26 kilometers per hour
C.
27.3 kilometers per hour
John's average speed for the whole race would be; 12.8 kilometers per hour
How to calculate the average speed?The first part of the race was 14 km long, and he completed it in 1 hour.
Now, formula for speed is;
Speed = distance/time
Thus, John's speed in the first part of the race would be;
14/1 = 14km/hr
The second part was 18 km long, and he completed this part in an hour and a half. This means that his speed in the second part of the race is;
18/1.5 = 12km/hr
Average speed = Total distance/total time
Total distance for both parts of the race is;
14 + 18 = 32km
Total time for the race is;
1 + 1.5 = 2.5 hours
John's average speed for the whole race would be;
32/2.5 = 12.8 kilometers per hour
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Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
The correct answer is option is a) x^4 – 6x^2 – 27 = 0 , d) 6(2x + 4)2 = (2x + 4) + 2 , e) 6x^4 = -x^2 + 5.
How do you write a quadratic form?
A quadratic equation can be expressed using the formula au^2+bu+c=0. where u is a mathematical expression. In each case, the leading term's exponent is equal to the middle term's exponent multiplied by two.
What is quadratic standard form?
Standard form refers to the quadratic function f(x) = a(x - h)2 + k, where an is not equal to zero. The graph opens either upward or downward depending on the value of a. The vertex is the point, while the line of symmetry is the vertical line x = h.
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Help me thank u very kuchhh
Answer: see below
Step-by-step explanation:
slope intercept form
y=mx+b
m=slope
The first question:-5/2 is the sloop
second question: 5/2 is the sloop
Multiply. Write the answer in simplest form.
4 2/3 x 9/10
Answer:
[tex] 4\frac{1}{5} [/tex]
Step-by-step explanation:
[tex] 4\frac{2}{3} \times \frac{9}{10} [/tex]
[tex] \frac{14}{3} \times \frac{9}{10} [/tex]
[tex] \frac{126}{30} [/tex]
[tex] \frac{21}{5} [/tex]
-7/12=1 5/6+d what is d?
Answer:
-3/2
Step-by-step explanation:
[tex]-\frac{7}{12}=1 \frac{5}{6}+d \\ \\ -\frac{7}{12}=\frac{11}{12}+d \\ \\ -7=11+12d \\ \\ -18=12d \\ \\ d=-3/2[/tex]
(quickly!) What is the value of x
The value of x for the given triangle is x = 86°.
What is triangle?
Three edges and three vertices make up a triangle, which is a polygon. It is among the fundamental shapes in geometry. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, any three points that are not collinear determine a singular triangle and a singular plane at the same time.
From the given triangle we have to find the value of x.
By triangle's property.
(x - 45)° + (x + 3)° = (x + 44)°
2x - 42 = x + 44
2x -x = 44 + 42
x = 86°
Hence, the value of x for the given triangle is x = 86°.
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on graphs of linear relationships slope describes the what of a line
Answer: it describe the steepness of the line
Step-by-step explanation:
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Bruno recorded 2/12 of his new album in
August, 1/3 of his new album in July, and the
rest in June.
What fraction of the album did he record in June?
The fraction of the album he recorded in June is 1/2
How to determine this?When all the fractions of the album will be = 1
Bruno recorded 2/12 was recorded in August
2/12 to the lowest term = 1/6
And 1/3 was recorded in July
So,
The fraction of the rest of the album in June is unknown
Let fraction recorded in June will be = x
x = 1 - 1/6 - 1/3
x = 1/1 - 1/6 - 1/3
x = [tex]\frac{18 - 3 - 6}{18}[/tex]
x = [tex]\frac{9}{18}[/tex]
x = [tex]\frac{1}{2}[/tex] to lowest term
Therefore, he recorded 1/2 of his Album in June
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-14 – x = -21 pls help
Answer:
x = 7
Step-by-step explanation:
Given equation,
→ -14 - x = -21
Now the value of x will be,
→ -14 - x = -21
→ -x = -21 + 14
→ -x = -7
→ [ x = 7 ]
Hence, the value of x is 7.
Answer:
x=7
Step-by-step explanation:
Isolate the variable by dividing each side by factors that dont contain the variable
The probability of rain on Monday is .1. The probability of rain on Tuesday is .8. What is the probability of rain on both Monday and Tuesday?
Answer:
The probability of rain on both Monday and Tuesday is .08, or approximately 8%.
Step-by-step explanation:
The probability of an event occurring on two separate days (such as rain on Monday and Tuesday) is calculated by multiplying the probabilities of the two events occurring separately. In this case, the probability of rain on both Monday and Tuesday is given by:
Probability of rain on Monday * Probability of rain on Tuesday = .1 * .8 = .08
Therefore, the probability of rain on both Monday and Tuesday is .08, or approximately 8%.
It's important to note that this probability assumes that the likelihood of rain on each day is independent of the other day. In other words, the probability of rain on Tuesday does not depend on whether or not it rained on Monday. If this is not the case, the probability of rain on both days may be different.