The standard form of a line is simply a special way of writing the equation of a line. You are probably already familiar with the slope-intercept form of a line, y = mx + b. The standard form is just another way to write this equation and is defined as Ax + By = C, where A, B, and C are real numbers, and A and B are both not zero (see note below about other requirements). As you will see in the lesson below, every line can be expressed in this form.
Note that the requirements on A, B, and C vary a bit from textbook to textbook. While they technically can be any real numbers, it is most common to write them as integers and to keep A positive. It is also common to require that A, B, and C share no common factors.
Ax+By=C
THE STANDARD FORM OF A LINE: Ax+By=C
The result is referred to as the standard form of the line: Ax+By=C. We should always be able to convert from one form of an equation to another. For example, if we are given a line in the slope-intercept form, we should be able to express it in the standard form, and vice versa
he standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations
Now ,
A=0
B=0
A and B are not both zero, the graph of Ax + By = C is always a line.
when ,
The graph of Ax + By = C, where A and B are not both zero
A[tex]\neq[/tex]0
B[tex]\neq[/tex]0, is a line.
Divide both sides by B. Because the form Ax + By = C can describe any line,
it is called the standard form of an equation for a line.
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Write a method called listlength() that takes in a list of strings and returns a list of their lengths as integers. you must create a new list for your answer.
Following are examples of the listlength() methods -
listLength(list("Guava" "apple", "orange", "pineapple")) -> list(0, 1, 2, 3)listLength(list("HI")) -> list(2)listLength(list()) -> list()What is the function of listlength() method?It counts the string characters.
What are the different methods to get string length in python?Len(), a built-in method in Python, may be used to determine a list's size or length. The iterable that is accepted as an input by the len() function counts and returns the number of elements that are present in the list.Using a for loop in a Python program to determine the length of the list is seen as an antiquated or simple approach.The length hint() method in the Python operator module may be used to determine the total number of entries in a list.To learn more about string methods from given link
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how do you factor x^6-27x^9 completely
Answer: -x^6(3x-1)(9x^2+3x+1)
Step-by-step explanation:
x^6-27x^9=
x^6(1-27x^(9-6))=
x^6(1-27x^3)=
-x^6(27x^3-1)=-x^6(3x-1)(9x^2+3x+1)
1. Solve: -3.9 + 2.7
the volume 216 whats the lenght in inches
Answer:
so i the answer is 216 only
42. (a) find the unit vectors that are parallel to the tangent line to the curve y − 2 sin x at the point sy6, 1d. (b) find the unit vectors that are perpendicular to the tangent line. (c) sketch the curve y − 2 sin x and the vectors in parts (a) and (b), all starting at sy6, 1d.
Vectors is a quantity that has both magnitude and direction as well. A vector that has 1 magnitude is called unit vector. Unit vector is represented by the symbol '^'.
To find a Unit vector we divide the vector by its magnitude.
First find the slope of the tangent line, slope of a tangent line for a point f(x) is given by f'(x). Hence at point (π/6,1) where x = π/6, the slope of the tangent line is :
[tex]f(x)=2sinx\\f'(x)=2cosx\\f'(\pi /6)=2cos(\pi /6)=2.\frac{\sqrt{3} }{2}=\sqrt{3}[/tex]
The slope of the tangent line at this point is [tex]m=\sqrt{3}[/tex]
Finding a unit vector parallel to the tangent line. since slope is the ratio y and x then we can set an arbitrary vector with slope 4 by letting x=1 and y = √3 or v=[1,√3]. this vector has slope √3 and this is parallel to the tangent line, However this is not unit vector because its magnitude is not equal to 1 so we can divide this vector by its magnitude to find the unit vector.
[tex]u_v=\frac{v}{|v|} =\frac{1 \sqrt{3} }{\sqrt{1^{2}+(\sqrt{3})^2 } } \\=\frac{1}{\sqrt{4} } ,\frac{\sqrt{3} }{\sqrt{4} } =\frac{1}{2}, \frac{\sqrt{3} }{2} =[\frac{1}{2},\frac{\sqrt{3} }{2} ][/tex]
If a line has slope of m then all lines perpendicular of it will have a slope of -1/m
So we are looking for a unit vector of slope of -1/√3
Using the same logic we have unit vector that are perpendicular to the tangent line are [tex][\frac{\sqrt{3} }{2},-\frac{1}{2} ][/tex]
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Find the product (2x + 9) (9x + 11)
Answer:
Step-by-step explanation:
18x^2 + 22x + 81x + 99
18x^2 + 103x + 99
Awat Withdrawals $18 from his bank account once each day for five days what integer represents the change in amount in the account used pencil and paper find the true that would represent the changing them out the account if awat deposit $18 into his bank once each day for five days explain the difference between the integer for the withdraws and the integers for the deposit
-90
90
Since it is withdrawing, we are taking away -$18 every day for 5 days.
(-18)*5 = -90
Since it is a deposit, we are adding to the amount in her account, +$18 for 5 days.
18*5 = 108
The difference is that one is taking away and one is adding each day, resulting in negative or positive change.
An agreement with a bank to retain money and maintain transaction records. a plan for working with a firm on a regular basis. a set-up where a person uses a specific company's email or Internet services. The word "account" typically alludes to a ledger or record-keeping activity. In the financial sector, it can be used in a wide variety of ways. An account in banking is a contract whereby a company, generally a bank or credit union, takes a customer's financial assets and retains them on the customer's behalf at the customer's choice.
Savings accounts are one type of account that consumers can open to help them amass liquid assets.
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☆*: .｡. o(≧▽≦)o .｡.:*☆ wasting my points
Answer:
Step-by-step explanation:
Totally rad!
Determine the correct METRIC length of the cockroach in this image.
A 1.0 in
B 2.5 cm
C 7.5 cm
D 3.0 in
Answer:
B
Step-by-step explanation:
7.5cm - 5cm = 2.5cm
So it is B :)
Directions: Find the next five terms, then write a conjecture.
7. ⬆️,➡️,⬇️
Conjecture:
The next five terms are ← ↑ → ↓ ← and the conjecture is each arrow is rotated 90 degrees clockwise to get the next
How to find the next five terms, then write a conjecture?The first three terms are given as
↑ → ↓
From the above pattern, we have the following highlights:
Each arrow is rotated 90 degrees clockwise to get the next
Using the above as a guide, we have the next five terms to be:
← ↑ → ↓ ←
Also, we have the conjecture to be:
Each arrow is rotated 90 degrees clockwise to get the next
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Which table represents a linear function?
Find the product of 3.2 x 1012 and 4.25 x 109. Write the final answer in scientific notation.
The product of the numbers written as a scientific notation is 1.36 × 10²²
Product of numbersFrom the question, we are to determine the product of the given numbers
The given numbers are
3.2 x 10¹² and 4.25 x 10⁹
The product of the numbers can be determined as shown below
3.2 × 10¹² × 4.25 × 10⁹
= 3.2 × 4.25 × 10¹² × 10⁹
= 13.6 × 10¹² ⁺ ⁹
= 13.6 × 10²¹
= 1.36 × 10¹ × 10²¹
= 1.36 × 10¹ ⁺ ²¹
= 1.36 × 10²²
Hence, the product of the numbers written as a scientific notation is 1.36 × 10²²
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HELPS!!! WILL MARK BRAINLIEST!!!!
20x+50=150
Find x
Answer:
x = 5
Step-by-step explanation:
why do i have a limit that's weird i shouldn't have a limit to something i've signed up for
Answer:
A limit on what? And what website
Step-by-step explanation:
Directions: Translate equation DO NOT SOLVE!
(8) "two times the sum of number and 5 is 20"
Answer: 2(n +5) = 20
Step-by-step explanation:
Answer:
2(n+5)=20
Step-by-step explanation:
n+5 is the sum. Two times of the sum is 2*(n+5) which is 2(n+5). This is set to equal 20.
Answer quick please :)
Select the correct answer.
The first term of a geometric series is -3, the common ratio is 6, and the sum of the series is -4, 665. Using a table of values, how many terms
are in this geometric series?
OA 6
OB. 5
OC. 10
OD. 4
This geometric progression has 5 terms
This is a geometric progression or geometric series whose sum of n terms is given by the formula
Sn = a[([tex]r^{n\[/tex] – 1)/(r – 1)]
Where Sn is sum of n terms of geometric progression, a is the first term of the series , r is the common ratio
Here we are required to find the number of terms in the geometric progression whose first term is -3 and common ratio is 6
-4665 = -3 [( [tex]6^{n}[/tex]-1)/(6-1)
1555=( [tex]6^{n}[/tex]-1)/5
7775= [tex]6^{n}[/tex]- 1
7776 = [tex]6^{n}[/tex]
[tex]6^{5}[/tex] = [tex]6^{n}[/tex]
So, n=5
Therefore this geometric progression has 5 terms
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5a/b+c=10, solve for a
Answer:
a = b(10-c)/5
Step-by-step explanation:
5a/b + c = 10
5a/b = 10-c
5a = b(10-c)
a = b(10-c)/5
what three numbers are next in the sequence 2,3,6,11,18? and how do you get these numbers?(answer needed as soon as possible)
The next three numbers in the sequence are 27, 38, and 51
SequenceFrom the question, we are to determine the next three numbers in the given sequence
The given sequence is
2,3,6,11,18
The difference between the 1st and 2nd terms is 3 -2 = 1
The difference between the 2nd and 3rd terms is 6 -3 = 3
The difference between the 3rd and 4th terms is 11 - 6= 5
The difference between the 4th and 5th terms is 18 - 11= 7
We can observe that the successive odd numbers are being added to the terms
Thus,
The sixth term will be 18 + 9 = 27
The seventh term will be 27 + 11 = 38
The eight term will be 38 + 13 = 51
Hence, the next three numbers in the sequence are 27, 38, and 51
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What is the value of the expression when a = 6, b = 4, and c = 8?
2a3b−c
A.1
B.3
C.8
D.12
Answer: 27
Step-by-step explanation:
A student performs several experiments in which he swings a pendulum for 20-second duration. He uses a string that is 27 cm long, and he tests pendulum masses of different sizes, varying from 2 to 12 grams. He records the number of swings each pendulum makes in 20 seconds. What is the independent quantity and the dependent quantity.Be sure to include the appropriate units of measure
Using it's concepts, we have that:
The independent variable is the pendulum mass.The dependent variable is the number of swings.What is the relation between a function and the dependent and independent variables?A function has the following format: y = f(x).
In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.
That is, the input of the function is the independent variable and the output is the dependent variable.
For this problem, we have that the number of swings is dependent on the mass of the pendulum, hence:
Number of Swings = f(mass).
Thus:
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How should this model be completed to represent 642/11 ??
Enter the answer in the box.
Model be completed to represent 642/11 is 29.1818181818
[tex]\frac{642}{11}[/tex] = 58.3636363636
58.3636363636 = 583.636363636 to the nearest tenth
58.3636363636 = 58.36 to the nearest hundredth
58.3636363636 = 58.364 to the nearest thousandth
= 0 to the nearest tenth
= 0 to the nearest hundredth
= 0 to the nearest thousandth
Other Divisions Math homework are
642 divide by half plus 20
([tex]\frac{642}{2}[/tex]) + 20 = 341
642 divide by half plus 40
([tex]\frac{642}{2}[/tex]) + 40 = 361
[tex]\frac{642}{11}[/tex] divided by 2
([tex]\frac{642}{11}[/tex]) ÷ 2 = 29.1818181818
Division is one among the four basic operations of arithmetic, the ways in which numbers are combined to make new numbers. the opposite operations are addition, subtraction, and multiplication.
At an elementary level the division of two natural numbers is, among other possible interpretations, the method of calculating the number of times one number is contained within another.7 This number of times needn't be an integer. for instance , if 20 apples are divided evenly between 4 people, everyone receives 5 apples (see picture).
The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is that the number of times the second number is completely contained in the first number, and a remainder, which is that the part of the first number that remains, when within the course of computing the quotient, no further full chunk of the dimensions of the second number can be allocated. for instance , if 21 apples are divided between 4 people, everyone receives 5 apples again, and 1 apple remains.
For division to always yield one number instead of a quotient plus a remainder, the natural numbers must be extended to rational numbers or real numbers.
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a couple decides to have 4 children. if they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?
3/8 is the probability that they will have exactly 2 girls and 2 boys.
What does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Got to have 4 children
Boy and Girl are equally likely
Hence, P( boy) = P( girl) = 1/2
This is like performing binomial distribution.
P( excatly 2 boys and 2 girls)
=4C2(1/2)^2 (1/2)^2
=6/16
=3/8
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consider a sample with data values of 28, 26, 24, 15, 30, 34, 20, and 26. compute the range. 19 correct: your answer is correct. compute the interquartile range. 14 incorrect: your answer is incorrect. compute the sample variance. (round your answer to two decimal places.) 34.6 correct: your answer is correct. compute the sample standard deviation. (round your answer to two decimal places.) 5.9 correct: your answer is correct.
According to the given statement the values are:
The range = 19
Interquartile Range will be = 8.25
Sample Variance =33.93
Sample Standard deviation = 5.82
What is Interquartile Range?The dispersion of your data's middle quartile is measured by the interquartile range (IQR). It is the range for your sample's middle 50%. Assess geographical variability where the majority of your numbers are by using the IQR. Larger numbers suggest a wider dispersion of your data's center region.
According to the given data:
finding the range = Maximum value + Minimum value
= 34 - 15
= 19
The range = 19When ordering the observations, we obtain:
15,20,24,26,26,27,30,34
Where ,
n = 8
Q1=(n+14)the observation's term value
=(94)the observation's term value
=(2.25)the observation's term value
=2nd observation +0.25[3rd-2nd]
=20+0.25[24-20]
=20+0.25(4)
=20+1
=21
Q3=(3(n+1)4)the observation's term value
=(3⋅94)the observation's term value
=(6.75)the observation's term value
=6th observation +0.75[7th-6th]
=27+0.75[30-27]
=27+0.75(3)
=27+2.25
=29.25
Now finding the Interquartile Range
= Q3 -Q1
= 29.25 - 21
=8.25
The Interquartile Range will be = 8.25
Sample Variance S2=∑x2-(∑x)2nn-1
=5338-(202)28/7
=5338-5100.5/7
=237.57
=33.9286
Sample Variance =33.93
Sample Standard deviationS=√∑x2-(∑x)2nn-1
=√5338-(202)28/7
=√5338-5100.5/7
=√237.5/7
=√33.9286
=5.8248
Sample Standard deviation = 5.82
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It cost Fawzia $12.00 to send 80 text messages. How many text messages did she send if she spent $19.95?
Answer: she would have sent 133 text messages
hope this helps
R
The following transformations are to be performed, in order, on the parallelogram.
• Translate 2 units in a positive y-direction.
. Translate 6 units in a positive x-direction.
• Reflect about the x-axis.
Which of the following describes the location of vertex Q after the transformations?
OA (2,-4)
B. (-2,-8)
C. (2,-8)
OD. (-2,4)
18÷ 3 2/3
Can someone help me with this q
the 45
Step-by-step explanation:
679
Answer:
54/11 (or) 4 10/11
Step-by-step explanation:
Let's solve the problem,
→ 18 ÷ 3 2/3
→ 18 ÷ (11/3)
→ 18 × (3/11)
→ 54/11 = 4 10/11
Hence, the answer is 54/11.
A number cube labeled 1 through 6 is rolled.
What is the probability of the cube landing on an even number?
Answer: 3/6 or 1/2 or 50%
Step-by-step explanation: 1, 2, 3 4, 5, 6 are each face
2, 4, and 6 are even.
3 out of the 6 are even (3/6)
reduce (1/2)
1/2 = 50%
The tangent function has asymptotes at where and where? and they occur every
? radians around the circle.
There are two vertical asymptotes at angles of 0.5π radians and 1.5π radians and it occurs every π radians.
What are the family of vertical asymptotes of the tangent function?
Tangent function is a kind of trigonometric function, that is, a kind of transcendent function. This function has a period of π radians and for f(x) = tan x, the vertical asymptotes are contained in the points:
x = 0.5π + i · 2π, where i is an integer.
Hence, there are two vertical asymptotes at angles of 0.5π radians and 1.5π radians and it occurs every π radians.
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Add.
7/4 + 2/3
help pls!!
Answer: 2 5/12
Step-by-step explanation: you multiply each number to 12 as the bottom number it’s hard to explain
Mary used 10 2/3 yards of fabric to make 4 identical curtain panels.
What equation can be used to model the total number of yards of fabric, y. needed to make x curtain panels? Write the equation in the form
The equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels is y = (10 2/4 ÷ 4) × x
How to compute the expression?It should be noted that Mary used 10 2/3 yards of fabric to make 4 identical curtain panels.
Therefore, the equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels will be:
y = (10 2/4 ÷ 4) × x
where
y = number of yards
x = number of panels
Therefore, the equation is y = (10 2/4 ÷ 4) × x
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