the exponential function is n(t) =n° (1+r)∧t, where t is the power refers the time in months after opening and n denotes average customer.
what means growing exponentially?when the rate of increases is occurred very rapidly. In this question, the trendy restaurant has earned reputation.
How will be the exponential function?Given, average number of customers after 11 months of opening = n(11) =310
average number of customers after 15 months of opening= n(15) =456
during this 4 month increases of customer =456 -310 =146
increasing rate of customer per month = 146/4 = 36.5
now increasing rate in percentages = 36.5 %
exponential growth rate, r= 0.365
let, n° is the initial number of customer while opening at t=0 month
now, the exponential function n(t) that model's average number of customers, n after t months of being open will be
n(t) = n° ( 1+r)∧t
we are given that after 11 months of opening average customer n(11) = 310
now, 310 = n° (1+ 0.365)∧11
n° = 10
hence, the exponential function = n(t) = 10(1+r)∧t
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Gabriella has 60 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 209 square meters. Solve for the dimensions (length and width) of the field.
The length and width of the rectangular plot of land is (209 / (60 - l)) and (60 - (209 / (60 - l))), respectively.
The formula to calculate the dimensions of a rectangular plot of land is area = length x width, or A = l x w. In this problem, the area of the land is 209 square meters, so A = 209. We know that Gabriella has 60 meters of fencing to build a four-sided fence around the land, so the length and width of the field must add up to 60 meters. This can be written as l + w = 60. To solve for the length and width of the field, we can first substitute the value for the area of the land into the equation for area: A = l x w. This equation can be rewritten as l x w = 209. We now have two equations that can help us solve for the length and width of the field.
We can solve this system of equations using substitution. We can substitute the equation l + w = 60 into the equation l x w = 209. This simplifies the equation to l x (60 - l) = 209. We can then solve for l by dividing both sides of the equation by (60 - l). This results in l = (209 / (60 - l)). We can then substitute this into the equation l + w = 60 to solve for w. This simplifies to w = (60 - (209 / (60 - l))).
Therefore, the length and width of the rectangular plot of land is (209 / (60 - l)) and (60 - (209 / (60 - l))), respectively.
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Please help me because I need to find the answer please
The difference between the number of away fans at the semi-final and at the final exists 50.
What is meant by ratios?When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion.
To determine how much larger one number is than the other, two numbers of the same unit are compared to determine their connection, which is known as a ratio.
When two quantities of the same unit are compared, the ratio is used to determine how much larger one quantity is than the other. If b is not equal to zero, it is expressed as a/b or a: b.
The number of away fans at the semifinal is
250 × 4/(6 + 4) = 250 × 4/10 = 100
(total number × ratio of a nay fans)
the number of away fans at the final is
500 × 3/(7 + 3) = 500 × 3/15 = 150
(total number × ratio of away fans)
The difference is 150 - 100 = 50
Therefore, the difference between the number of away fans at the semi-final and at the final exists 50.
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What is a surface area in math?
Answer: the amount of space covering the outside of a three-dimensional shape.
Step-by-step explanation:
What is the formula of mean method?
The formula of mean method is [tex]\frac{Sum of all values}{Number of values}[/tex].
The formula for the mean, also known as the average, is:
mean = [tex]\frac{sum of all values}{number of values}[/tex]
For example, if you have a list of numbers [1, 2, 3, 4], the mean would be calculated as follows:
mean = (1 + 2 + 3 + 4) / 4 = 10 / 4 = 2.5
The mean is a measure of central tendency that gives you an idea of the typical value in a set of numbers. It is calculated by adding up all the values in the set and dividing the sum by the number of values.
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What is domain in sets?
The set of all initial elements in ordered pairs constitutes the domain (x-coordinates).
Given that,
We have to find what us domain in sets.
We know that,
What is a domain?We learned the distinction between a relation and a function in Function Basics.
We are dealing with relationships expressed as ordered pairs in both scenarios.
The domain refers to all possible values that can be used as inputs into a relation or function.
The range refers to all of the values that are produced as the result of a relation or function.
The set of all initial elements in ordered pairs constitutes the domain (x-coordinates).
The set of all second elements in ordered pairs (y-coordinates) is the range.
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What is the equation of a line that is perpendicular to 2y 3x 1?
-2/3 is the slope of equation of a line that is perpendicular to 2y = 3x - 1.
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
We know that the equation of the line in its slope-intercept form is:
y = mx+b
Where m = slope
b = y - intercept
A line that is perpendicular to it is y = (-1/m) x + b
The slope of the perpendicular line is -1/m
Rewriting the given equation 2y = 3x - 1, we get:
y = (3/2) x - 1/2
So, the slope of the perpendicular line is the reciprocal of 3/2 which is multiplied by -1.
The slope of the line = -2/3
Therefore, the slope of a line that is perpendicular to the line whose equation is 2y = 3x - 1 is -2/3.
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The complete question is as follows:
What is the equation of a line that is perpendicular to 2y = 3x - 1?
Whats 416 divided by 3 with remainder
Answer:
416 / 3 = 128 with a remainder of 2.
Step-by-step explanation:
When 416 is divided by 3 can be expressed as 138 with a remainder of 2.
When we divide 416 by 3, the quotient represents the whole number result of the division, while the remainder represents the amount left over.
Dividing 416 by 3 gives us:
416/3 = 138 + 2/3
Quotient: 416/3 = 138
Remainder: 416/3 = 2
However, there is a remainder of 2. The remainder represents the amount that is left over after dividing as much as possible. In this case, after dividing 416 by 3, there is 2 left over that cannot be evenly divided.
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What is root 4 called?
The root 4 is called quad root.
When a number is raised to the root 4, then it is called quad root of that number as the term quad in Latin refers to 4, just the way when a number is raised to the root 2 it is called square root of that number, when a number is raised to the root 3, it is called cube root of that number.
For example, the quad root of the number 256 is (256) ^1/4 which results to 4 as the answer since 4 x 4 x 4 x 4 = 256.
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solve pls brainliest
Answer:
1/ 3
2/ 1 1/2
3/ -3
4/ 1 1/2
5/ 12
6/ 8
Step-by-step explanation:
1/2(a - 6) + a = 9
1/2a - 3 + a = 9
1 1/2a - 3 = 9
1 1/2a = 12
a= 8
prove that 1 - cosx / sinx = sinx / 1 + cosx
how?
Answer:
see explanation
Step-by-step explanation:
using the identity
cos²x = 1 - sin²x
consider the left side
[tex]\frac{1-cosx}{sinx}[/tex]
multiply numerator/ denominator by (1 + cosx)
= [tex]\frac{(1-cosx)(1+cosx)}{sinx(1+cosx)}[/tex] ← expand numerator
= [tex]\frac{1-cos^2x}{sinx(1+cosx)}[/tex]
= [tex]\frac{sin^2x}{sinx(1+cosx)}[/tex] ← cancel sinx on numerator/ denominator
= [tex]\frac{sinx}{1+cosx}[/tex]
= right side , thus proven
Consider the linear function y=5x+12y=5x+12 and the linear function represented by the table of values below.
Answer:
Step-by-step explanation:
y intercept = 12 the one with no x
use process of elimination
function=straight line
I need some help understanding these questions, is there anyone willing to help? I'd really appreciate it!
Consider how the structure of the standard form of a linear function
reveals its key characteristics.
For the equation Ax + By = C , determine the slope, x -intercept,
and y -intercept.
Which form of a linear equation is more efficient for determining each characteristic?
- Slope
- x -intercept
- y -intercept
Answer:
Slope: slope-intercept form, point-slope form, or slope formX-intercept: intercept form, standard formY-intercept: slope-intercept form, intercept formStep-by-step explanation:
You want to know how the form of a linear equation can be used to reveal its key characteristics.
Key CharacteristicsThe characteristics of a linear equation that are of interest for this problem are ...
slopex-intercepty-interceptForms of a linear equationA linear equation can be written in many forms. Some of these forms make it easy to determine one or more of the key characteristic listed above. Some of the more common forms are Slope-Intercept form, Point-Slope form, and Standard form. There are a number of others.
Slope-Intercept formThe slope-intercept form is ...
y = mx + b
where m is the slope, and b is the y-intercept. This form makes it easy to determine ...
slopey-interceptThis equation cannot be used to describe a vertical line.
Alternate Slope-Intercept formWe can rearrange the above equation to reveal the x-intercept.
y = m(x -a)
where m is the slope and 'a' is the x-intercept. This form makes it easy to determine ...
slopex-interceptThis equation cannot be used to describe a horizontal line (except y=0).
Point-Slope formThe equation of a line with slope m through point (h, k) can be written as ...
y -k = m(x -h)
This makes it easy to determine ...
slopea point on the line (not necessarily an intercept)This equation cannot be used to describe a vertical line.
Standard formThe standard form equation of a line is similar in style to the standard form equations for other geometric figures (circle, ellipse, hyperbola). This form is ...
Ax +By = C
where A, B, C are mutually prime (integers), and A ≥ 0. If A = 0, then B > 0. That is, the leading coefficient is positive. Integers are preferred for the coefficients, but some lines have irrational slope or other key characteristics, so integers may not be able to be used in all places.
The key characteristics cannot be read from the equation directly, but they are one step away:
slope = -A/Bx-intercept = C/Ay-intercept = C/BSolving for the intercepts is especially easy, so we list this form as one that can be efficient for determining the intercepts.
Intercept formA very nice form for efficiently determining the intercepts, or efficiently writing an equation from the intercepts is ...
x/a +y/b = 1
where 'a' is the x-intercept, and 'b' is the y-intercept. This form makes it very easy to determine ...
x-intercepty-interceptYou may notice that dividing the standard form equation by C and rearranging the coefficients will give you this form:
Ax +By = C
(A/C)x +(B/C)y = 1 . . . . . . . divide by C
x/(C/A) +y/(C/B) = 1 . . . . . . . intercept form
General formThe general form of a polynomial equation of any degree is ...
f(x, y) = 0
The general form of a linear equation is ...
Ax +By +C = 0
This is simply a rearrangement of the Standard form equation. Equations written in this form can be helpful for ...
finding the distance from a point to the linesolving a system of equations by "addition" or matrix methodsVarious 2-Point formsWhen two points are given, and you want an equation of the line, various forms are available for using those coordinates. These forms make use of the fact that the slope of a line is the same everywhere, so the ratio of any difference of y-coordinates to the corresponding difference of x-coordinates is a constant (the slope). Again, slopes of 0 or "undefined" can cause trouble with certain of these forms. Here are several different arrangements of 2-point forms:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)\\\\(x_2-x_1)(y-y_1)=(y_2-y_1)(x-x_1)\\\\\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}=m\qquad\text{Slope form}\\\\\\\dfrac{x-x_1}{y-y_1}=\dfrac{x_2-x_1}{y_2-y_1}\qquad\text{inverted from the above}\\\\\\\dfrac{y-y_1}{y_2-y_1}=\dfrac{x-x_1}{x_2-x_1}[/tex]
The last three "ratio forms" are variations of each other. Any such proportion can be written 4 ways. (3 are shown) The form not shown has the variables in the denominator, which is usually not useful.
All of these forms can be written in a "general form" by subtracting one side.
The slope can be read directly from the 1st and 3rd of the forms shown here. It is m = (y2-y1)/(x2-x1).
The slope form is useful for determining ...
slopeDeterminant formAnother 2-point form is one written as a determinant:
[tex]\left|\begin{array}{cc}x-x_1&x_2-x_1\\y-y_1&y_2-y_1\end{array}\right|=0[/tex]
__
Additional comment
It can be useful to recognize the various forms and their relationship to known points on the line or other key characteristics of the function. Any of the slope or point-slope forms make it easy to write the equations of parallel or perpendicular lines through a given point. (The standard and general forms can be used for this, too.)
zhi noticed that an odd number had appeared eight times in a row on the following roulette table. she now felt very strongly that an even number would be next. on a single spin, the probability of getting an even number is 18 over 38. considering the last eight spins resulted in odd numbers, what is the probability of getting an even number on the next spin? a.) 18 over 38 because each spin is independent. b.) 0 because each spin is independent. c.) 8 over 38 because each spin is dependent. d.) 1 over 38 because each spin is dependent.
The probability of getting an even number on the next spin is a.) 18 over 38 because each spin is independent.
Probability is honestly how possibly some thing is to happen. Whenever we are uncertain approximately the final results of an occasion, we are able to communicate approximately the chances of positive outcomes—how possibly they are. The evaluation of occasions ruled via way of means of possibility is referred to as statistics. Probability is calculated via way of means of dividing the quantity of methods the occasion can arise via way of means of the overall quantity of outcomes. Probability and odds are one-of-a-kind concepts. Odds are the possibility that some thing occurs divided via way of means of the possibility that it would not happen.
Thus, the correct option is a.
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Name:
IP: ACP Rev
1. A downtown shop rents scooters for a one-time
cost of $20.50 plus $7.50 per hour. Which equation
can be used to find y, the total cost that a group of
people must pay to rent x scooters for 8 hours?
The Total Cost that people must pay to rent x scooters is given by the equation y = 80.5x
What is Linear Equation in Two Variables?
A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.
Solution:
Total Cost = y
Number of Scooters Rented = x
y = (20.5$ + 7.5*8 $)x
y = (20.5 + 60)x
y = 80.5x
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What is it called when you do 1 2 3 4?
Natural Numbers The numbers we use to count or arrange are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Whole Numbers the sum of natural numbers and zero. not a fraction or decimal.
what is counting ?The counting-on method can be used by mathematicians to add numbers. With this approach, a student first adds the larger number, then "counts on" with the other addends to arrive at the sum. If the number sentence is 4 + 3, the student will understand that 4 is the greater number and will add three additional numbers, such as the integers "4... 5, 6, 7."
here ,
For those of you who are not aware with this series, it indicates that the sum of all natural numbers, i.e., 1, 2, 3, 4, and so on, up to infinity .
Is equal to -1/12 and has come to be known as the Ramanujan Summation .
Whole Numbers the sum of natural numbers and zero. not a fraction or decimal.
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Solve 13t+ 6| = 9
A. n = -5
B. n = 1
C. n = -1 or 1
D. n = -5 or 1
Answer: t 13/3 ≈0.230769231
Step-by-step explanation:
solve factored. was she correct??
Answer:
No, she is wrong
Step-by-step explanation:
(4x - 6)^2 can be write as
(4x -6) ( 4x-6)
16x^2 - 24x -24x + 36
16x^2 -48x + 36
So, she is wrong!
Hey there!
(4x - 6)^2
= (4x - 6)(4x - 6)
FACTOR/DISTRIBUTE
= 4x(4x) + 4x(-6) - 6(4x) - 6(-6)
SIMPLIFY
= 16x^2 - 24x - 24x - 36
COMBINE the LIKE TERMS
= 16x^2 - 48x - 36
Therefore, the answer should be:
16x^2 - 48x - 36
Therefore, your answer should be: “No, because the equation should’ve been 16x^2 - 48x - 36. She didn’t factor the equation correctly”
Good luck with your assignment & enjoy your day!
~Amphitrite1040:)
John wants to purchase at least 4 books and 5 notebooks from a stationery shop. The
cost of each book is $8 and the cost of each notebook is $4. Which inequality correctly
represents the minimum amount of money he should carry?
The inequality that represents the minimum amount of money he should carry is 4x+5y ≥ 52
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
Let x be the cost of each books
Let y be the cost of each notebook
Cost of 4 books = $32
Cost of 5 notebooks = $20
Total cost = 32+20 = $52
At least shows the inequality ≥
So, the inequality that represents the minimum amount of money he should carry is
4x+5y ≥ 52
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What will be the median of the given data if the mean is 4.5 5 7 7 8 a 5 4 3 1 2?
The median for a given set of observations is 4.
What is mean?The mean is the average of a set of variables in mathematics and statistics. The mean may be calculated in a variety of methods, including the simple arithmetic mean (add the numbers and divide the total by the number of observations), geometric mean, and harmonic mean. A data set's mean (average) is calculated by summing all of the numbers in the set and then dividing by the number of values in the set. When a data collection is arranged from least to largest, the median is the midway value. The mode is the number that appears the most frequently in a data collection.
Here,
given set of observation,
=5,7,7,8,a,5,4,3,1,2
4.5=(5+7+7+8+a+5+4+3+1+2)/10
45=42+a
a=3
median=5,7,7,8,3,5,4,3,1,2
=1,2,3,3,4,5,5,7,7,8
median=10/2
=5th term
=4
The median for given set of observation is 4.
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How to learn maths fast?
Learning mathematics quickly requires dedication and hard work.
What is mathematics?
Mathematics is the science of numbers, shapes, and patterns. It is used to describe and explain the physical world and to solve problems. Mathematics is a language that helps us to understand and communicate ideas. It is a tool used to organize and understand data, determine relationships, and make predictions.
According to the given question:
The first step to learning math quickly is to determine your level of understanding. It is important to identify any weaknesses in order to develop a plan to improve them. Once the strengths and weaknesses are identified, it is important to set realistic goals and to create an action plan to reach those goals.
It is also important to find a good tutor or mentor to help guide the learning process. A tutor or mentor can provide guidance, resources, and practice problems to help increase understanding of the subject. Additionally, they can help identify problem areas and provide feedback that can help improve learning.
Finally, it is important to take advantage of online resources. There are many online tutorials, websites, and videos that can help improve the learning process.
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What is a transformation in math grade 7?
A transformation in mathematics is a process of manipulating a polygon.
A transformation in maths is nothing but a process that manipulates a polygon or any other two-dimensional object on a plane or coordinate system. A transformations describe how two-dimensional figures move around a coordinate system.
The original shape of the object before any transformation is called the Pre-Image and the final shape and position of the object is called as the Image.
In mathematics, there are five different transformations:
Dilation, Reflection, Rotation, Shear and Translation
Therefore, transformation is a process of manipulating a polygon.
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What are the 3 triangle similarity theorems?
Triangle similarity theorems are essential to geometry and can be used to compare two triangles. The three triangle similarity theorems are:
Side-Side-Side (SSS) Similarity TheoremAngle-Angle-Side (AAS) Similarity TheoremAngle-Side-Angle (ASA) Similarity Theorem3 Triangle similarity theoremsThe Side-Side-Side (SSS) Similarity Theorem: If the three sides of one triangle are proportional to the three sides of a second triangle, then the two triangles are similar. The Angle-Angle-Side (AAS) Similarity Theorem: If two angles of one triangle are equal to two angles of a second triangle, and the included side of the first triangle is proportional to the included side of the second triangle, then the two triangles are similar. The Angle-Side-Angle (ASA) Similarity Theorem: If two angles of one triangle are equal to two angles of a second triangle, and the sides between them are proportional, then the two triangles are similar.Learn more about similar triangles: https://brainly.com/question/14285697
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Is √ 3 is polynomial or not?
Yes, 3x² is a polynomial, but a special form of a polynomial with just one term which is called monomial.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given expression is 3x².
In the given expression three times of x square, x is the variable.
For an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions.
Yes, this is a polynomial, but a special form of a polynomial with just one term which is called monomial.
Hence, 3x² is a polynomial.
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(0,-9);r=9 find the equation for the circle
Answer: x^2 + y^2 + 18y + 81 = 0
Step-by-step explanation:
The equation of a circle with center at the point (0, -9) and radius 9 is given by the following equation:
(x - 0)^2 + (y + 9)^2 = 9^2
This can be simplified to the following:
x^2 + y^2 + 18y + 81 = 0
This is the equation of a circle with center at (0, -9) and radius 9.
JS 19. Evaluate the integral || curlĒ dĞ using Stoke’s Theorem, where F =-yi+xj+ryck and S is the part of the sphere r2 + y2 + 22 = 4 that lies above the cy-planes, oriented upward. A. 27 B. 0 C. 87 D. -87 E. 47
The integral || curl F || dĞ is equal to -2. The correct answer is therefore option D that is -87.
To evaluate the integral || curl F || dĞ using Stoke's Theorem, we need to find a vector field F and a surface S such that the boundary of S is a closed curve C and the integral is equal to the flux of the curl of F through S. Using the given information, we can find the components of F as:
F = (-y, x, r)
The curl of F is given by:
curl F = (0, 0, 1)
The surface S is the part of the sphere r2 + y2 + z2 = 4 that lies above the cy-planes, oriented upward. This surface can be parameterized by:
x = rcosφcosθ
y = rcosφsinθ
z = rsinφ
where 0 ≤ φ ≤ π and 0 ≤ θ ≤ 2π.
The boundary of S is the curve C, which is the intersection of the sphere and the cy-plane. This curve can be parameterized by:
x = rcosθ
y = rsinθ
z = 0
where 0 ≤ θ ≤ 2π.
Using Stoke's Theorem, the integral || curl F || dĞ is equal to the flux of curl F through S, which is given by:
∫|| curl F || dĞ = ∫curl F · ndC
where n is the unit normal vector to the surface S.
Substituting the expressions for curl F and the parameterizations of S and C, we get:
∫|| curl F || dĞ = ∫(0, 0, 1) · (cosφcosθ, cosφsinθ, sinφ)dC
= ∫(sinφ)dC
= ∫sinθdθ
= [-cosθ]θ=0θ=2π
= -2
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Statistics question
Walmart claims that their checkout scanners correctly price 98.9% of the items sold. How many items would you expect to buy, on average, to find one that scans incorrectly? Round your answer up to the next integer
a) 2
b) 91
c) 99
d) 500
e) 989
Answer:
(b) 91
Step-by-step explanation:
The probability of an item scanning correctly is 98.9%, so the probability of an item scanning incorrectly is 1 - 98.9% = 1.1%.
The expected number of items to buy to find one that scans incorrectly is 1 / 1.1% = 91. This means that you would expect to buy 91 items on average to find one that scans incorrectly.
Rounding up to the next integer, the answer is 92. Therefore, the correct answer is (b) 91.
Find the perimeter of the triangle
(21-x) in.
(2x - 3) in.
(x + 5) in.
The Perimeter of the triangle is 23+2x in³
We know that formula of the Perimeter of the triangle is:
Perimeter= A+B+C
where A=(21-x)in.
B=(2x-3)in.
C=(x+5)in.
Solution:
Perimeter = (21-x)+(2x-3)+(x+5)
Perimeter = (18+x)+ (x+5)
Perimeter = 23+2x in³
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How do you solve a slope step by step?
In order to calculate the slope, m, one can use either the classic line equation, y = mx + b, or the slope formula, [tex]m = (y_{2} -y_{1} )/(x_{2} - x_{1} )[/tex]. The slope can be calculated or discovered through observation.
How do you calculate slope step by step?When a straight line's equation is not available, determining its slope involves three stages. Determine the first two points on the line. Choose one to be (x1, y1) and the other to be in step two (x2, y2). Step three is to compute slope using the slope equation.
If you have the coordinates of two points on a line, you can use the slope formula to determine that line's slope. The slope equation is given by [tex]m=(y_{2}- y_{1} )/(x_{2} -x_{1} )[/tex], which is the ratio of the change in the y values to the change in the x values. x1 and y1 are the coordinates of the first point. A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
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Find the 81st term of the arithmetic sequence 8,7,6
16. Write and solve an equation to find two consecutive odd integers such that their sum is twenty.
Answer:
9 and 11
Step-by-step explanation:
there is a difference of 2 between consecutive odd integers.
let n and n + 2 be the integers , then
n + n + 2 = 20
2n + 2 = 20 ( subtract 2 from both sides )
2n = 18 ( divide both sides by 2 )
n = 9
and n + 2 = 9 + 2 = 11
the two consecutive odd numbers are 9 and 11