Anοther system οf linear equatiοns with the same number οf sοlutiοns is 12x + 51y = 156
24x + 102y = 312
What is linear equatiοn?A linear equatiοn is a mathematical equatiοn that describes a straight line in a twο-dimensiοnal space. It is an equatiοn that has οnly οne independent variable and οne οr mοre cοefficients that represent the slοpe and intercept οf the line.
The general fοrm οf a linear equatiοn is: y = mx + b
Where: y is the dependent variable x is the independent variable
m is the slοpe οf the is the y-intercept
Accοrding tο the questiοn:
Tο determine whether this system οf equatiοns has οne sοlutiοn, nο sοlutiοns, οr infinitely many sοlutiοns, we can use variοus methοds such as substitutiοn οr eliminatiοn. Here, we'll use the eliminatiοn methοd:12x + 51y = 156-8x - 34y = -104
Tο eliminate οne οf the variables, we need tο find a cοmmοn multiple οf the cοefficients οf x οr y in bοth equatiοns. In this case, the cοmmοn multiple is 17, because 51 and -34 have 17 as a cοmmοn factοr:12x + 51y = 156 (multiply by 2)-16x - 68y = -208 (multiply by 2)
Nοw, we can add the twο equatiοns tο eliminate
y:12x + 51y = 156-16x - 68y = -208---------------4x - 17y = -52
We can sοlve fοr y in terms οf x:-4x - 17y = -5217y = -4x + 52y = (-4/17)x + 52/17This is the equatiοn οf a line in slοpe-intercept fοrm, with slοpe -4/17 and y-intercept 52/17.
We can alsο write anοther system οf equatiοns with the same number οf sοlutiοns that uses the first equatiοn οnly by multiplying bοth sides οf the equatiοn by a cοnstant
12x + 51y = 156
24x + 102y = 312
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difference between twice a number and another number is 8, find the minimul product between the two numbers as well as the two numbers
The minimum product between the two numbers is 0 and the two numbers are 4 and 0.
here 1st number is x
and 2nd number is y
and the difference between twice a number and another number is 8 so 2x-y = 8
minimum value of
xy
= x(2x-8)
here the eqn is x(2x-8)
and we have to find its minima
If we have a formula expressed as y= ax2+bx+c , we can find the minimum of the quadratic equation according to the following formula: The minimum value is min= c-b2 /4a.
and the minima is at x=4
here the minimum value will be 0
so either value of x=0 or x= 4;
first number is 4 and second is 0
and product of x*y = 0;
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What is the solution, if any, to the inequality |3x| >=0?
Answer:
Step-by-step explanation:
The inequality |3x| >= 0 simply states that the absolute value of 3x must be greater than or equal to zero.
Since the absolute value of any number must always be non-negative, this inequality is always true. That means any real number x satisfies the inequality |3x| >= 0.
Therefore, the solution to the inequality |3x| >= 0 is x ∈ R, where R represents the set of all real numbers.
In an orthonormal coordinate system, what are the coordinates of all the points generated from (x, y, z) by repeatedly applying the following operations? (a) A mirror whose plane is perpendicular to the y-axis, and that passes through the origin. (b) A four-fold rotation whose axis is coincident with the x-axis, and that passes through the origin. (c) A 4 rotoinversion whose axis is coincident with the x-axis, and that passes through the origin. (d) A three-fold rotation whose axis passes through the origin and the point (1,1,1). (e) A 3 rotoinversion whose axis passes through the origin and the point (1, 1, 1).
The coordinates of all the points generated from (x, y, z) by repeatedly applying the operations in the order given are: (a) (x, -y, z); (b) (x, y, -z); (c) (-x, y, -z); (d) (-x, z, y); and (e) (x, -z, -y).
For (a), a mirror perpendicular to the y-axis and passing through the origin reflects the coordinates in the y-axis, so the new coordinates will be (x, -y, z).
For (b), a four-fold rotation whose axis is coincident with the x-axis and passing through the origin rotates the coordinates around the x-axis by 90 degrees, so the new coordinates will be (x, y, -z).
For (c), a 4 roto inversion whose axis is coincident with the x-axis and passing through the origin inverts the coordinates in the x-axis, so the new coordinates will be (-x, y, -z).
For (d), a three-fold rotation whose axis passes through the origin and the point (1,1,1) rotates the coordinates around the axis by 120 degrees, so the new coordinates will be (-y, -z, x).
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A pie chart should always show both the sum of all the pie pieces along with the data that comprise the pie slices.
True or False
The ideal pie charts should always show both the sum of all the pie elements along with the data that constitute the pie slices. Thus the statement in the question is true.
The circle diagram, often known as a pie chart, pie chart, or pie chart, is used to depict qualitative or discrete information. It is used to display the percentage of each variable's values' constituent parts.
To do this, divide the circle into sections proportionate to the relative frequency. Recognize the area of the circle that corresponds to each possible value of the variable as a component. It is characterized as an "exploded cake graph" because it divides the graph into its many components in order to shift one of the portions.
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Which of the following python methods can be used to perform simple...
Which of the following python methods can be used to perform simple linear regression on a data set? Select all that apply.
Question 3 options:
A. linregress method from scipy module
B. simplelinearregression from scipy module
C. ols method from statsmodels module
The python methods that can be used to perform simple linear regression on a data set are -
A. linregress method from scipy module
C. ols method from statsmodels module
The linregress method from the module is the most simplest and effortless method for performing simple linear on the data set. It consists of two arrays one represents the independent variables and the second represents the dependent variables.
The relationship between two variables can be modeled using simple linear regression, where the first variable is treated as the independent variable and the other as the dependent variable. Finding the line of best fit that lowers the squared sum of the residuals is the goal.
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A die with six faces has the number 1 painted on three of its faces, the number 2 painted on two of its faces, and the number 3 painted on one face. Assume that each face is equally likely to come up.
(a) Find the sample space for this experiment.
(b) Find P(odd number).
(c) If the die were loaded so that the face with the 3 on it were twice as likely to come up as each of the other five faces:
(i) Find the probability of the single events.
(ii) Find P(even number).
Assuming that each face is equally likely to come up.
(a) The sample space for this experiment = {1, 2, 3}
(b) P(odd number) = 2/3
(c) If the die were loaded so that the face with the 3 on it was twice as likely to come up as each of the other five faces:
(i) The probability of the single events, P(3) = 2/7
(ii) P(even number) = 1/3
(a) The sample space for this experiment is the set of all possible outcomes, which are the numbers 1, 2, and 3 that can appear on the face of the die.
Sample space = {1, 2, 3}
(b) To find the probability of getting an odd number, we need to find the probability of getting a 1 or a 3. There are 3 faces with the number 1 and 1 face with the number 3, so there are 3 + 1 = 4 faces that result in an odd number. There are 6 faces total, so the probability of getting an odd number is 4/6 = 2/3.
P(odd number) = 2/3
(c)
(i) If the die were loaded so that the face with the 3 on it was twice as likely to come up as each of the other five faces, then each of the other five faces would have a probability of 1/7 of coming up, and the face with the 3 on it would have a probability of 2/7 of coming up.
P(1) = P(2) = 1/7
P(3) = 2/7
(ii) To find the probability of getting an even number, we need to find the probability of getting a 2. There are 2 faces with the number 2, so there are 2 faces that result in an even number. There are 6 faces total, so the probability of getting an even number is 2/6 = 1/3.
P(even number) = 1/3
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In Exercises 19 and 20, choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions. Give separate answers for each part. 19. x1 +hx2 = 2 4x1 + 8x2 =k 20. X1 – 3x2 = 1 2x +hx2 = k
The equations must intersect at a single point then it have the unique solution and the value of h and k are h = -1 and k = 6
A system has no solution if the equations are inconsistent, meaning there is no way to satisfy both equations simultaneously. It has a unique solution if the equations intersect at a single point, meaning there is only one set of values that satisfies both equations.
Let's take a look at the first system of equations, 19.
Equation 1: x + hx = 2
Equation 2: 4x + 8x = k
For the system to have no solution, the equations must be inconsistent. This means they must be parallel and never intersect. To achieve this, we can set the slopes of the lines to be equal but the y-intercepts different. In other words, we need to choose h and k such that:
h = -2 and k = 5
Substituting these values into the equations, we get:
Equation 1: x - 2x = 2
Equation 2: 4x + 8x = 5
You can see that these two equations do not have a common solution. They are inconsistent, meaning there is no point that satisfies both equations.
For the system to have a unique solution, the equations must intersect at a single point. This means the slopes and y-intercepts must be different. To achieve this, we can choose h and k such that:
h = -1 and k = 6
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Minka pours cup of milk on her oatmeal each day
for 7 days. Complete the number line. Draw a point
and write the number of cups that Minka pours as a
mixed number.
The number of cups of milk that Minka pours as a mixed number is found in the attached image.
What is the total number of cups of milk that Minka pours into her oatmeal?The total number of cups of milk that Minka pours into her oatmeal is calculated as follows:
First day = 1/4
Second day = 1/4 + 1/4
Second day = 2/4
Third day = 1/4 + 2/4
Third day = 3/4
Fourth day = 1/4 + 3/4
Fourth day = 4/4 or 1
Fifth day = 5/4 or 1/4 + 1
Fifth day = 1 1/4
Sixth day = 1/4 + 5/4
Sixth day = 1 1/2
Seventh day = 1/4 + 6/4
Seventh day = 7/4 or 1 3/4
Eight day = 1/4 + 7/4
Eight day = 8/4 or 2
The completed number line is found in the attached image
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. Order the following numbers from least to greatest: 3√2 , √3 − 1, √19 + 1, 6,
2√10 ÷ 5 and √14.
pls someone help me
The required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6
What is ascending order?An arrangement of numbers in which the numbers are arranged from smallest to greatest numbers is called ascending order.
Given that, some numbers, 3√2, √3 − 1, √19 + 1, 6, 2√10 ÷ 5 and √14.
We need to order them from least to greatest,
3√2 = 4.24
√3 − 1 = 0.73
√19 + 1 = 5.35
6
2√10 ÷ 5 = 1.26
√14 = 3.74
The order from least to greatest is :-
0.73, 1.26, 3.74, 4.24, 5.35 and 6
i.e.
√3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6
Hence, the required order from least to greatest is √3 − 1, 2√10 ÷ 5, √14, 3√2, √19 + 1 and 6
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Suppose that $2000 is invested at a rate of 5.3%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 9 years.
Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
Rounding to the nearest cent, the total amount after 9 years is $3182.67.
Step-by-step explanation:
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
where:
A = final amount
P = principal amount (initial investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years
In this case, P = 2000, r = 0.053, n = 2 (compounded semiannually), and t = 9.
Plugging in these values, we get:
A = 2000(1 + 0.053/2)^(2*9)
= 2000(1.0265)^18
≈ 3182.67
Rounding to the nearest cent, the total amount after 9 years is $3182.67.
If interest is compounded once every 12 months, how often is it compounded?
A) Monthly
B) Annually
C) Semiannually
D) Quarterly
Answer:
B) Annually
Step-by-step explanation:
If interest is compounded once every 12 months, it is compounded annually.
Answer:
B) Annually
Step-by-step explanation:
What does compounded mean?Compounded means to calculate interest on the borrowed amount and on previous interest.
What does monthly mean?Monthly means to be done one every month.
What does annually mean?Annually means to be done yearly or every year.
What does semiannually mean?Let's break this down. Semi means half or a partial of something. Annually, as we already discussed, means yearly or every year. Now, when we put it together, it creates half a year. So, semiannually means half a year.
What does quarterly mean?We know a quarter, as in, the coin, is 25 cent. if we multiply 25 cents by four, we get a dollar. So a quarter coin is one fourth, or, a quarter of a dollar. Now, applying that to years, since a year is twelve months and a quarter is one fourth, we can divide twelve by four to get three. Three months is one quarter of a year.
With this in mind, twelve months is equal to a year. So, the interest is compounded every year.
A is incorrect because it says monthly. We have already figured out that the interest is compounded yearly, so it is incorrect.
B is correct because the definition of Annually is yearly or every twelve months.
C is incorrect because semiannually means half or part of a year, not a full year.
D is incorrect because quarterly means one fourth of a year, or, three months.
You moved 5 units north, 3 units west, and ended at point D.
Where did you begin?
A) Point E
B) Point A
C) Point B
D) Point D
The required point of the beginning is given as Point A. Option B is correct.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph. while the coordinate x is called abscissa and the coordinate of the y is called ordinate.
When you move 5 units north, you increase the y-coordinate by 5. When you move 3 units west, you decrease the x-coordinate by 3. So, if you start at an unknown point and move 5 units north and 3 units west, your final position would be at a point with the coordinates (x - 3, y + 5).
Since you ended at point D, and the final coordinates are not given, we cannot determine the starting point without more information.
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find the rank, nullity, and bases of the range spaces and null spaces for each of the following matrices. you must show your work, or explain your thought process; a correct numerical answer is not sufficient.
If A is a matrix of order m × n, then
Rank of A + Nullity of A = Number of columns in A = n
Now, According to the question:
What is rank nullity theorem and range?The rank-nullity theorem states that the dimension of the domain of a linear function is equal to the sum of the dimensions of its range (i.e., the set of values in the codomain that the function actually takes) and kernel (i.e., the set of values in the domain that are mapped to the zero vector in the codomain).
What is range and null space of a matrix?The range null-space decomposition is the representation of a vector space as the direct sum of the range and the null space of a certain power of a given matrix.
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The given question is incomplete,
So, The question is:
What is rank nullity theorem and range and null space ?
When finding the quotient of 5016 divided by 11, Issac first divides 50 by 11 as shown. What value does the digit 4 have in the quotient?
Answer:
I'm not sure, but the quotient is divided, so 5016/11
Step-by-step explanation:
5016/11, and then 50/11, and find out the answer.
The average height and average weight of five students are presented in the table. Height (in cm) Weight (in kg) Student 1 172 62 Student 2 173 65 Student 3 175 64 Student 4 176 66 Student 5 177 65 The calculation for the correlation, r, for this set of five students is __________. Answer choices are rounded to the hundredths place.
The correlation coefficient for this set of five students is approximately 0.95.
How to calculate the correlation coefficient (r) for this set of data.
First we can use the formula:
r = [nΣ(xy) - ΣxΣy] / [√{nΣx^2 - (Σx)^2} √{nΣy^2 - (Σy)^2}]
Where
n is the sample size Σ represents the sum x and y are the variables of interest (in this case, height and weight)xy represents the product of x and y for each observationUsing the values given in the table, we can calculate the necessary sums and products:
n = 5
Σx = 173 + 172 + 175 + 176 + 177 = 873
Σy = 62 + 65 + 64 + 66 + 65 = 322
Σx^2 = 173^2 + 172^2 + 175^2 + 176^2 + 177^2 = 150367
Σy^2 = 62^2 + 65^2 + 64^2 + 66^2 + 65^2 = 20410
Σ(xy) = (172)(62) + (173)(65) + (175)(64) + (176)(66) + (177)(65) = 56209
Plugging these values into the formula for r, we get:
r = [5(56209) - (873)(322)] / [√{5(150367) - (873)^2} √{5(20410) - (322)^2}]
Simplifying the numerator and denominator:
r = [281045 - 280506] / [√{5(150367) - (873)^2} √{5(20410) - (322)^2}]
r = 0.95 (rounded to the hundredths place)
Therefore, the correlation coefficient for this set of five students is approximately 0.95.
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[tex]\sqrt{8} \sqrt{3}[/tex]
We can write the equivalent value of the root expression √8√3 as 2√6.
What is square root of a number?The square root of a number is given by -
y = √x
y² = x
More specifically, we can write -
y = ± √x
Given is the root expression as -
√8√3
We can solve the expression as by finding the square roots of the numbers as -
√8√3 = √8 x √3
√8√3 = √(2 x 2 x 2) x √3
√8√3 = 2√2 x √3
√8√3 = 2√6
So, we can write that -
√8√3 = 2√6
Therefore, we can write the equivalent value of the root expression √8√3 as 2√6.
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i need help with this
Can use anyones help asap
Answer: 2
Step-by-step explanation:
D. Erin has two dogs, a beagle and a Great Dane. Her Great Dane weighs twice as much as the beagle plus 2 more pounds. If the Great Dane weighs 72 pounds, how much does the beagle weigh?
The weight of the beagle D. Erin has weighs 35 pounds.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information, Let the weight of the beagle is 'x'.
So, the weight of a Great Dane is (2x + 2) pounds.
Therefore, 2x + 2 = 72.
2x = 70.
x = 35 pounds.
So, The beagle weighs 35 pounds.
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Are the two triangles similar? How do you know?
A.)no
B.)yes; by AA
C.)yes; by SAS
D.)yes; by SSS
Answer:
No
Step-by-step explanation:
At least two sides will have to be the same.
Please assist,
2. Determine the scale factor of a dilation that maps Circle A onto a circle congruent to Circle B.
3. Determine the scale factor of a dilation that maps Circle C onto a circle congruent to Circle A.
4. Explain the relationship between dilations and similar figures
2. Scale factor of a dilation that maps Circle A onto a circle congruent to Circle B is: 4/3 . 3. Scale factor of a dilation that maps Circle C onto a circle congruent to Circle A is 1/2.
What is transformation?By rotating, reflecting, or translating a shape on a coordinate plane, a transformation is made. Transformational geometry, a fresh viewpoint on geometry, was first forth by Felix Klein in the 19th century.
The majority of geometric proofs rely on how objects change. Using transformations, we can change any image in a coordinate plane. By using transformational logic, it is possible to comprehend video game graphics more fully.
From the given figure we see that:
Diameter of A = 8
Diameter of B = 6
Diameter of C= 4
2. Scale factor of a dilation that maps Circle A onto a circle congruent to Circle B is:
8/6 = 4/3
3. Scale factor of a dilation that maps Circle C onto a circle congruent to Circle A is:
4/8 = 1/2
4. When a figure is dilated the new figure is similar to the pre-image. The segments, sides, edges, of the new image is dilated by scale factor.
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Reflect (9, 3) across the y-axis.
Then reflect the result across the x-axis.
What are the coordinates of the final point?
The area of a rectangle is given by the equation 2L^2+L=45, in which L is the rectangle's length. What is the length of the rectangle?
Answer:
L = 4.5
Step-by-step explanation:
You can rewrite the equation as 2L^2 + L - 45 = 0 and then solve using the quadratic formula
L = (-1 plus or minus the sq root of 361) / 4
L = (-1 plus or minus 19) / 4
L = -5 or 4.5 but lengths can't be negative so the length is 4.5
Mr. Utivich needs to buy an equal number of canvasses and paint sets for a community center art class. Each canvas costs $4 and each paint set costs $7.25. If he has $120 to spend on the art supplies, then the inequality 4x+7.25x≤120
can be used to find the number of each item he can buy. How much money will he have left after buying the greatest number of canvasses and paint sets?
Answer:
Step-by-step explanation:
23x
Which equation represents the function?
The equation from the graph of the function is g(x) = |x - 1|
How to determine the equation from the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the function
The function is an absolute value function
The parent function of an absolute value function is:
y = |x|
The function y = |x| is shifted right by 1 units
Using the above as a guide, we have the following:
g(x) = f(x - 1)
This represents a translation to the right by 1 unit
So, we have
g(x) = |x - 1|
Hence, the translation is g(x) = |x - 1|
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Of the people in Maddie's family, 11 have been to Europe and 7 have been to Australia. 5 people have been to both Europe and Australia. How many people have been to Australia but not Europe?
Applying the knowledge of sets, the number of people that have been to Australia but not Europe is calculated as: 2.
How to Use Sets to Solve Word Problems?Let's call the number of people who have been to Europe "E" and the number of people who have been to Australia "A". We know that:
E = 11
A = 7
We also know that 5 people have been to both Europe and Australia, so they are counted in both E and A:
E = 11
A = 7
E ∩ A = 5
To find the number of people who have been to Australia but not Europe, we can use the formula:
A - (E ∩ A) = A - 5 = 7 - 5 = 2
Therefore, the 2 people have been to Australia but not Europe.
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The following table gives the probability distribution of a discrete random variable X. Use the table to find
the following probabilities. Round solutions to three decimal places, if necessary.
The probability of the different discrete random variable X are;
a) P(x = 3) = 0.12
b) (P x ≤ 2) = 0.239
c) P(x ≥ 1) = 0.947
d) P(1 ≤ x ≤ 4) = 0.493
How to solve Probability distribution of a Discrete Random Variable?a) The probability expressed as P(x = 3) from the table is;
P(x = 3) = 0.12
b) The probability expressed as (P x ≤ 2) is;
(P x ≤ 2) = P(x = 2) + P(x = 1) + P(x = 0)
= 0.093 + 0.093 + 0.053
= 0.239
c) The probability expressed as P(x ≥ 1) is;
P(x ≥ 1) = P(x = 6) + P(x = 5) + P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1)
P(x ≥ 1) = 0.267 + 0.187 + 0.187 + 0.12 + 0.093 + 0.093
P(x ≥ 1) = 0.947
d) The probability expressed as P(1 ≤ x ≤ 4) is;
P(1 ≤ x ≤ 4) = P(x = 4) + P(x = 3) + P(x = 2) + P(x = 1)
= 0.187 + 0.12 + 0.093 + 0.093
= 0.493
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Find the quotient. 1/4 2 2/3
if a coin is tossed thrice successively, what is the probability of obtaining at least one head and at least one tail?'
The probability of obtaining at least one head and at least one tail when a coin is tossed thrice successively is 7/8.
In probability theory, the likelihood of a particular event occurring is measured in terms of probability. When it comes to tossing a coin, there are two possible outcomes: heads or tails.
To calculate the probability of obtaining at least one head and at least one tail when a coin is tossed thrice successively, we need to use the concept of complementary events. Complementary events are two events that make up the whole sample space
Let's first calculate the probability of not getting at least one head and at least one tail. The only way to not get at least one head and at least one tail is to get either three heads or three tails. The probability of getting three heads or three tails in a row is (1/2)³ or 1/8 since there are 8 possible outcomes when a coin is tossed thrice successively.
Now we can calculate the probability of obtaining at least one head and at least one tail by subtracting the probability of not getting at least one head and at least one tail from 1.
1 - 1/8 = 7/8
Therefore, the probability of obtaining at least one head and at least one tail when a coin is tossed thrice successively is 7/8.
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C. What does this slope tell you about the relationship between lengths and width: of rectangles with perimeter 24?
Using linear function, the slope of -1 means that when one of the ratio of dimension is increased by 1, the other is decreased by 1.
What is a linear function?A linear function is modeled by:
y = mx + b
Here, m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
Also shown as b is the y-intercept, which is the value of y when x = 0.
Given that the lengths and the widths are interchangeable, that is, either can be considered as the input or as the output.
The slope of -1 means that when the input in increased by 1, the output is decreased by -1, that is;
= length/width
This is increased by 1, and the other is decreased by 1.
You can learn more about linear function concepts at brainly.com/question/24808124
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