The surface will be zero at the planes x=-3, x=3, y=0, and y=3, and will increase as we move away from the minimum in either direction along the y-axis.
The given function is Z = 4x^2(y-2)^2. To graph this function, we can first consider the planes z=1, x=-3, x=3, y=0, and y=3. These planes will create a rectangular prism in the xyz-plane. Next, we can look at the behavior of the function within this rectangular prism. When y=2, the function will have a minimum at z=0. This minimum will be located at x=0. For values of y greater than 2 or less than 0, the function will increase as we move away from the minimum at (0,2,0). Therefore, the graph of the function Z = 4x^2(y-2)^2 will be a three-dimensional surface that is symmetric about the plane y=2 and has a minimum at (0,2,0). The surface will be zero at the planes x=-3, x=3, y=0, and y=3, and will increase as we move away from the minimum in either direction along the y-axis.
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Find the volume of the solid enclosed by the paraboloid z = 4 + x^2 + (y − 2)^2 and the planes z = 1, x = −3, x = 3, y = 0, and y = 3.
A company manufactures two types of cabinets, type 1 and type 2. It produces 110 total cabinets each week. Last week, the number of type 2 cabinets produced exceeded twice the number of type 1 cabinets produced by 20. If x is the number of type 1 cabinets produced and y is the number of type 2 cabinets produced, the system of equations that represents this situation is x + y = 110 and y = 2x + 20.
X for type 1 cabinets = 30
Y for type 2 cabinets = 80
And that proven that type 2 cabinets (Y) produced exceeded more than twice the number of type 1 cabinets (X)
As per the equations stated
X + Y = 110 ……….. (1)
Y = 2x + 20 …...... (2)
We substitute Y at equation (1) with equation (2), to find X
X + Y = 110
X + (2X + 20) = 110
3X + 20 = 110
3X = 110 – 20
3X = 90
X = 90 / 3
X = 30
Then, We substitute value X at equation (1 ) with the value that we have discovered before
X + Y = 110
30 + Y = 110
Y = 110 – 30
Y = 80
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Which has exactly 12 angles?
A dodecagon or 12-gon is a twelve-sided polygon.
One of the polygonal shapes with 12 sides, 12 vertices, and 12 angles is the dodecagon. A dodecagon is a two-dimensional plane figure, just like other polygons. 12 equal sides and 12 equal angles make up a standard dodecagon polygon.
Dodecagons that are irregular have uneven sides and angles. Dodecagons can also be concave or convex polygons. The dodecagon's inner angles add up to 1800° in total.
The word dodecagon is derived from Greek words, ‘dodeka‘ which means ‘twelve’, and ‘gon‘ means ‘sides’.
Thus, A dodecagon or 12-gon is a twelve-sided polygon.
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A line pae through the point (–6,5) and (8,–2). What i it equation in point-lope form?
The equation of the line passing through the point (-6, 5) and (8, -2) in point-slope form is y - 5 = -0.5(x + 6).
The point-slope form of a line is
y - y1 = m(x - x1)
where (x1, y1) is a point on the line, and m is the slope of the line.
To find the equation of a line given two points, we can use either point and find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)
So, we can use the point (-6, 5) and (8, -2)
m = (y2 - y1) / (x2 - x1) = (-2 - 5) / (8 - (-6))
m = -7/14
m = -1/2
Now we can use this slope and the point (–6,5) to find the equation of the line in point-slope form:
y - 5 = -1/2(x - (-6))
y - 5 = -0.5(x + 6)
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Four glasses of milk and 2 snack bars have a total of 86 carbohydrates (carbs), and 2 glasses of milk and 3 snack bars have a total of 69 carbs. Determine how many carbs are in one glass of milk and in one snack bar.
Answer:
One glass of milk: 15 carbs
One snack bar: 13 carbs
Step-by-step explanation:
This problem is an example of systems of linear equations. We can set this problem up by defining variable. I used [tex]m[/tex] for the glass of milk and [tex]b[/tex] for the snack bar.
First, we have: 4 glasses of milk and 2 snacks bar have a total of 86 carbs. We can write this as
[tex]4m+2b=86[/tex]
Next: 2 glasses of milk and 3 snack bars have a total of 69 carbs.
We can write this as
[tex]2m+3b=69[/tex]
Now we set it up.
[tex]4m+2b=86[/tex]
[tex]2m+3b=69[/tex]
By dividing both sides of the first equation by 2, we can use the subtraction method to get rid of the variable [tex]m[/tex]. Now we have
[tex]2m+b=43[/tex]
[tex]2m+3b=69[/tex]
Subtract like terms and solve for [tex]b[/tex]
[tex]-2b=-26[/tex]
[tex]b=13[/tex]
Now we substitute [tex]b[/tex] back into the original equation to find [tex]m[/tex].
[tex]2m+(13)=43[/tex]
[tex]2m=30[/tex]
[tex]m=15[/tex]
There you have it. I hope this helps!
I am atempting my math homework but I do not understand this question It says "Vera spent 0.04 of of the earnings on a new phone apps What percent of monthly earnings did she spend on phone apps" Can someone help?
The percent of monthly earnings that Vera spends on phone apps is 4%.
How to express the percentage?.The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.
Since Vera spent 0.04 of of the earnings on a new phone apps, the percent of monthly earnings did she spend on phone apps will be:
= 0.04.
= 4/100
= 4%
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Darnell can buy a particular brand of fruit juice in a 6-ounce bottle or a 10-ounce bottle. The juice in a 10-ounce bottle contains 150 calories. How many calories are in the juice in a 6-ounce bottle
Answer:
90 calories in a 6 ounce bottle
Step-by-step explanation:
6oz/x
10oz/150
150 divided by ten is 15
15 times 6 equals 90
Answer: 90 calories is in 6 ounce bottle which is 90
2+sqrt{4-p} = sqrt {2p-4}
Please show work.
The value of the given expressions is p = -1.281, though it is also possible for p = 0.781 to be the value.
what is equation ?Take into consideration the equation 3x + 5 = 14, in which 3x + 5 and 14 are two expressions that are separated by the word "equal." The standard form, slope-intercept form, and point-slope form are the three primary formats for linear equations. In a mathematical expression known as an equation, the equals sign appears. Algebra is used in a variety of equations. When you don't know how much to compute in math, you use algebra to approximate the answer.
given
-4p^2=2p-4
p=(-1-sqrt(17))/4=-1.281
p=(-1+sqrt(17))/4=0.781
The value of the given expressions is p = -1.281, though it is also possible for p = 0.781 to be the value.
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What is the slope of the line through (-9,6(−3,9)
Answer:
0.6 cause I got it correct.
PLEASE HELP
is this equation an exponential decay of 40% or 30%
y=0.4(0.7)^t
Answer:
30%
Step-by-step explanation:
The level of decay is determined by the number raised to the power.
y = 0.4(0.7)^t
If you had 1^t, there would be no decay or growth since 1^t is always 1.
Instead, you have 0.7^t
As t increases, 07^t decreases. That is where the decay comes from.
Now look at 0.7
In the general decay equation, you have
y = a(1 - r)^t
r is the rate of decay.
Here we have 0.7
0.7 = 1 - 0.3
the rate of decay is 0.3 or 30%
Answer:
The equation y = 0.4(0.7)^t represents an exponential decay of 30%. The decay rate is determined by the value in the parentheses, which in this case is 0.7. To calculate the decay rate, you can subtract this value from 1, giving you 1 - 0.7 = 0.3, or 30%.
Step-by-step explanation:
What is the coefficient of x² in the polynomial x³ 4x² 7x 2?
So on solving the provided question we can say that coefficient of x^2 in x³ +4x² -7x -2 is 1.
What is the coefficient?A coefficient in mathematics is a polynomial, a series, or the multiplicative coefficient of a particular term in an expression. Typically numeric, however any expression is permitted. The term "parameter" can also refer to the coefficients themselves if they are variables. A number times a variable equals a coefficient. Coefficient examples include: The coefficient is 14 in phrase 14c 14c 14c. The coefficient is 1 for word g. multiplies the variable by this amount. example Given that "z" is a variable and that 6z is the definition of the term, the coefficient is 6. One is the coefficient of the square of x.
here,
coefficient of x^2 in x³ +4x² -7x -2 is 1
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A manufacturer records the number of errors each work station makes during the week. The data are as follows 6 3 2 3 5 20 254201 Which of these choices display the correct dotplot?
O A. Number of Errors for the Week for Workstations
O B. Number of Errors for the Week for Workstations 0 10 10
O C. Number of Errors for the Week
O D. Number of Errors for the Week for Workstations for Workstations 10 10
The correct dot plot for the given data would be option A. Number of Errors for the Week for Workstations.
A dot plot is a graph that displays the frequency of a data set by plotting a dot above the number for each occurrence of that number. The x-axis represents the data values and the y-axis represents the frequency of each data value.
In this case, the data represents the number of errors each workstation makes during the week, so the correct way to display the data in a dot plot would be to have the x-axis represent the number of errors and the y-axis represents the frequency of each error. Each dot on the dot plot would be above the number of errors for each workstation.
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Are these answers correct?? If not, please help
Answer:
Step-by-step explanation:
Question 4 I got something different x= 5, y= -4 (double check my work to make sure i used correct equation and all)
Also for slopes does your teacher want you to include the "x". Cuz when I think of slope its only the "m" part which means it should only be -1, -4 but its your call.
Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. 1 /x^2 + x^4
The partial fraction decomposition of the function is[tex]\\& \Rightarrow \frac{1}{x^2+x^4}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1}\end{aligned}[/tex]
In algebra, a rational fraction—that is, a fraction where the numerator and denominator are both polynomials—can be partially decomposed or expanded by adding a polynomial (potentially zero) and one or more fractions with a lower denominator to the original fraction.
In symbols, the partial fraction decomposition of a rational fraction of the [tex]{\textstyle {\frac {f(x)}{g(x)}},}[/tex]
[tex]{\displaystyle {\frac {f(x)}{g(x)}}=p(x)+\sum _{j}{\frac {f_{j}(x)}{g_{j}(x)}}}[/tex]
Where p(x) is a polynomial, [tex]g_{j}[/tex] for each j is a power of an irreducible polynomial (which cannot be factored into polynomials of positive degrees), and [tex]f_{j}[/tex] for each j is a polynomial with a smaller degree than this irreducible polynomial's degree.
The numerical values of the coefficients is [tex]\frac{1}{x^2+x^4}$[/tex].
Now,
[tex]$\begin{aligned} x^2+x^4 & x^2+x^4 \\ = & x^2\left(1+x^2\right)\end{aligned}$[/tex]
Therefore, the form of the partial fraction decomposition is
[tex]\begin{aligned}& \frac{1}{x^2\left(1+x^2\right)}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1} \\& \Rightarrow \frac{1}{x^2+x^4}=\frac{A}{x}+\frac{B}{x^2}+\frac{C x+D}{x^2+1}\end{aligned}[/tex]
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What does range () function returns Mcq?
The range is found by finding the vertex and noting that it is the minimum or maximum (depending on direction) of the function. You can find the vertex by using -b/2a for the x value and then plugging in to get y value.
What is a function?
A mathematical phrase, rule, or rule that establishes the link between explanatory variables or a dependent variable In mathematics, curves exist everywhere, and they are crucial for constructing physical links in the sciences.
A Method can be defined by a module, an object, or another function. An internal feature of a class is called a method. Methods are listed inside a base class to make the connections between it class and thus the method clear. A method can be called or invoked using different syntax. We can convert a type into an object before being able to access its methods.
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a light year is defined as 5.88 times 10^12 miles: the distance that light travels in 1 year. How far will light travel in 3 years?
The distance that light will travel in 3 years, given the speed it travels in one year is
How to find the speed travelled ?The notion of a Light Year allows us to quantity the distance that light travels in an entire year. This has allowed scientists to quantify with more ease, the distance to other galaxies and planets.
The distance that light travels in a year is 5. 88 x 10¹² miles.
In 3 years therefore, the distance would be:
= 3 x ( 5.88 x 10 ¹²)
= 17.64 x 10 ¹² miles
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unit 8 right triangles and trigonometry homework 7 law of cosines
The value of x will be cos^-1 549/900.
What is Law of Cosine ?
The relationship between a triangle's side lengths and the cosine of its angle is known as the law of cosines. Additionally known as the cosine rule.
We know that ,
a²= b²+c² - 2bc cosα, where α is the angle between b and c.
Here, b = 18 , c= 25, a = 20 and cos x
So, a²= b²+c² - 2bc cosα
(20)² = (18)² + (25)² - 2×18×25 cos x
400 = 324 + 625 - 900 cos x
900cos x = 549
cos x = 549/900
hence, x = cos^-1 549/900
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x^2 = 361 Which represents the solution of the given equation?
Answer: X=19
Step-by-step explanation:
x^2=361
Square root both sides to get rid of the exponent above x.
[tex]\sqrt{x^2}[/tex]=[tex]\sqrt{361}[/tex]
x=19
Solve the inequality and write the solution in set-builder notation. r - 8 < 7
r<15 because I am smart dont doubt me
find x and mut pleaase
The formula for a circle's sector's area is /360o (r2), where r is the circle's radius and is the sector's angle.
Formula for a Sector's Circumference
The following is the formula for a circle's sector's perimeter:
Sector perimeter equals radius plus radius plus arc length.
Sector perimeter equals 2 radius plus arc length.
The relation is used to compute arc length:
Arc length is equal to l = (/360) 2r.
Therefore,
Sector perimeter: 2 Radius + ((/360) 2r)
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Assuming that r is the circle's radius and that is the sector's angle, the formula for the area of a circle's sector is /360o (r2).
What are sectors in a circle?A circular sector (also known as a circle sector or a disc sector; symbol: ) is the area of a disc (a closed region bordered by a circle) enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger as the major sector.
The radius of the circle, r, and the sector angle (in degrees) that the arcs at its centre subtend are also given. A = 1/2 r2 gives the area if the subtended angle is provided in radians.
The area, A, of just the segment may be calculated using the following formula if you know the circle's radius, r, and the sector's central angle,, in degrees.
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Translate the following arguments into symbolic form. Then determine whether each is valid or invalid by constructing a truth table for each.
If national elections deteriorate into TV popularity contests, then smooth-talking morons will get elected. Therefore, if national elections do not deteriorate into TV popularity contests, then smooth-talking morons will not get elected.
Symbolic Form:
P: National elections deteriorate into TV popularity contests
Q: Smooth-talking morons will get elected
The argument can be expressed as:
If P then Q
Therefore, if not P then not Q
This is a valid argument as it follows the logical form of Modus Ponens. We can verify this using a truth table:
P | Q | P → Q | ¬P | ¬P → ¬Q
T | T | T | F | T
T | F | F | F | T
F | T | T | T | T
F | F | T | T | T
The truth table shows that the argument is valid because the final column (¬P → ¬Q) is true for all four cases. This indicates that if the symbolic form of premise (P) is false, then the conclusion (Q) must also be false.
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Jose swam 8 kilometers against the current in the same amount of time it took him to swim 16 kilometers with the current. The rate of the current was 1 kilometer per hour. How fast would Jose swim if there were no current?
The rate at which Jose will swim if there was no current would be = 2 km / hour
What is speed ?Speed is defined as the scalar quantity that is used the express the relationship of the distance of a moving object with respect to its time.
Jose swims with the current of the water and against the current of the water within the same time.
When swimming with the current he covers = 8 km
The rate he used with the current = 1 km / hour
When he is swimming against the current he covers = 16 km
Therefore the rate at which he swims against the current = 16/8 = 2km/hour.
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can somebody help me I been doing this all day please dont guess its for a test
decide if thee absolute value inequality is an "and" compound inequality, an "or" compound inequality or nether.
1. |5+m|<13
a. and b. or c. neither
2. 4|y+6|≥3
a. and b. or c. neither
3. |g - 3| = -2
a. g=5 or -5 b. g = 1 or -1 c. null set
Answer: its number 2
Step-by-step explanation:
You swam 4 sets of 200 yards and your friend swam 5 sets of 150 yards. How many more yards did you swim?
You swam 50 yards more than your friend.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, you swam 4 sets of 200 yards and your friend swam 5 sets of 150 yards.
Total number of yards you swam 4×200
= 800 yards
Total number of yards your friend swam 5×150
= 750 yards
Number of yards more you swam =800-750
= 50 yards
Therefore, you swam 50 yards more than your friend.
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All three members of the Harrison family want to take a cruise with Luxury Starline. Estimate how much the family would spend if a cruise costs $1,825 per person by rounding the cost per person to the nearest thousand. $
In the word problem ,the total cost for cruise for total family is $5475.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
Here the Total members of the Harrison family = 3
Cost of cruise per person = $1825
Now, Total cost for cruise of Harrison family is,
=> Total members × Cost per person
=> 3 × 1825
=> $5475
Hence the total cost for cruise for total family is $5475.
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Segment JK has endpoints J(2,4) and K(6,2). You dilate the segment using a dilation centered at the origin with a scale factor of 1/2 and then reflect the image over the x-axis. Where is the final image of K?
The final image of K would be at (3,-1) after the given sequence of transformation Segment JK.
What is Dilation?Dilation is a process for creating similar figures by changing the size.
Segment JK has endpoints J(2,4) and K(6,2).
A dilation by a factor of 1/2 means that each coordinate value will be multiplied by 1/2.
The dilation of segment JK with a scale factor of 1/2 would shrink the segment by half, so the coordinates of K would be (3,1).
Reflecting over the x-axis would change the sign of the y-coordinate, so the final image of K would be at (3,-1).
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Peter stands at the vertex A of a square ABCD. He can make one step at a time either clockwise or counter-clockwise (the length of the step equals the side-length of the square). In how many ways he can make 8 steps and land at the same vertex A?
Therefore 128 ways that Peter can make 8 steps and land back at vertex A.
How many ways can Peter make 8 steps to Vertex A?There are two possible directions for each step that Peter can take, either clockwise or counter-clockwise.
Therefore, for 8 steps, there are 2^8 = 256 possible ways that Peter can make the steps. However, only half of these ways will end with Peter back at vertex A, since the other half will have him end at the opposite vertex.
Therefore, there are 256/2 = 128 ways that Peter can make 8 steps and land back at vertex A.
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graph 2y-4x<8 please
We have drawn the graph of the given linear inequality.
What is linear inequality?
A linear inequality is a mathematical statement involving a linear function and one of the symbols <, >, ≤, or ≥. The general form of a linear inequality in one variable is:
ax + b <, >, ≤, or ≥ c
where a, b, and c are constants, and x is the variable.
To graph the inequality 2y - 4x < 8, we first need to put it in slope-intercept form, y = mx + b, so we can see the slope and y-intercept of the line. We can do this by adding 4x to both sides:
2y - 4x < 8
2y < 4x + 8
Then we divide both sides by 2 to get y by itself:
y < 2x + 4
Now we have y = 2x + 4 in slope-intercept form, where the slope is 2 and the y-intercept is 4. To graph the line, we can use the y-intercept as a starting point and use the slope to find additional points on the line.
To graph the line, we can follow these steps:
Plot the y-intercept, which is (0,4) on the graph.
Using the slope of 2, find a second point by going up 2 units and over 1 unit. This point is (1,6)
Draw a line through these two points.
Hence, we have drawn the graph of the given linear inequality.
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The volume of a sphere is given by the equation $V=\frac{1}{6\sqrt{\pi}}S^{3/2}$V=
1
6√πS3/2 , where cap s$S$S is the surface area of the sphere. Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meters. Use 3.14 for pi$\pi$π .
The volume of a sphere, to the nearest cubic meter is; 44 cubic meter
How to find the Volume of a sphere?
We are given that the formula for the volume of a sphere is;
V = [1/(6√π)]S^(3/2)
where;
V is volume
S is the surface area of the sphere
π = 3.14
We are given that surface area is 60 square meters. Thus, we will now have;
V = [1/(6√3.14)]60^(3/2)
V = 43.713 m³
Approximating to the nearest cubic meter gives;
V = 44 cubic meter
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John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle from the ground to the top of the tree is 33 degrees. How tall is the tree?
The height of the tree, given the angle from the ground and the distance from the base of the tree, is 64. 94 feet.
How to find the height of the tree ?Assuming that this situation was modelled as a right angled triangle, then the angle from the ground to the top of the tree would be such that the distance from the base of the tree would be the adjacent measure and the height of the tree would be the opposite measure.
This means that the relevant operation to use would be Tan.
Using the Tan operation, and assuming the height of the tree was x, the formula would be:
Tan (33 degrees ) = x / Distance from base
Tan (33 degrees ) x / 100
x = 64. 94 ft
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(Linear Relationships MC) An indoor soccer field can be rented for personal use. The total cost for renting the field can be found by using the equation y=225x + 200 The x-variable is the number of hours the field is being rented, the constant is the flat rate for renting the field, and the y-variable is the total cost, in dollars Which statement is true based on the given equation? The equation shows a linear relationship, but not a proportional relationship The equation shows a linear relationship and a proportional relationship The equation does not show a linear relationship or a proportional relationship The equation shows a proportional relationship but not a linear relationship
first statement is true, the equation shows a linear but not proportional.
what is linear equation?The equation which has two variables with first order term and only a constant available in the equation is termed as linear equation. Example of a linear equation, y =mx + b
Which statement is true for this question?
Given, an equation, y = 225x + 200
where x and y are two variables
x denotes the number of hours the field is being rented
y denotes the total cost
constant 200 implies the flat rate for renting the field.
If we compare this equation to the standard form of linear equation, y = mx + b, where m = slope and b is the y intercept.
we will find that the above two equation is similar and therefore the equation given in question is a linear relationship.
the coefficient 225 is the slope of equation and the constant 200 is the y intercept.
this given equation is not a proportional relationship.
The first statement is true.
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