Answer: $9.57
Step-by-step explanation: 47.85/5 = 9.57. Therefore each book costs $9.57.
The sum of two numbers is 6. Theirdifference is 12. Find the numbers.
Given:
Sum of two numbers-6
Difference of two numbers-12
Required:
To calculate the number
Explanation:
Consider first number-9
Consider second number--3
Sum =9+(-3)=9-3=6
Difference=9-(-3)=12
Required answer:
Option B
Suppose the price of your dream house is $239,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30 year fixed rate mortgage at 10%. a.) Find the required down payment, b.) Find the amount of the mortgage. c.) How much must be paid for the three points at closing? d.) Find the monthly payment (excluding escrowed taxes and insurance) e.) Find the total cost of interest over 30 years.
a) The required down payment is $47,800.
b) The mortgage loan is $191,200.
c) The amount for the three points at closing is $5,736, which is 3% of the mortgage.
d) The monthly payment (excluding escrowed taxes and insurance) is $-1,677.92.
e) The total interest cost for the mortgage over its 30-year period is $412,850.06.
What is the down payment?The down payment is an upfront payment required to reduce the mortgage loan and assure the financier that the mortgagee is financially ready to engage in the mortgage transaction.
The price of a dream house = $239,000
Down payment = 20% = $47,800 ($239,000 x 20%)
Mortgage loan = $191,200 ($239,000 - $47,800)
Three points at closing = 3% of $191,200
= $5,736
Periodic Payment:N (# of periods) 360 months (30 years x 12)
I/Y (Interest per year) = 10%
PV (Present Value) = $191,200
FV (Future Value) = $0
Results:
PMT = $-1,677.92
Sum of all periodic payments = $-604,050.06
Total Interest = $412,850.06
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The sum of the angle measures of a triangle is 180 degrees angles of a triangle measure 40 and 70 degrees , so Katy concludes that the third angle measures 70inductive or Deductive ??i need help
From the fact that the sum of the angle measures of a triangle must be equal to 180º and that two angles have measures of 40º and 70º, we can deduce that the third angle must have a measure of 70º.
Therefore, this was a deductive argument.
The domain is ? Type your answer in interval notation
The graph of the function is
The domain of the function is determined as the x -value of the function that satisfy the given function.
[tex](-\infty,-4)\cup(-4,1)\cup(1,\infty)[/tex]The weight (W kg) of a decaying radio active substance after n years is given by W= Wo(1/2)^n/100, where Wo kg is the initial weight of the substance. 1. Find the number of years for the radioactive substance to decay to half of its initial weight.
We have the equation:
[tex]W=W_0(\frac{1}{2})^{\frac{n}{100}}[/tex]And we want to find the value n, correspondign to the number of years necessary in order to the substance to decay in half.
Let's say that we have 1 Kg of the substance, this is Wo, the initial weight. Since we want to find the the decay of half the substance we use W = 1/2
And write:
[tex]\frac{1}{2}=1\cdot(\frac{1}{2})^{\frac{n}{100}}[/tex]Now we can use a property of logarithms:
[tex]\ln (a^b)=b\ln (a)[/tex]Thus applying natural log on both sides:
[tex]\ln (\frac{1}{2})=\ln (\frac{1}{2}^{\frac{n}{100}})[/tex]By the property:
[tex]\ln (\frac{1}{2})=\frac{n}{100}\ln (\frac{1}{2}^{})[/tex]We can divide on both sides by ln(1/2):
[tex]\begin{gathered} 1=\frac{n}{100} \\ n=100 \end{gathered}[/tex]The number of years for the radioactive substance to decay to half its initial weigh are 100 years.
The step to get rid of the ln(1/2) is:
[tex]\begin{gathered} \ln (\frac{1}{2})=\frac{n}{100}\ln (\frac{1}{2}^{}) \\ \frac{\ln (\frac{1}{2})}{\ln (\frac{1}{2})}=\frac{n}{100}\frac{\ln (\frac{1}{2}^{})}{\ln (\frac{1}{2})} \\ 1=\frac{n}{100}\cdot1 \\ 1=\frac{n}{100} \end{gathered}[/tex]
Write an equation of a line that passes through the point (7, 3) and is parallel to the line y = negative 2 over 3 x + 3.
We are asked to determine the equation of a line that is parallel to:
[tex]y=-\frac{2}{3}x+3[/tex]Two lines are parallel if their slopes are in the following relationship:
[tex]m_2=-\frac{1}{m_1}[/tex]Therefore, if m1 is the slope of the given line and m2 is the slope of the parallel line we may determine the value of the slope of the parallel line by replacing it in the relationship. Let's remember that when a line is written in the form:
[tex]y=mx+b[/tex]Where "m" is the slope. Therefore, m1 is -2/3. Replacing in the relationship we get:
[tex]m_2=-\frac{1}{-\frac{2}{3}}=\frac{3}{2}[/tex]Now, we go back to the general form of a line equation and replace the value of the new slope:
[tex]y=\frac{3}{2}x+b[/tex]The value "b" is the y-intercept and can be found using the point through which the line passes:
[tex]3=\frac{3}{2}(7)+b[/tex]Now we solve the operations:
[tex]3=\frac{21}{2}+b[/tex]Subtracting 21/2 from both sides:
[tex]3-\frac{21}{2}=b[/tex]Solving the operations:
[tex]-\frac{15}{2}=b[/tex]Now we replace in the line equation:
[tex]y=\frac{3}{2}x-\frac{15}{2}[/tex]And thus we get the equation of the parallel line.
hey mr or ms could you help me out with this problem?
Point = (8,-4)
When coordinate points (x,y) are rotated by 90° the image became (y,-x)
So, for this case:
Image: (-4,-8)
13B5Find the length of AC.A. AC = 3B. AC= 8C. AC = 12D. AC= 13.9
Question:
Find the length of AC.
Solution:
Applying the Pythagorean Theorem, we get:
[tex]AC\text{ = }\sqrt[]{CB^2_{}-AB^2}\text{ = }\sqrt[]{13^2_{}-5^2}[/tex]this is equivalent to:
[tex]AC\text{ = }\sqrt[]{13^2_{}-5^2}\text{ = }\sqrt[]{144}=12[/tex]then, we can conclude that the length of AC side is:
[tex]AC\text{ }=12[/tex]
The dollar value v(t) of a certain car model that is t years old is given by the following exponential function.v(t) = 19, 900 * (0.84) ^ tRound your answers to the nearest dollar as necessary.Find the initial value of the car and the value after 11 years.
Given
[tex]v(t)=19900(0.84)^t[/tex]a) The car has its original (initial) value when no time has passed since it was bought; in other words t=0. Then,
[tex]\text{ initial value: }v(0)=19900(0.84)^0=19900*1=19900[/tex]The initial value is 19900.
b) After 11 years, t=11; then,
[tex]\begin{gathered} v(11)=19900(0.84)^{11}=2923.64894... \\ \Rightarrow v(11)\approx2924 \end{gathered}[/tex]Rounded to the nearest tenth, the second answer is 2924
express this number in standard form:[tex]1.304 \times {10}^{7} [/tex]
To write this in standard form, we need to look at the power of 10. In this case, it's a 7. Then, we need to shift the decimal point 7 places to the right:
[tex]1.304\cdot10^7=13,040,000[/tex]We can see that behind the 1 (where was the decimal point before) now there are 7 numbers, then what we do is correct.
Write the next 5 terms of this sequence. Given: a1=3 and d = 5
To find the number of term, we will use the formula;
[tex]U_{n\text{ = }}a+(n-1)d[/tex]when n= 1
[tex]U_1=\text{ 3 + (1-1)5}[/tex][tex]=\text{ 3+0}=3[/tex]for the second term
n = 2
[tex]U_2=\text{ 3 + (2-1)5}[/tex]= 3 + 5
=8
For n= 3
[tex]U_3=3+\text{ (3-1)5}[/tex]=3 + 2(5)
=3 + 10
=13
For n=4
[tex]U_4=3+(4-1)5[/tex]=3+3(5)
= 3 + 15
= 18
For n= 5
[tex]U_5=3+(5-1)5[/tex]= 3 + 4(5)
= 3 + 20
= 23
Therefore, the terms; 3, 8, 13, 18 and 23
Write two equivalent fractions.
2/3
Answer:
5/10
15/30
Step-by-step explanation:
The triangles are similar, so the lengths of corresponding sides are in the same ratio.
One pair of corresponding sides is 5 and 10.
10 is twice 5.
5/10
The other pair of corresponding sides is 15 and ?.
? must be twice 15, so ? is 30.
15/30
James wants to have earned $7,592 amount of interest in 16 years. Currently he finds that hisannual interest rate is 9.04%. Calculate how much money James needs to invest as his principal inorder to achieve this goal.Round answers to the nearest hundredth (two decimal places) of a year.
We know that
• The earnings are $7,592.
,• The time is 16 years.
,• The annual interest rate is 9.04%.
This problem is about simple interest, its formula is
[tex]A=P(1+rt)[/tex]Where A = 7,592, r = 9.04, t = 16, and P is the principal.
Let's replace each value.
[tex]7,592=P(1+0.0904(16))[/tex]Notice that 9.04% is equivalent to 0.0904.
Now, we solve it for P.
[tex]\begin{gathered} 7,592=P(1+1.4464) \\ 7,592=P(2.4464) \\ P=\frac{7,592}{2.4464} \\ P\approx3,103.34 \end{gathered}[/tex]Therefore, James needs to invest $3,103.34 as his principal in order to achieve the goal.GEOMETRY ITS DUE AT 2:15 PLEASE .
1) Write an equation perpendicular to 2x + 3y = 18 that passes through the point (1, 5).
2) Write an equation parallel to y = 2x + 6 that passes through the point (0, 7).
The required equation for the line is y = x + 4 that perpendicular to y = -x + 4 and passes through the point (1, 5).
The required equation is y = 2x + 7 that parallel to y = -3x+7 passes through the point (0, 7).
What is the slope of the line?The slope of a line is defined as the angle of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
The equation of the line which is given as
2x + 3y = 18
3y = -2x + 18
y = -2x/3 + 6
Here the slope of the line, m = -1/3
Let the required line would be as
⇒ y₀ - y₁ = m₀ (x₀ - x₁ )
The required line passes through the point (1, 5)
Here x₁ = 1 and y₁ = 5 and m₀ = 1/3 (Since required line perpendicular)
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 5 = 1 (x - 1)
⇒ y = x - 1 + 5
⇒ y = x + 4
Therefore, the required equation for the line is y = x + 4 that perpendicular to y = -x + 4 and passes through the point (1, 5).
The equation of the line which is given as
y = 2x + 6
Here the slope of the line, m = 2
The given coordinates of the line;
points on the line (0, 7)
Let the required line would be as
⇒ y - y₁ = m (x - x₁ )
Here x₁ = 0 and y₁ = 7 and m = 2
The equation of the line is obtained by substituting these values into the above equation;
⇒ y - 7 = 2 (x - 0)
⇒ y - 7 = 2x
⇒ y = 2x + 7
Therefore, the required equation is y = 2x + 7 that parallel to y = -3x+7 passes through the point (0, 7).
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which phrase best describesuse the commutative property to simplify the expression 1/4 + 1/3 + 3/4 communisim
By using commutative property the result after solving expression (1/4 + 1/3 + 3/4) will be 7/4.
What is the commutative property of addition?
The commutative property of addition for three numbers is given by -
a + (b + c) = (a + b) + c
Given is the following expression -
1/4 + 1/3 + 3/4
We have the following expression -
1/4 + 1/3 + 3/4
Now, lets solve the expression by adding first two terms first and than add the third term to result of the addition of first two terms. Mathematically -
(1/4 + 1/3) + 3/4
Let (1/4 + 3/4) = K
Than the expression becomes -
K + 3/4
Now, first solve K, we will get -
K = 1/4 + 3/4
K = 4/4 = 1
Now, adding the resultant [K] to third term -
1 + 3/4
1/1 + 3/4
(4 + 3)/4
7/4
So, using commutative property, we have solved the expression (1/4 + 1/3 + 3/4) and the final value will be 7/4.
Therefore, by using commutative property the result after solving expression (1/4 + 1/3 + 3/4) will be 7/4.
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Help in solving question 5 please. System needs to be solved using the elimination method. Thanks!
Given: A system of linear equations in three variables x, y, and z as follows-
[tex]\begin{gathered} 2x+y-z=9 \\ -x+6y+2z=-17 \\ 5x+7y+z=4 \end{gathered}[/tex]Required: To solve the system using elimination.
Explanation: Let the given system as-
[tex]\begin{gathered} 2x+y-z=9\text{ ...}(1) \\ -x+6y+2z=-17\text{ ...}(2) \\ 5x+7y+z=4\text{ ...\lparen3\rparen} \end{gathered}[/tex]We can solve the system by reducing the system to a system of 2 variables. Suppose we would like to remove the variable z.
Multiplying equation (1) by 2, adding to equation (2) as follows-
[tex]\begin{gathered} (4x+2y-2z)+(-x+6y+2z)=18+(-17) \\ 3x+8y=1\text{ ...}(4) \end{gathered}[/tex]Now, add equations (1) and (3) as follows-
[tex]\begin{gathered} (2x+y-z)+(5x+7y+z)=9+4 \\ 7x+8y=13\text{ ...}(5) \end{gathered}[/tex]Now, equations (4) and (5) represent a system of linear equations in two variables. Subtracting the equations as follows-
[tex]\begin{gathered} (3x+8y)-(7x+8y)=1-13 \\ -4x=-12 \\ x=3 \end{gathered}[/tex]Substituting x=3 in equation (4)-
[tex]\begin{gathered} 9+8y=1 \\ 8y=-8 \\ y=-1 \end{gathered}[/tex]Substituting x=3 and y=-1 in equation (1) as follows-
[tex]\begin{gathered} 6-1-z=9 \\ z=-4 \end{gathered}[/tex]Final Answer: The solution to the system is-
[tex]\begin{gathered} x=3 \\ y=-1 \\ z=-4 \end{gathered}[/tex]According to the histogram, how many students live between 1 and 1.9 miles from school?
ANSWER
B. 25
EXPLANATION
We want to identify the number of students that live between 1 and 1.9 miles from school.
To do this, we have check the frequency corresponding to the bar for 1 - 1.9 miles on the frequency axis.
From the histogram, we see that the number of students that live between 1 and 1.9 miles from the school is 25.
The correct answer is option B.
Help with number 1 pls make sure when you’re done to highlight the answer in bold
Answer:
Step-by-step explanation:
[tex]undefined[/tex]An automobile windshield wiper 11 inches long rotates through an angle of 60∘. If the rubber part of the blade covers only the last 10 inches of the wiper, find the area of the windshield cleaned by the windshield wiper. Answer exactly or round to the nearest tenth of a square inch
the area of the windshield, cleaned by the windshield wiper is mathematically given as 0.096inche^2
This is further explained below.
What is a windshield?The term "acute area of the windshield glazing" refers to the section of the windshield that measures eight and one-half inches by eleven inches and is located immediately in front of the driver's line of sight, as seen in the image.
Then, let's call the part of the windshield labeled "ABC" A.
[tex]A=\frac{1}{2} r^2 \theta[/tex]
Now, substituting the given values we get,
[tex]\begin{aligned}&A=\frac{1}{2} r^2 \theta \\&A=\frac{1}{2} \times(7)^2 \times \frac{\pi}{180} \\\end{aligned}$$[/tex]
A=0.4276
Then let the area of the windshield, ADE, be denoted by the letter A',
[tex]A^{\prime}=\frac{1}{2} r^2 \theta[/tex]
Now, after replacing those values with the ones we were provided,
[tex]\begin{aligned}&A^{\prime}=\frac{1}{2} r^2 \theta \\&A^{\prime}=\frac{1}{2} \times(1)^2 \times 60 \times \frac{\pi}{180} \\&A^{\prime}=0.5236\end{aligned}[/tex]
In conclusion, In order to calculate the area of the windshield, you need to take the difference between A and A'.
0.5236-0.4276=0.096
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I NEED HELP PLEASE!!!!!!!!!!
a) The inverse of a statement : If If two angles are not supplementary then the angles are not a linear pair. FALSE
b) The converse of a statement : If the angles are a linear pair, then the two angles are supplementary. TRUE
c) The contrapositive of a statement : If the angles aren't supplementary, then they aren't linear pair . FALSE
The given statement is : If two angles are supplementary then the angles are a linear pair .
(a) The inverse of a statement : If If two angles are not supplementary then the angles are not a linear pair.
This statement is FALSE because supplementary angles do not have to be adjacent, whereas a linear pair must be adjacent and create a straight line. So, no, supplementary angles are not always linear pairs. However, linear pairs are always supplementary.
(b) The converse of a statement : If the angles are a linear pair, then the two angles are supplementary.
This statement is TRUE because in a linear pair, if the two angles have a common vertex and a common arm, then the non-common side makes a straight line and the sum of the measure of angles is 180°. Linear pairs are always supplementary.
(c) The contrapositive of a statement : If the angles aren't supplementary, then they aren't linear pair .
This statement is FALSE because if they are adjacent and share a vertex and one side. See the first picture below. They might not form a linear pair, like in a parallelogram.
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PLEASE HELP!!!
Can someone help me out with this math problem.(CALCULUS 2)
picture of problem attached below.
The centre of mass of 40g, (1,3); 30g, (2,-1); 70g, (0,0) and 50g (0,-2) is located at (10/19,-1/19).
The formula to find the coordinates (X,Y) of centre of mass of a discrete particles system is,
X = (m₁x₁+m₂x₂+m₃x₃+m₄x₄)/(m₁+m₂+m₃+m₄)
Y = (m₁y₁+m₂y₂+m₃y₃+m₄y₄)/(m₁+m₂+m₃+m₄)
As we know,
m = 40
m = 30
m = 70
m = 50
Putting all the values in the formula,
for X coordinate,
X = [(40×1)+(30×2)+(70×0)+(50×0)]/(40+30+70+50)
X =(40+60+0+0)/(190)
X = 100/190
X = 10/19
For Y coordinate,
Y = [(40×3)+(30×-1)+(70×0)+(50×-2)]/(40+30+70+50)
Y= (120-30+0-100)/(190)
Y = -10/190
Y = -1/19
So, the centre of mass of the discrete particle system is at (10/19,-1/19)
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Factor: x^6-5x^4-5+x
The value of the given expression x^6 -5x^4 - 5 + x simplified as; x^4(x^2 - 5) - (5 + x)
How to factor the expression?The statement is given as ;
Factor: [tex]x^6 -5x^4 - 5 + x[/tex]
From the given expression, we have
[tex]x^6 -5x^4 - 5 + x[/tex]
Group the expression in two part;
So, we have;
[tex]x^6 -5x^4 - 5 + x = (x^6 - 5x^4) - (5 + x)[/tex]
Now Factorize each group of the expression;
[tex]x^6 -5x^4 - 5 + x = x^4(x^2 - 5) - (5 + x)[/tex]
The given expression cannot be further simplified.
Hence, the value of [tex]x^6 -5x^4 - 5 + x is x^4(x^2 - 5) - (5 + x)[/tex]
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Find the y-intercept of line on the graph.
Answer:
-3
Step-by-step explanation:
the 'y- intercept ' is ACTUALLY the 'y-axis intercept'.......this is where the graph crosses the y - axis ....for this graph this is -3
Solve the system of equations.y= x2 + 3x - 4y = 2x - 4A. (-1,6) and (0,4)O B. (-1,-6) and (0, -4)C. (0,-4) and (1, -2)O D. (0,4) and (1,-6)
Answer:
(0,-4) and (-1,-6) or B
Step-by-step explanation:
Notice that equation 1 and equation 2 are both equal to y.
Substitute equation 2 into equation 1:
[tex]2x-4=x^2+3x-4[/tex]
Simplify:
[tex]x^2+x=0[/tex]
Factor:
[tex]x(x+1)=0[/tex]
Notice that the zeros for x are x = 0 and x = -1.
Now plug both values into either equation 1 or 2 to find y:
[tex]y=0^2+3(0)-4 = -4[/tex]
[tex]y=(-1)^2+3(-1)-4=-6[/tex]
Therefore, our values are (0,-4) and (-1,-6) or option B
What are the coordinates of P', the image of P(-4, 0) under the translation (x-3, y + 6)?
Answer:
I really don't understand much about math sometimes I need help
which expression is a factor xsquared - 5x-6
The Factors of x² - 5x + 6 are (x-3) (x-2)
Step 1: Add the constant term to the first term's coefficient. i.e (6 x 1) = 6
Step 2:Find the two factors of 6 whose total matches the middle term's coefficient., i.e -5.
Thus, the factors are -3 and -2 as,
-3 × (-2) = 6 (Product)
-3 + (-2) = -5 (Sum)
The polynomial may be expressed as follows after dividing the middle term by the two components, -3 and -2:
x² - 3x - 2x + 6 = 0
⇒ x(x-3) -2(x-3) = 0
⇒ (x-3)(x-2) = 0
Thus, the Factors of x² - 5x + 6 are (x-3) (x-2).
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18- A clothing store sells a shirt costing $20 for $33 and a jacket costing $60 for $93.
(i) If the markup policy of the store is assumed to be linear, write an equation that expresses retail price R
in terms of cost C.
(ii) What does a store pay for a suit that retails for $240?
(i) (a) R = 1.5C + 12
(b) R = 1.5C+3
(c) R = 3C + 1.2
(d) R = 3C +1.5
(ii) (a) 158
(b) 185
(c) 155
(d) 188
I cant solve this and I need steps while solving it.
Let the graph of g be a vertical stretch by a factor of 2 followed by a translation 3 units down of the graph of f(x) = x^2 Write a rule for g.
The equation for the function after the transformation is f'(x) = 2x^2 - 3
How to write the image for the function?The initial equation is given as
f(x) = x²
The above represents the parent function
The sequence of transformations is given as
Vertically stretched by a factor of 2Shifted a distance of 3 units downThe rules of the above sequence of transformations are
Vertically stretched by a factor of 2: (x, 2y)Shifted a distance of 3 units down: (x, y - 3)When the rules are applied, we have
Stretch: f(x) = 2x^2Shifted: f'(x) = 2x^2 - 3Hence, the equation in its final position is f'(x) = 2x^2 - 3
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Andrew has $9,000 in a savings account that earns 5% interest per year. How much will he have including interest in 1 year?
Andrew will have $9,450 in his savings account that earns 5% interest per year.
According to the question,
We have the following information:
Principal amount in Andrew's savings account = $9,000
Interest rate = 5% per year
Time = 1 year
We know that we use the following formula to find the simple interest on any amount:
Simple interest = (principal*rate*time)/100
Simple interest = (9000*1*5)/100
Simple interest = $450
Now, the total amount in his savings account will be the sum of the amount earned from the interest and the principal amount submitted by him.
Total amount = interest+principal
Total amount = 450+9000
Total amount = $9,450
Hence, he will have $9,450 in his savings account.
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Mike is training for a race. He wants his pace to be proportional throughout the race. The table relates the number of hours he ran and the distance that he traveled. Hours 0.5 1.0 1.5 2.0 Miles 3 6 8 12 Mile then graph these points (hours, miles) to determine whether or not his pace was proportional. Mike determined his pace was proportional because the graph passes through the origin. Which statement best describes his error? Multiple choice question. cross out A) The graph passes through the point (1, 1). cross out B) The graph does not pass through the origin. cross out C) The graph both passes through the origin and is a straight line. cross out D) While the graph does pass through the origin, it is not a straight line.
The statement which best describes Mike's error is that: D) While the graph does pass through the origin, it is not a straight line.
What is a graph?A graph can be defined as a type of chart that's commonly used for the graphical representation of data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
In Mathematics, the graph of any proportional relationship is characterized by a straight line with the points passing through the origin (0, 0) because as the values on the x-coordinate (x-axis) decreases or increases, the values on the y-coordinate (y-axis) decreases or increases simultaneously.
In this context, we can reasonably infer and logically deduce that even though Mike's graph passes through the origin, his error is that it is not a straight line.
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