An equation that shows the proportional relationship between cups (c) and tablespoons (n) is: B. c = 0.0625n
What is a proportion?A proportion is an equation which is typically used to indicate the equality of two (2) ratios. Therefore, proportions can be used in mathematics to show that two (2) ratios are equivalent and then used to calculate or determine all of the unknown quantities.
Mathematically, a proportional relationship can be represented by the following equation:
y = kx
Where:
y and x represent the variables in a proportional relationship.k is the constant of proportionality.Let the cups be represented by c.
Let the tablespoons be represented by n.
Next, we would determine the constant of proportionality (k) as follows:
c = kn
Making k the subject of formula, we have:
k = c/n
k = 0.5/8 ≡ 1.5/24
k = 0.0625.
Substituting the parameters into the equation for a proportional relationship, we have;
c = kn
c = 0.0625n
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Answer:
C = (8/.5)n
Step-by-step explanation:
.5 = 8
1.5 = 24
C = (8/.5)n
Because
8 divided by .5 = 16
16 * .5 = 8
Ex.2
8 divided by .5 = 16
16 * 1.5 = 24
Can someone pls help me it would mean a lot
The position where where angle, θ would be located is at: angle F (∠F).
What is a right angle?A right angle can be defined as a type of angle that is formed by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angle has a measure of 90 degrees.
Additionally, all right angles are are formed as a linear pair and they are marked with a right angle symbol.
In conclusion, the measure of the angle in this right angle triangle would be calculated by using the tangent function as follows:
Tanθ = Opposite side/Adjacent side
Tanθ = 6/4
Angle, θ = tan⁻¹(6/4)
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GAME DESIGN A computer software designer is creating a new video game. The designer wants to create a secret passage that is halfwaybetween the castle and the bridge. Where should the secret passage be located?
Answer:
8.5 and 10.5
Step-by-step explanation:
add your x1 and x2 coordinate and divide them by 2 to get your x.
and for the y add your y1 and y2 coordinate and divide them by 2 to get your y.
The x1, x2, y1, and y2 in this situation would be (5,14) (being the bridge)
and (12,7) being the castle.
x1 = 5
x2 = 12
y1 = 14
y2 = 7
Where can I find angles measurements that is Missing each set of supplemenry angles?
Remember that
If the sum of two angles is equal to 180 degrees, then the angles are supplementary
so
In this problem
Let
x ----> the missing angle
x+34.6 =180 degrees -----> by form a linear pair (supplementary angles)
solve for x
x=180-34.6
x=145.4 degreesA rock climber completing a two-minute training session climbed 12 meters higher on the wall during the second minute of the session. at the end of the two-minute session, the climber was back to the same spot she was at when the session started. what value represents the climber's change in elevation during the first minute of the training session
The value represents the climber's change in elevation during the first minute of the training session is 1/5.
Given,
During the second minute of a two-minute training session, a rock climber completed a 12-meter ascent up the wall. The climber returned to the identical location she had been in at the beginning of the two-minute session.
Let x be the distance climbed by the climber is x m
During the first minutes(60 seconds): distance climbed =[tex]\frac{x}{60}[/tex]
In the 2nd minute, they climbed 12 m higher than in the 1st minute.
Now, the distance climbed by the climbed in the Second minute = [tex]\frac{x+12}{60}[/tex]
Now, the change in the elevation during the first minute of the training session= [tex]\frac{x+12}{60}-\frac{x}{60} = \frac{12}{60}=\frac{2}{10}=\frac{1}{5}[/tex]
Hence, the value represents the climber's change in elevation during the first minute of the training session is [tex]\frac{1}{5}[/tex]
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Danny recipe calls for 3 cups of flour He would like to combine some wheat flour and some white flour to equal 3 cups Write two mixed numbers that have a sum of 3
Answer:
1 1/2 + 1 1/2
Step-by-step explanation:
1 1/2 (or 1.5) plus 1 1/2 equals 3
Mrs. Holmes’s physics class uses 3D-printing software to create miniature bridges that can hold at least 5 pounds. Teams will print multiple parts of the bridges and then assemble the parts. One team wants at least 6 inches between the bridge's upper and lower rail. The lower rail of the bridge contains points (2, 10) and (16, 3). Will the bridge meet the team's specifications if the upper rail contains points (5, 1)? If yes, how far apart are the rails? Let every unit represent an inch. Round your answer to the nearest hundredth, if needed.
Answer:
I litteraly have the same problem and no clue how to do I
Step-by-step explanation:
A turtle and a rabbit are in a race to see who is first to reach a point 100 feet away. The turtle travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continues at a constant speed of 40 feet per minute for the last 50 feet. Determine which animal won the race and by how much time.
a poster of area 15360 cm215360 cm2 has blank margins of 10 cm10 cm wide on the top and bottom and 6 cm6 cm wide on the sides. find the dimensions that maximize the printed area. (use decimal notation. give your answers as whole or exact numbers.)
The dimensions that maximize the area are, 96cm and 84cm.
What is area?
The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Let the height of poster be h and breadth be b,
bh = 15630cm square........(1)
Height of the printed area=h-10-10 = h - 20
(decrement of 10 from top and bottom)
the breadth of the printed area b-6-6 = b-12
(decrement of 9 from both sides)
for maximum printed area:
A=(h-20)(b-12) should be maximum
[tex]A = (h - 20)(\frac{15360 }{h}-12)[/tex]
From equation (1)
[tex]A = 15360-12h-\frac{307200}{h} +240[/tex]
A = 15600 - 12h - (307200/h)
differentiate with respect to h (it should be=0)
[tex]\frac{dA}{dh}= 0-12 + \frac{307200}{h^2}[/tex]
[tex]12 = \frac{307200}{h} \\h = 160 cm[/tex]
from equation (1),
[tex]bh = 15630cm^2\\b = 96cm[/tex]
dimension of printed area,
= h - 20
= 160 - 20
= 140 cm
= b - 12
= 96 - 12
= 84 cm
Therefore, the dimensions that maximize the area are, 96cm and 84cm.
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The options are relational/irrational and is equal to an integer/has a square root in its denominator
because, the quotient has an integer in its denominator
Explanation
A rational number is a number that is expressed as the ratio of two integers
[tex]\frac{p}{q}[/tex]hence
for
[tex]\frac{20}{\sqrt{16}}[/tex]we can solve the root in the denominator, so we have
[tex]\begin{gathered} \frac{20}{\sqrt{16}} \\ \frac{20}{\sqrt[]{16}}=\frac{20}{4} \end{gathered}[/tex]so, as the number can be expressed as the ratio of two integers ( 20 and 4) we can conclude
[tex]\text{the quotient }\frac{20}{\sqrt[]{16}}\text{ is a rational number}[/tex]because, the quotient has an integer in its denominator
I hope this helps you
13. When feeding, a juvenile whale shark filters about 600 cubic meters of water through its
mouth each hour. About 2.8 kilograms of food are filtered out from the water each hour.
120
a. Graph the function that represents the amount a of water filtered by the whale shark as a
function of the number of minutes.
m
b. The whale shark feeds for 7.5 hours each day. Graph the function that represents the amount f
of food (in pounds) filtered by the whale shark as a function of the number d of days.
Answer:214.29
Step-by-step explanation:600 divided by 2.8
possibly the answer
in Mrs raps advisory 20 students saw the action movie and 5 didn't what is the ratio of students who saw the movie to the total students simplify the ratio
Answer:
4 : 5
Explanation:
We are told that 20 students saw the movie and 5 didn't, meaning there were in total 20 + 5 = 25 students; therefore, the ratio is
[tex]\frac{\text{saw the movie}}{\text{total students}}=\frac{20}{25}[/tex]To simplify the ratio, we divide both the numerator and the denominator by 5. This gives
[tex]\frac{20\div5}{25\div5}[/tex][tex]\frac{4}{5}[/tex]Hence, the ratio of the students who saw the movie to the total number is 4 : 5.
Transpose and solve for x
15x³=723
Answer:
x = 241 1/3
————
5 1/3
Step-by-step explanation:
Answer:
x = ^3(square root )of 18075 or 5.24875253...
-----------------------
5
Step-by-step explanation:
isolate the variable by deviding each side by factors that dont contain the variable
hope this helped have a good day ^^
g(n) = 3n - 4f(n) = n^3 - 2nFind (gºf)(n)
hello
let's get the functions out first
[tex]g(n)=3n-4[/tex][tex]f(n)=n^3-2n[/tex][tex]g\cdot f(n)=\text{ ?}[/tex][tex]\begin{gathered} g.f(n)=(3n-4)\cdot(n^3-2n) \\ g\mathrm{}f(n)=3n^4-6n^2-4n^3+8n \\ g\mathrm{}f(n)=3n^4-4n^3-6n^2+8n \end{gathered}[/tex]How many times smaller is 1.9 × 10^3 than 4.085 × 10^5?
1.9 × 10^3 is 215 times smaller than 4.085 × 10^5.
The basic formula for the area of a rectangle is length x width, but the basic formula for volume is length x width x height. The calculation does not change depending on how you refer to different measurements. For example, you can use depth instead of height.
Every 3D object occupies a certain space. This space is measured by its volume. Volume is defined as the space occupied within the bounds of an object in three-dimensional space. Also called the capacity of the object. The volume of an object is the amount of space it fills. Large capacity is measured in cubic meters m3. Smaller volumes are measured in cubic centimeters cm3 or cubic millimeters mm3.
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3. Smartphones come with an app that keeps track of the amount of time that the phone is being used. For teenagers, the distribution of amount of time they use their phone is approximately normal with mean = 7.75 hours per day and standard deviation = 1.25 hours per day.
(a) What percent of teenagers use their phone less than 5 hours per day?
(b) What percent of teenagers use their phone more than 10 hours per day?
(c) What proportion of teenagers use their phone between 6 to 8 hours per day?
(d) What is the 75th percentile of this distribution?
Using the normal distribution, it is found that:
a) 1.39% of teenagers use their phone less than 5 hours per day.
b) 3.59% of teenagers use their phone more than 10 hours per day.
c) 49.85% of teenagers use their phone between 6 to 8 hours per day.
d) The 75th percentile of the distribution is of 8.59 hours.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the fraction presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the daily amounts they use their phone are given as follows:
[tex]\mu = 7.75, \sigma = 1.25[/tex]
The proportion that use their phone for less than 5 hours a day is given by the p-value of Z when X = 5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (5 - 7.75)/1.25
Z = -2.2
Z = -2.2 has a p-value of 0.0139.
Thus the percentage is of 1.39%.
The proportion that use their phone for more than 10 hours a day is one subtracted by the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (10 - 7.75)/1.25
Z = 1.8
Z = 1.8 has a p-value of 0.9641.
1 - 0.9641 = 0.0359 = 3.59% (percentage).
The proportion between 6 and 8 hours a day is the p-value of Z when X = 8 subtracted by the p-value of Z when X = 6, hence:
X = 8:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (8 - 7.75)/1.25
Z = 0.2
Z = 0.2 has a p-value of 0.5793.
X = 6:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (6 - 7.75)/1.25
Z = -1.4
Z = -1.4 has a p-value of 0.0808.
0.5793 - 0.0808 = 0.4985 = 49.85% (percentage).
The 75th percentile is X when Z = 0.675, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
0.675 = (X - 7.75)/1.25
X - 7.75 = 0.675 x 1.25
X = 8.59 hours.
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ames determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements are true? Check all that apply. 7 x + 4 and 3 x + 5 + 4 x minus 1 When x = 2, both expressions have a value of 18. The expressions are only equivalent for x = 4 and x = 6. The expressions are only equivalent when evaluated with even values. The expressions have equivalent values for any value of x. The expressions should have been evaluated with one odd value and one even value. When x = 0, the first expression has a value of 4 and the second expression has a value of 5. The expressions have equivalent values if x = 8.
The statements are true about the given expressions include the following:
When x = 2, both expressions have a value of 18.The expressions have equivalent values for any value of x.The expressions have equivalent values if x = 8.How to determine whether the expressions are equivalent?In order to determine whether these expressions are equivalent, we would evaluate the two expressions based on each of the statements:
"When x = 2, both expressions have a value of 18"
7x + 4 = 7(2) + 4 = 14 + 4 = 18.
3x + 5 + 4x - 1 = 3(2) + 5 + 4(2) - 1 = 6 + 5 + 6 - 1 = 18.
"The expressions are only equivalent for x = 4 and x = 6." is false has demonstrated above.
"The expressions have equivalent values for any value of x." is true.
Let x = 1;
7x + 4 = 7(1) + 4 = 7 + 4 = 11.
3x + 5 + 4x - 1 = 3(1) + 5 + 4(1) - 1 = 3 + 5 + 4 - 1 = 11.
Let x = 10;
7x + 4 = 7(10) + 4 = 70 + 4 = 74.
3x + 5 + 4x - 1 = 3(10) + 5 + 4(10) - 1 = 30 + 5 + 40 - 1 = 74.
"The expressions should have been evaluated with one odd value and one even value." is false because all values of x are solutions.
"When x = 0, the first expression has a value of 4 and the second expression has a value of 5." is false because the two expressions are equivalent expressions.
In conclusion, "The expressions have equivalent values if x = 8." is true because the two expressions are equivalent expressions.
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Explain what the slope and intercept mean in each situation.
A graph represents the perimeter, y, in units, for an equilateral triangle with side length x units. The slope of the line is 3 and the y-intercept is 0.
The amount of money, y, in a cash box after x tickets are purchased for carnival games. The slope of the line is 14 and the y-intercept is 8.
The number of chapters read, y, after x days. The slope of the line is 54 and the y-intercept is 2.
The graph shows the cost in dollars, y, of a muffin delivery and the number of muffins, x, ordered. The slope of the line is 2 and the y-intercept is 3.
The slope intercept form of the each situation is given by
a) y = 3x + 0
b) y = 14x + 8
c) y = 54x + 8
d) y = 2x + 3
What is slope intercept form?
Slope intercept form- The equation of the line in slope-intercept form is given by:
y = mx + c
Here,
(x, y) = Every point on the line
m = Slope of the line
c = y-intercept of the line
a) In situation one
slope of the line = 3 and y- intercept = 0 =c
The equation becomes y = 3x+ 0
y = 3x
b) slope of the line = 14 and y intercept = 8
y = 14x + 8
c) slope of the line = 54 and y- intercept = 2
y = 54x + 2
d) slope of the line = 2 and y- intercept = 3
y = 2x + 3
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read the attachment.
Answer: C, D
Step-by-step explanation:
Answer C is correct because 2/5 is 0.4 and 0.55 is greater than 0.4.
Answer D is correct because 2/5 is 0.4 and 3/4 is 0.75 therefore 0.75 is greater than 0.4.
Answer:
C and D
Step-by-step explanation:
On the number line, the first point is 2/5. 2 divided by 5 gets you .4, so that's why it's at .4. .55 is the next point. .55 is a bigger number than .4, so it would be an answer.
3 divided by 4 gets you .75. 3/4=.75. 2/5=.4. .75 is greater than .4. 3/4 is greater than 2/5
Write the function in vertex form.
y = 3x² - 8x + 13
The function is y=
Answer:
y = 3(x - [tex]\frac{4}{3}[/tex] )² + [tex]\frac{23}{3}[/tex]
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
given
y = 3x² - 8x + 13
using the method of completing the square
the coefficient of the x² term must be 1 so divide first 2 terms by 3
y = 3(x² - [tex]\frac{8}{3}[/tex] x) + 13
add/subtract ( half the coefficient of the x- term )² to x² - [tex]\frac{8}{3}[/tex] x
y = 3(x² + 2(- [tex]\frac{4}{3}[/tex] )x + [tex]\frac{16}{9}[/tex] - [tex]\frac{16}{9}[/tex] ) + 13
= 3(x - [tex]\frac{4}{3}[/tex] )² + 3(- [tex]\frac{16}{9}[/tex] ) + 13
= 3(x - [tex]\frac{4}{3}[/tex] )² - [tex]\frac{16}{3}[/tex] + [tex]\frac{39}{3}[/tex]
= 3(x - [tex]\frac{4}{3}[/tex] )² + [tex]\frac{23}{3}[/tex] ← in vertex form
which term number -385 for the sequence: -25, -35, -45, -55
question in the screenshot
Answer:
4.2
Step-By-Step explanation:
12.5+1.5=14
14 times 3= 42
42/10= 4.2
Pls help Lila's mom is decorating her room and placed acircular rug near her window for story time.How much space does this rug take up if its diametermeasures 25 feet?
Step1: Write the area of the circular Rug
The area of the circle is
[tex]\Pi r^2[/tex]From the question the diameter is 25feet, hence the radius is
[tex]\begin{gathered} \text{radius}=\frac{diameter}{2} \\ =\frac{25}{2} \end{gathered}[/tex]Step2: substitute the value into the formula
[tex]\begin{gathered} \text{area of circular rug=area of a circle=}\Pi r^2 \\ =\frac{22}{7}\times\frac{25}{2}\times\frac{25}{2} \\ =\frac{13750}{28} \\ =491.07ft^2 \end{gathered}[/tex]Hence the area of the circular rug is 491.07 square feet
The will take approximately 491square feetyou
32 Développe et réduis les expressions
suivantes :
A = (x + 4)(x + 3)
B = (y + 3)(2y + 8)
C = (3z + 4)(5 + 6z)
D = (7t+8)(3 + 5f)
the determinant of a is the product of the pivots in any echelon form u of a, multiplied by (1)r, where r is the number of row interchanges made during row reduction from a to u.
The determinant of a is the product of the pivots in any echelon form u of a, multiplied by (1)r, where r is the number of row interchanges made during row reduction from a to u is False.
Given:
The determinant of a is the product of the pivots in any echelon form u of a, multiplied by (1)r, where r is the number of row interchanges made during row reduction from a to u.
Definition of det A:
det A = (-1)^r * (product of pivots in echelon form) if A is invertible or 0 when A is not invertible.
From definition of det A we can simply say the given statement is false - This can only hold if A is an invertible matrix, but the problem does not state this.
Reduction to an echelon form may also include scaling a row by a nonzero constant, which can change the value of the determinant.
Therefore the determinant of a is the product of the pivots in any echelon form u of a, multiplied by (1)r, where r is the number of row interchanges made during row reduction from a to u is False.
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Hello I need help with A please make it easy and simple to understand
distanceSolution:
Given that a toy car placed on the floor travels at a constant acceleration for 3 seconds reaching a velocity of 4v m/s, we have
It slows down with a constant deceleration of 0.5 m/s² for 4 seconds before hitting a wall and stopping. This is as shown below:
Thus, the velocity-time graph for the toy car is as shown below:
The total distance traveled by the toy car is evaluated by calculating the area of the triangle ABC. Thus,
[tex]\begin{gathered} \text{Total distance traveled = }\frac{1}{2}\times7\times4 \\ =14\text{ meters} \end{gathered}[/tex]Hence, the
I need help on this question its due in tomorrow.
The perimeter of the semi circle is 56.54 cm
How to find the perimeter of a semi circle?The perimeter of a figure is the sum of the whole sides of the figure.
The perimeter of the semi circle is the sum of the whole sides of the semi circle.
Therefore,
perimeter of the semi circle = 2πr / 2 + 2r
perimeter of the semi circle = πr + 2r
where
r = radiusperimeter of the semi circle = 3.14 × 11 + 2r
perimeter of the semi circle = 34.54 + 2(11)
perimeter of the semi circle = 34.54 + 22
Therefore,
perimeter of the semi circle = 56.54 cm
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The question is in the photo. Complete C and D.
x = -12
Explanations:Given the following equation
[tex]-\frac{1}{2}x=6[/tex]We are to find the variable x. To do that, we will multiply both sides by -2 as shown:
[tex]\begin{gathered} -\frac{1}{2}x\times-2=6\times-2 \\ x=6\times-2 \\ x=-12 \end{gathered}[/tex]This shows that the value of x for the equation to be true is -12
Check
If x = -12, on substiituting;
[tex]\begin{gathered} =-\frac{1}{2}(-12) \\ =\frac{-12}{-2} \\ =\text{ 6} \end{gathered}[/tex]Since the result is equivalent to 6, this shows that the solution x = -12 is correct.
A line passes through the points (-4,-3) and (2, 6). Determine the slope of the line.
• m = 2/3
O The slope is undefined.
Om = 0
Om =3/2
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{6 +3}{2 +4} \implies \cfrac{ 9 }{ 6 } \implies {\Large \begin{array}{llll} \cfrac{ 3 }{ 2 } \end{array}}[/tex]
Evaluate the following expression, given that x = -6 and y =12.
|2x+5| - 8y
The value of expression |2x+5| - 8y is -89 when x = -6 and y =12
What is Expression?Expression is a combination of numbers, variables and Operators.
The given expression is mod two x plus 5 minus eight y.
|2x+5| - 8y
This expression has addition, subtraction and multiplication operators.
Given value of x is minus six and y is equal to twelve.
x=-6 and y=12
plug in values of x and y in expression
|2(-6)+5|-8(12)
|-12+5|-96
|-7|-96
The value in mod will be always taken as positive
7-96
-89
Hence the value of expression |2x+5| - 8y is -89 when x = -6 and y =12.
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At store a 3 lb of apples cost $12 at store B the cost is given by y = 2x where Y is the cost in dollars and X is the number of pounds of apples the cost of apples at store C is shown in the graph what is the unit price of apples at store a explain how you found this unit price
The most appropriate choice for equation of line in slope intercept form will be given by
Unit price of apple in store A = $4
Unit price of apple in store A = $2
Unit price of apple in store A = $3
What is equation of line in slope intercept form?
Equation of line in slope intercept form is given by y = mx + c
Where, m is the slope of the line and c is the y intercept of the line
The distance from the origin to the point where the line cuts the x axis is called x intercept
The distance from the origin to the point where the line cuts the y axis is called y intercept
Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis
If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by [tex]tan\theta[/tex]
If the line passes through ([tex]x_1,y_1[/tex]) and ([tex]x_2, y_2[/tex])
slope = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Unit price of apple in store A = [tex]\frac{12}{3}[/tex] = $4
For store B
Putting x = 1
y = [tex]2 \times 1[/tex]
y = 2
Unit price of apple in store B = $2
For store C
From the graph,
At x= 1, y = 3
Unit price of apple in store C = $3
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Complete Question
The graph has been attached
