The tuxedo was rented for 4 days.
Let's start by assigning variables to the unknowns. Let "x" be the number of additional days rented, and "d" be the total number of days rented (including the first day).
From the given information, we know that the flat fee for the rental is $150, so the cost of the additional days is the total cost minus the flat fee, which is $300 - $150 = $150. We also know that the cost for each additional day is $50. Therefore, we can set up the equation:
$150 + $50x = $300
Subtracting $150 from both sides, we get:
$50x = $150
Dividing both sides by $50, we get:
x = 3
So the tuxedo was rented for 3 additional days, making the total number of days rented:
d = 1 + 3 = 4
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The supply and demand function of a good are p=Qs+8, p=-3Qd+80.find
A.the equilibrium price and quantity if the government imposes a fixed tax of $36 on each good.
B.find the corresponding value of the government tax revenue.
The equilibrium price and quantity if the government imposes a fixed tax of $36 on each good is $26 and the corresponding value of the government tax revenue is $648
To find the equilibrium price and quantity, we need to set Qs = Qd and solve for the price.
Qs = Qd
=> p = -3Qd + 80 = Qs + 8
=> -3Qd + 80 = Qd + 8 (substituting Qs = Qd)
=> 4Qd = 72
=> Qd = 18
=> Qs = 18
Therefore, the equilibrium price is:
p = Qs + 8 = 18 + 8 = 26
Now, if the government imposes a fixed tax of $36 on each good, the new supply function becomes:
p = Qs + 8 - 36
=> Qs = p - 28
And the demand function remains the same:
p = -3Qd + 80
Setting Qs = Qd and substituting Qs and Qd in terms of p, we get:
p - 28 = -3Qd + 80
=> -3Qd = p - 52
=> Qd = (52 - p) / 3
The government tax revenue is the product of the tax and the quantity sold, which is:
Tax revenue = tax per unit × quantity sold
=> Tax revenue = 36 ×Qs
Substituting Qs = 18, we get:
Tax revenue = 36 × 18 = $648
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Write the equation of the line perpendicular to y=-1/3x+5 and passes through the point (1,-10)
Answer:
Step-by-step explanation:
First, we need to determine the slope of the line we want to find since it is perpendicular to the given line. The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line.
The given line has a slope of -1/3, so the slope of the line we want to find is 3 (the negative reciprocal of -1/3).
Now we can use the point-slope form of the equation of a line to find the equation of the line passing through (1,-10) with a slope of 3:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the point. Substituting the values we have:
y - (-10) = 3(x - 1)
Simplifying:
y + 10 = 3x - 3
Subtracting 10 from both sides:
y = 3x - 13
Therefore, the equation of the line perpendicular to y=-1/3x+5 and passing through the point (1,-10) is y = 3x - 13.
I WILL GIVE BRAINLIST!!! HELP PLS
The evaluated probability that a randomly choosing a point within the circle falls in the red-shaded triangle is 0.30,
To evaluate this probability, we have to calculate the ratio of the area of the red-shaded triangle to the area of the circle.
The area of the circle is derived as πr²
Here,
r = radius of the circle.
In this case, r = 5.
Staging the values
π(5)² = 25π.
So, the area of the circle is 25π.
The area of the red-shaded triangle can be evaluated by using the formula for the area of a triangle which is
[tex]1/2 * base * height[/tex]
In this case, the base is 6 and the height is 8. So, the area of the red-shaded triangle is
1/2 x 6 x 8
= 24.
Hence, the probability that a randomly selected point within the circle falls in the red-shaded triangle is
P = (Area of red-shaded triangle) / (Area of circle)
= 24 / (25π)
= 24 / 25 x 3.14
= 24 / 78.5
≈ 0.30
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Now It's Time to Practice on Your Own
What is the area of a regular octagon with a side length of 6 mm and an apothem length of 7.243 mm?
Round your answer to the nearest hundredth.
URGENT
Answer:
173.83
Step-by-step explanation:
An octagon has 8 sides (octa-, right, like octopus)
"regular" means all the sides are the same length.
The apothem is given, 7.243, it goes from the center to the middle of a side, at a right angle. See image. Make a triangle. Use area formula for triangle.
A = 1/2bh
Multiply by 8, bc there are 8 of these identical triangles.
OR, use the area formula for an n-sided regular polygon:
A = 1/2asn
see image.
logan is buying his baby sister a stacking toy with his allowance. the cost of a wooden stacking toy is $25.50. a plastic stacking toy costs 1/3 the price of the wooden toy. sales tax on either would be 6%. how much more will logan pay if he buys the wooden toy instead of the plastic toy?
Logan will pay $18.02 more if he buys the wooden stacking toy instead of the plastic stacking toy.
The cost of the plastic stacking toy is 1/3 the cost of the wooden stacking toy:
Cost of plastic toy = (1/3) x $25.50 = $8.50
If Logan buys the wooden toy, he will pay:
Cost of wooden toy = $25.50
To find the amount of sales tax on either toy, we can multiply the cost of the toy by the tax rate of 6%:
Sales tax = 6% x cost of toy
Sales tax on the wooden toy = 6% x $25.50 = $1.53
Sales tax on the plastic toy = 6% x $8.50 = $0.51
If Logan buys the wooden toy, he will pay an extra:
Total cost difference = Cost of wooden toy - Cost of plastic toy + Sales tax on wooden toy - Sales tax on plastic toy
Total cost difference = ($25.50 - $8.50) + ($1.53 - $0.51)
Total cost difference = $17 + $1.02
Total cost difference = $18.02
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The area covered by a certain population of bacteria increases according to a continuous exponential growth model. Suppose that a sample culture has an initial area of 6.5 and an observed doubling time of 22 minutes.
Let t be the time (in minutes) passed, and let y be the area of the sample at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
A formula relating y to t is y = 6.55[tex]e^{k(22)}[/tex]ln(26/6.5)t)
Let's consider a sample culture of bacteria with an initial area of 6.5. We observe that the population of bacteria doubles in size every 22 minutes. We want to find a formula that relates the area of the sample culture, denoted as y, to the time passed, denoted as t.
Let's call this proportionality constant k. We can then write the differential equation that describes the growth of the population as:
dy/dt = ky
where dy/dt is the rate of change of the area with respect to time.
We can solve this differential equation by separation of variables. We first separate the variables and then integrate both sides:
dy/y = k dt
∫(dy/y) = ∫k dt
ln|y| = kt + C
where C is a constant of integration. To solve for C, we use the initial condition that the area of the sample culture is 6.5 when t = 0. This gives:
ln|6.5| = k(0) + C
C = ln|6.5|
Substituting this value of C back into the solution, we get:
ln|y| = kt + ln|6.5|
ln|y/6.5| = kt
Finally, we can solve for y to get the formula we were looking for:
y = 6.5[tex]e^{kt}[/tex]
where k is the proportionality constant that depends on the doubling time of the bacteria. We can use the fact that the population doubles in size every 22 minutes to find k. If the population doubles, then the area of the population quadruples. This means that after 22 minutes, the area is 6.5 x 4 = 26. We can use this to find k:
26 = 6.5[tex]e^{k(22)}[/tex]
[tex]e^{k(22)}[/tex] = 26/6.5
k(22) = ln(26/6.5)
k = (1/22)ln(26/6.5)
Substituting this value of k back into the formula we derived earlier, we get the exact expression relating y to t:
y = 6.55[tex]e^{k(22)}[/tex]ln(26/6.5)t)
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6. The ratio of the circumference (C) of a circle to its diameter (d) is approximately 3.1. Which of the following does not show that ratio
A. C = 40.3, d = 13
B. C = 29.7, d=9
C. C= 21.7, d= 7
D. C= 37.2, d = 12
The ratio is not approximately 3.1.
Option B is the correct answer.
We have,
Let's use the formula for the ratio of the circumference to the diameter of a circle:
C/d = pi (where pi is approximately 3.14).
Therefore, the ratio should be approximately 3.14, not 3.1.
Using the given answer choices:
A. C/d = 40.3/13 = 3.1... approximately correct
B. C/d = 29.7/9 = 3.3... not correct
C. C/d = 21.7/7 = 3.1... approximately correct
D. C/d = 37.2/12 = 3.1... approximately correct
Therefore,
The ratio is not approximately 3.1.
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Need help with this a lil confused
I am also in confused
need help now will give brainlist
Answer:
your selection is correct. The slope is positive. As x increases y increases.
A composite figure is made up of two rectangles and a right triangle. The figure and its dimensions in centimeters are shown in the diagram. What is the area of the composite figure in square centimeters?
The area of the composite figure is 336 centimeters²
Since, A right triangle or right angled triangle, or more formally an orthogonal triangle, formerly referred as rectangle triangle, is a triangle in which one angle is a right angle, that is in which two sides are perpendicular to each other. It forms the basis of trigonometry on the basis of its sides and angles.
Now, The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm2 and m2. Area of a shape is a two dimensional quantity.
Divide the composite figure into smaller shapes.
A is a rectangle with width 6cm and length 12cm
Hence, Area of A= 12 x 6 = 72cm²
B is a triangle with base 6cm and height 8cm
Therefore area of triangle=1/2 x base x height
= 1/2 x 6x 8 = 24cm²
C is a rectangle with breadth 30cm and length 8cm
Area of figure C =30 x 8 = 240cm²
So, total area of the figure is =(72+24+240)cm²
=336cm²
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Complete question is,
What is the area of this composite figure?
A figure is comprised of 1 rectangle and 2 triangles. The rectangle has a length of 16 centimeters and width of 10 centimeters. Both triangles have a base of 16 centimeters and height of 6 centimeters.
96 centimeters squared
160 centimeters squared
208 centimeters squared
256 centimeters squared
Select two numbers that make the inequality true.
2x – 3 > 1
A. 3/2
B. 10/2
C. 1
D. 2
E. 6.3
Answer:
B. 10/2, E. 6.3
Step-by-step explanation:
First, you need to solve for x by isolating it on one side of the inequality. You can do this by adding 3 to both sides and then dividing by 2:
2x - 3 > 1
2x - 3 + 3 > 1 + 3
2x > 4
2x / 2 > 4 / 2
x > 2
Next, you need to find two numbers that are greater than 2 and plug them into the inequality to check if they make it true. You can choose any numbers that are larger than 2, but it is easier to pick from the given options. For example, let’s try A. 3/2 and B. 10/2:
A. x = 3/2
2(3/2) - 3 > 1
3 - 3 > 1
0 > 1, False
B. x = 10/2
2(10/2) - 3 > 1
10 - 3 > 1
7 > 1, True
Then, you need to repeat the same process for the remaining options until you find another number that makes the inequality true. For example, let’s try C. 1, D. 2, and E. 6.3:
C. x = 1
2(1) - 3 > 1
2 - 3 > 1
-1 > 1 False
D. x = 2
2(2) - 3 > 1
4 - 3 > 1
1 > 1, False
E. x = 6.3
2(6.3) - 3 > 1
12.6 - 3 > 1
9.6 > 1, True
Finally, you need to select the two numbers that make the inequality true from the options. The answer is B. and E. B. 10/2 and E. 6.3 are two numbers that make the inequality true.
can someone please do 13 &14
The results for each composite function at each x-value are listed below:
Case 13: (f ° g) (1) = 26 (Right choice: D)
Case 14: (f + g) (3) = 20 (Reight choice: E)
How to evaluate a composite functionIn this problem we find two cases of composite functions that must be evaluated at given x-value. The procedure is described below:
Perform the operations between the two functions.Evaluate the function at given x-value. Mark the right choice.Now we proceed to solve for each case:
Case 1: f(x) = x² + x - 4, g(x) = 3 · x + 2
(f ° g) (x) = [(3 · x + 2)² + (3 · x + 2) - 4]
(f ° g) (1) = [(3 · 1 + 2)² + (3 · 1 + 2) - 4]
(f ° g) (1) = (5² + 5 - 4)
(f ° g) (1) = 26
Case 2: f(x) = x² + x, g(x) = x² - 1
(f + g) (x) = (x² + x) + (x² - 1)
(f + g) (x) = 2 · x² + x - 1
(f + g) (3) = 2 · 3² + 3 - 1
(f + g) (3) = 18 + 3 - 1
(f + g) (3) = 20
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can someone please write this in exponential form
Using the exponential function we can rewrite the expression as:
[tex]H = 10^{-4}[/tex]
How to write this in exponential form?Here we start with the equation:
log₁₀(H) = -4
We can rewrite the logarithm part as follows:
log₁₀(H) = ln(H)/ln(10)
Then we can rewrite:
ln(H)/ln(10) = -4
ln(H) = -4*ln(10)
Now we can move the coefficeint -4 as a exponent:
[tex]ln(H) = ln(10^{-4})[/tex]
Now apply the exponential equation to both sides:
[tex]exp(ln(H)) = exp(ln(10^{-4}))[/tex]
[tex]H = 10^{-4}[/tex]
That is what we wanted.
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Explain reasoni my
The measure of exterior angle 1 is 120 degrees. (option a)
In this case, we are given two interior angles of the polygon, which are 60 degrees and 25 degrees. The sum of the measures of the interior angles of a polygon with n sides is given by the formula (n-2) x 180 degrees. Therefore, for this polygon, the sum of its interior angles can be calculated as
=> (n-2) x 180 = (3-2) x 180 = 180 degrees.
Next, we can use the fact that the sum of an exterior angle and its adjacent interior angle is always 180 degrees. Therefore, we can calculate the measure of the exterior angle 1 as follows:
Exterior angle 1 + Interior angle 1 = 180 degrees
Exterior angle 1 + 60 degrees = 180 degrees (since we know that Interior angle 1 is 60 degrees)
Exterior angle 1 = 180 degrees - 60 degrees
Exterior angle 1 = 120 degrees
Hence the correct option is (a).
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Joe painted 3/4 of a bedroom in a 1/2 of a day. How many days will it take for joe to paint one bedroom?
[tex]\begin{array}{ccll} bedroom&day\\ \cline{1-2} \frac{3}{4}&\frac{1}{2}\\[1em] 1&d \end{array}\implies \cfrac{~~ \frac{ 3}{4 } ~~}{1}~~ = ~~\cfrac{~~ \frac{1 }{2 } ~~}{d}\implies \cfrac{3}{4}=\cfrac{1}{2d} \\\\\\ 6d=4\implies d=\cfrac{4}{6}\implies d=\cfrac{2}{3} ~~ \textit{of a day}[/tex]
There are 26 boys and 20 girls in a class.
The boys and the girls have some counters.
The mean number of counters that the boys have is 28.
The mean number of counters that the girls have is 19.
Work out the mean number of counters the 46 children have.
Computing the total number of counters in the class as 1,108, the mean number of counters that the 46 children have is 24.
What is the mean?The mean refers to the average value.
The average is the quotient of the total value divided by the number of items in the data set.
The number of boys in the class = 26
The number of girls in the class = 20
The total number of boys and girls in the class = 46
The mean number of counters that the boys have = 28
The total number of counters that the boys have = 728 (28 x 26)
The mean number of counters that the girls have =19
The total number of counters that the girls have = 380 (19 x 20)
The total number of counters that the class has = 1,108 (728 + 380)
The average or mean number of counters in the class = 24 (1,108 ÷ 46)
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which of the following is a true statement
A. A trapezoid is a type of parallelogram
B. A trapezoid is a type of quadrilateral
C. A polygon is a type trapezoid
Answer:
the answer is B
Step-by-step explanation:
all trapezoids are quadrilaterals
Could the points (-4, 3), (-1, 1) and (1, 3) for the vertices of a right triangle? Why or why not?
The points (-4, 3), (-1, 1), and (1, 3) cannot form the vertices of a right triangle.
To determine if the points (-4, 3), (-1, 1), and (1, 3) can form the vertices of a right triangle
we need to check if the square of the length of one side of the triangle is equal to the sum of the squares of the lengths of the other two sides.
We calculated the distances between the three points using the distance formula, and checked if any of the three sides of the triangle satisfied the Pythagorean theorem, which relates the sides of a right triangle.
Since none of the three sides satisfied the Pythagorean theorem, the given points cannot form the vertices of a right triangle.
Therefore, the points (-4, 3), (-1, 1), and (1, 3) cannot form the vertices of a right triangle.
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multiply three 1,5. -5,6. 0,0
what are the coordinates of the center of a circle whose equation is (x+10)^2 + (y-8)^2=17
The solution is :
the center of the circle is (-10,8)
Third option is correct.
Here, we have,
The equation of the circle is (x+10)^2 + (y-8)^2=17
This equation can be rewritten as
(x- (-10) )^2 + (y-8)^2=17
The standard form of the circle is given by
(x- h )^2 + (y-k)^2=r^2
, where (h,k) is the center of the circle.
On comparing the given equation of circle with the standard form
h = -10, k = 8
Hence, the center of the circle is (-10,8)
Third option is correct.
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The complex solution to a quadratic equation is x equals start fraction negative six plus or minus square root of negative 432 end square root over six end fraction full stop Write this solution in standard form, x = a ± bi, where a and b are real numbers. Justify your answer by showing your work. (5 points)
So expressing the given complex solution x = (- 6 ± √(-432))/6 as x = a ± bi we can write that x = -1 ± 2√3i and the values of a and b are -1 and 2√3 respectively.
Given that the standard form of writing a complex solution is,
x = a ± bi, where a and b are the real numbers and i = √(-1)
Given that one of this type of solution is,
x = (- 6 ± √(-432))/6
x = -6/6 ± √(-432)/6, differentiate denominators with each numerator
x = -1 ± √((-1)*144*3)/6
x = -1 ± 12√3i/6
x = -1 ± 2√3i
Comparing with x = a ± bi we get, a = -1 and b = 2√3.
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The average weekly salary of two employees is $5500. One makes $450 more than the other. Find their salaries.
One employee makes
and the other makes S
X
S
Based on an equation, the salaries of the two employees whose average weekly salary is $5,500 are as follows:
X = $5,25
S = $5,725.
What is an equation?An equation is a mathematical statement that shows that two or more algebraic expressions are equal or equivalent.
While equations use the equal symbol, mathematical or algebraic expressions combine variables with numbers, constants, and values using mathematical operands.
The average weekly salary of two employees = $5,500
The number of employees = 2
Th,e total weekly salaries of the two employees = $11,000 ($5,500 x 2)
Let the salary of Employee One = x
Let the salary of Employee Two = s
x = s - 450
Equation:11,000 = s - 450 + s
11,450 = 2s
s = $5,725
x = $5,275 ($5,725 - $450)
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Identify the type of arrangement used in the picture to pack cans
The type of arrangement used in the picture to pack cans is a linear arrangement.
What is the arrangement about?
If the cans are arranged in a straight line, this would be called a linear arrangement. In a linear arrangement, the objects are arranged in a single line or row.
This type of arrangement is commonly used for packing and displaying items that need to be easily accessible or for creating a uniform and organized appearance. It can be used for packing cans, bottles, or other similarly shaped objects.
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Identify the type of arrangement used in the picture to pack cans
Two angles are vertical. The first angle measures (2x + 15)°, and the second measures (4x + 9)°.
The value of x is 3 when the two angles are vertical.
Vertical angles are formed when two lines meet each other at a point.
They are always equal to each other.
The first angle measures (2x + 15)°, and the second measures (4x + 9)°.
2x+15 = 4x+9
We have to find the value of x
Take the variable terms on one side and constants on other side
15-9=4x-2x
6=2x
Divide both sides by 2
x=3
Hence, the value of x is 3 when the two angles are vertical.
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The legs of a right triangle measure 36 and 77 units. What is the measure of the hypotenuse? Answer as a number only
Using the Pythagorean theorem: a^2 + b^2 = c^2, where a=36, b=77, and c is the hypotenuse.
36^2 + 77^2 = c^2
1296 + 5929 = c^2
7225 = c^2
c = √7225
c = 85
The hypotenuse is 85 units
A vase is shaped like a triangular prism. The volume of the vase is 540 cm. The area of the base is 120 cm. What is the height of the vase?
[tex]\textit{volume of a prism}\\\\\ V=Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ V=540\\ B=120 \end{cases}\implies 540=120h\implies \cfrac{540}{120}=h\implies \cfrac{9}{2}=h[/tex]
Answer:
1.5cm height giving ace
The tenth through thirteenth terms of an arithmetic sequence are given by a10=47, a11=53. a12=59, and a13=65. Which formula can be used to find a n?
A. an=6n-13
b. an=6n+37
c. an=6n+41
d. an=6n-47
e, an=6n-7
Answer: e, an=6n-7.
Step-by-step explanation: Any pair of consecutive terms can be used to determine the arithmetic sequence's common difference (d), which can then be used in conjunction with the given term to determine the nth term using the following formula:
an = a1 + (n - 1) d.
Let's use the pair a11=53 and a10=47 to find d:
d = a11 - a10 = 53 - 47 = 6
Now we can use the formula to find any term of the sequence. Let's use the given value of a13=65 to find a13:
a13 = a1 + (13 - 1)d
65 = a1 + 12(6)
65 = a1 + 72
a1 = -7
Therefore, the formula that can be used to find the nth term of the arithmetic sequence is:
an = -7 + (n - 1)6
Simplifying this expression, we get:
an = 6n - 7.
please help i'll give 10 points
The the distance between these points (6,0) and (26,0) is 20 units.
We have,
The distance between two points is the length of the line joining the two points. Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
Given that,
endpoints are (6,0) and (26,0) of the line segment.
The distance= √(26-6)²-(0-0)²
=20 units
Hence, The the distance between these points (6,0) and (26,0) is
20 units.
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the following mapping statements describe the transformation of the vertices of the quadrilateral.
A(-3, 2)→ A'(-1,0)
B(-2, 2)→ B'(0, 0)
C(2, 1) → C'(0, -1)
D(-3, 1)→ D'(−1,−1)
which function correctly describes the transformation
1. (x,y) → (x+2, y+2)
2. (x,y) → (x +2, y)
3. (x,y) →(x+2, y-2)
4. (x,y) →(x,y -2)
Answer:1
Step-by-step explanation:
Question 8 of 10
What is the slope of the line shown below?
(-3,-1)
(5, 1)
OA. 1/1
OB. 4
OC. -4
OD. - 1/2
The slope of the line shown is equal to: A. 1/4.
How to calculate the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using this mathematical equation;
Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Rate of change (slope) = rise/run
Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)
Rate of change (slope) = (1 + 1)/(5 + 3)
Rate of change (slope) = 2/8
Rate of change (slope) = 1/4.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 1/4.
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