With the help of slope we conclude that Ashley needs to read 100 pages every 10 hours to finish the book in 30 hours.
What is slope?Slope is a measure of the steepness of a line, and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
According to given information:To find out how many pages Ashley needs to read every 10 hours, we need to look at the slope of the line on the graph. The slope tells us the rate of change of the number of pages read per hour.
We can use the formula for slope, which is:
slope = (change in y) / (change in x)
In this case, the "change in y" is the number of pages Ashley needs to read in 30 hours minus the number of pages she needs to read in 0 hours (which is the starting point of the graph). The "change in x" is 30 hours minus 0 hours. So we have:
slope = (number of pages in 30 hours - number of pages in 0 hours) / (30 hours - 0 hours)
Using the graph, we can see that the number of pages Ashley needs to read in 30 hours is 300. The number of pages she needs to read in 0 hours (or the starting point of the graph) is 0. So we have:
slope = (300 - 0) / (30 - 0) = 10
This means that Ashley needs to read 10 pages per hour to finish the book in 30 hours. To find out how many pages she needs to read every 10 hours, we can multiply the hourly rate by 10:
10 pages per hour * 10 hours = 100 pages
Therefore, Ashley needs to read 100 pages every 10 hours to finish the book in 30 hours.
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Convert: 83.36m= cm
pls help
Answer: 8,336
Step-by-step explanation:
So 1 meter is equal to 100 centimeters. All you have to do is multiply 83.36 by 100.
83.36 * 100 = 8,336
Hope this helps!!! :)
C. The table below shows the ages in years of 42 children at a birthday party. AGE(YEARS) NO OF CHIDREN 7 2x 8 3x 9 4x-1 10 X 11 X-2 (i). Find the value of x. (ii). Calculate, correct to the nearest whole number the mean age. (iii). Find the probability of selecting at random a child whose age is less than 9 years. 12 x-3 CURT
(1) The value of X is equal to 4 (2) The mean age is 3. (3) The probability of randomly selecting a child under the age of 9 is approximately 0.83.
How to calculate the average?
The formula for calculating the average of given numbers is equal to the sum of all values divided by the total number of values. There are three main types of averages: mean, median, and mode. All of these techniques work slightly differently and often give slightly different typical values.
(i). Given that there are a total of 42 children on the birthday, finding the value of x:
2x + 3x (4x-1) + x + (x-2) + (x-3) = 42
11x - 6 = 42
11x = 48
x = 4
Therefore, the value of x is equal to 4.
(ii). To find the average age, we need to calculate the sum of all the ages and divide by the total number of children:
Average age = (7 x 2 + 8 x 3 + 9 x (4-1) +10 x 4 +11 x (4-2) 12 x (4-3)) / 42
= (14 + 24 + 27 + 40 + 22 +12) / 42
= 139/42
= 3.31
Rounded to the nearest whole number, the average age is 3.
(iii). The probability of randomly selecting a child under 9 is obtained by adding the number of children aged 7, 8 or 9 (because we want children under 9) and dividing by the total number of children:
Number of children under 9 years = 2x + 3x + (4x-1)
Number of children under 9 years = 9x - 1
Number of children under 9 = 9(4)–1
Number of children under 9 years = 35
Probability of choosing a child under 9 = number of children under 9 / total number of children
Probability of choosing a child under 9 = 35/42
The probability of choosing a child under 9 years old is ≈ 0.83
Thus, the probability of randomly selecting a child under the age of 9 is approximately 0.83.
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Which equation best represents the relationship between X and Y in the graph?
A- y = 3x + 3
B- y = 3x - 1
C- y = 1/3x + 3
D- y = 1/3x - 1
15 POINTS
please help
#2
AA Similarity Theorem is required to prove that both triangles are similar
What is AA Similarity Theorem
AA (Angle-Angle) Similarity Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
In other words, if two angles of one triangle are equal to two angles of another triangle, then the third angles must also be equal, and the two triangles are said to be similar.
One of the equal angle is marked while the other is equal using the concept of vertical angle theorem. Angles formed where the line intersect are the ones equal by vertical angle theorem
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First 5 terms 3 8 13 18 23 explain why 387 is not a term of the sequence
Answer:
I believe it’s because they were adding by 5 with each number in the sequence.
Step-by-step explanation:
if you take 3+_= 8 what goes in the missing spot? 5 would, so we look at the next number and see if it’s a pattern. 13 so 8+_= 13 we know that’s 5 as well. So there’s a pattern of +5 hence why 7 is not part of the sequence.
complete the vector to describe the transformation
The translation vector for the rectangle is described by T(x, y) = (- 3, - 6).
How to derive the translation vector of an entire figure
In this problem we must derive the translation vector between a rectangle and its image set on Cartesian plane (let assume that the origin is on the lower left corner of the square). The translation formula is:
B(x, y) = A(x, y) + T(x, y)
Where:
A(x, y) - Coordinates of the original point.B(x, y) - Coordinates of the image.T(x, y) - Translation vector.If we know that A(x, y) = (6, 9) and B(x, y) = (3, 3), then the translation vector is:
T(x, y) = B(x, y) - A(x, y)
T(x, y) = (3, 3) - (6, 9)
T(x, y) = (- 3, - 6)
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Explain what the constant of proportionality means in the equation y = 5/2 x
Answer:
[tex]y = \frac{5}{2} x[/tex]
[tex] \frac{y}{x} = \frac{5}{2} [/tex]
The constant of proportionality is the ratio of y to x. Here, the ratio of y to x is 5 to 2. We see that y is directly proportional to x.
he solution to the system of equations shown is (2, 0).
3x − 2y = 6
x + 4y = 2
When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14
.
Which system of equations will also have a solution of (2, 0)?
Answer:
Multiplying the first equation by 2, we get:
6x - 4y = 12
Adding the second equation, we get:
6x - 4y + x + 4y = 2 + 12
Simplifying, we get:
7x = 14
This is the same equation given in the problem statement. So any system of equations that has this equation and the second equation will also have the solution (2, 0). For example:
3x - 2y = 6
7x = 14
In 2014, Michelle's annual base salary was $87,000. She also earned 3% commission of her annual sales of $500,000. What was Michelle's income during 2014?
Answer: Michelle's income during 2014 was her base salary plus her commission.
Her commission was 3% of $500,000, which is 0.03 x $500,000 = $15,000.
So her total income for 2014 was $87,000 + $15,000 = $102,000.
Step-by-step explanation:
Which pair does not represent the probabilities of complementary events?
4/7 and 3/7
16% and 84%
0.25 and 0.50
0 and 1
0 and 1 are the numbers that do not represent the probabilities of complementary events.
What is probability?Probability is a measure of the possibility or chance that an event will occur.It is a value between 0 and 1, with 0 indicating that the event will not happen and 1 indicating that the event will almost likely happen. The number of favourable outcomes divided by the total number of possible outcomes is the probability of an event. Probability is utilised extensively in a wide range of professions, including mathematics, statistics, science, economics, and engineering.
According to the given information:In probability theory, complementary events are two events that together encompass all possible outcomes, and their probabilities add up to 1. The complement of an event A is the absence of A, indicated by A'. Therefore, the probability of the complement of A is 1 minus the probability of A, or P(A') = 1 - P(A).
In the given pair, 0 represents the probability of an impossible event, and 1 represents the probability of a certain event. These events are not complementary, as there is no other event that can occur apart from a certain event, and their probabilities do not add up to 1. Therefore, this pair does not represent the probabilities of complementary events.
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Determine the domain of the graph above
The domain of the graph in this problem is given as follows:
C) -3 ≤ x ≤ 4.
How to obtain the domain of the graph?To determine the domain of a graph, you need to identify the set of all possible input values (also known as the independent variable) that produce a valid output (also known as the dependent variable) on the graph.
On a graph, the input values are represented by the values of x of the graph.
On the graph in this problem, we have that it assumes values of x between -3 and 4, with closed intervals, hence the domain is given as follows:
-3 ≤ x ≤ 4.
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Question 9 (10 points)
A rectangular mattress has a length that is twice it's width. The width is known to be
1 meter across, what is the area of the mattress?
O2 sq. meters
none of these
3 sq. meters
6 sq. meters
1/18 is the area of the mattress. none of these of the option.
What is a quick rectangle answer?
A quadrilateral of the kind represented by a square has equal sides that are equal to one another and four vertices that are equal to 90 degrees. The equiangular quadrilateral is hence another name for it. Since a rectangle's opposite sides are parallel and equal, a parallelogram is another word for a rectangle. With four sides, four corners, and four right angles (90°), a square form is a closed 2-D object. A square's opposing sides are comparable and equal.
Based on the given conditions, formulate = 1/2 * 1/1 + 2 * 1/2 * 2/1+2
= [tex]\frac{2/3}{2 * 3 * 2}[/tex]
= [tex]\frac{2}{3} * \frac{2}{2 * 3 * 2}[/tex]
Cross out the common factor = 1/3 * 1/3 * 2
= 1/3 * 3 * 2
= 1/18
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Miranda is standing at the corner of a 7 m by 11 m field. She needs to go to the corner diagonally opposite from where she is standing. How much shorter is it if she cuts across the diagonal instead of walking around the perimeter of the field? Round your answer to the nearest hundredth of a meter.
Therefore, Miranda saves approximately 22.96 meters by cutting across the diagonal instead of walking around the perimeter of the field.
What is perimeter?Perimeter is the total length of the boundary or outer edge of a two-dimensional shape, such as a square, rectangle, triangle, or circle. It is the distance around the shape, and is measured in units such as centimeters, meters, feet, or inches. To find the perimeter of a shape, you simply add up the lengths of all its sides. For example, the perimeter of a square with sides of length 5 cm would be 4 × 5 cm = 20 cm. The perimeter of a rectangle with length 6 cm and width 4 cm would be 2 × (6 cm + 4 cm) = 20 cm.
If Miranda walks around the perimeter of the field, she will travel a distance equal to the perimeter of a rectangle, which can be calculated as follows:
[tex]Perimeter = 2(Length + Width) = 2(7m + 11m) = 2(18m) = 36m[/tex]
To cut across the diagonal of the field, Miranda will travel a distance equal to the length of the diagonal of the rectangle. This can be found using the Pythagorean theorem:
[tex]Diagonal = \sqrt(Length^2 + Width^2) = \sqrt(7m^2 + 11m^2) = \sqrt(170m^2) \approx 13.04m[/tex]
So, the distance Miranda saves by cutting across the diagonal is:
[tex]36m - 13.04m \approx 22.96m[/tex]
Rounding to the nearest hundredth of a meter gives:
≈ 22.96m to 2 decimal places
Therefore, Miranda saves approximately 22.96 meters by cutting across the diagonal instead of walking around the perimeter of the field.
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Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 2.7, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 1.6, 1.4
Determine the scale factor used.
2
3
one third
one half
The scale factor is 1/3.
What is the scale factor?
The difference in scale between an original object's scale and a new object that is its representation but is larger or smaller is known as a scale factor. For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
Here, we have
Given: Triangle D has been dilated to create triangle D′.
To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:
4.8 / 1.6 = 3
4.2 / 1.4 = 3
2.7 / x = 3
Knowing that the scaling for each edge is 3, we can solve for x.
2.7 / 3 = x
0.9 = x
The edges for D are 4.8, 4.2, and 2.7 respectively to D’ scaled by 1/3. So we can determine that the edges for D’ are 1.6, 1.4, and 0.9 respectively to D scaled by 3.
So if we go D’ to D, we scale by 3. If we go D to D’, we scale by 1/3.
Hence, the scale factor is 1/3.
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If w = 10 units, x = 5 units, and y = 6 units, what is the surface area of the figure? Round your answer to the nearest tenth. (1 point) Figure is composed of a right square pyramid on top of a square prism. The sides of the square pyramid are equal to the sides of the square prism, the length and width of the square prism is w, the height of the square prism is x, and the height of the square pyramid, which forms a right angle with the center, is y.
The surface area of the figure is 456.2 units²,
How to determine the surface area?The area of the square base is:
base area = w² = (10 units)² = 100 units²
The lateral area is 4 times the area of one rectangular face:
lateral area = 4wx = 4(10 units)(5 units) = 200 units²
The area of one triangular face is half the product of its base length (w) and its slant height (h). The latter is found using the Pythagorean theorem:
h² = y² +(w/2)² = (6 units)² +((10 units)/2)² = 61 units²
h = √61 units
So, the area of 4 triangles is ...
area of triangular faces = 4(1/2)wh = 2(10 units)(√61 units) ≈ 156.2 units²
Now we have the areas of the parts, so we can add them together to get the total surface area:
surface area = base area + lateral area + area of triangular faces
= 100 units² + 200 units² + 156.2 units²
therefore, surface area = 456.2 units²
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Name
Date
- Sarah received a coupon for 15% off the total purchase price at a shoe store. Let p be the
original price of the purchase. Use the expression p-0.15p for the new price of the purchase.
Write an equivalent expression by combining like terms.
Expand the expressions and simplify 5(x + 4) + 3(x + 2) =
8x + 4
6x + 18
8x+ 26
7x - 18
Answer:
8x+26
Step-by-step explanation:
distribute the 5 into the numbers in the parentheses. you get (5x+20) then do the same with 3(x+2) which wll be (3x+6) now add like terms, which are 5x+3x=8x and 20+6=26. boom 8x+26.
8x + 26
multiply the outside number by the inside numbers and add them. remember, if the variable is singular example x, then it equals 1 :) I hope this helps you understand, I'm currently doing algebraic expressions.
In an election, suppose that 40% of voters support a new tax on fast food. If we poll 165 of these voters at
random, the probability distribution for the proportion of the polled voters that support a new tax on fast food
can be modeled by the normal distibution pictured below. Complete the boxes accurate to two decimal
places.
The values accurate to two decimal places for -2 standard deviation, mean, and +2 standard deviation are 0.30, 0.40, and 0.49, respectively.
What are the values of the mean and the standard deviation?We can use the following formulas to calculate the mean and standard deviation of the sampling distribution:
Mean: μ = p = 0.40 (since the population proportion is 0.40)
Standard deviation: σ = √((p(1-p))/n)
σ = √((0.40(1-0.40))/165)
σ = 0.049
Now we can calculate the values for -2SD, mean, and +2SD as follows:
-2SD: μ - 2σ = 0.40 - 2(0.049) = 0.30
Mean: μ = 0.40
+2SD: μ + 2σ = 0.40 + 2(0.049) = 0.49
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HELP PLEASE !
Using the table given in the photo, please help me understand and answer these questions. any help would be very appreciated!!!
The average rate is given as 0.2895 gallons per hour
What is gallons per hour?Gallons per hour (GPH) is a unit of measurement used to express the rate of flow of a liquid, typically fuel.
It represents the number of gallons of fuel that can flow through a particular system or device in one hour.
For example, the GPH of a car's fuel pump indicates how many gallons of fuel it can deliver to the engine in one hour. This unit is commonly used in the context of measuring the fuel efficiency of vehicles or other machinery.
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Which is the best estimate of the difference between 67/8 and 1/82
Answer:
8.36
Step-by-step explanation:
67 - 1
8. 82
= 2747 - 4
328
=2743
328
= 8.36
A recliner is discounted by $190. If the original price is $800, estimate the sale price by first rounding each number to the nearest hundreds
all u got to do is subtract
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the system of equations algebraically. Show all of your steps.
y=x2+2x
y=3x+20
There are two solutions for given system of equations: (5, 35) and (-4, 8).
What does "system of equations" and its solution means ?A system of equations is a grouping of two or more equations with numerous variables that are treated as a whole. The solution to a system of equations is the set of variable values that satisfies all of the equations in the system at the same time.
Typical approaches for resolving equation systems include:
Substitution MethodElimination MethodMatrix MethodGraphical MethodGiven system of equations is,
[tex]y=x^2+2x[/tex]..................(1)
[tex]y=3x+20[/tex]..................(2)
Solving equations algebraically,
Equating the formulas for 'y' in both equations:
[tex]x^2 + 2x = 3x + 20[/tex]
Rearranging the equation :
[tex]x^2 - x - 20 = 0[/tex]
Here, we got a quadratic equation,Solving for values of x,
[tex](x - 5)(x + 4) = 0[/tex]
[tex]x - 5 = 0 \\x=5\\or\\x + 4 = 0\\x=(-4)[/tex]
For values of 'y', putting values of x in equation (1),
for x = 5,
[tex]y = 5^2 + 2(5)=25 + 10 = 35[/tex]
Thus, (5, 35) is one of the solution.
for x= -4,
[tex]y = (-4)^2 + 2(-4)=16 - 8 = 8[/tex]
Thus, (-4, 8) is other solution.
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Each tile is 3/4 of inch by 3/4 of an inch what is the area of each tile
Answer:
9/16 of a square inch
Step-by-step explanation:
[tex] \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} [/tex]
Answer:
9 /16 inches^2
Step-by-step explanation:
To find the area of the tile, multiply the length by the width
A = 3/4 * 3/4
A = 9 /16 inches^2
Find the range of the relationship
Answer:
The range is {-7, -4, -1, 2, 5}.
If a Meat-E-Um pizza is cut into 6 pieces, about how much should one slice cost? (Round if needed)
Using division operation, if a Meat-E-Um pizza is cut into 6 pieces and the total cost is $36.60, the cost per slice is $6.10.
What is division operation?Division operation is one of the four basic mathematical operations. Other mathematical operations are addition, subtraction, and multiplication.
Division operation involves the following parts: dividend, divisor, and quotient.
The total cost of the Meat-E-Um pizza = $36.60
The number of pieces the pizza is cut = 6
The unit cost of each slice = $6.10 ($36.60 ÷ 6)
Thus, a slice of a Meat-E-Um pizza cut into 6 pieces will cost $6.10 per slice.
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Question Completion:The total cost of a Meat-E-Um pizza is $36.60.
someone help me plss
The fraction of the panel, that is left after cutting out the hole is [tex]\frac{11}{12}[/tex]
What are the areas of some common plane figuresThe area of a rectangle equals the product of its 2 sides. The area of a triangle is equal to half of the product of the base and height.. If we choose one of the sides as the base, then for area calculation, for height we have to use the height of the opposite vertex from this base. To find it, we have to drop a perpendicular from the opposite vertex onto the base. The area of a parallelogram is the product of the length of the base and the perpendicular distance between the two parallel sides of the parallelogram. Area of a trapezium = half of the product of the distance between the parallel sides and the sum of the length of the parallel sides. Area of a circle is [tex]\pi r^2[/tex], in which r is the radius of the given circle. Sometimes the plane figure maynot be a standard shape. In that case we have to divide the figure into suitably many parts such that, each part is a standard figure whose area we can calculate. Also sometimes we can represent an area as the difference of the area of two standard figures. In that case to find the area we have to take the difference of the areas of the two standard figures.
In our question. Initial area of the panel is (3)(2) = 6 square ft.
Area of the cutout = (1)([tex]\frac{1}{2}[/tex]) = [tex]\frac{1}{2}[/tex] square ft.
Using the formula, fraction left = [tex]\frac{6 - \frac{1}{2}}{6} = 1 - \frac{1}{12} = \frac{11}{12}[/tex]
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Required fraction left is 11/12 square feet.
What is area of rectangle?
A rectangle is a geometric shape that has four sides and four right angles. It is a type of quadrilateral and is characterized by its two pairs of parallel sides. The opposite sides of a rectangle are congruent, which means they have the same length, and the adjacent sides are perpendicular to each other.
The area of a rectangle is the total amount of space inside the rectangle and is calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is Area = length x width
For example, if a rectangle has a length of 6 units and a width of 4 units, the area can be calculated as:
Area = 6 units x 4 units = 24 square units
The area of the panel is 3 feet x 2 feet = 6 square feet
The area of the hole is 1 foot x 1/2 foot = 1/2 square feet
Therefore, the area left is 6 square feet - 1/2 square feet = 11/2 square feet
The fraction left is (11/2 square feet) / (6 square feet) = 11/12
Therefore, the required correct option is C.
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Use π = \frac{22}{7}: Henry bought exactly the right amount of fencing to put around his circular herb garden, which has a diameter of 14 feet. Then he decides to make the garden larger by doubling the diameter. How much more fencing does Henry need to purchase to enclose the new garden?
The answer of the given question based on the circle is , Henry needs to purchase an additional 44 feet of fencing to enclose the new garden.
What is Circumference?Circumference is distance around edge of circular object. It is same as perimeter of circle. The circumference of a circle can be calculated using the radius of the circle, which is half the diameter.
The circumference of circle with diameter d is given :
C = πd
Using the given diameter of 14 feet, the circumference of the original garden is:
C1 = πd1 = (22/7) * 14 = 44 feet
When the diameter is doubled to 28 feet, the circumference of the new garden is:
C2 = πd2 = (22/7) * 28 = 88 feet
To find how much more fencing Henry needs to purchase to enclose the new garden, we need to subtract the original circumference from the new circumference:
C2 - C1 = 88 - 44 = 44 feet
Therefore, Henry needs to purchase an additional 44 feet of fencing to enclose the new garden.
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Ejercicio 2.- La temperatura ambiente a las 8 am era de 61 grados Farenheit. Fue aumentando de forma lineal hasta la 1 pm en que el termómetro marcó 81 grados. a) Escriba una ecuación lineal que muestre la temperatura en función de la hora en ese intervalo. b) Calcule con esa ecuación la temperatura a las 11:15 am. Aproxime a la décima de grado Farenheit si fuera necesario. oprondamos a hacer ecuaciones y resolver
a)Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es T(h) = 4h + 29
b) Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
what is aproximadamente ?
"Aproximadamente" is a Spanish word that means "approximately" or "roughly" in English. It is often used to indicate that a value or measurement is not exact, but rather an estimation or approximation.
In the given question,
a) La ecuación lineal que relaciona la temperatura con la hora en ese intervalo es:
T(h) = m*h + b
donde T es la temperatura en grados Farenheit, h es la hora en formato de 24 horas, m es la pendiente de la recta y b es el término independiente.
Primero encontramos la pendiente m:
m = (81 - 61) / (13 - 8) = 4
Luego, encontramos el término independiente b utilizando uno de los puntos:
61 = 4*8 + b
b = 29
Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es:
T(h) = 4h + 29
b) Para encontrar la temperatura a las 11:15 am, primero convertimos el tiempo a horas decimales:
11:15 am = 11 + 15/60 = 11.25 horas
Luego, sustituimos este valor en la ecuación lineal:
T(11.25) = 4(11.25) + 29 = 75.25
Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
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For #1 - 6, use the information given to write the equation of the line in slope intercept form.
1. Line where slope is -32 and y-intercept is 7
1. Line where slope is 5 and x -intercept is 2
1. Line going through the points (-1, -5) and (4, -2)
1. Line going through the points (0, 1) and (2, -2)
1. Line where m = 4 and and b = -76
1. Line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0
An equation of a line where slope is -32 and y-intercept is 7 is y = -32x + 7.
An equation of a line where slope is 5 and x-intercept is 2 is y = 5x - 10.
An equation of a line that is going through the points (-1, -5) and (4, -2) is y = 3x/5 - 22/5
An equation of a line that is going through the points (0, 1) and (2, -2) is y = -x/2 + 1
An equation of a line where m = 4 and and b = -76 is y = 4x - 76.
An equation of a line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0 is y = 3x + 0.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 + 5)/(4 + 1)
Slope (m) = 3/5
At data point (-1, -5) and a slope of 3/5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 5 = 3/5(x + 1)
y = 3x/5 + 3/5 - 5
y = 3x/5 - 22/5
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A bus traveled on a level road for 2 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 3 hours. Find the average speed on the level road if the entire trip was 225 miles.
By answering the presented question, we may conclude that As a result, the average speed on the flat road is 57 miles per hour.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
Let's apply the formula:
distance = time speed
The bus went for 2 hours on the level road, hence the distance travelled is:
1 distance = x 2
The bus went for 3 hours on the twisting route, hence the distance travelled is:
3 distance2 = (x - 20)
Because the bus's total distance travelled is 225 miles, we may write:
distance1 plus distance2 equals 225
Substituting distance1 and distance2 expressions yields:
x × 2 + (x - 20) × 3 = 225
When we simplify this equation, we get:
2x + 3x - 60 = 225
5x = 285\sx = 57
As a result, the average speed on the flat road is 57 miles per hour.
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