The answer of the given conditions is 255/3 =83, 368/16 = 23 and 2 210/65 = 34.
What are the numerator and denominator?
For example, 4/5 is a fraction, and the line separating the numbers 4 and 5 is the fraction bar. Here the number above the fraction bar is the numerator, and the one below the fraction bar is the denominator. A numerator represents the number of parts out of the whole, which is the denominator.
3 divided by 255 is equal to 3/255.
16 divided by 368 is equal to 16/368.
65 divided by 2 210 is equal to 65/2210.
Note that for 2 and 3 the numerator and denominator have been swapped and the division is not correct, it should be 368/16 = 23 and 2 210/65 = 34
Hence, the answer of the given conditions are 255/3 =83, 368/16 = 23, and 2 210/65 = 34.
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subtract the polynomial multiple questions 100points+brainleist
1) (-x^{2} -5x-3)-(-7x^{2} -8x-8)
2) (-2x^{3}+x) -(7x-3-7x^{3})
3) (3x^{3} +3x^{2} +9)-(5x^{3} -7x^{2} +6x-9)
4) (5x^{3} +5x^{2} +5)-(6x^{3} -6x^{2} +8x-5)
5) (5x^{3} +3x^{2} +5) - (7x^{3} -9x^{2} +8x-5)
The polynomials are subtracted to give;
1. 6x²- 5x⁻³ - 8x⁻⁸
2. 5x³+ x - 7x⁻³
3. -2x³ + 10x² -6x + 18
4. 11x³ + 11x² + 8x + 10
5. -2x³ + 12x² - 8x + 10
What are algebraic expressions?These are expressions that are composed of terms, coefficients, factors, variables and constants.
They are also composed of mathematical or arithmetic operations such as;
ParenthesesDivisionAdditionMultiplicationSubtractionBracket, etcPolynomials are algebraic expression with non-negative integer exponentiation of variables.
From the information given, we have the expressions;
1.{ (-x²) - 5x⁻³} - ( -7x² - 8x⁻⁸)
collect like terms
-x² + 7x² - 5x⁻³ - 8x⁻⁸
Add like terms
6x²- 5x⁻³ - 8x⁻⁸
2. (-2x³ + x) - ( 7x⁻³ - 7x³)
collect like terms
-2x³ + 7x³ + x - 7x⁻³
add like terms
5x³+ x - 7x⁻³
3. (3x³ + 3x² + 9) - (5x³ -7x² +6x - 9)
collect like terms
3x³- 5x³ + 3x² + 7x² -6x + 9 + 9
-2x³ + 10x² -6x + 18
4.5x³ + 5x² + 5 - (-6x³ - 6x² + 8x - 5)
collect like terms
5x³ + 6x³ + 5x² + 6x² + 8x + 5 + 5
11x³ + 11x² + 8x + 10
5. 5x³ + 3x² + 5 - (7x³ - 9x² + 8x - 5)
collect like terms
5x³ - 7x³ + 3x² + 9x² - 8x + 5 + 5
-2x³ + 12x² - 8x + 10
Hence, polynomials are also described as algebraic expressions
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tan40*cot50-sec40*csc50
I know the answer is -1, but I'm not sure how to get it.
[tex]\tan 40^{\circ} \cot 50^{\circ}-\sec 40^{\circ} \csc 50^{\circ}\\\\=\tan 40^{\circ} \tan 40^{\circ}-\sec 40^{\circ} \sec 40^{\circ}\\\\=\tan^2 40^{\circ}-\sec^2 40^{\circ}\\\\=-1[/tex]
a golf course has 18 holes. a guidebook provided to golfers includes useful information about each hole. the individuals in this data set are shown below. a 4-column table with 6 rows. column 1 is labeled hole number with entries 1, 2, 3, 4, 5, 6. column 2 is labeled yards with entries 312, 530, 147, 350, 410, 185. column 3 is labeled bunkers with entries 2, 5, 1, 0, 2, 1. column 4 is labeled difficulty level with entries moderate, moderate, easy, moderate, hard, moderate. which of the variables in the data set is a categorical variable? hole number yards bunker difficulty level
The variable "difficulty level" in the data set is a categorical variable.
What is variable in math?A variable in math is a symbol or letter that is used to represent a number or set of numbers in an equation or expression. Variables can be anything such as x, y, a, b, c, etc. Variables are used to represent unknown values or values that can change. They allow equations and expressions to be flexible and can help make problem-solving easier.
Categorical variables are those that have discrete categories or labels, such as "moderate", "easy", and "hard". They are usually qualitative in nature and do not have numerical values. In this case, the difficulty level of each hole is indicated by a label, which can be used to classify the hole accordingly.
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Answer:
difficulty level
Step-by-step explanation:
took the test
as a part of a customer loyalty program, a restaurant's computer chooses orders at random to receive a free appetizer. each order has a 111 in 181818 chance of receiving a free appetizer. (each order is limited to one free appetizer.) let xxx be the number of orders the restaurant fills in a day until they give away the first appetizer. assume that each order getting the appetizer is independent. find the probability that the restaurant first gives away an appetizer on the 6^{\text{th}}6 th 6, start superscript, start text, t, h, end text, end superscript order of the day.
The probability of the 6th order being the order with the free appetizer is 0.0417 (approx).
The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.
The probability of getting a free appetizer is 1/18.
The probability of not getting a free appetizer is 17/18.
If the restaurant gives away an appetizer on the 6th order, then there must have been 5 orders before the 6th one that had no free appetizer, followed by the one with the free appetizer.
[tex]P (X = 6) = P(N N N N N F)[/tex]
= 17/18 x 17/18 x 17/18 x 17/18 x 17/18 x 1/18
[tex]= \frac{17^4}{18^5}[/tex] ≈ 0.0417
Thus, the probability of the 6th order being the order with the free appetizer is 0.0417 (approx).
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Eleri wants to be fit for the adventure holiday.
She runs 2 laps of a running track.
Each lap is 400m
Eleri thinks she has run 1km in total
Is Eleri correct?
Show why you think this
Show your working and your answer here
Eleri wants to be fit for the adventure holiday and to achieve that she runs 2 laps of a running track. Each lap is 400m and she thinks she has run 1km in total. To determine if Eleri is correct, we must first understand the basic units of measurement for distance and how they relate to one another.
A lap of a running track is a distance of 400m. The prefix "kilo" in the unit "kilometer" represents 1000. Therefore, a kilometer is equal to 1000 meters. To convert meters to kilometers, we divide the number of meters by 1000. To convert kilometers to meters, we multiply the number of kilometers by 1000.
To determine the total distance Eleri ran, we must multiply the number of laps by the distance of each lap. 2 laps x 400m per lap = 800m. This is the total distance Eleri ran in meters.
To determine if Eleri ran 1km, we must convert 800m to kilometers. Therefore, to convert meters to kilometers, we divide 800 by 1000. 800m / 1000 = 0.8km.
Therefore, Eleri did not run 1km, she ran 0.8km.
To further demonstrate the accuracy of our calculation, we can use dimensional analysis by using the conversion factor of 1000m = 1km.
800m / (1000m/1km) = 0.8km
This confirms that Eleri ran 0.8km, not 1km.
In conclusion, Eleri is not correct in her assumption that she ran 1km. She actually ran 0.8km which is 800 meters. This was determined by understanding the basic units of measurement for distance, converting the distance from meters to kilometers, and using dimensional analysis to verify our calculations.
Answer:
Step-by-step explanation:
no she is not correct she only ran 0.8 km
o ne year ago, gill was five times as old as her horse. one year from now the sum of their ages will be 22. how old is gill now?
Answer: Gill is 16 now
Step-by-step explanation: If the horse was 3 one year ago, and gill is five times as old as it, shed be 15. one year from now, the horse is 5 and Gill is 17, which combined, is 22. If she is 17 in one year, she is 16 now.
For which interval(s) is the function increasing and decreasing?
y = |2x² + x - 6|
The function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).
What is a function?
A function is a mathematical relation between a set of inputs (often called independent variables, or the domain) and a set of outputs (often called dependent variables, or the range). A function assigns exactly one output for each input. It can be represented by an equation, such as y = f(x), where x is the input and y is the output.
To find the interval(s) in which the function is increasing and decreasing, we can first find the critical points of the function by setting the derivative equal to 0 and solving for x.
The derivative of y = |2x² + x - 6| is not a defined function, it is not differentiable, it is a piece-wise defined function, it has a break at x = -3/2
Hence, the function is decreasing in the interval (-∞,-3/2) and (3/2, ∞) and increasing in the interval (-3/2, 3/2).
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F(x) = 2x² +1
g(x) = 3x - 5
f-g
Answer: The answer is. 2x² - 3x + 6. Step-by-step explanation: f(x) = 2x² + 1. g(x) = 3x - 5. To find f - g(x) subtract g(x) from f(x).
I hope this helps! Have a Wonderful day! <3
The point T is plotted on the coordinate grid. Plot the point T’ the reflection of T over the y-axis
The coordinate point T' the reflection of T over the y-axis is (4, -5).
What is the reflection on y-axis?When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given that, the point T is plotted on the coordinate grid.
The coordinate point on the grid is (-4, -5).
The reflection of point (x, y) across the y-axis is (-x, y).
Here, (-4, -5)→(4, -5)
Therefore, the coordinate point T' the reflection of T over the y-axis is (4, -5).
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andrew buys 8 pounds of apples for $12.00. he wants to know and use the unit rate of the cost per pound. true or false: using the unit rate of the cost per pound, do 5 pounds of apples cost $7.50?
The unit price for the apples is $1.5 per pound. The statement is true.
Now, According to the question:
How to calculate the Unit rate of the cost per pound?
8 pounds of Apple costs $12
The unit rate is
8= 12
1= x
We can write, by cross - multiply
8x = 12
x= 12/8
x= 1.5
Hence, the unit rate of the cost per pound is $1.5
And, 5 pounds of apples cost $7.50
cross multiply,
5× 12/8
60/8 = 7.50
5 pounds of apples = 7.50
Hence, The unit price for the apples is $1.5 per pound. The statement is true.
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Find the missing number so that the equation has no solutions.
4x + 10= __x + 8
The missing coefficient of the linear equation 4 · x + 10 = __ · x + 8 such that it has no solutions is equal to 4.
How to determine the value of coefficient such that a linear equation has no solution
In this problem we find a linear equation of the form a · x + b = c · x + d, where a, b, c, d are real coefficients. This kind of equation has no solution for the case when a = c. The complete procedure is shown below.
First, write the incomplete expression:
4 · x + 10 = __ · x + 8
Second, add the missing coefficient according to the definition for linear equations with no solutions:
4 · x + 10 = 4 · x + 8
Third, use algebra properties to simplify the expression:
10 = 8 (CRASH!)
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Identify the initial amount a and the rate of decay r (as a percent) of the exponential function y=0.5(34)t. evaluate the function when t=3. round your answer to the nearest tenth.
The exponential function y = 0.5(34)t has the form y = a*b^t, where a is the initial amount and b is the rate of decay. In this case, a = 0.5 and b = 34.
How is this calculated?To find the rate of decay as a percent, we need to find the decimal form of b and then convert it to a percent. To find the decimal form, we need to take the square root of b = 34.
√34 = 5.83
To convert this decimal to a percent, we need to multiply it by 100.
5.83 * 100 = 583%
Therefore, the rate of decay is 583%.
Now we can use these values to evaluate the function when t = 3.
y = 0.5(34)^3
y = 0.5(363)
y = 181.5
So when t = 3, the value of y is 181.5, rounded to the nearest tenth.
Note that the initial amount a = 0.5, the rate of decay r = 583% and the function at t = 3 is 181.5.
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you are driving on a highway and are about 140 miles from a state border. you set your cruise control at 60 miles per hour and plan to turn it off within 30 miles of the border on either side. find the minimum and maximum numbers of hours you will have cruise control on.you will travel at least hour(s) and at most hour(s) with cruise control on.
The minimum number of hours you will have cruise control on is 1.83 hour(s) and the maximum is 2.83 hour(s).
To find the minimum and maximum numbers of hours you will have cruise control on, you need to calculate the distance you will travel with cruise control on and divide it by your speed.
The minimum distance you will travel with cruise control on is
140 miles - 30 miles = 110 miles.
The maximum distance you will travel with cruise control on is
140 miles + 30 miles = 170 miles.
To convert these distances into hours, you will divide them by your speed of 60 miles per hour.
Minimum hours: 110 miles / 60 mph = 1.83 hours
Maximum hours: 170 miles / 60 mph = 2.83 hours
Therefore, the minimum number of hours you will have cruise control on is 1.83 hour(s) and the maximum is 2.83 hour(s).
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assume your professor has given you 60 minutes to complete a specific assignment. you have worked on the assignment for 45 minutes but have not yet completed the assignment. a friend stops by and asks you to go out for a couple of hours. what should you do?
The best course of action would be to politely decline the offer and explain to your friend that you still have to finish the assignment.
What is minutes?Minutes is a record of the proceedings of a meeting or other event. It is typically written by the secretary of the meeting and contains a summary of the main points discussed, decisions taken, and any action points arising from the meeting. Minutes are an important part of any organization as they provide a record of the decisions taken and an opportunity for review. Minutes can also help to keep everyone on track and ensure that everyone is aware of their responsibilities.
Even though your friend may be disappointed, they will understand. It is important to prioritize your school work and stay on top of assignments, so you should continue to work on the task at hand.
If you find yourself struggling to stay focused, it can help to break down the assignment into manageable chunks and set a timer for each chunk. This can also help you stay on track with the time limit that your professor gave you. Additionally, taking a few minutes to get up and stretch or grab a snack can help you stay energized and productive.
If you need additional help, reach out to your professor or a tutor. You can also ask a classmate for help or advice. Your professor likely will not mind if you ask for an extension on the assignment, as long as it is reasonable and you provide a valid reason.
Remember, it is important to prioritize your school work and stay on top of assignments. It is ok to take breaks and accept help, but be sure to stay focused on the task at hand.
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A line passes through points (3,14) and (9,20). Write a linear function rule in terms of x and y for this line.
Answer:
y = x + 11
Step-by-step explanation:
the equation of a straight line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (3, 14 ) and (x₂, y₂ ) = (9, 20 )
m = [tex]\frac{20-14}{9-3}[/tex] = [tex]\frac{6}{6}[/tex] = 1 , then
y = x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (3, 14 )
14 = 3 + c ⇒ c = 14 - 3 = 11
y = x + 11 ← equation of line
A line passes through points (3,14) and (9,20), linear function rule in terms of x and y for this line is y = x + 11
A linear function in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula: m = (y2 - y1) / (x2 - x1). Plugging in the point values from the problem, we get:m = (20 - 14) / (9 - 3) = 6/6 = 1
The y-intercept be found by plugging in any one of the point values and the slope into the equation y = mx + b and solving for b. Using the point (3,14), we get:
14 = 1*3 + b
b = 11So the linear function in terms of x and y is:
y = x + 11
A linear function is a type of mathematical function that, when graphed, defines a straight line. It is defined by the equation y = mx + b, where x and y are variables, m is the line's slope, and b is the y-intercept (the point where the line crosses the y-axis). The slope (m) of the line represents its steepness, and the y-intercept (b) represents the point at which the line intersects the y-axis.
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pls help due tomorrow!!!!
Answer:
Any real value.
Step-by-step explanation:
Ok, so I am just gonna simplify the question a little bit.
[tex]\frac{x-8+3}{5}[/tex] = (x - 5)/5 or x/5 - 1..
Wait a minute, the question doesn't make sense.
The question is true for any value of x as | x | > 0 and - | x | will be < 0 no matter what.
Which of the following graphs does NOT describe y as a function of x?
Answer:
the first one
Step-by-step explanation:
using the vertical line rule, we can see that a vertical line would intersect the first graph more than once at any point to the right of the vertex. this cannot be said for the other graphs
A 9-kilogram bag of rice costs $12.96. What is the unit price?
Answer:
$1.44
Step-by-step explanation:
9kg costs $12.96
1kg costs ($12.96*1kg)÷9kg
=$1.44
given the function defined in the table below,find the average rate of change,in simplest form,of the function over the interval 12
Answer: The average rate of change over the interval 12 < x < 30 is -4/3
Step-by-step explanation:
The average rate of change over an interval is defined as the change in the output (f(x)) divided by the change in the input (x) over that interval. In this case, the interval is 12 < x < 30. To find the average rate of change, we need to evaluate the function at the endpoints of the interval and subtract the value at the start point from the value at the end point, and divide that by the change in x.
Given the table:
f(30) = 16 and f(12) = 40
The average rate of change over the interval 12 < x < 30 is:
(f(30) - f(12)) / (30 - 12) = (16 - 40) / 18 = -24/18 = -4/3
So the average rate of change over the interval 12 < x < 30 is -4/3
It's worth noting that this is only the average rate of change, and the function may have different rates of change at different points within the interval 12 < x < 30.
what is the value of the expression (x-3y)2, when x =4 and y= -3
Answer: 26
Step-by-step explanation:
Simplify
2x-6y
Plug in numbers
2(4)-6(-3)
Answer:
26
Step-by-step explanation:
We want to find the value of the following expression:
[tex](x-3y)2[/tex]
We are given the following variable values:
[tex]x=4[/tex]
[tex]y=-3[/tex]
Start by simplifying the given expression with the distributive property:
[tex]2x-6y[/tex]
Now, plug in the provided variable values:
[tex]2(4)-6(-3)[/tex]
Simplify:
[tex]8+18[/tex]
Finally, add to get the simplified expression:
[tex]26[/tex]
Flavia bought a pair of roller blades. the regular price was 129.50. they were bought for 40% off and the sales tax was 15%. determine each of these amounts:
On solving the provided question, we can say that equation of cost of the roller blades is $ 89.66
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Let the total cost = A
initial cost = $ 129.50
he discount percentage = 40 %
So , the equation will be
= 129.50 - ( 40/100 ) x 129.50
= 129.50 - 51.8
= $ 77.7
sales tax percentage = 15 %
So , the equation will be
= 77.7 + ( 15/100 ) x 77.7
= 77.7 + 11.655
= $ 89.655
final cost is A = $ 89.66
final cost of the roller blades is $ 89.66
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What is half of 1 2 US?
Answer: 6
12 divided by 2 is 6 or 6 + 6 = 12
If 4^3rootx^10+(5x^3)^3root8x, what is the sum of in simplest form?
The sum of the expression 4∛(x¹⁰) + 5x³∛(8x) in the simplest form will be 14x³ ∛x.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 4∛(x¹⁰) + 5x³∛(8x)
Simplify the expression, then we have
⇒ 4∛(x¹⁰) + 5x³∛(8x)
⇒ 4∛[(x³)³ · x] + 5x³∛(2³ · x)
⇒ 4x³ ∛x + 10x³ ∛x
⇒ 14x³ ∛x
The sum of the expression 4∛(x¹⁰) + 5x³∛(8x) in the simplest form will be 14x³ ∛x.
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a rectangular prism measures 2 yd by 10 yd by 5 yd. if the dimensions of the box were all doubled, how would the surface area of the box change?
If the dimensions of the box were all doubled, then the surface area of the box be 640 square units.
Use the concept of prism defined as:
A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat sides, and identical bases.
Without bases, the prism's faces are parallelograms or rectangles. And any n-sided polygon, whether a triangle, square, rectangle, or other, might serve as the prism's basis.
Given that,
The dimension of the rectangular prism = 2yd x 10yd x 5yd
Since we know that,
Dimension of prism = length x breadth x height
length x breadth x height = 2yd x 10yd x 5yd
Therefore,
Length = 2 yd
Breadth = 10 yd
Height = 5 yd
Now if dimension doubled the,
The dimension of the new prism = 4yd x 20yd x 10yd
Then,
Length 'l' = 4 yd
Breadth 'b'= 20 yd
Height 'h' = 10 yd
Since we know that,
The surface area of a rectangular prism is,
A=2(bl+hl+hb)
Substitute the values,
A = 2(20x4 +10x4 + 10x20)
A = 640 square units.
Hence the surface area is 640 square units.
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Which algebraic expression is equivalent to 9(4x + 8) - 4
Answer: 36x + 68
Step-by-step explanation:
Expanding it, you get:
36x + 72 - 4
= 36x + 68
Please help me I don’t understand math 2
Answer:
3rd choice
a rotation of 90° counterclockwise about the origin and a translation down 1 unit
Step-by-step explanation:
This is just asking you what operations you need to perform to get figure N from figure M. Such a set of operations is called a transformation.
In this case we see that to get figure N we have to rotate figure M 90° in a counterclockwise direction. That would be the first transformation
From the choices you can eliminate the first two choices which deal only with clockwise rotation
Translation transformation is one where the figure is shifted horizontally or vertically
All we have to do is figure out if, after 90° counterclockwise rotation of M whether it was shifted 1 unit up or 1 unit down
Look at the point (-3, 1) in figure M.
When a figure is rotated 90° counterclockwise, each if its original coordinates (x, y) become new coordinates (-y, x)
In other words the coordinates are interchanged in the transformed figure and the sign of the new x-coordinate is changed from the original y value
So (-3, 1) should become (-1, -3)
But in figure N, that point has become (-1, -4) which is (-1, -3-1). This indicates the figure has been shifted down which corresponds to a translation down by 1 unit
Answer: 3rd choice
a rotation of 90° counterclockwise about the origin and a translation down 1 unit
The two images I have attached may help you understand better. First one is just the rotation of M. Second one is the rotated figure shifted down which results in figure N
Calcula el área de las bases y el área lateral, de un cilindro de 10cm de radio y 20cm de altura.
El area de las bases es 628 cm^2 (ambas bases) y el area lateral es 1,256 cm^2
¿Como calcular el area de las caras del cilindro?Tenemos un cilindro con un radio de 10 centimetros y 20 centimetros de altura.
El cilindro tiene dos tapas que son circulares, el area de estas se calcula como el area de un circulo cualquiera, esta sera:
A = 2*( pi*R^2)
Donde R es el radio y pi = 3.14, entonces tendremos:
A = 2*(3.14*(10cm)^2)
A = 628 cm^2
El area lateral será igual que el producto entre la altura y la circunferencia:
A' = 2*pi*R*H
Donde H es la altura.
Remplazando los valores que conocemos obtendremos:
A' = 2*3.14*(10cm)*20cm
A' = 1,256 cm^2
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the area covered by a lake is 11 square kilometers. It is decreasing exponentially at a rate of 2 percent each year represented by A(t)=11x(.98)^t. By what factor does the area decrease in 10 years? By what factor does the area decrease each month?
Answer:
The lake decreases by a factor of 3.038 in 10 years (to 3.038 km^2).
The lake decreases by a factor of 0.00167 each month.
Step-by-step explanation:
Use the given relationship A(t)=11x(.98)^t and find the value of A for t=10 years.
A(10) = 11*(0.98)^10
A(10) = 3.621 km^2
The lake has decreased by a factor of (11km^2/3.621km^2) or 3.038.
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The lake decreases each month by (0.02/12) or 0.00167 each month.
Find the slope of the ordered pairs below
Answer:
[tex]\boxed{\sf \:Slope(m)=2}[/tex]
Step-by-step explanation:
Let's use the slope formula to find the slope of (2,2) and (3,4):-
Slope formula :- m=(y2-y1)/(x2-x1)
[tex]\sf \left(x_1,\:y_1\right)=\left(2,\:2\right)[/tex]
[tex]\sf \:\left(x_2,\:y_2\right)=\left(3,\:4\right)[/tex]
[tex]\sf m=\cfrac{4-2}{3-2}[/tex]
[tex]\sf m=\cfrac{2}{1}[/tex]
[tex]\sf m=2[/tex]
Therefore, the slope is 2!!
_____________________
Hope this helps!
Have a great day!
For how many integer values of M is M/20 strictly between 1/3 and 3/5?
There are 5 integer values of M that satisfy the given inequality.
An integer is a whole number, which means it is a number that can be written without a fractional or decimal component. Integers include positive numbers (e.g. 1, 2, 3), negative numbers (e.g. -1, -2, -3), and zero.
They are also often represented using the symbol "Z". Integers are a subset of the set of real numbers.
If M/20 is strictly between 1/3 and 3/5, then we have the following inequalities:
1/3 < M/20 < 3/5
To solve this, we can multiply both sides of the inequality by 20 to get rid of the denominator on the left side:
6 < M < 12
This tells us that M is an integer that lies strictly between 6 and 12 (i.e., 6 < M < 12), and the integers between 6 and 12 are 7, 8, 9, 10, and 11. Therefore there are 5 integer values of M that satisfy the inequality.
To know more about inequalities refer to:
brainly.com/question/30231190
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