Therefore , the solution of the given problem of expressions comes out to be 16 ounces are equal to 1 pound.
Expression : What is it?There is a need for mathematical operations like multiplying, splitting, joining, and currently removing. If they were combined, it would read as follows: A mathematical formula, some data, and an equation Values, elements, and mathematical operations like additions, deductions, errors, subdivisions, and algebraic formulas all go into making a declaration of truth. It is possible to assess and analyse words and sentences.
Here,
=> 6x - 3 is an expression that is equal to 3(2x-1).
We can spread the 3: to see why this is true.
=> 3(2x-1) = 6x - 3
There are 5,280 feet in a mile, as the saying goes.
5280 feet make up a mile.
Simply put, this phrase means that 5,280 feet is equal to 1 mile.
One way to say "there are 16 ounces in a pound" is:
A pound weighs 16 ounces.
Simply put, this phrase means that 16 ounces are equal to 1 pound.
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3. Colin is painting his basement floor. The dimensions are shown on the diagram below:
If one can of paint will cover 3.5 m², and each can costs $15.25, what is the total cost including 13% HST.
2.3 m
2.5 m
32m
1.8 m
The total cost of painting his basement floor is $51.70.
How to calculate total cost ?To find the total cost of the paint including HST, we first need to calculate the total area of the basement floor that needs to be painted. We can do this by multiplying the length by the width:
Area of basement floor = length x width
Area of basement floor = 2.5 m x 2.3 m + 1.8 m x 2.3 m
Area of basement floor = 5.75 m² + 4.14 m²
Area of basement floor = 9.89 m²
Now, we can calculate the number of cans of paint needed:
Number of cans = Area of basement floor / Area covered by each can
Number of cans = 9.89 m² / 3.5 m²
Number of cans = 2.8257
Number of cans = 3
The total cost of the paint without HST would be:
Total cost = Number of cans x Cost per can
Total cost = 3 x $15.25
Total cost = $45.75
To calculate the HST, we need to multiply the total cost by the HST rate (13% or 0.13):
HST = Total cost x HST rate
HST = $45.75 x 0.13
HST = $5.95 (rounded to two decimal places)
Finally, we can find the total cost including HST by adding the total cost and the HST:
Total cost including HST = Total cost + HST
Total cost including HST = $45.75 + $5.95
Total cost including HST = $51.70
Therefore, the total cost of the paint including 13% HST is $51.70.
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2
A worker earned #80 per hour for a 38-hour week in a company. The company pays overtime at
a time and a half. In one week he earned #3640. Find the total numbers of hours he worked that
week.
3
Kasham travelled from Lagos to Akure, a distance of 350km. The first 210km she spent 3hours
and the remaining distance she spent 2hours 45minutes. (a) Calculate the speed for each part
of the journey. (b) Calculate the average speed for the whole journey in (i) km/h (ii) m/s to 1d.p
Answer:
2. Total Hours= 38+5 = 43
Step-by-step explanation:
2. Wage at Normal rate80 *38 = 3040
Extra Sum of Money then Normal wage 3640-3040 = 600
Overtime rate 80*1.5= 120
Overtime hours 600/120=5
3. (a) 210/3 = 70km/hr
140/(2.75*) = 50.91 km/hr
*2.75= 2+ (45/60)
Solve the system by the addition method.
5x + 6y=5
10x+12y = 10
The solution for the given system of equations is (1,0) using the addition method.
What is addition method?The addition method, also known as the elimination method, is a technique used to solve a system of linear equations by adding the two equations together in such a way that one of the variables is eliminated.
According to question:Multiply the first equation by -2:
-10x - 12y = -10
Add the second equation to the first:
-10x - 12y = -10
10x + 12y = 10
0 + 0 = 0
We can solve one of the original equations for x in terms of y and then replace into the equation to represent the solutions in terms of y. For instance, when we solve the first equation for x, we obtain:
5x + 6y = 5
5x = 5 - 6y
x = (5 - 6y)/5
By substituting this into the second equation, we get:
10x + 12y = 10
10((5 - 6y)/5) + 12y = 10
2(5 - 6y) + 12y = 10
10 - 4y = 10
-4y = 0
y = 0
So the solution to the system is (x, y) = ((5 - 6y)/5, y) = (1, 0)
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Triangle ABC is shown. Use the graph to answer the question. triangle ABC on a coordinate plane with vertices at negative 8 comma 1, 0 comma 1, negative 4 comma 5 Determine the coordinates of the image if triangle ABC is translated 8 units to the right. A′(−14, 1), B′(−8, 1), C′(−12, 5) A′(−6, 9), B′(0, 9), C′(−4, 13) A′(0, 1), B′(8, 1), C′(4, 5) A′(2, −7), B′(8, −7), C′(4, −3)
The cοοrdinates οf the image if triangle ABC is A′(0, 1), B′(8, 1), C′(4, 5).
What is Triangle?A triangle is a clοsed, twο-dimensiοnal geοmetric figure with three straight sides and three angles. It is οne οf the basic shapes in geοmetry.
A triangle is a pοlygοn with three edges and three vertices. It belοngs tο the basic geοmetric shapes. A triangle with vertices A, B, and C is knοwn as triangle ABC. Any three pοints in Euclidean geοmetry that are nοt cοllinear result in a distinct triangle and a distinct plane.
The cοοrdinates οf the image if triangle ABC is translated 8 units tο the right are:
A′(0, 1), B′(8, 1), C′(4, 5).
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Write the equation of a rational function that has been translated left 2 units and shifted up 1 unit.
The equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)
What is a function?A relation is a function if it has only One y-value for each x-value.
A general form of a rational function is:
f(x) = (ax + b) / (cx + d)
To translate this function left 2 units, we need to replace x with x + 2. This gives us:
f(x + 2) = (a(x + 2) + b) / (c(x + 2) + d)
To shift this function up 1 unit, we need to add 1 to the numerator. This gives us:
f(x + 2) = (a(x + 2) + b + 1) / (c(x + 2) + d)
Therefore, the equation of a rational function that has been translated left 2 units and shifted up 1 unit is: f(x) = (a(x - 2) + b + 1) / (c(x - 2) + d)
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please help me with this
The linear function that models the scatter plot is given as follows:
y = 7/8x + 6.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.For the equation in this problem, we have that:
The slope is positive, as when x increases, y increases.The intercept is also positive, as the graph is composed only by positive values.Hence the option that satisfies the sign of the slope and the intercept is given as follows:
y = 7/8x + 6.
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Find the cube root of these expression
³√5׳√5׳√5=
We can simplify this expression by multiplying the cube roots together:
³√5 × ³√5 × ³√5 = ³√(5 × 5 × 5)
Simplifying the product inside the cube root, we get:
³√(125)
Therefore, the cube root of 5 × 5 × 5 is equal to:
³√5׳√5׳√5 = ³√125 = 5
Please help geometry question Pythagorean theorem
Therefore , the solution of the given problem of triangle comes out to be L = 3(√(h²) + ((w/2²))) + 3h .
What is a triangle exactly?A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular.
Here,
Given the height and breadth of the top of the frame, we can use the Pythagorean theorem to determine the length of each side of the triangle.
Let's assume the height is h feet and the width of the top of the frame is w feet. The triangle's side lengths can then be calculated as follows:
=> s =√((h²) + ((w/2)²))
We must add up the lengths of all the pipe segments that will be used to build the frame in order to determine the total quantity of steel pipe required.
The following formula can be used to determine how much steel tubing is required:
=> L = 3s + 3h
where h is the height of the frame and s is the length of each edge of the triangle.
Using the method instead of s, we obtain:
=> L = 3(√(h²) + ((w/2²))) + 3h
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In addition to physical safeguards on all machinery, what else is considered a crucial part of providing safeguard against machine-related hazards
To have an effective safeguarding system, specific and detailed training of workers must also be included.
What constitutes the foundation of the safety system?
Any portion of the operator's body, including the hands, arms, and other body parts, must not come into touch with potentially harmful moving parts.
A strong safety system completely avoids the chance of the operator or another worker putting their bodies in close proximity to dangerous moving parts.
What are the two main sorts of protection strategies?
There are primarily two types of safeguarding: hard guards and safeguarding gadgets. Hard guards act as a physical barrier between workers and moving parts.
Safeguarding devices, however, stop unintentional access to dangers. A machine that needs two hands to operate it, for instance, ensures that neither hand may enter the danger zone.
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y= a(1+r)t
1. The sales of McDonald's for one year is $650,000. Their sales are increasing at a rate of
4% per year. What will be their sales after 5 years?
a=
r=
t =
2. The population of a school is 800 students and is increasing at a rate of 2% per year.
What will be their population after 6 years?
a=
r=
t =
3.There are 70 northern sea otters that are seeing a growth at a rate of 18%.What will their population be after 4 years?
a=
r=
t=
4. Annual sales for a furniture stores are $375,000 and are increasing at a rate of 6.75% each year.What will their sales me after 9 years?
a=
r=
t=
5. The population of Indiana showed an annual growth rate of 0.6%.Their population in 1999 was 273,000,000. What will their population be in 2007?
a=
r=
t=
1) If the sales of McDonald's for one year is $650,000 and increasing at 4% annually (exponential growth), their sales after 5 years will be $790,824.
2) If the population of a school is 800 students and is increasing at a rate of 2% per year (exponential growth), after 6 years, the population will be 901.
3) With 70 northern sea otters growing at a rate of 18% annually (exponential growth), after 4 years, the population will be 136.
4) If the annual sales for a furniture stores are $375,000 and increasing (exponential growth) at a rate of 6.75% each year, the sales after 9 years will be $675,060.
5) If the population of Indiana showed an annual growth rate of 0.6% (exponential growth) and their population in 1999 was 273,000, the population in 2007 will be 286,383.
What is exponential growth?Exponential growth refers to the consistent increase in quantity over time and at a constant growth rate.
Exponential growths are modeled using the exponential growth function y = a(1+r)^t.
1. McDonalds:
y= a(1+r)^t
Where a = $650,000
r = 0.04 (4%)
t = 5 years
Sales after 5 years, y= a(1+r)^t
= $650,000 (1.04)^5
= $650,000 × 1.2166529
= $790,824
2) School Population:
Current population = 800
Annual increasing rate = 2%
a = 800
r = 2%
t = 6 years
Population after 6 years, y= a(1+r)^t
= 800(1.02)^6
=901
3) Northern Sea Otters:
a = 70
r = 18% or 0.18
t = 4 years
Population after 6 years, y= a(1+r)^t
= 70(1.18)^4
= 136
4) Furniture Stores:
a = $375,000
r = 6.75% or 0.0675
t = 9 years
Sales after 9 years, y = a(1+r)^t
= 375,000(1.0675)^9
= $675,060
5) Indiana Population:
a = 273,000
r = 0.6% or 0.006
t = 8 years (2007 - 1999)
Population after 8 years, y = a(1+r)^t
= 273,000(1.006)^8
= 286,383
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Write an inequality that represents 12more than w is at least 45?
Answer:
The inequality that represents the given statement is:
12 + w ≥ 45
Step-by-step explanation:
Help due in 30 mins
.
The cost of a Boston Red Sox baseball cap is $24.00. The local sporting goods store sells it for 30.00, Find the markup rate?
Answer:
25%
Step-by-step explanation:
$30-$24 =$6
$6×100
________ =25 percent
24
Using the grouping method put this equation into factored form
A chef has three blocks of butter each block weighs 1 pound she cut each blocks into fifths how many 1/5 pounds pieces of butter does the chef have
Answer:
Chef will have 15 pieces of butter.
Step-by-step explanation:
Chef has 3 blocks of butter,
weight of each block = 1 pound
she cuts each block into fifth pieces,
3 / 1/5 = 15 pieces
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Sam is collecting money for an animal shelter. He collects $150.00 each day for 6 days. The shelter will use 35% of the money he collects to buy pet food. The rest of the money will be used to buy cleaning supplies.
How much of the money that Sam collects will be used to buy cleaning supplies?
According to the solving Sam will spend $585.00 of the money he collects on cleaning materials.
What do the percentages mean?%, a relative figure signifying hundredths of any amount. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Mathematical percentile is a related topic.
According to the given information:Sam collects $150.00 each day for 6 days, so the total amount he collects is:
$150.00/day x 6 days = $900.00
The shelter will use 35% of the money he collects to buy pet food. To find out how much money will be used to buy pet food, we can multiply the total amount Sam collects by 35% (or 0.35):
$900.00 x 0.35 = $315.00
So, $315.00 of the money that Sam collects will be used to buy pet food. To find out how much money will be used to buy cleaning supplies, we can subtract the amount used to buy pet food from the total amount collected:
$900.00 - $315.00 = $585.00
$585.00 of the money that Sam collects will be used to buy cleaning supplies.
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Dividing integers. The temperature dropped 32° F in 4 hours. Suppose the temperature dropped by an equal amount each hour. What integer describes the change?
Answer:
To find the integer that describes the change in temperature, we can divide the total temperature drop by the number of hours:
32 ÷ 4 = 8
Therefore, the temperature dropped by 8 degrees Fahrenheit each hour. The integer that describes the change is -8, since the temperature decreased.
Answer: To find the integer that describes the change in temperature, we need to divide the total change in temperature (32° F) by the number of hours over which the temperature dropped (4 hours). This will give us the amount that the temperature dropped by each hour.
So, dividing 32 by 4, we get:
32 ÷ 4 = 8
Therefore, the temperature dropped by 8 degrees Fahrenheit each hour.
Step-by-step explanation:
A bookstore needs to sell at least 235 books. The number of books the store sells is described by 745-30b,where is the price per book.
Select the answer choice in each blank to make the statement true.
The range of the (profit per book)
Sold should be
(greater than $30 )
(between $0 and $17)
(greater than $17)
(between $17 and $30)
The parentheses are the choices for the answer.
The choice in the blank to make the statement true will be D. between $17 and $30)
How to explain the informationRevenue = Price per book × Number of books sold = (745 - 30P) b
Since the store needs to sell at least 235 books, we have:
Revenue ≥ 235 × Price per book = 235(745 - 30P)
Simplifying this inequality, we get:
745b - 30Pb ≥ 235 × 745
P ≤ (745/30) - (235/b)
Since we want to find the minimum profit per book sold, we need to maximize the value of (235/b). The maximum value of (235/b) occurs when b is minimized
If we assume that the cost per book is constant, then the profit per book sold will increase as the price per book increases. Therefore, we can say that the minimum profit per book sold that would enable the store to sell at least 235 books is greater than $17.
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The mean score on the Stats exam
was 75 points with a standard deviation of 5 points,
and Gregor's z-score was -2. How many points did he
score?
Gregor scored 65 points on the Stats exam.
How to determine the number of points he scoredWe can use the formula for calculating z-score:
z = (x - μ) / σ
Where
z is the z-score,x is the raw score, μ is the population meanσ is the population standard deviation.We are given that the population mean (μ) is 75 and the population standard deviation (σ) is 5.
We are also given that Gregor's z-score (z) is -2.
We can plug these values into the formula and solve for x:
-2 = (x - 75) / 5
Multiplying both sides by 5, we get:
-10 = x - 75
Adding 75 to both sides, we get:
x = 65
Hence, the score is 65 points
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4(1 + 9x) theres alot lol
Answer:
4 + 36x
Step-by-step explanation:
4(1 + 9x)
= 4 + 36x
So, the answer is 4 + 36x
Can someone help me with this? As detailed as possible?
F1 = 1167.35N and F2 = 1932.65N are the contact support forces on the beam
How to calculate the contact support forces on the beam?For the torques, let the axis be at support 2 and consider torques and the counterclockwise rotation is positive.
Let m = mass of athlete and M = mass of beam.
Thus, the equilibrium of torques will be:
Mg(1.96) - mg(0.54m) - F1(3.92) = 0
Substitute the values and solve for F1:
(250 * 10 * 1.96) - (60 * 10 * 0.54) - 3.92F1 = 0
3.92F1 = 4900 - 324
3.92F1 = 4576
F1 = 1167.35N
Note: The weight of the beam is acting at the center and the distance from center to axis at support 2 is 1.96m.
Balancing forces in the vertical direction, we have:
F1 + F2 - Mg − mg = 0
1167.35 + F2 - (250 * 10) − (60 * 10) = 0
1167.35 + F2 - 2500 - 600 = 0
F2 = 1932.65N
Note: upward forces (supports) are positive and downward forces are negative.
Thus, the contact support forces on the beam are F1 = 1167.35N and F2 = 1932.65N.
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the following data gives the amount in thousand spend s on feeding by fourty
household in ibadan in febuary 2023
32,22,19,18,43,42,40,43,18,21,31,26,22,25,47,40,26,32,34,22,35,38,34,41,36,25,22,45,48,26,28,38,35,19,47,28,26,35,38,35.
( a) construct a frequency distribution using class interver
(b) hence compute the (1) class mark for each class (2)class boundary for each class (3) cummulate frequency of the distribution (4) relative frequency of the classes (5) relative cummulative frequency.
The frequency distribution is calculated below
How to construct the frequency distributionThe dataset is given as
32,22,19,18,43,42,40,43,18,21,31,26,22,25,47,40,26,32,34,22,35,38,34,41,36,25,22,45,48,26,28,38,35,19,47,28,26,35,38,35.
To construct a frequency distribution using class intervals, we calculate the class width as follows:
Class width = Range / Number of intervals
So, we have
Class width = (48 - 18)/5 = 6
Now we can construct the frequency distribution table:
Class Interval Frequency
18 - 23 9
24 - 29 8
30 - 35 9
36 - 41 7
42 - 47 6
48 - 53 1
The class mark for each class can be calculated as:
Class mark = (Lower limit + Upper limit) / 2
For the class boundaries, we use the following formula
Lower boundary = Lower limit - 0.5
Upper boundary = Upper limit + 0.5
For the cumulative frequency of the distribution, we need to add up the frequencies of each class and all the preceding classes.
Lastly, for the relative frequency we divide each frequency by the total frequency (40)
Using the above as a guide, we have
Interval Frequency Boundaries Mark CF
18 - 23 9 17.5 - 23.5 20.5 9
24 - 29 8 23.5 - 29.5 26.5 17
30 - 35 9 29.5 - 35.5 32.5 26
36 - 41 7 35.5 - 41.5 38.5 33
42 - 47 6 41.5 - 47.5 44.5 39
48 - 53 1 47.5 - 53.5 50.5 40
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a broker invested 1,600 in a particular stock. the table shows the value og the stock and the number of weeks since the investment. wgich function best models the value of the stock v(n), in dollars, m weeks since the investment for the given period?
The exponential function that best models the value of the stock after n weeks is given as follows:
v(n) = 1600(1 + r)^n.
How to define the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which:
a is the value of y when x = 0.b is the rate of change.The initial investment was of 1600, hence the parameter a is given as follows:
a = 1600.
The rate of change is obtained multiplying two consecutive values on the table, and will have the following format:
b = 1 + r.
In which r is the growth rate.
Missing InformationThe problem is incomplete, hence the general procedure to obtain the function is presented.
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Prove for any real number, |x−6|+x>3. Please use proof by cases, explaining each as you go.
The proof of |x−6|+x>3 is shown below.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
We have |x−6|+x>3.
Now, opening the absolute value
|x−6|+x>3
-(x- 6) + x >3
-x + 6 +x > 3
6 > 3
Thus, |x−6|+x>3 has been proved.
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On a grid, a middle school is located at (-5, 3), and a library is located at (2, 3). If 1 unit represents 1 mile on the grid, how far is the library from the middle school, in miles?
Answer: To find the distance between two points on a grid, we can use the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the coordinates of the middle school are (-5, 3), and the coordinates of the library are (2, 3). So we have:
distance = sqrt((2 - (-5))^2 + (3 - 3)^2)
distance = sqrt((2 + 5)^2 + 0^2)
distance = sqrt(7^2)
distance = 7
Therefore, the library is 7 miles away from the middle school.
Step-by-step explanation:
If x= 1, solve for y.
y = 3.5x
y = [?]
3.5
you plug in 1 in the x spot then solve
3.5 (1)
which then equals 3.5
that means that's what Y equals
which equation describes the line that passes through the points (1,3) and (-2,6)
y= -x+4
y= -2x+6
y= -2x+3
y= -x+3
hi
im pretty sure the answer is:
y= -x+4
If you can please help !! (the question is provided below)
Answer:
The distance between the student and the mirror is 7.5 feet.
Step-by-step explanation:
We can use similar triangles to solve this problem.
Let's call the distance between the student and the mirror "d". We can create a right triangle with the student's height as one leg, the distance "d" as the other leg, and the hypotenuse being the line from the student's eyes to the top of the school. Let's call the length of this line "h".
We can also create a second right triangle with the height of the school as one leg, the distance from the school to the mirror as the other leg, and the hypotenuse being the same line from the student's eyes to the top of the school.
Since these two triangles share an angle (the angle formed by the line from the student's eyes to the top of the school and the ground), they are similar triangles. This means that the ratios of their corresponding sides are equal.
We can set up the following proportion:
(student height) / d = (school height) / (distance from school to mirror)
Plugging in the given values, we get:
4.5 / d = 30 / 50
Simplifying, we get:
4.5 / d = 3 / 5
Cross-multiplying, we get:
3d = 22.5
Dividing by 3, we get:
d = 7.5
Therefore, the distance between the student and the mirror is 7.5 feet.
The distance of the student to the mirror, is 7.5 ft
What are similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Given that, a mirror is placed outside a school the distance from the school to the mirror is 50 ft and the height of the school is 30 ft we need to find the distance of the student to the mirror,
This arrangement is creating two similar triangles, here we will use the properties of the similar triangles, to find the distance of the student to the mirror,
Therefore,
30 / 4.5 = 50 / d
d = 50 x 4.5 / 30
d = 225 / 20
d = 7.5
Hence, the distance of the student to the mirror, is 7.5 ft
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Fill in the table, write an equation, find the LCD, and find the average rate.
The LCD we can use to simplify the equation is (2-r)(2+r) = 4 - r².
What is LCD?The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.
1. We can use the formula:
distance = rate × time
For the upstream journey:
distance = 4 miles
rate = 2 - r (since Dara is paddling against the current)
time = 4/(2-r) hours
For the downstream journey:
distance = 4 miles
rate = 2 + r (since Dara is paddling with the current)
time = 4/(2+r) hours
We can fill in the table as follows:
Distance (mi) Avg Speed (mph) Time (h)
With Current: 4 2+r (4)/(2+r)
Against Current: 4 2-r (4)/(2-r)
2. We know that the total time for the round trip is 6 hours:
4/(2-r) + 4/(2+r) = 6
3. Multiplying both sides by the LCD (2-r)(2+r), we get:
4(2+r) + 4(2-r) = 6(2-r)(2+r)
Simplifying, we get:
8 = 12 - 2r²
Rearranging, we get:
r² = 2
Taking the square root of both sides, we get:
r = ±√2
Since the current is flowing in one direction, we take the positive square root:
r = √2 ≈ 1.41 miles per hour
The LCD we can use to simplify the equation is (2-r)(2+r) = 4 - r².
4. To the nearest hundredth, the rate of the current is approximately 1.41 miles per hour, which is option B: About 1.15 miles per hour (rounded to two decimal places).
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in any given month there are at least 20 workdays each week, then how many workdays would roger have in the month if the month starts on a monday ? (hint: Draw a calendar to show how you arrive at your answer)
Roger would have 20 workdays in the month if it starts on a Monday and there are at least 20 workdays each week.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Assuming a month has four weeks, each with at least 20 workdays, we can calculate the total number of workdays in the month starting on a Monday as follows:
Week 1: Monday to Friday = 5 workdays
Week 2: Monday to Friday = 5 workdays
Week 3: Monday to Friday = 5 workdays
Week 4: Monday to Friday = 5 workdays
So the total number of workdays in the month is:
5 + 5 + 5 + 5 = 20
Therefore, Roger would have 20 workdays in the month if it starts on a Monday and there are at least 20 workdays each week.
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A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine whether or not the diagonals of polygon ABCD bisect each other. In your final answer, include all of your calculations.
Answer:
Step-by-step explanation:
midpoint of AC
[tex]x=\frac{1-1}{2} =0\\y=\frac{4-4}{2} =0\\mid ~point~of~AC=(0,0)[/tex]
midpoint of BD
[tex]x=\frac{4-4}{2} =0\\y=\frac{-1+1}{2} =0\\midpoint ~of~BD=(0,0)[/tex]
so diagonals bisect each other.