The length of one side of the square is x - 6 units
How to determine the lengthThe formula for calculating the area of a square is expressed as;
A = a²
Such that the a is the length of its side
From the information given, we have that;
Area = x^ 2 − 12 x + 36
solve the quadratic expression, we have that;
x² - 6x - 6x + 36
group in pairs
(x²- 6x) - (6x + 36)
factorize the terms
x(x - 6) - 8(x - 6)
Then, we have;
(x - 6) and (x - 6) units
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Let g(x.y)= 15x2 +2y2. Compute g(3,3), g(0,-2), and g(a,b). g(3,3)= _____
The function g(x, y) is defined as 15x^2 + 2y^2. To compute g(3,3), g(0,-2), and g(a,b), we substitute the given values into the function.
To find g(3,3), we substitute x = 3 and y = 3 into the function g(x, y) = 15x^2 + 2y^2:
g(3,3) = 15(3)^2 + 2(3)^2
g(3,3) = 135 + 18
g(3,3) = 153
To find g(0,-2), we substitute x = 0 and y = -2 into the function g(x, y) = 15x^2 + 2y^2:
g(0,-2) = 15(0)^2 + 2(-2)^2
g(0,-2) = 0 + 8
g(0,-2) = 8
To find g(a,b), we substitute x = a and y = b into the function g(x, y) = 15x^2 + 2y^2:
g(a,b) = 15a^2 + 2b^2
Note: The function g(a,b) cannot be simplified further without knowing the values of a and b.
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What is the approximate length, in inches of the scrap wood when they are, placed end to end
Answer:
D. 53
Step-by-step explanation:
To calculate total length, just add all those lengths:
5.5 + 6 + (6.5 x 3) + (7 x 2) + 8
5.5 + 6 + 19.5 + 14 + 8
11.5 + 19.5 + 14 + 8
31 + 14 + 8
45 + 8
53
3 Let a represent a positive number and let b represent a negative number. Tell whether each statement is True or False. A. The difference (a - b) could be negative. True False True False b. The difference (b - a) cannot be positive. C. The sum (a + b) could be positive. True False d. The sum (b + a) must be negative. True False
Using various laws of integers we can say that if a is a positive integer and b is a negative integer, statement A is False, B is True, C s True and D is false.
Here we are given that a is a positive integer while b is a negative integer.
A. The statement says that the difference (a - b) could be negative.
According to the subtraction law of integers, when a negative number is subtracted from a positive number, that is we have
2 - (-3)
Here the 2 minus signs will make a positive to give
2 + 3 = 5
Hence (a - b) will be a positive number since b is negative.
B.
The difference (b - a) cannot be positive.
Since a is positive and b is negative, according to the above example we will get
-3 - 2 = -5
Hence it is true that the difference (b - a) can't be positive.
C.
The sum (a + b) could be positive.
Here, we can see that a is a positive number while b is a negative number. In the light of above example, we will get
2 - 3 = -1
Here the sum is nagative as 3 > 2, but if we had
3 + (-2), then the answer would have been 1. Hence (a + b) can be positive. Hence the statement is true.
D.
The sum (b + a) must be negative.
Integers have commutative properties. Hence a + b = b + a
Hence if a + b can be positive, then b + a can also be positive.
Hence the statement is False.
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To the nearest whole cubic centimeter, what is the volume of the prism?
The volume of the prism in 120 cubic centimeter.
What is volume?Volume is a measure of the amount of space occupied by a three-dimensional object. It is a scalar quantity that characterizes the "size" or "capacity" of an object in three dimensions.
What is prism?A prism is a three-dimensional geometric shape that has two parallel and congruent bases connected by lateral faces that are typically rectangular or parallelogram-shaped. Prisms are classified based on the shape of their base, such as rectangular prisms, triangular prisms, pentagonal prisms, hexagonal prisms, and so on. The lateral faces of a prism are perpendicular to the bases, and the bases are usually parallel to each other.
According to the given information:
Given the measures of prism is length = 8cm, breadth = 6 cm, height = 5 cm
The formula for volume of prism = 1/2 l*b*h
= 1/2 8*6*5
= 120 cubic centimeter
Hence the volume of prism is 120 cubic centimeter.
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If Juan does not read any books before day 4 and he starts reading at the same
rate as Patti for the rest of the month, how many books will he have read by
day 12?
A. 5
B. 10
C. 15
D. 20
If Juan does not read any books before day 4 and he starts reading at the same rate as Patti for the rest of the month, he would have read 6 books by day 12. The correct option is A.
If Juan does not read any books before day 4, it means he has missed out on the opportunity to read for the first three days. Assuming Patti and Juan have been reading at the same rate since day 4, we can calculate the total number of books they would have read by day 12.
Patti reads one book per day, so by day 12, she would have read a total of 9 books (from day 4 to day 12). If Juan starts reading at the same rate as Patti from day 4, he would also have read 9 books by day 12.
However, we have to account for the fact that Juan did not read any books before day 4. This means that he missed out on the opportunity to read 3 books (one book per day for the first three days). Therefore, by day 12, Juan would have read a total of 6 books (3 books missed + 3 books read from day 4 to day 12).
Therefore, the answer is A. Juan would have read 5 books less than Patti by day 12, since Patti would have read a total of 9 books and Juan would have only read 6.
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Spencer spent 10 minutes on the phone while routing 5 phone calls. If he routes 28 phone calls, how much time will Spencer have spent on the phone in total? Solve using unit rates
Spencer will be on the phone for 56 minutes in total if he routes 28 calls.
To solve problemUsing unit rates, we can calculate how long Spencer will spend on the phone when routing 28 calls if he spent 10 minutes on the phone while routing 5 calls.
The amount of time spent on each phone call is the unit rate. In this instance, the unit fee is 10 minutes / 5 phone calls = 2 minutes each call.
In order to determine how much time Spencer will spend on the phone when routing 28 calls, we can use this unit rate as follows:
Time on phone = unit rate times the number of calls.Time on phone = 2 minutes per phone call x 28 phone callsTime on phone = 56 minutesTherefore, Spencer will be on the phone for 56 minutes in total if he routes 28 calls.
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Francium is a radioactive element discovered by Marguerite Perey in 1939 and named after her country. Francium has a half-life of 22 minutes.
a) Write an exponential function that models the mass how many grams remain from a 480-gram sample after t minutes.
b) How many grams remain after 2 hours?
After 2 hours, approximately 4.38 grams of Francium remain from the 480-gram sample.
What is Algebraic expression ?
An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It may contain one or more terms, with each term separated by a plus or minus sign. Algebraic expressions are used in algebra to represent mathematical relationships and formulas.
a) To write an exponential function that models the mass of Francium remaining after t minutes, we can use the formula:
N = N0 * [tex](1/2)^{(t / t1/2)}[/tex]
where N is the amount remaining after time t, N0 is the initial amount, t1/2 is the half-life, and (t/t1/2) means raised to the power of t/t1/2.
In this case, the initial amount is 480 grams, the half-life is 22 minutes, and we want to find the amount remaining after t minutes. Therefore, the exponential function that models the mass of Francium remaining after t minutes is:
N = 480 * [tex](1/2)^{t/22}[/tex]
b) 2 hours is equal to 120 minutes. To find how many grams of Francium remain after 2 hours, we can substitute t = 120 into the exponential function we found in part a):
N = 480 *[tex](1/2)^{ (120 / 22) }[/tex] ≈ 4.38 grams
Therefore, after 2 hours, approximately 4.38 grams of Francium remain from the 480-gram sample.
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CAN SOMEONE HELP PLEASE!
A restaurant is serving a special lunch combo meal that includes a drink, a main dish, and a dessert. Customers can choose from 5 drinks, 6 main dishes, and 3 desserts.
How many different combo meals are possible?
Select from the drop-down menu to correctly complete the statement.
Customers can create (14, 39, 60, 120) different lunch combo meals.
y were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. find the probability that
The value is calculated by dividing the total number of occurrences by 200 favourable examples that do not possess a college degree is 0.33 is the determined probability value.
The favourable number of cases is 200.
The total number of cases is 600.
The calculation of the required probability is,
Probability = Favourable cases Total number of cases 200 600 = 0.33
Occurrences refer to events or incidents that happen in a particular time or place. These events can be both positive and negative and can occur in various contexts, such as personal experiences, historical events, natural phenomena, and scientific observations.
Occurrences can be significant or insignificant, depending on their impact on individuals or society as a whole. Some occurrences may be routine and expected, while others may be unexpected and unpredictable. The study of occurrences is important in many fields, including history, sociology, psychology, and environmental science. By analyzing past occurrences, researchers can gain insights into patterns of behavior and trends that can inform future decisions and policies.
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Complete Question:-
The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. The probability that an employee of the company does not have a college degree is:
Which of the data sets below have striking deviations? Select all that apply.
A) 65, 68, 61, 63, 71
B) 99, 95, 93, 97, 98
C) 22, 83, 85, 88, 91
D) 45, 47, 43, 45, 97
E) 72, 78, 71, 67, 35
Mr. Thayer wants to measure the height of the CN tower. He stands 320 m from the base of the tower. He uses an inclinometer to measure the angle from the (horizontal) ground to the top of the tower, and it is 60°. Assume Mr. Thayer's eyes are 1.6 m above the ground.
The height of the CN tower which is 320m away from the Mr.Thayer is 555.85 meters.
Please look at the attached diagram for a clear explanation,
From the diagram point A represents, the Mr.Thayer's eyes, point B represents Mr.Thayer's foot, point C represents the base of the CN tower along with point E represents the top of the tower.
From the following diagram lets find out the height of the tower,
In right-angled triangle ADE, Tan theta = opposite/adjacent
So, Tan (60°) = DE/AD
√3 = DE/320m
DE = 320m x √3
DE= 554.25m
DE represents the height of the CN tower from the eyes of Mr.Thayer.
To find out the total height of the CN tower, the height of Mr.Thayer + the height of the CN tower from Mr. Thayer's eyes = 554.25m + 1.6m = 555.85m.
From the above explanation, we can conclude that the height of the CN tower from the base = 555.85m.
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a qualitative researcher studied womens decisions to delay birth until their late 30s. initial participants referred other women who had made similar decisions. what type of sampling approach i sbeing used with such referrals
The sample is being used with such referrals of a qualitative researcher studied women's decision to delay childbearing until their late 30s is Snowball, option C.
A non-probability sampling technique called snowball sampling entails the recruitment of new units by existing units to make up the sample. Research regarding people with certain characteristics who would be hard to find otherwise can benefit from snowball sampling (e.g., people with a rare disease).
Snowball sampling, sometimes referred to as chain sampling or network sampling, starts with one or more research participants. Following then, it proceeds based on recommendations from those individuals. This procedure is repeated until the required sample is obtained or a saturation point is reached.
The selection is based on a variety of factors, including:
A minimum of five years must have passed from the beginning of the relationship.Now the pair must cohabitate.The pair must reside in a specific region.The pair must be able to provide examples of changes or difficulties they have faced together (e.g., long-distance, illness or loss of a loved one).Learn more about Snowball sample:
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Complete question;
A qualitative researcher studied women's decision to delay
childbearing until their late 30s. Initial study participants
referred friends who had made similar decisions. What type
of sample is being used with such referrals?
A.Convenience
B.Volunteer
C.Snowball
D. Purposive
The equation of the line of best fit for the exam grade per hour studied is
y = 6x + 60. What is the residual for 1 hours of studying?
The predicted exam grade for 1 hour of studying is 66. Therefore the residual for 1 hours of studying can be calculated as Residual = Actual Exam Grade - 66.
To find the residual for 1 hour of studying, we first need to determine the predicted exam grade and compare it to the actual exam grade for that specific data point.
Using the line of best fit equation y = 6x + 60, we can find the predicted exam grade for 1 hour of studying:
y = 6(1) + 60
y = 6 + 60
y = 66
So, the predicted exam grade for 1 hour of studying is 66. To calculate the residual, you need the actual exam grade for 1 hour of studying. If that information is not provided, the residual cannot be calculated. If the actual grade is provided, subtract the predicted grade from the actual grade to find the residual:
Residual = Actual Exam Grade - Predicted Exam Grade
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if a1=5 and an=an-1 -1 then find the value of a4
a4 = 2
It is given that,
[tex]a_{1} = 5[/tex], and
[tex]a_{n} = (a_{n-1}) - 1[/tex]
Therefore, it can be said,
[tex]a_{2} = a_{1} - 1\\a_{3} = a_{2} - 1\\a_{4} = a_{3} - 1\\[/tex]
That is,
[tex]a_{2} = 5-1=4\\a_{3} = 4-1=3\\a_{4} = 3-1=2[/tex]
So, a4 = 2
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help pls. my mom is mad bc i don’t have this done.
_______________________________
A = L × B = 7.3cm × 9cm= 65.7cm= 65.7cm × 90m= 5,913m²_______________________________
Which list correctwhich list correctly identifies the steps to solving a word problem?ly identifies the steps to solving a word problem?
There is no one definitive list of steps to solving a word problem, as different types of problems may require different approaches.
However, a general set of steps that can be useful in solving many word problems is:
1. Read the problem carefully to understand what it is asking.
2. Identify the relevant information and the unknown quantity you need to find.
3. Translate the problem into an equation or set of equations that relate the given information to the unknown quantity.
4. Solve the equation(s) to find the value of the unknown quantity.
5. Check your answer to make sure it makes sense in the context of the problem.
Additional steps or variations on these steps may be necessary depending on the specific problem, but this general framework can be a useful starting point.
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Each year Wenford Hospital records how long patients wait to be treated in the Accident
and Emergency department.
In 2015 patients waited 11% less time than in 2014.
In 2015 the average time patients waited was 68 minutes.
(a) Work out the average time patients waited in 2014.
Give your answer to the nearest minute.
The average time patients waited in 2014 was approximately 76 minutes, calculated by dividing the 2015 waiting time by 0.89 as patients waited 11% less time in 2015.
Let's call the average time patients waited in 2014 as per Wenford Hospital records "x" (in minutes). According to the problem statement, patients waited 11% less time in 2015 compared to 2014, so,
0.89x = 68
Solving for x,
x = 68 / 0.89
x ≈ 76.4
Therefore, the average time patients waited in 2014 was approximately 76 minutes (rounded to the nearest minute).
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for each pair of numbers verify lcmm,n∙gcdm,n=mn. 60,90 220,1400 3273∙11, 23∙5∙7
lcmm,n∙gcdm,n=mn is verified for all three pairs of numbers. We can verify lcmm,n∙gcdm,n=mn for each pair of numbers as follows:
For 60 and 90:
lcm(60,90) = 180
gcd(60,90) = 30
180 * 30 = 5400
60 * 90 = 5400
Since both sides of the equation are equal to 5400, the equation is verified.
For 220 and 1400:
lcm(220,1400) = 3080
gcd(220,1400) = 20
3080 * 20 = 61600
220 * 1400 = 61600
Since both sides of the equation are equal to 61600, the equation is verified.
For 3273∙11 and 23∙5∙7:
lcm(3273∙11, 23∙5∙7) = 15015
gcd(3273∙11, 23∙5∙7) = 161
15015 * 161 = 2418315
3273∙11 * 23∙5∙7 = 2418315
Since both sides of the equation are equal to 2418315, the equation is verified.
Therefore, lcmm,n∙gcdm,n=mn is verified for all three pairs of numbers.
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Water flows into an empty reservoir at a rate of 3200+ 5t gal/hour. What is the quantity of water in the reservoir after 11 hours? Answer:_____ gallons.
To find the quantity of water in the reservoir after 11 hours, we need to integrate the rate of flow with respect to time from 0 to 11. The quantity of water in the reservoir after 11 hours is 38,225 gallons.
∫(3200 + 5t) dt from 0 to 11
= [(3200 * 11) + (5/2 * 11^2)] - [(3200 * 0) + (5/2 * 0^2)]
= 35,200 + 302.5
= 35,502.5 gallons
Therefore, the quantity of water in the reservoir after 11 hours is 35,502.5 gallons.
To find the quantity of water in the reservoir after 11 hours with the rate of 3200 + 5t gal/hour, we need to first find the total amount of water that flows into the reservoir within that time.
Step 1: Identify the given rate of flow: 3200 + 5t gal/hour.
Step 2: Integrate the flow rate function with respect to time (t) to find the total quantity of water. The integral of the function will give us the quantity of water in gallons:
∫(3200 + 5t) dt = 3200t + (5/2)t^2 + C, where C is the constant of integration.
Since the reservoir is initially empty, the constant C will be 0.
Step 3: Substitute t=11 hours into the integrated function to find the total quantity of water:
Q(11) = 3200(11) + (5/2)(11)^2
Q(11) = 35200 + 3025
Step 4: Add the values to find the total quantity of water in gallons:
Q(11) = 38225 gallons
The quantity of water in the reservoir after 11 hours is 38,225 gallons.
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You are buying shingles for a roof. Each bundle of shingles will cover 27 square feet. The roof consists of two rectangular parts, and each 70 feet by 30 feet. How many bundles of shingles do you need?
Answer:
156 bundles
Step-by-step explanation:
Total area of the roof = 2(70 x 30) = 4200 sf
(4200 sf) / (27sf/bundle) = 155.56 ≈ 156 bundles
Rita and Jan are working on a school project together. Rita has completed 0.3 of her portion, and Jan has completed a portion as well. Use the model to complete the equation below and find how much of the total project Rita and Jan have completed.
answer the question.
Answer:
rita and john are susseful the job
js school
A shoe store donated a percent of every sale to charity. The total sales were $7,200 so the store donated $144. What percent of $7,200 was donated to charity?
The percentage of $7,200 that was donated to charity would be = 2%
How to calculate the percentage of the total sales that was donated?To calculate the percentage of the total sales that was donated, the following should be carried out.
The total sales at the shoe store = $7,200
The amount of money that was donated = $144
Therefore to calculate the percentage the following is done ;
= 144/7200 × 100/1
= 14400/7200
= 2%
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Grams of
Peanuts
Grams of
Raisins
14
4
21
6
35
10
Enter the number of grams of peanuts in a bag for every 1 gram of raisins.
For every 1 gram of raisins, there are 3.5 grams of peanuts in a bag.
To find the number of grams of peanuts for every 1 gram of raisins, you need to set up a ratio and solve for the missing value.
1. Set up the ratio: grams of peanuts / grams of raisins.
2. You are given three sets of values: (14, 4), (21, 6), and (35, 10).
For the first set (14, 4):
3. Calculate the ratio: 14 grams of peanuts / 4 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.
For the second set (21, 6):
4. Calculate the ratio: 21 grams of peanuts / 6 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.
For the third set (35, 10):
5. Calculate the ratio: 35 grams of peanuts / 10 grams of raisins = 3.5 grams of peanuts per 1 gram of raisin.
Your answer: For every 1 gram of raisins, there are 3.5 grams of peanuts in a bag.
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Find the equation of a line that goes throught point -2,-5 and is parallel to y = x + 2
The equation of the line that goes through the point (-2, -5) and is parallel to y = x + 2 is y = x - 3.
To find the equation of a line that goes through the point (-2, -5) and is parallel to y = x + 2, we will follow these steps:
1. Identify the slope of the given line.
2. Use the slope and the given point to find the equation of the new line.
Step 1: Identify the slope of the given line.
The equation of the given line is y = x + 2. This is in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope (m) is 1, as it is the coefficient of x.
Step 2: Use the slope and the given point to find the equation of the new line.
Since the new line is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also 1.
Now, we will use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point.
Plugging in the values, we have:
y - (-5) = 1(x - (-2))
y + 5 = 1(x + 2)
Now, let's rewrite the equation in slope-intercept form:
y + 5 = x + 2
y = x + 2 - 5
y = x - 3
So, the equation of the line that goes through the point (-2, -5) and is parallel to y = x + 2 is y = x - 3.
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Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form Passing through (-9,2) and parallel to the line whose equation is y = – 3x + 3
The equation of the line in point-slope form is y - 2 = -3(x + 9), and in slope-intercept form is y = -3x - 25.
To find the equation of the line passing through(- 9,2) and parallel to the line y = – 3x 3, we need to use the fact that resemblant lines have the same pitch.
The pitch of the given line y = – 3x 3 is-3,
so the pitch of the resemblant line we want to find is also-3. Point- pitch form Using the point- pitch form, the equation of the line is given by
y- y1 = m( x- x1),
where( x1, y1) is the given point and
m is the pitch.
Substituting the given values,
we get y- 2 = -3( x-(- 9))
y- 2 = -3( x 9)
y- 2 = -3 x- 27
y = -3 x- 25
Hence in slope-intercept form is y = -3x - 25.
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Pls help me with this question quick
Based on the equation, when Lisa sells 24 copies of Math is Fun, her total pay will be $3140.
How to calculate the amountThe equation relating P to N is:
P = 1700 + 60N
This is because her base salary is $1700, and she earns an additional $60 for each copy of Math is Fun she sells.
In order to find her total pay if she sells 24 copies of Math is Fun, we simply need to substitute N = 24 into the equation:
P = 1700 + 60(24)
P = 1700 + 1440
P = 3140
Therefore, if Lisa sells 24 copies of Math is Fun, her total pay will be $3140.
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Quinn is a budding fashion designer known for incorporating geometry into her creations. Her newest design is a simple black blouse patterned with same-size right triangles in different funky colors. The longer leg of each right triangle will be twice as long as the shorter leg, and the hypotenuse of each triangle will be 6 inches long. To the nearest tenth of an inch, what will be the length of the shorter leg of each triangle?
To the nearest tenth of an inch, the length of the shorter leg of each right triangle will be 2.7 inches.
What is the triangle?A triangle is a polygon with three sides and three angles. The sum of the three angles in a triangle always adds up to 180 degrees. There are many different types of triangles, including equilateral triangles (where all three sides are equal in length and all three angles are 60 degrees), isosceles triangles (where two sides are equal in length and two angles are equal in measure), and scalene triangles (where no sides are equal in length and no angles are equal in measure).
According to the given informationLet x be the length of the shorter leg of each right triangle. Then, the longer leg will be twice as long, so its length will be 2x. Using the Pythagorean theorem, we can write:
x² + (2x)² = 6²
Simplifying and solving for x, we get:
x² + 4x² = 36
5x² = 36
x² = 7.2
x ≈ 2.7
Therefore, to the nearest tenth of an inch, the length of the shorter leg of each right triangle will be 2.7 inches.
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4 Find the value xa where the function is discontinuousFor the point of discontinuity, give (a) f) if it exists. (b) lm (0) Im . () im 16), and (ej identity which conditions for continuity are not man -O (Use a coma o separate answers as needed Select the choice below and necessary, tal in the trawer box within your choice ОА ка) OB) is undefined (b) Select the choice below and necessary, tu in the answer box within your chale ΟΑ. lim) OB lim does not exist
So, the answer is:
(a) f(x) does not exist at xa = 16.
(b) lim f(x) as x approaches 16 does not exist.
(c) None of the conditions for continuity are met at xa = 16.
To find the value of xa where the function is discontinuous, we need to look for any points where the function is undefined or where the left and right limits of the function are not equal.
(a) From the given information, we know that the function is undefined at xa = 16. So, this is the point of discontinuity.
(b) To find the left and right limits at xa = 16, we need to approach the point from both sides of the function. So,
lim f(x) as x approaches 16 from the left (denoted as lim-) = Im = 0
lim f(x) as x approaches 16 from the right (denoted as lim+) = Im = 16
Since the left and right limits are not equal, the limit as x approaches 16 does not exist. So,
lim f(x) as x approaches 16 (denoted as lim) does not exist.
(c) To determine which conditions for continuity are not met, we need to check if the function satisfies the three conditions for continuity at xa = 16.
i) The function must be defined at xa = 16. Since the function is undefined at xa = 16, this condition is not met.
ii) The left and right limits of the function must exist and be equal at xa = 16. Since the left and right limits are not equal, this condition is not met.
iii) The value of the function at xa = 16 must be equal to the limit of the function at xa = 16. Since the limit does not exist, this condition is also not met.
Therefore, none of the conditions for continuity are met at xa = 16.
So, the answer is:
(a) f(x) does not exist at xa = 16.
(b) lim f(x) as x approaches 16 does not exist.
(c) None of the conditions for continuity are met at xa = 16.
Note: The terms "discontinuous" and "continuity" are used throughout the explanation to describe the concept and the point of interest. The term "function" refers to the given function that we are analyzing.
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A mover notes the weights of a table and 4 chairs and records t+4C >_100 on his invoice. What is he communicating?
The choices are,
A. The table and 4 chairs each weigh more than 100 pounds.
B. The table and 4 chairs weigh at most 100 pounds.
C. The table and 4 chairs weigh around 100 pounds, give or take a little.
D. The table and 4 chairs at
least 100 pounds
The mover is communicating that the weight of the table and 4 chairs combined, represented as t+4C, is greater than or equal to 100 pounds.
The expression t+4C represents the total weight of the table and 4 chairs. The mover's invoice states that this total weight is greater than or equal to 100 pounds, which means that the combined weight of the table and chairs is at least 100 pounds. Therefore, the correct answer is D, "The table and 4 chairs weigh at least 100 pounds."
To solve this mathematically, we can use algebraic inequalities. The inequality t+4C >_ 100 can be rearranged as t >_ 100-4C. This means that the weight of the table t must be greater than or equal to 100 minus four times the weight of a single chair C.
If each chair weighs less than 25 pounds, then the total weight of the table and 4 chairs combined will be at least 100 pounds. So D is correct answer.
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Maddy is an event coordinator who helps
raise money for a children's hospital. At
last year's event, she sold 1200 tickets at
$8 each.
Part A: This year Maddy will reduce ticket
prices by 25%. What will be the price of a
new ticket? Explain your reasoning.
D
Part B: Based on the new price, how many
more tickets will Maddy need to sell to
raise the same amount of money as last
year? Explain your reasoning.
The price of a new ticket after reducing the ticket price by 25% is $6. Maddy will need to sell 400 more tickets this year to raise the same amount of money as last year.
Number of tickets sold = 1200
Cost of each ticket = $8
Part A:
If Maddy lowers ticket costs by 25%, The price of a new ticket will be:
Ticket price = $8 - (25% of $8)
Ticket price = $6
The New ticket price will be calculated by multiplying 0.75 for reducing the 25% tickets
New ticket price = $8 x 0.75 = $6
Part B:
To find how many tickets Maddy requires to sell to equal the same amount of money collected in the previous year:
Total revenue = total number of tickets x Ticket price
1200 tickets x $8 per ticket = $9,600
= $9,600 / $6
= 1,600
Total tickets need to sell = 1600-1200 = 400
Therefore we can conclude that Maddy will need to sell 400 more tickets this year.
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