The values of x make the quadratic equation (x-2)² =2 is 2 + √2.
To find the values of x that make the quadratic equation (x-2)² = 2 true, we need to solve for x.
First, we can take the square root of both sides of the equation:
x - 2 = ±√2
Next, we can add 2 to both sides of the equation:
x = 2 ± √2
Therefore, the two solutions for x are:
x = 2 + √2
x = 2 - √2
These are the two values of x that make the quadratic equation (x-2)^2 = 2 true.
To check these solutions, we can substitute each value back into the original equation:
[(2 + √2) - 2]² = 2
Simplifying:
√2² = 2
2 = 2
This solution works. Now let's check the other solution:
[(2 - √2) - 2]² = 2
Simplifying:
-√2² = 2
-2 = 2
This solution does not work, so we discard it. Therefore, the only value of x that makes the quadratic equation (x-2)² = 2 true is: x = 2 + √2.
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2x + 3y = 8
-4x + 6y = 8
X-Z = -4
Nilai x+y+z adalah
Answer:
0
Step-by-step explanation:
Untuk menyelesaikan masalah ini, kita perlu menyelesaikan sistem persamaan linear dua variabel pertama dan sistem persamaan linear tiga variabel:
Sistem Persamaan Linear Dua Variabel:
2x + 3y = 8 ... (1)
-4x + 6y = 8 ... (2)
Untuk menyelesaikan sistem persamaan ini, kita dapat menggunakan metode eliminasi:
Langkah 1: Kalikan Persamaan (1) dengan 2 dan Persamaan (2) dengan 1. Kita memperoleh:
4x + 6y = 16 ... (3)
-4x + 6y = 8 ... (4)
Langkah 2: Tambahkan Persamaan (3) dan Persamaan (4). Kita memperoleh:
12y = 24
Langkah 3: Bagi kedua sisi dengan 12. Kita memperoleh:
y = 2
Langkah 4: Substitusikan y = 2 ke dalam Persamaan (1) atau (2). Kita memperoleh:
2x + 3(2) = 8
2x + 6 = 8
2x = 2
x = 1
Jadi, solusi dari sistem persamaan linear dua variabel adalah (x, y) = (1, 2).
Sistem Persamaan Linear Tiga Variabel:
x - z = -4 ... (5)
x + y + z = ?
2x + 3y = 8
Untuk menyelesaikan sistem persamaan ini, kita dapat menggunakan metode substitusi:
Langkah 1: Substitusikan x = 1 dan y = 2 dari sistem persamaan linear dua variabel ke dalam Persamaan (3). Kita memperoleh:
2(1) + 3(2) = 8
2 + 6 = 8
8 = 8
Langkah 2: Substitusikan x = 1 dari sistem persamaan linear dua variabel ke dalam Persamaan (5). Kita memperoleh:
1 - z = -4
z = 5
Langkah 3: Substitusikan x = 1 dan z = 5 ke dalam Persamaan (6). Kita memperoleh:
1 + y + 5 = ?
y = -6
Jadi, solusi dari sistem persamaan linear tiga variabel adalah (x, y, z) = (1, -6, 5).
Maka nilai x + y + z adalah:
x + y + z = 1 + (-6) + 5 = 0
Jadi, nilai x + y + z adalah 0
a car moves at a speed of 90 meters per minute. what is its speed in meters per second?
Answer:
There are 60 seconds in a minute, so to convert meters per minute to meters per second, we need to divide by 60.
90 meters per minute ÷ 60 = 1.5 meters per second
Therefore, the car's speed is 1.5 meters per second.
Step-by-step explanation:
Step-by-step explanation:
There are 60 in a minute, so to convert meters per minute to meters per second, we need to divide by 60
90 meters per minute ÷ 60 = 1.5 meters per second
The distribution of the ages of of all IRSC students is known to be normally distributed with a mean of 20.9
years and a standard deviation of 5.9 years. Use this information to determine the following probabilities.
Round solutions to four decimal places, if necessary.
The probability that a random sample of 55 students has a mean age of less than 19.2 age years is 0.3866 and the probability that a random sample of 55 students has a mean age between 18.8 and 23 years is 0.27808.
What is the probability that a random sample has a mean age of less than 19.2a. To find P(x < 19.2), we need to find the area under the normal distribution curve to the left of x = 19.2. We can use the formula for z-score to standardize the value of x:
z = (x - μ) / δ = (19.2 - 20.9) / 5.9 = -0.2881
Looking up the area to the left of z = -0.2881 in a standard normal distribution table or using a calculator, we find that the probability is approximately 0.3869. So P(x < 19.2) is 0.3866.
b. To find P(18.8 < x < 23.0), we need to find the area under the normal distribution curve between x = 18.8 and x = 23.0. Again, we can standardize the values of x and use a standard normal distribution table or calculator:
z1 = (18.8 - 20.9) / 5.9 = -0.3559
z2 = (23.0 - 20.9) / 5.9 = 0.3559
Looking up the area between z1 = -0.3559 and z2 = 0.3559 in a standard normal distribution table or using a calculator, we find that the probability is approximately0.27808. So P(18.8 < x < 23.0) is 0.27808.
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make a table for the function d = 3t which gives the distance traveled at the rate of 3 mi per hr. then graph the function
The table for the function d = 3t is
t (hours) d = 3t (miles)
0 0
1 3
2 6
How to make a table for the functionThe equation of the function is given as
d= 3t
The above is a linear function
To make a table for the function d = 3t, we can choose some values of t and then calculate the corresponding values of d using the given equation.
Since the equation represents distance traveled at a rate of 3 miles per hour, we can assume that t represents time in hours and d represents distance in miles.
Let's choose some values of t and calculate the corresponding values of d:
t (hours) d = 3t (miles)
0 0
1 3
2 6
3 9
4 12
5 15
The graph is attached
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The value of the of your quarters incense is a function of and the number of quarters. You have finally output when the input is 10
The value of the of your quarters incense is a function of and the number of quarters, then the output when input is 10 is 250.
Quarters:
In mathematical terms, quartering is the division of a whole into 4 equal parts, where 1 is the part referred to and 4 is the number of parts the whole is divided into.
Let the quarter be 25 cents then value(v) of quarter (cents) is functions of n then equation,
v = 25n
Putting input (n =10)
V = 25× 10
= 250
The independent value is: n
The dependent value is : v
The equation is: v = 25n
And, the output when input is 10 is 250.
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Write the equation of a circle with center at ( 3, -5 ), and a radius of 3.
A. (x - 3)² + (y + 5)² =9
B. 3 (x - 3)² + (y + 5)² =9
C. (x + 3)² + (y - 5)² =9
D. (x + 3)² + (y - 5)² =3
Answer:
The equation of a circle with center (h, k) and radius r is given by:
(x - h)² + (y - k)² = r²
So, substituting the values given in the question, we get:
(x - 3)² + (y + 5)² = 3²
Simplifying, we get:
(x - 3)² + (y + 5)² = 9
Therefore, the correct option is A) (x - 3)² + (y + 5)² = 9.
Step-by-step explanation:
Math Problem #2
Ten bags each contain a different number of marbles. The number of marbles in
each bag ranges from 1 to 10. Five friends take two bags each. Amina got 5
marbles. Breanna got 7 marbles. Chyna got 9 marbles. Deion got 15 marbles. How
many marbles did Emila get?
Show your work.
Emila gοt a tοtal οf 2 + 7 = 9 marbles.
Let's first find οut which bags each friend gοt. Since each friend tοοk twο bags, we can subtract the marbles each friend gοt frοm the tοtal number οf marbles in the twο bags tο find οut the number οf marbles in the οther bag.
Amina gοt 5 marbles, sο the tοtal number οf marbles in her twο bags must be 1 + 4 οr 2 + 3. Let's assume she gοt bags with 1 and 4 marbles.
Then, the bags left fοr the οther friends are:
Bag 2: Breanna οr Chyna
Bag 5: Breanna οr Chyna
Bag 6: Deiοn οr Emila
Bag 7: Deiοn οr Emila
Bag 8: Available tο any friend
Bag 9: Available tο any friend
Bag 10: Available tο any friend
Breanna gοt 7 marbles, sο the tοtal number οf marbles in her twο bags must be 3 + 4. Therefοre, Chyna gοt bags with 2 and 5 marbles.
Chyna gοt 9 marbles, sο the tοtal number οf marbles in her twο bags must be 4 + 5. Therefοre, Deiοn gοt bags with 1 and 8 marbles.
Deiοn gοt 15 marbles, sο the tοtal number οf marbles in his twο bags must be 6 + 9. Therefοre, Emila gοt bags with 2 and 7 marbles.
Therefοre, Emila gοt a tοtal οf 2 + 7 = 9 marbles.
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11
10
9
8765
4
321
y
3
2
1
S
6 7 8 9 10 11
O A. y = x
B. y = x
C. y = 6x
OD. y = 2x
The proportional relationship defined by the table is given as follows:
y = 2x.
What is a proportional relationship?A proportional relationship is defined according to the equation presented as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
From the table, when the input variable x is increased by one, the output variable y is increased by 2, hence the constant of proportionality is given as follows:
k = 2.
Meaning that the equation is given as follows:
y = 2x.
Missing InformationThe graph of the relation is given by the image presented at the end of the answer.
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Find the measure of each bolded arc. Round to the nearest hundredth.
The length of the shaded arc is 68.71 metres squared.
How to find the length of an arc?The arc of a circle is defined as the part or segment of the circumference of a circle. Therefore, the length of the bolded arc can be found as follows:
length of an arc = ∅ / 360 × 2πr
where
r = radius∅ = central angleTherefore,
r = 26 / 2 = 13 m
∅ = 360 - 57 = 303 degrees
length of an arc = 303 / 360 × 2 × 3.14 × 13
length of an arc = 24736.92 / 360
length of an arc = 68.7136666667
length of an arc = 68.71 metres squared
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is skewed
IQR, because Desert Landing is symmetric
Range, because Sunny Town is skewed
Range, because Desert Landing is symmetric
A. IQR or B. IQR is the correct response since Sunny Town is symmetrical or Sunny Town is asymmetrical.
How do distributions work?The pattern of data distribution across various values or intervals is referred to as a distribution. The form, centre, and dispersion of a set of data can be described and examined in this manner.
We need to measure the fluctuation of the temperature data in both locations in order to decide which place has the most stable temperature. The interquartile range (IQR), which quantifies the spread of the middle 50% of the data, is the ideal measure of variability for this application.
As a result, depending on how the distributions are shaped, the answer is either A. IQR because Sunny Town is symmetric or B. IQR because Sunny Town is skewed. The IQR would be a suitable tool to gauge the data's spread if Sunny Town's temperature data were symmetric. The IQR would also be useful to measure the spread of the data if Sunny Town's temperature data were skewed. Therefore, the range would not be a suitable indicator of variability if the temperature data from either location were not skewed.
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2x/5 - 2 = 5 (find value of x)
What is sinK? Triangle L M K. Angle L is 90 degrees. Hypotenuse K M is 13, adjacent K L is 5, opposite L M is 12. A. StartFraction 12 Over 13 EndFraction c. StartFraction 5 Over 13 EndFraction b. StartFraction 13 Over 12 EndFraction d. StartFraction 5 Over 12 EndFraction
According to the trigonometric functions, the answer is A. StartFraction 12 Over 13 EndFraction.
What are trigonometric functions?
Trigonometric functions are mathematical functions that relate the angles of a right triangle to the ratios of its sides. There are six primary trigonometric functions:
Sine (sin): the ratio of the opposite side to the hypotenuse of a right triangle.
Cosine (cos): the ratio of the adjacent side to the hypotenuse of a right triangle.
Tangent (tan): the ratio of the opposite side to the adjacent side of a right triangle.
Cosecant (csc): the reciprocal of the sine function, i.e. the ratio of the hypotenuse to the opposite side of a right triangle.
Secant (sec): the reciprocal of the cosine function, i.e. the ratio of the hypotenuse to the adjacent side of a right triangle.
Cotangent (cot): the reciprocal of the tangent function, i.e. the ratio of the adjacent side to the opposite side of a right triangle.
To find sin(K), we need to use the definition of sine which is the opposite side over the hypotenuse:
sin(K) = opposite / hypotenuse
In this case, the opposite side is LM and the hypotenuse is KM. We are given that KM = 13 and LM = 12, so we can plug these values into the formula:
sin(K) = 12/13
Therefore, the answer is A. StartFraction 12 Over 13 EndFraction.
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find W (hypotenuse) if the angle is 15 degrees and the opposite side has a length of 7 cm
[tex]\sin(15^o )=\cfrac{\stackrel{opposite}{7}}{\underset{hypotenuse}{h}}\implies h=\cfrac{7}{\sin(15^o )}\implies h\approx 27.05[/tex]
Make sure your calculator is in Degree mode.
Answer: W ≈ 16.6
Step-by-step explanation:
The Pythagorean Theorem equation is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] =[tex]c^{2}[/tex]
First do [tex]15^{2} +7^{2} =w^{2}[/tex]
Which equals [tex]274=w^{2}[/tex]
Then do[tex]\sqrt{274} =w[/tex]
so w ≈ 16.6
Wills mobile contract gives him 700 minutes of calls each month. Will made 113 minutes of calls during the first week how much call time does he have left during this month? give your answer in hours and minutes. How much total call time does wills phone have in the first 7 months. Give your answer in days hours and minutes
Will has 587 mins (9h 47m) of call time left for the month and used 791 mins (13h 11m) in the first 7 months. He has 4,909 mins (81h 49m) left for the remaining 5 months. His phone has 5,700 mins (95d 4h 20m) of call time in a year.
Will has 587 minutes of call time left for the rest of the month, which is 9 hours and 47 minutes (587/60). In the first 7 months, Will has used 791 minutes (113 minutes per month for 7 months), which is 13 hours and 11 minutes. He has 4,909 minutes (7 months x 700 minutes per month - 791 minutes used) or 81 hours and 49 minutes left for the remaining 5 months. In total, Will's phone has 5,700 minutes (12 months x 700 minutes per month) or 95 days, 4 hours and 20 minutes of call time in a year.
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2.7c-4.5=3.6c-9
solve for c
Answer:
2,7c-3,6c =-9+4,5
-0,9c=-4,5
c=5
Answer:
c=5
Step-by-step explanation:
2.7c-4.5=3.6c-9
+4.5 +4.5
2.7c = 3.6c -4.5
-3.6c -3.6c
-0.9c = -4.5
-0.9c/-0.9= -4.5/-0.9
c= 5
Counting principles ounting principles the fundamental Court Understand and Question A company is planning its 4-week winter advertising campaign. The marketing team is planning to mail one of the following different types of advertisements, at random, to their city's residents each week. They have the following types of advertisements ready to send: Week 1 Postcard Leaflet Week 2 Flyer Catalog Calendar Week 3 Brochure Poster Week 4 Business card koupon How many different possible ways can a resident receive an advertisement in the mail? Provide your answer belowe FEEDBACK MORE INSTRUCTION SUBMIT DINO Alicia
There are 24 different possible ways a resident can receive an advertisement in the mail.
The counting principle states that if there are "a" ways to do one thing, and "b" ways to do another thing, then there are "a × b" ways to do both things. In this case, we need to multiply the number of different types of advertisements for each week to find the total number of different possible ways a resident can receive an advertisement in the mail.
Week 1: 2 different types of advertisements (postcard or leaflet)
Week 2: 3 different types of advertisements (flyer, catalog, or calendar)
Week 3: 2 different types of advertisements (brochure or poster)
Week 4: 2 different types of advertisements (business card or coupon)
Total number of different possible ways = 2 × 3 × 2 × 2 = 24
Therefore, there are 24 different possible ways a resident can receive an advertisement in the mail.
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A 2-pound bag of corn costs $3.20. What is the price per ounce?
Answer:
$0.10
Step-by-step explanation:
2 pound = 32 ounces
32 ounces = $3.20
What is the price per ounce?
3.20 / 32 = $0.10
So, the price per ounce is $0.10
What is the GCF of the terms in the polynomial? 18d4e2−45d2+36d
Answer: 18d
Step-by-step explanation:
To find the greatest common factor (GCF) of the terms in the polynomial 18d^4e^2 − 45d^2 + 36d, we need to factor each term into its prime factors and then identify the common factors with the highest exponent for each variable.
The prime factors of each term are:
18d^4e^2 = 2 x 3^2 x d^4 x e^2
45d^2 = 3^2 x 5 x d^2
36d = 2^2 x 3^2 x d
To find the common factors, we need to look for factors that appear in all terms. The common factors with the highest exponent for each variable are:
2^1, 3^2, and d^1.
Therefore, the GCF of the terms in the polynomial is:
2 x 3^2 x d = 18d
Hence, the GCF of the terms in the polynomial 18d^4e^2 − 45d^2 + 36d is 18d.
Evaluate the expression when m = -2
m^2 + 6m +9
To promote his new business, Claudio made 300 tamales to give to pedestrians. The expression above describes the number of tamales remaining after passing out samples to p pedestrians. If Claudio passed out samples to 160 pedestrians, how many tamales would remain?
The answer is 140 tamales would remain.
What is an expression?An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, among others. It is a mathematical phrase that represents a value or a set of values when evaluated.
We are given that Claudio made 300 tamales to give to pedestrians. Let the number of tamales Claudio passed out to pedestrians be represented by p.
If we assume that Claudio passed out p tamales, then the number of tamales remaining would be:
300 - p
If Claudio passed out samples to 160 pedestrians, then the number of tamales remaining would be:
300 - 160 = 140
Therefore, 140 tamales would remain.
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At an ice cream shop, the cost of 4 milkshakes and 2 ice cream sundaes is $23.50. The cost of 8 milkshakes and 6 ice cream sundaes is $56.50.
Order the steps below for solving this system of linear equations using the elimination method.
Write the correct number, 1 for first through 4 for last, in front of each step listed.
Choices: Solve for y, Substitute the value for y into one of the equations to determine the value of x, Subtract from the other equation, and Multiply the equation 4x + 2y = 23.50 by 2.
Step 1:
Step 2:
Step 3:
Step 4:
x = 3.375 and y = 5 provide the system of equations' answer.
How Do You Solve an Equation System?The process of figuring out the unknown variables while keeping the equations balanced on both sides is known as the system of equations method. We solve an equation system by identifying the value of the variable that makes the condition of all the provided equations true. There are numerous methods for solving a system of equations.
Multiply the equation 4x+2y=23.50 by 2.
From the other equation, subtract.
Calculate y using a solution.
To find the value of x, substitute the value for y into one of the equations.
To eliminate one variable (either x or y) while utilising the elimination method, the equations are added or subtracted.
To start, we can multiply the first equation by 2 to get rid of the 2y term:
8x + 4y = 47
Next, we can subtract the second equation from this equation to eliminate the 8x term:
2y = 10
y = 5
Now that we have solved for y, we can substitute this value into one of the original equations (let's use the first one) to solve for x:
4x + 2(5) = 23.50
4x + 10 = 23.50
4x = 13.50
x = 3.375
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Erin is planning on putting tile down in her
kitchen around the island. How many square feet
of tile will she need to purchase?
16 ft
16 ft
3 ft
Island
7 ft
12 ft
2 ft
4ft
10ft
Erin will need to purchase 48ft² of tile for her kitchen island.
In order to calculate the square footage of tile needed for Erin’s kitchen island, we will use the formula for the area of a rectangle: A = lw, where A is the area, l is the length, and w is the width.
The first step is to measure the length and width of the island. Let’s assume that the length is 16ft and the width is 3ft.
Next, we will use the formula to calculate the area of the island: A = lw
A = 16ft x 3ft
A = 48ft²
Finally, Erin will need to purchase 48ft² of tile for her kitchen island.
To double check our calculations, we can also calculate the area of each individual side of the island. For example, the area of the 16ft side is 16ft x 2ft = 32ft². The area of the 3ft side is 3ft x 7ft = 21 ft². When we add the areas together, 32ft² + 21ft² = 53ft². Since 53ft² is greater than 48ft², it is clear that calculating the area of the entire island is the correct solution.
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The Fashion Center made the following leather jacket purchases during the year. At the end of the year, there are 46 jackets in The Fashion Center's
inventory. Use the FIFO method to find the inventory value of the 46 remaining jackets.
$4,875
$5,000
$5,125
$4,500
March
June
September
30 jackets at $175
25 jackets at $150
35 jackets at $125
30 jackets at $100
The total value of the remaining inventory is $5,000. So correct option is B.
Describe Inventory?Inventory refers to the stock of goods or materials that a business or organization has on hand for the purpose of selling, manufacturing, or producing. It can include finished goods ready for sale, work in progress, or raw materials waiting to be processed or used. Proper management of inventory is essential to ensure that a business can meet customer demand while minimizing costs associated with carrying excess inventory or stockouts. Inventory management techniques involve tracking inventory levels, determining optimal reorder points, and controlling the flow of goods in and out of the inventory.
Using the FIFO method, we assume that the first jackets purchased are the first ones sold, so the value of the remaining inventory is calculated as follows:
The first 30 jackets are from the beginning inventory and cost $175 each.
The next 16 jackets (out of the 25 purchased in March) cost $150 each.
The next 10 jackets (out of the 35 purchased in June) cost $125 each.
The last 0 jackets (out of the 30 purchased in September) cost $100 each.
So the total value of the remaining inventory is:
30 x $175 + 16 x $150 + 10 x $125 + 0 x $100 = $5,000
Therefore, the answer is B. $5,000.
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\Graph the following system of equations.
y = 3x + 9
6x + 2y = 6
What is the solution to the system?
There is no solution.
There is one unique solution (−1, 6).
There is one unique solution (0, 3).
There are infinitely many solutions. (not this one already checked)
The solution to the system of equations. is (x, y) = (-1, 6).
What is a System of Equations?Simplifying this equation, we get:
6x + 6x + 18 = 6
12x + 18 = 6
Subtracting 18 from both sides:
12x = -12
Dividing both sides by 12:
x = -1
Now that we know x = -1, we can substitute this value into either equation to find y. We'll use the first equation:
y = 3x + 9
y = 3(-1) + 9
y = 6
Therefore, the solution to the system is (x, y) = (-1, 6).
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A number, k, is 15.29 when truncated to
2 d.p.
Write an inequality to show the lower and
upper bounds of k.
the error interval will be [15.29, 15.3).
What is error?
Error is the difference between an actual value and an estimate, or approximate, representation of that value in applied mathematics. The discrepancy between the population's average and the average of a sample taken from that population is a frequent example in statistics. The discrepancy between an irrational number's true value and the values of rational expressions like 22/7, 355/113, 3.14, or 3.14159 serves as an example of round-off error in numerical analysis. A truncation error happens when an infinite series is ignored for all but a small number of terms. For instance, the sum of the infinite series can be used to express the exponential function ex.
Find the error interval of 15.29:
[15.29, 15.3)
Hence the error interval will be [15.29, 15.3).
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Class A has 18 pupils and class B has 24 pupils.
Both classes sit the same maths test.
The mean score for class A is 76.
The mean score for both classes is 66.
What is the mean score (rounded to 1 DP) in the maths test for class B?
Answer: 56
Step-by-step explanation:
66 x 2 = 132
132-76 = 56
(76+52) divided by 2 = 66
Hence the mean score for class B is 56.
The circumference of a circle is 6π ft. What is the area, in square feet? Express your answer in terms of
�
π.
Answer:
9π
Step-by-step explanation:
circumference=6ft
radius=3ft
radius squared=9ft
area=9ft ×π
area=9π
Mr. Denson has a square shaped patio enclosed with a fence. The entire length of the fence around the perimeter of the patio is 72 meters. What is the area of his square-shaped patio?
The area of Mr. Denson's square-shaped patio that enclosed the fence is 324 m².
What is the area?The area is represented as the number of unit squares that cover the surface of an enclosed figure or object, measured in square units like cm² and m².
The area is the product of the two sides (length and breadth).
The perimeter of a square = 4a, where a is one length of the square.
If 4a = 72 meters, a = 18 meters (72/4).
The area of the square-shaped patio = 324 m² (18 x 18).
Thus, Mr. Denson should know that his square-shaped patio has an area of 324 m².
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It takes 3 people 4 hours to paint a wall. Assume that all people paint at the same rate. B) How long would it take 5 people to paint the same wall? Give your answer in hours and minutes
It would take 5 people to paint the same wall is 1 hour and 20 minutes or 1:20.
It is clear that workers twice as fast as people when painting the same surface. This means that John will always draw twice as much area as people at any given time if they are working at the same time. So if they plan well and finish painting the room at the same time, John will paint twice as much area as people.
There is only one possibility:
3 people = 4 hours
Divide by 3.
1 person = 4/3 or 1 1/3 hours
There are 60 minutes in 1 hour. Multiply 1/3 by 60.
(1/3)× 60 = 60/3 = 20
1/3 of an hour is 20 minutes.
It would take 1 person 1 hour and 20 minutes to paint the wall
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Find the jacobian of the transformation. X = 6v + 6w2, y = 4w + 4u2, z = 9u + 9v2
To get the transformation's Jacobian, we must first compute the partial derivatives of each new variable with respect to each old variable: x/u = 0, x/v = 6 + 0 = 6, and x/w = 0 + 12w = 12w.
∂y/∂u = 8u ∂y/∂v = 0 ∂y/∂w = 8w + 0 = 8w z/u = 9 plus 0 = 9 z/v = 0 plus 18v = 18v z/w = 0 As a result, the transformation's Jacobian matrix is: [(x,y,z)/(u,v,w)] = J = \s[ 0 6 12w ] [ 8 0 8w ] [ 9 18v 0 ] A transformation's Jacobian is a matrix of partial derivatives that illustrates how changing the old variables impacts changing the new variables. We have three new variables x, y, and z in the provided transformation, which are functions of three old variables u, v, and w. To get the transformation's Jacobian, we must compute the partial derivatives of x, y, and z with respect to u, v, and w. We discover that x's partial derivative with respect to u is zero, x's partial derivative with respect to v is six, and x's partial derivative with respect to w is twelve. Likewise, y's partial derivative with regard to u.
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