Answer: We can simplify the given equation as follows:
sin(x/2) = sqrt(2) - sin(x/2)
2sin(x/2) = sqrt(2)
sin(x/2) = sqrt(2)/2
x/2 = pi/4 or x/2 = 3pi/4 (using the standard angles for sin)
x = pi/2 or x = 3pi/2
However, we need to check if these solutions satisfy the original equation since we simplified it along the way.
For x = pi/2, we have:
sin(pi/4) = sqrt(2) - sin(pi/4)
sqrt(2)/2 = sqrt(2) - sqrt(2)/2
sqrt(2)/2 = sqrt(2)/2
This is true, so x = pi/2 is a solution.
For x = 3pi/2, we have:
sin(3pi/4) = sqrt(2) - sin(3pi/4)
-sqrt(2)/2 = sqrt(2) - (-sqrt(2)/2)
-sqrt(2)/2 = sqrt(2)/2
This is not true, so x = 3pi/2 is not a solution.
Therefore, the only solution in the interval [0, 2pi) is x = pi/2.
Step-by-step explanation:
The cheek for a large fitting is to be laid out in three sections. This will involve two 1-in. (25.4-mm) standing seams. The full allowance for each seam will be N-m.
A. 1% in. (27.0 mm).
B. 2 in. (50.8 mm).
C. 24 in. (57.2 mm).
D. 3 in (76.2 mm).
If h(x) = 5 + x and k (x) = StartFraction 1 Over x EndFraction, which expression is equivalent to (k circle h) (x)?\
A: StartFraction (5 + x) Over x EndFraction
B: StartFraction 1 Over (5 + x) EndFraction
C: 5 + (StartFraction 1 Over x EndFraction)
D: 5 + (5 + x)
Answer:
B: (k circle h)(x) = StartFraction 1 Over (5 + x) EndFraction
Step-by-step explanation:
To find the expression that is equivalent to (k circle h)(x), we first need to find k(h(x)).
k(h(x)) = k(5 + x) = 1/(5 + x)
Therefore, the expression that is equivalent to (k circle h)(x) is 1/(5 + x), which is option B:
(k circle h)(x) = StartFraction 1 Over (5 + x) EndFraction
what is the answer to this math equation i am very bad at division and dont understand it (564873 / 5) * 2 + 6
Answer:
225955.2
Step-by-step explanation:
How much pure alcohol must a pharmacist add to 10cm^(3) of a 8% alcohol solution to strengthen it to a 80% solution? cubic centimeters
36 cm³ of pure alcohol is added to 10 cm of an 8% alcohol solution to strengthen it to an 80% solution.
What is the solution?
A particular kind of homogenous mixture made up of two or more substances is known as a solution. A solute is a substance that has been dissolved in a solvent, which is the other substance in the mixture.
Here, we have
Given: a pharmacist adds 10cm^(3) of an 8% alcohol solution to strengthen it to an 80% solution.
Let x represent the volume of pure alcohol (100%) in cm³ needed to be added.
x × 100% + 10 cm³ × 8% = 80% × (x + 10 cm³)
x × 1 + 10 × 0.08 = 0.8 × (x + 10)
x + 0.8 = 0.8x + 8
0.2x = 7.2
x = 36 cm³
Hence, 36 cm³ of pure alcohol is added to 10 cm of an 8% alcohol solution to strengthen it to an 80% solution.
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What is the equation of a straight line that passes through (2, 0)
and has a gradient of −3 ?
Answer:
Step-by-step explanation:
La ecuación de una línea recta que pasa a través de un punto \ ((x_1,y_1)\) y tiene un gradiente \ (m\) se puede escribir en la forma punto-pendiente1:
\ [y - y_1 = m (x - x_1)\]
En tu caso, el punto es \ ((2,0)\) y el gradiente es \ (-3\). Sustituyendo estos valores en la fórmula anterior, obtenemos:
\ [y - 0 = -3 (x - 2)\]
Simplificando esta ecuación, obtenemos:
\ [y = -3x + 6\]
Esta es la ecuación de la línea recta que buscas.
Espero que te haya sido útil. ¿Tienes alguna otra pregunta?
Espero que te haya sido útil.
Bi
2.When that square is cut by a diagonal, two isosceles triangles
2. Suppose the side of the original square Is 10 cm. Find
are formed. The area of one of the resulting triangles is A =
1
2
the area of one of the triangles.
The area of a square is represented by the formula A =
O 12.5cm
RASVATITANTAR
O 50 cm
CPP9P51.00
فريد
O 25 cm
O 100 cm
SURTNEY
DELL
S
Submit Answer
9:23 AM
3/31/2023
the area of one of the isosceles triangles formed by cutting the square by a diagonal is 25√(7) square cm.
Find the area of triangle?
To find the area of one of the isosceles triangles formed by cutting the square by a diagonal, we can use the fact that the area of a triangle is given by the formula:
A = (1/2)bh
where A is the area of the triangle, b is the base, and h is the height.
In this case, the base of the isosceles triangle is one of the sides of the original square, which is 10 cm. The height can be found by using the Pythagorean theorem, since the diagonal of the square and the height of the isosceles triangle form a right triangle:
d² = h² + (10/2)²
where d is the length of the diagonal, which can be found using the Pythagorean theorem:
d² = 10² + 10² = 200
d = √(200) = 10√(2)
Substituting this value for d in the first equation, we get:
(10√(2))² = h²+ (10/2)²
200 = h² + 25
h²= 175
h = √(175) = 5√(7)
Now we can use the formula for the area of a triangle to find the area of one of the isosceles triangles:
A = (1/2)(10)(5√(7))
A = 25√(7) square cm
Therefore, the area of one of the isosceles triangles formed by cutting the square by a diagonal is 25√(7) square cm.
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HELP ASAAAP
This scatter plot shows the recommended number of hours of sleep for people and their ages.
The equation represents the linear model for this data.
y=−0.25x+13
According to the model, what is the recommended amount of sleep for a 25-year-old person?
According to the model, the recommended amount of sleep for a 25-year-old person is equal to 6.75 hours of sleep.
What is a line of best fit?In Mathematics and Statistics, a line of best fit is also referred to as a trend line and it can be defined as a statistical or analytical tool that is typically used by researchers and mathematicians in conjunction with a scatter plot, in order to determine whether or not there is any form of association and correlation between a data set.
Based on the scatter plot, we can logically deduce that a linear equation which represents the line of best fit include the following:
y = -0.25x + 13
For a 25 years old person, the recommended hours of sleep can be calculated as follows;
y = -0.25x + 13
y = -0.25(25) + 13
y = -6.25 + 13
y = 6.75 hours of sleep.
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the graph of y=f(x) is shown below find all values of x where f(x)=1
the values of x where f(x) = 1 for the function y = x^2 - 2x + 1 are x = 0 and x = 2.
general steps to find all values of x where f(x) = 1 for a given function y = f(x):
1. Set f(x) equal to 1: f(x) = 1.
2. Solve the equation for x. This may involve algebraic manipulation or using techniques such as factoring, completing the square, or using the quadratic formula, depending on the form of the equation.
3. If the equation has multiple solutions, list them all as the values of x where f(x) = 1. If the equation has no solutions, then there are no values of x for which f(x) = 1.
For example, if the function is y = x^2 - 2x + 1, then setting f(x) = 1 gives:
x^2 - 2x + 1 = 1
Simplifying this equation by subtracting 1 from both sides, we get:
x^2 - 2x = 0
Factoring out x, we get:
x(x - 2) = 0
This equation is satisfied when either x = 0 or x = 2. Therefore, the values of x where f(x) = 1 for the function y = x^2 - 2x + 1 are x = 0 and x = 2.
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marking as brainlist please help!!
Answer:
x=7 and 1/6
Step-by-step explanation:
LOOK AT THE PICTURE! Because the transversal (line that goes through A and B) is straight, then:
(Angle C)+(20x+10)=180 deg
Angle C=(180 deg)-20x+10 deg
Angle C=170-20x
We know that 4x+2 is equal to angle C (marked in the picture) because of alternate interior angles are congruent theorem. So:
170-20x=4x+2
172=24x
x=7 and 1/6
A bag contains 8 counters labeled with the numbers 3, 4, 4, 5, 5, 6, 6, and 6. Select all of the true statements The probability of drawing a 2 is 0. The probability of drawing a 7 is 1. The probability of drawing a number 5 or greater is greater than the probability of drawing a number less than 5. The probability of drawing a 3 or a 6 is 12 . The least likely number to draw is 4.
The true statements are, The probability of drawing a 2 is 0 and The probability of drawing a number 5 or greater is greater than the probability of drawing a number less than 5.
What is probability?Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.
Here the given , Total number of outcomes = N {3,4,4,5,5,6,6,6} = 8
Now probability = No of Favorable outcome/ Total outcome.
Here Option A , Number of 2 = 0.
Then probability of getting 2 = 0/8 = 0.
Option B, Number of 7 = 0
Then probability of getting 7 =0/8 = 0
Option C , Number of 5's = 2
probability of getting 5 = 2/8 = 1/4
Number of less than 5 = 3
Probability of getting less than 5 = 3/8
Here 1/4 > 3/8 . Then The probability of drawing a number 5 or greater is greater than the probability of drawing a number less than 5.
Option D, Here least number in given is 3 not 5.
Hence the true statements are, The probability of drawing a 2 is 0 and The probability of drawing a number 5 or greater is greater than the probability of drawing a number less than 5.
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20. There are 100 packs of 100 sheets of paper on a table. Melissa must transfer 82 sheets from each
pack onto a cart. She can count at a maximum speed of 3 sheets per second and needs a minimum of 3
seconds more for putting each pack onto a cart. What is the minimum amount of time she will need to
accomplish the task?
a) 15 minutes
b) 8 minutes
c) 10 minutes
d) 12 minutes
e) 13 minutes
The minimum time that Melissa will need to accomplish the task are 15 minutes.
How much time will Melissa require to complete this task?To start let's calculate the time she needs to count the sheets Melissa will transfer:
Sheets to be counted: 18 (Melissa can just count 18 sheets rather than 82 as there are 100 sheets in a pack) 100 - 82 = 18.
Time to count 3 sheets: 1 second
1 second = 3 sheets
x = 18 sheets
x = 18 x 1 / 3 = 6 seconds
6 seconds + 3 seconds to transfer the package = 9 seconds
Finally, let's calculate the total time by multiplying by the number of packs.
9 x 100 = 900 seconds / 60 = 15 minutes.
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An employee makes $15 per hour for up to 40 hours per week. For every hour over 40 hours worked in a week, the employee's pay is 1 1/2 regular hourly pay. The employee has to pay 30% of his income in taxes.
What is the employee's net pay after taxes if he works 52.5 hours in one week? Enter the answer in the box.
The employee's net pay after taxes if he works 52.5 hours in one week is $616.875.
What is the net pay?The net pay is the difference between the gross periodic pay or earnings less statutory deductions, including income taxes.
Normal hourly rate = $15
Normal weekly hours = 40 hours
Overtime rate = 1¹/₂ of $15 = $22.50
Income tax rate = 30%
Total hours worked in one week = 52.5 hours
Overtime hours = 12.5 (52.5 - 40)
Normal weekly gross pay = $600 ($15 x 40)
Overtime pay = $281.25 ($22.50 x 12.5)
Total pay for the week = $881.25
Income tax = $264.375 ($881.25 x 30%)
Net pay = $616.875 ($881.25 - $264.375)
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What is the probability of rolling an even number and spinning "A," given the sample space below?
1 2 3 4 5 6
A A1 A2 A3 A4 A5 A6
A A1 A2 A3 A4 A5 A6
B B1 B2 B3 B4 B5 B6
B B1 B2 B3 B4 B5 B6
1/6
1/2
1/4
1/12
Step-by-step explanation:
even number=6
A=12
:.6/12
=1/2
How can I solve this?
Answer:
Step-by-step explanation:
first.. simplify
5.9x^2 + 8.5x +4.5x^2+5x (add the others together in a different problem)
then subtract the two numbers (i hope this helps!)
Which angle between -0° and -36° is coterminous with 887?
Answer:
Step-by-step explanation:
To find the coterminal angle with 887, we can add or subtract any multiple of 360°.
Adding a multiple of 360°:
887 + n(360)
where n is an integer.
Subtracting a multiple of 360°:
887 - n(360)
where n is an integer.
To find the angle between -0° and -36°, we need to subtract a multiple of 360° from 887 to get an angle between -0° and -36°.
887 - n(360) = -x
where x is the angle between -0° and -36°.
We can solve for x:
x = 887 - n(360)
We want x to be negative, so we need to choose a value of n such that 887 - n(360) is less than 0.
If we set n = 3, then:
x = 887 - 3(360) = 47
So, the angle between -0° and -36° that is coterminal with 887 is 47 degrees.
Help!! please!!!!!!!!PLEASE!!!!!!!PLEASE PLEASE M BEEGGNG.
The independent events are given below:
Rolling a dice and flipping a coin:
Spinning two spinners each round:
The Dependent EventsGrabbing an S out of the scrabble bag and then grabbing an M:
These are dependent events because the outcome of the first event affects the outcome of the second event. The number of possible outcomes for the second event depends on the outcome of the first event.
For example, if the S is not replaced in the bag after it is picked, then the probability of picking an M on the second draw will be different if an S was picked on the first draw.
Pulling a candy, eating it, and pulling another out of a bag:
These are dependent events because the outcome of the first event affects the outcome of the second event. After one candy is removed from the bag, the total number of candies in the bag decreases, which affects the probability of selecting a certain type of candy on the second draw.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
16
Step-by-step explanation:
Because this is a right triangle the two angles besides the right angle add up to 90°
33 + 3x + 9 = 90
Combine like terms
42 + 3x = 90
Isolate the x ( subtract 42 from both sides)
3x = 48
Divide both sides by 3
x = 16
Answer:
X= 16
Step-by-step explanation:
right angle = 90°
And we have 33° already
90 + 33 = 123
Triangle is 180
180 - 123 = 57
Write in an equation
57 = 3x + 9
57- 9 = 48
48= 3x
48/ 3 = 16
X= 16
Here’s the question
The value of 2 miles = 3520 yards and 3 miles = 5280 yards. 2 yards = 6 feet and 3 yards = 9 feet. 2 feet = 2 x 12 inches = 24 inches and 3 feet = 36 inches.
What is SI unit conversion?The International System of Units (SI) units may be used in trade and commerce, grants and other business-related activities, educational information, and as guidelines in publications to improve understanding of the metric system. The SI units may be interpreted or modified for use in the United States by the Secretary of Commerce through the National Institute of Standards and Technology.
Multiply the number of miles by 1760:
1 mile = 1760 yards
2 miles = 2 x 1760 yards = 3520 yards
3 miles = 3 x 1760 yards = 5280 yards
Multiply the number of yards by 3, since there are 3 feet in a yard.
1 yard = 3 feet
2 yards = 2 x 3 feet = 6 feet
3 yards = 3 x 3 feet = 9 feet
Multiply the number of feet by 12, since there are 12 inches in a foot.
1 foot = 12 inches
2 feet = 2 x 12 inches = 24 inches
3 feet = 3 x 12 inches = 36 inches
Hence, the value of 2 miles = 3520 yards and 3 miles = 5280 yards. 2 yards = 6 feet and 3 yards = 9 feet. 2 feet = 2 x 12 inches = 24 inches and 3 feet = 36 inches.
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Luis plays basketball for WVC. For the free throws, he makes the
shot 75% of the time. He must now attempt two free throws. Probability that Luis makes the first
shot is 0.75. The probability Luis makes the second shot is 0.75. The probability Luis makes the
second free throw given that he made the first is 0.85. Calculate the probability that Luis makes
both free throws.
Please write your answer as a decimal. Round your answer to the third decimal place.
Let's use the conditional probability formula to calculate the probability that Luis makes both free throws:
P(both free throws) = P(makes first) * P(makes second | makes first)
We are given that:
P(makes first) = 0.75
P(makes second | makes first) = 0.85
So we can substitute these values in the formula:
P(both free throws) = 0.75 * 0.85
P(both free throws) = 0.6375
Therefore, the probability that Luis makes both free throws is 0.6375, or 0.638 rounded to the nearest thousandth.
Solve the formula 3x+4y=10 for y
Answer:formula 3x + 4y = 10 can be solved for y as y = (10 - 3x) / 4.
Step-by-step explanation:
To solve for y, we need to isolate y on one side of the equation.
3x + 4y = 10
Subtract 3x from both sides:
4y = 10 - 3x
Divide both sides by 4:
y = (10 - 3x) / 4
Molly is 54 3/4 inches tall. Nancy is 1 1/2 inches taller than Molly and Jane is 1 1/5 inches taller than Nancy. How tall is Jane?
Answer:
Jane is 57 9/20 inches tall.
Step-by-step explanation:
what is the circumference of a circle with a diameter of 21 cm?
The circumference of a circle with a diameter of 21 cm is 65. 94cm
How to determine the circumferenceThe equation for the formula that is used to determine the circumference of a circle is expressed as;
C = 2πr
Such that the parameters are enumerated as;
C is the circumference of the circleπ takes the constant value of 3.14 or 22/7r is the radius of the circleAlso, the formula for calculating the radius of a circle is expressed as;
Radius = Diameter/2
Substitute the value
Radius = 21/2 = 10. 5cm
Substitute the value for circumference
Circumference = 2 × 3.14 × 10. 5
Find the value
Circumference = 65. 94cm
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La raíz cuadrada de 81 dividida en el cuadrado de 3
Answer:
27 duh lord help them please and me
What is the least number of plums that can be shared equally among 6, 9 or 12 children? (A) 27 (B) 36 (C) 54 (D) 72
The least number of plums that can be shared equally among 6, 9, or 12 children is the smallest common multiple (LCM) of 6, 9, and 12.
Prime factorizing each number, we get:
6 = 2 * 3 9 = 3 * 3 12 = 2 * 2 * 3
Taking the highest power of each prime factor, the LCM is:
LCM = 2 * 2 * 3 * 3 = 36
Therefore, the least number of plums that can be shared equally among 6, 9, and 12 children is 36, which is option (B).
Answer:
Step-by-step explanation: answer is choice B or 36
That would be finding the Lcm of least common multiple of the three numbers. Which is 36
hope it helps!
Three grams of musk oil are required for each bottle of Mink Caress, a very popular perfume made by a small company in western Siberia. The cost of the musk oil is $1.50 per gram. Budgeted production of Mink Caress is given below by quarters for Year 2 and for the first quarter of Year 3:
Cost of Raw Materials for 4 years is = $ 297,000 $ 459,000 $ 630,000 $ 423,000
Define Budgeted productionBudgeted production refers to the expected level of production that a company plans to achieve during a specific period of time, typically a year. It is a key component of the budgeting process and involves estimating the amount of goods or services that a company will produce and sell in the upcoming period, based on various factors such as market demand, production capacity, and available resources.
Part 1:Direct Materials Budget in Bottles & Grams
Year 2
First Second Third Fourth Total
Budgeted production, 60,000 90,000 150,000 100,000 450,000
Add Desired Ending Inventory
20 % 0f the Production 18,000 30,000 20,000 14,000 82,000
Less Beginning Inventory
36,000/ 3 12,000 18,000 30,000 20,000 80,000
D.
Materials 66,000 102,000 140,000 94,000 452,000
Grams in a Bottle 3 3 3 3 3
Raw Materials 198,000 306,000 420,000 282,000 1356,000
Costs $1.50 $1.50 $1.50 $1.50 1.50
Costs Raw Materials $ 297,000 $ 459,000 $ 630,000 $ 423,000
Total Raw Material Cost is $2,034,000.
Part 2:"Unit cost of raw materials"
Direct Materials Budget in Bottles & Grams
Year 2 Year 3
First Second Third Fourth First
Budgeted production
Production = 60,000 90,000 150,000 100,000 70,000
Desired Ending Inventory
20 % of the Production = 18,000 30,000 20,000 14,000
Less Beginning Inventory
36,000/3 = 12,000/18,000 30,000 20,000 14,000 for musk oil.
D.
Materials Budget = 66,000 102,000 140,000 94,000
Grams in a Bottle = 3 3 3 3
gms = 198,000 306,000 420,000 282,000 for raw materials
Costs(given) = $1.50 $1.50 $1.50 $1.50
Costs of Raw Materials are $ 297,000, $ 459,000, $ 630,000, and $ 423,000 for 4 years.
Therefore, the correct answer are :
Total Raw Material Cost is $2,034,000.
Cost of Raw Materials for 4 years is = $ 297,000 $ 459,000 $ 630,000 $ 423,000
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The complete question is:
Three grams of musk oil are required for each bottle of Mink Caress, a very popular perfume made by a small company in western Siberia. The cost of the musk oil is $1.50 per gram. Budgeted production of Mink Caress is given below by quarters for Year 2 and for the first quarter of Year 3:
Year 2 Year 3
First Second Third Fourth First
Budgeted production, in bottles 60,000 90,000 150,000 100,000 70,000
Musk oil has become so popular as a perfume ingredient that it has become necessary to carry large inventories as a precaution against stock-outs. For this reason, the inventory of musk oil at the end of a quarter must be equal to 20% of the following quarters production needs. Some 36,000 grams of musk oil will be on hand to start the first quarter of Year 2.
Required:
Prepare a direct materials budget for musk oil, by quarter and in total, for Year 2. (Round "Unit cost of raw materials" answers to 2 decimal places.)
Use the confidence interval to find the estimated margin of error. Then find the sample mean.
A biologist reports a confidence interval of (4.1,4.9) when estimating the mean height (in centimeters) of a sample of seedlings.
The estimated margin of error is
Thus, estimated margin of error is 0.4. Sample mean height of seedlings is 4.5 cm.
Explain about the margin of error?The degree of error in survey findings from random sampling is known as the margin of error in statistics. A wider margin of error for statistics denotes a reduced possibility of relying on a survey's or poll's findings, meaning that there will be less confidence in the results' ability to accurately reflect a community.
In order to admit that sample findings will vary between sample to sample and may differ from the actual population situation, you must add a margin of error to your statistical results.
Given data:
confidence interval of (4.1,4.9)
upper limit k = 4.9.
Lower limit r = 4.1.
So,
margin of error E = (k - r)/2
E = (4.9 - 4.1)/2
E = 0.4
Thus, estimated margin of error is 0.4.
Sample mean height of seedlings:
x = k - E
x = 4.9 - 0.4
x = 4.5
Thus, Sample mean height of seedlings is 4.5 cm.
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The regular price of a color TV is $445.81. During a sale, Hill TV is selling the TV for $393.36. Determine the percent decrease in the price of the TV.
The regular price of the TV is $445.81, and the sale price is $393.36.
To find the percent decrease in the price, we can use the formula:
percent decrease = (original price - sale price) / original price x 100%
Substituting the given values, we get:
percent decrease = ($445.81 - $393.36) / $445.81 x 100%
percent decrease = $52.45 / $445.81 x 100%
percent decrease = 0.1175 x 100%
percent decrease = 11.75%
Therefore, the percent decrease in the price of the TV is 11.75%.
What describes the movement of a figure that is translated according to the rule below?
x,y→(x+4, y-6).
4 units tο the right and 6 units dοwn, withοut changing its size οr οrientatiοn describes the mοvement οf a figure that is translated accοrding tο the rule belοw.
What is mοvement οf a figure?In geοmetry, a mοtiοn is an isοmetry οf a metric space. Fοr instance, a plane equipped with the Euclidean distance metric is a metric space in which a mapping assοciating cοngruent figures is a mοtiοn.
The rule [tex]$\rm (x,y) \to (x+4,y-6)$[/tex] defines a translatiοn οf a figure in the plane. Specifically, each pοint in the οriginal figure is mοved 4 units tο the right and 6 units dοwn tο οbtain the cοrrespοnding pοint in the translated figure.
Fοr example, cοnsider the pοint (2, 3) in the οriginal figure. Applying the translatiοn rule, we οbtain (2+4 ,3-6) = (6,-3) as the cοrrespοnding pοint in the translated figure.
Similarly, any οther pοint (6, 4) in the οriginal figure is translated tο the pοint (6+4 ,4-6) = (10,-2) in the translated figure.
Geοmetrically, we can think οf the translatiοn as sliding the entire figure 4 units tο the right and 6 units dοwn, withοut changing its size οr οrientatiοn.
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PLEASE HELP ME!!! THANK YOU
The interval notation for the solution set is (-∞, -4] and the number line is on the image at the end.
How to find the solution set of the ienquality?Here we want to find the solution set of the inequality below:
x ≤ -4
First let's do the interval notation. This will be the set that contains all the numbers from negative infinity to -4 (with -4 included, so we need to have a closed set at that end)
This is written as:
(-∞, -4]
The use of the symbols [ ] means that the element belongs to the set.
Now to the number line, we will have a closed circle at x = -4 (because it is a solution) and a line that goes to the left of it. You can see an example in the graph at the end.
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22. 3.9 feet tall at the highest point.
23. 12.6 inches long.
24. 76.6 feet tall.
25. The height of the formation is 50.3m.
What is trigonometry?Trigonometry studies the relationships between sides and angles of triangles.
22. To calculate the height of the ramp, David can use the concept of trigonometry. The formula for finding the height of a right triangle is h = opposite side/sin(angle).
The opposite side is 3.5 feet and the angle is 20°.
Therefore, h = 3.5/sin(20°) = 3.9 feet. The ramp needs to be 3.9 feet tall at the highest point, rounded to the nearest tenth.
23. To calculate the length of the springboard, Eric can use the concept of trigonometry.
The opposite side is 6 inches and the angle is 14.5°. Therefore, a = 6/tan(14.5°) = 12.6 inches. The springboard is 12.6 inches long.
24. To calculate the height of the roller coaster, the concept of trigonometry can be used.
The opposite side is 98 feet and the angle is 55°.
Therefore, h = 98/sin(55°) = 76.6 feet. The roller coaster is 76.6 feet tall when it reaches the top of the first hill.
25. To calculate the height of the formation, Diego can use the concept of trigonometry.
The opposite side is 43m and the angle is 36°. Therefore, h = 43/sin(36°) = 50.3m.
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