This would make the inverse function a relation rather than a function, and it would fail the vertical line test.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It focuses on the study of trigonometric functions, which are functions that relate the angles of a triangle to the ratios of the lengths of its sides.
Inverse trigonometric functions are used to find the angle whose trigonometric ratio is given. For example, if we know that sin θ = 1/2, we can use the inverse sine function to find the angle θ, which is sin^-1(1/2) = 30°.
However, inverse functions must be functions, meaning that they must pass the vertical line test, where each input (x) produces exactly one output (y). To ensure that inverse trigonometric functions meet this criteria, we need to restrict the domain of the original trigonometric functions.
Trigonometric functions are not one-to-one functions, which means that multiple angles can produce the same value of a trigonometric ratio. For example, sin 30° = sin 150° = 1/2. If we were to define the inverse sine function as the inverse of the sin function without a domain restriction, we would have multiple possible outputs for the same input.
Therefore, this would make the inverse function a relation rather than a function, and it would fail the vertical line test.
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K
Refer to the figure shown to the right, which includes an isosceles
triangle with AB = BC. What is the measure of BCD if B measures
60°?
The measure of BCD is
By answering the presented question, we may conclude that Therefore, triangle the measure of BCD is 120°.
What is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles.
Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides.
Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees).
The region of a triangle may be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
Since triangle ABC is isosceles with AB = BC, angles A and C are also equal to each other. Let x be the measure of angles A and C. Then we have:
angle A + angle B + angle C = 180° (sum of angles in a triangle)
x + 60° + x = 180°
2x + 60° = 180°
2x = 120°
x = 60°
So angles A and C each measure 60°, making triangle ABC an equilateral triangle.
Now, angle BCD is an exterior angle of triangle ABC. By the Exterior Angle Theorem, the measure of angle BCD is equal to the sum of angles A and C:
angle BCD = angle A + angle C = 60° + 60° = 120°
Therefore, the measure of BCD is 120 degrees.
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Correct 0.0066 78 to
3 decimal places
0.006678 rounded to 3 decimal places is 0.0067.
We have,
To round 0.006678 to 3 decimal places, we need to look at the fourth decimal place (the digit 7).
Since 7 is greater than or equal to 5, we round up the last digit (8) by adding 1 to it.
Now,
The rounded number is 0.0067
So 0.006678 rounded to 3 decimal places is 0.0067.
Thus,
0.006678 rounded to 3 decimal places is 0.0067.
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Please help!! Correct answer gets brainliest!!
Option D (132 square centimeters)
Here is how I got my answer (Look at picture below):
• First, I did the rectangle outlined in red, 4×10=40
• Second, I did triangles outlined in yellow, [(4×3)÷2]×2=12
• Third, I did the rectangle outlined in blue, 10×5=50
• Fourth, I did the rectangle outlined in purple, 3×10=30
Lastly, I added up the sum which was 40+12+50+30=132
—————
Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle
—————
Explain what is assessment for learning (3) Discuss the importance of this assessment (3) Give examples on how you would implement this in your learning area (2) Explain what is the assessment used for learning (formative) (3) Discuss the importance of this assessment (3) Give examples on how you would implement this in your learning area (2) Explain what is the assessment used for promotional purposes (summative) (3) Discuss the importance of this assessment (3) Give examples on how you would implement this in your learning area (2)
Assessment for Learning is a type of assessment that is used to evaluate students' progress and understanding throughout the learning process.
Explain assessment?An evaluation that is brief and specifically focused on supporting planning and decision-making is known as a micro-assessment. A micro-assessment can be utilized to quickly and easily acquire data that is required for making decisions, establishing objectives or directions, or carrying out elevated or early planning.
Assessment for Learning:
Assessment for Learning is a type of assessment that is used to evaluate students' progress and understanding throughout the learning process. It is designed to provide teachers with feedback on how well their students are learning and to identify areas where students may need additional support. Assessment for Learning involves ongoing, interactive assessments that focus on identifying students' strengths and weaknesses.
Importance of Assessment for Learning:
It assists teachers in determining the areas in which students are having difficulty and in modifying their pedagogical approaches accordingly.
Implementation of Assessment for Learning in my Learning Area:
Provide regular feedback to students on their work, highlighting areas of strength and areas that need improvement.
Assessment Used for Learning (Formative):
Formative assessment is a type of assessment that is used to evaluate students' progress and understanding throughout the learning process. It is designed to provide teachers with feedback on how well their students are learning and to identify areas where students may need additional support. Formative assessment involves ongoing, interactive assessments that focus on identifying students' strengths and weaknesses.
Importance of Formative Assessment:
Teachers might then modify their pedagogical approaches in light of the areas in which their students are having difficulty.
Implementation of Formative Assessment in my Learning Area:
Provide regular feedback to students on their work, highlighting areas of strength and areas that need improvement.
Assessment Used for Promotional Purposes (Summative):
Summative assessment is a type of assessment that is used to evaluate students' learning at the end of a unit or course. It is designed to provide a summary of what students have learned and to determine whether they have met the expected learning outcomes.
Importance of Summative Assessment:
It provides a summary of what students have learned and helps to determine whether they have met the expected learning outcomes.
Implementation of Summative Assessment in my Learning Area:
Provide students with clear expectations and learning outcomes at the beginning of a unit or course.
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What is the value of the expression (10+5) + 6 x 8-12?
43
38
35
28
Question 7(Multiple Choice Worth 2 points)
(10.01 LC)
What is the value of the expression (14+ 2) + 6 x 3-12?
Answer:
51
Step-by-step explanation:
To find the value of the expression, you need to simplify it following PEMDAS (Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction) If you try and simplify the problem without following the order of operations, you won't always get the right answer.
You want to start by simplifying what is inside the parenthesis.
[tex](10+5)+6*8-12\\15+6*8-12[/tex]
Next you want to do the multiplication:
[tex]15+6*8-12\\15+48-12[/tex]
Now we can just combine the rest of the terms
[tex]15+48-12\\51[/tex]
Jim's speedboat can travel 21 miles upstream against a 3 mph current in the same amount of time it travels 23 miles downstream with a 3 mph current speed. Find the speed, in miles per hour, of the Jim's boat.
Answer:
69 mph
Step-by-step explanation
Let the speed of boat be x hence speed downstream is x+3 but speed upstream will be x-3
Speed is distance per unit time and time is same hence
24(x-3)=22(x+3)
24x-72=22x+66
2x=138
X=138/2=69
Therefore, the speed of boat is 69 miles per hour or
The boat in the problem travels different distances at different rates, but in the same amount of time for each trip. Distance is rate times time, d=r⋅t, which, solving for t, becomes
t=dr.
The trip against the current has rate r=s−3, so the time it takes to complete the trip is
t=20s−3.
The time it takes to complete the trip with the current is
t=22s+3.
The time to complete each trip is the same, so set the fractions equal to each other.
20s−3=22s+3
Multiply each side by (s−3)(s+3).
20(s−3)(s+3)(s−3)=22(s−3)(s+3)(s+3)
Simplify.
20(s+3)=22(s−3)
Distribute coefficients.
20s+60=22s−66
Combine like terms.
2s=126
Divide each side by 2 to find the solution,
s=69 mph.
Sorry if im wrong
solve for x in y=a(b-x)
Answer:
[tex]x = \frac{ab - y}{a} [/tex]
Step-by-step explanation:
[tex]y = a(b - x)[/tex]
[tex](b - x) = \frac{y}{a} [/tex]
[tex] - x = \frac{y}{a} - b[/tex]
[tex]x = b - \frac{y}{a} [/tex]
Make a the common denominator:
[tex]x = \frac{ab - y}{a} [/tex]
Each of these relationships reflects a correlation. Which relationship most likely reflects both correlation and causation?
The correct relationship most likely reflects both correlation and causation is Eating burgers more often is associated with eating french fries more often.
What is correlation?
Correlation refers to the statistical relationship between two variables. In other words, it measures how closely two variables are related to each other. A correlation can be positive, negative, or zero, depending on the direction and strength of the relationship between the variables.
However, correlation does not imply causation, which means that even if two variables are strongly correlated, it does not necessarily mean that one causes the other. There may be other underlying factors or variables that are responsible for the observed correlation.
The relationship that most likely reflects both correlation and causation is:
Eating burgers more often is associated with eating french fries more often.
This is because burgers and french fries are often served together at fast food restaurants, and the consumption of one is likely to lead to the consumption of the other.
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HELPPEPEPEPPEPEPPPPPPPPPPPPP MEEEEE QUICK QUICK
Answer:top one
Step-by-step explanation:
im doing it
94, 81, 94, 81, 97, 95, 96
Darnell said the median of this data is 81.
He is wrong.
Explain why he is wrong and be specific. Include the correct answer in your explanation.
Someone do this for me
∆ACE is similar to ∆BDE because angle A is equal to angle B and angle is common.
What are similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Therefore for ∆ACE to be similar to ∆BDE, their corresponding angles must be equal.
To show that the angles are equal,
<AEC = <DEB( vertically opposite angles )
<A = <B ( alternate angles)
therefore the value of angle C will be equal to the angle of D.
We can therefore say that ACE is similar to ∆BDE.
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Written as a simplified polynomial in standard form, what is the result when
(x - 7)? is subtracted from 6x?
Answer: 45r6
Step-by-step explanation:
The circumference of a circle is 18 inches. What is the radius?
C=18 in
Answer:
r=9
Step-by-step explanation:
the radius is half of the circumference because the equation for circumference is 2 X radius, so dividing the circumference by 2 will undo the problem.
(18/2 = 9 )
3 x−2 y=−11
x−3 y=−33
NO IDEA i'm only in 5th grade sorry.
Angel invests £1430 in a bank account. The account gathers compound interest at a rate of 0.5% per month. How much money will be in the account after 9 months? Give your answer in pounds to the nearest 1p.
Answer:
We can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the final amount
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time period in years
In this case, we have:
P = £1430
r = 0.005 (0.5% per month)
n = 12 (compounded monthly)
t = 9/12 = 0.75 (9 months is three-quarters of a year)
So we can plug in these values to find the final amount:
A = £1430(1 + 0.005/12)^(12*0.75)
A ≈ £1481.18
Therefore, the amount of money in the account after 9 months will be approximately £1481.18.
A pump moves 42 gallons in seven minutes find the unit rate
[tex]boommamama[/tex]
0.1 gallons per second is the unit rate in the given situation.
What is the unit rate?An item's unit rate is its price for one of them.
This is expressed as a ratio with a one as the denominator.
For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second.
Seven yards in one second and 70 yards in ten seconds are both ratios, but only one of them is a unit rate.
The denominator of a unit rate is always 1.
Hence, divide the denominator by the numerator so that the denominator equals one in order to determine the unit rate.
The unit rate is 50km/5.5 hours = 9.09 km/hour, for instance, if 50km are traveled in 5.5 hours.
So, in the given situation the unit rate would be:
0.1 gallons per second
Therefore, 0.1 gallons per second is the unit rate in the given situation.
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Solve for y.
8x-4y=-16
Y=?x+
y.8x-4y=-16Y=?x+To solve for y in the equation 8x - 4y = -16, we need to isolate y on one side of the equation. We can do this by subtracting 8x from both sides of the equation. 8x - 4y = -16 -4y = -16 - 8x Next, we can simplify the right side of the equation by factoring out -8. -4y = -8(2 + x) Finally, we can solve for y by dividing both sides of the equation by -4. y = 2 + 0.5x So the solution for y in terms of x is y = 2 + 0.5x.
Answer:
y=4+2x
Step-by-step explanation:
What’s the area of a square with sides lengths 2 2/5?
Prepare Journal Voucher of District Administration Office, Jhapa for its Budget Expenditure. (i) On 7th Shrawan office furniture purchased for Rs. 40,000 from Sharma furniture 1 store and payment made by issuing a payment order. (ii) Rs. 25,000 paid for house rent on 5th of Bhadra. (iii) Rs. 1,00,000/- paid for purchase of computers from Computer Land on 15th of Bhadra. (iv) Rs. 15,000 was paid for TADA to section officer on 25th of Bhadra. (v) Telephone charge Rs. 5,000 and electricity charge Rs. 6000 paid on 30th of Bhadra
Below is the Journal Voucher of District Administration Office, Jhapa for its Budget Expenditure.
What is budget expenditure?
Budget expenditure refers to the total amount of money spent by an organization, government, or individual during a specific period of time, as specified in their budget. A budget is a financial plan that outlines the expected income and expenses for a certain period of time, usually a year.
In this journal voucher, we have recorded the various expenses incurred by the District Administration Office, Jhapa during the month of Bhadra.
The first entry records the purchase of office furniture from Sharma Furniture Store for Rs. 40,000, paid by issuing a payment order.
The second entry records the payment of house rent for Rs. 25,000 on the 5th of Bhadra.
The third entry records the payment of Rs. 1,00,000 for the purchase of computers from Computer Land on the 15th of Bhadra.
The fourth entry records the payment of TADA to a section officer for Rs. 15,000 on the 25th of Bhadra.
The fifth entry records the payment of telephone charges of Rs. 5,000 and electricity charges of Rs. 6,000 on the 30th of Bhadra. The bank account is credited for each transaction, indicating that the expenses have been paid through the bank.
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How many hours is equal to 1 1\2 days
Answer: 132 hours
Step-by-step explanation:
First you divide 11/2 which equals 5.5 then you multiply it with 24, which is equal to 132
Johnathan is using a hose to fill his pool with water. The pool already had 2,000 gallons of water in it before he started, and the hose puts water into the pool at a rate of 360 gallons per hour. Let g represent the number of gallons that the hose has put into the pool after a given number of hours. Let h represent the number of hours that the hose has put water into the pool. Let w represent the total number of gallons of water in the pool. Complete the equations so that: Equation 1 shows the relationship between g and h. Equation 2 shows the relationship between g and w.
The problem states that Jonathan is using a hose to fill his pool with water. Initially, the pool already had 2,000 gallons of water in it before he started.
By doing step by step process we can get both equations solution:
The hose puts water into the pool at a rate of 360 gallons per hour.
Equation 1: g = 360h
Explanation: The number of gallons that the hose has put into the pool (g) is directly proportional to the number of hours that the hose has put water into the pool (h) at a constant rate of 360 gallons per hour. Therefore, we can express this relationship as g = 360h.
Equation 2: w = g + 2,000
Explanation: The total number of gallons of water in the pool (w) is equal to the number of gallons that the hose has put into the pool (g) plus the initial 2,000 gallons of water that were already in the pool. Therefore, we can express this relationship as w = g + 2,000.
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A father can do a job in a certain number of hours. His son takes twice as long to do the job. Working together, they can do the job in 6 hours. How many hours does it take the father to do the job alone?
F. 9
G. 10
H. 12.
J. 16
K. 18
Determine the measurement of EF.
EF = 3.47
EF = 3.16
EF = 1.39
EF = 1.1
Answer:
EF = 3.16
Step-by-step explanation:
Assume the triangles are similar.
BC/EF = BA/ED
7.9/EF = 11/4.4
11(EF) = 4.4 × 7.9
EF = 0.4 × 7.9
EF = 3.16
Joe starts his experiment with 83 speciman the specimen double every week write an equation to represent this scenario
Answer:
Step-by-step explanation:
Let S be the number of specimens and W be the number of weeks.
We know that initially Joe starts with 83 specimens, and every week the number of specimens doubles. Therefore, the equation that represents the scenario is:
S = 83 * 2^(W-1)
Here, (W-1) is used to account for the initial number of specimens already given in the problem.
This equation gives the number of specimens S after W weeks, taking into account the doubling of specimens every week.
Find the area of the irregular polygon.
A
80 in2
B
96 in2
C
120 in2
D
154 in2
The area of the rectangle is the product of its length and width, while the area of the triangle is half the product of its base and height. The total area of the polygon is 96 [tex]in^{2}[/tex] + 30 [tex]in^{2}[/tex] = 126 [tex]in^{2}[/tex].
What is an irregular polygon?A polygon that has sides of varying lengths and unequal angles is said to have irregular sides. A regular polygon, on the other hand, has equal-length sides and angles.
An irregular polygon can have any number of sides, any number of angles, and any shape for its sides. The area and perimeter of irregular polygons must be determined using particular formulae that take into consideration the unique characteristics of each individual polygon since irregular polygons can have a wide range of varied sizes and forms.
To find the area of an irregular polygon, we can divide it into smaller shapes such as triangles and rectangles, find the area of each shape, and add them together.
In this case, we can divide the polygon into a rectangle and a right triangle, as shown in the diagram below:
The area of the rectangle is the product of its length and width:
Area of rectangle = 8 in x 12 in = 96 [tex]in^{2}[/tex]
The area of the triangle is half the product of its base and height:
Area of triangle = 1/2 x 6 in x 10 in = 30 [tex]in^{2}[/tex]
Therefore, the total area of the irregular polygon is:
Area = Area of rectangle + Area of triangle
= 96 [tex]in^{2}[/tex] + 30 [tex]in^{2}[/tex]
= 126 [tex]in^2[/tex]
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Keisha is taking a road trip to her grandmother’s house. She drives the first 225 miles in 3 hours. She then stops for a one-hour lunch. Keisha arrive at her grandmother’s house after driving the remaining 220 miles in four hours. Create a distance time graph for Keisha’s trip.
Step-by-step explanation:
You should go ahead and label the x axis as hours and the y axis as distance and go in 25s
ex- 25 50 75 100 etc
Now plot the points on the graph according to the information given in the paragraph.
Please help will mark brainliest
Choose the inequality that represents the following graph.
Choose 1 answer:
A. x<2x
B. x ≤ 2x
C. x > 2x
D. x ≥ 2
Answer:
c
Step-by-step explanation:
the open circle means less than or equal too so it cant be B or D
and its pointing to the right so the mouth will eat the bigger number and the bigger number is X
Find each measurement indicated using Law Of Sines. Round your answers to the nearest tenth.
Answer:
14.0°
Step-by-step explanation:
[tex]\frac{sin(35)}{19} = \frac{sin(B)}{8}[/tex]
There is a B next to sin, but it represents m∠B. Note that both angles are in degrees.
Cross multiply the above equation.
8sin(35) = 19sin(B)
m∠B = [tex]sin^-1(\frac{8sin(35)}{19} )[/tex]
m∠B = 0.24391 rad
≅ 14.0°
The ratio of nitrogen to potassium in a sample of soil is 12:9. The sample has
36 units of nitrogen. How much potassium does the sample have?
The answer is 27 units of potassium. To determine the amount of potassium in the soil sample, we first need to use the given ratio of nitrogen to potassium to find the ratio between their respective quantities in the soil.
The ratio of nitrogen to potassium is 12:9, which can be simplified to 4:3 by dividing both sides by 3. This means that for every 4 units of nitrogen, there are 3 units of potassium in the soil sample. Since we know that the soil sample contains 36 units of nitrogen, we can use the ratio we just found to calculate the amount of potassium. To do this, we can set up a proportion: 4 units of nitrogen : 3 units of potassium = 36 units of nitrogen : x units of potassium
Solving for x, we cross-multiply and simplify:
4x = 3 * 36
4x = 108
x = 27
Therefore, the soil sample contains 27 units of potassium.
In summary, we used the given ratio of nitrogen to potassium to find the ratio between their respective quantities in the soil, and then set up a proportion using the known quantity of nitrogen to solve for the unknown quantity of potassium. The answer is 27 units of potassium.
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A machinist creates a solid steel part for a wind turbine. The part has a volume of 1,015 cubic centimeters. Steel can be purchased for $0.29 per kilogram and has a density of 7.95 g/cm^{3}
If the machinist makes 500 of these parts, what is the cost of steel to the nearest dollar.
Thus, the cost of steel for making 500 solid steel part for a wind turbine is found as: Total Price = $1170.04 .
Explain about the density of material?Atmospheric gases move according to their densities as one material rises above another. It affects what floats and what starts to sink in a body of water. A estimate of how compressed matter is is what density means. How much "stuff" is crammed into an area, to put it simply.
It is a calculable and manipulable formula in mathematics. Density is used to discuss population in various fields, such as the social sciences.
Density = mass / volume
mass = density * volume.
density of steel = 7.95 g/cm³
volume of steel = 1,015 cm³
Unit rate = $0.29 per kilogram
mass = 7.95 * 1,015 g
mass = 8069.25 g
mass of 500 parts = 500* 8069.25
mass of 500 parts = 4034625 grams
mass of 500 parts = 4034625/1000 = 4034.625 kg
Total Price = mass of 500 parts *Unit rate
Total Price = 4034.625 * 0.29
Total Price = $1170.04
Thus, the cost of steel for making 500 solid steel part for a wind turbine is found as: Total Price = $1170.04 .
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