In mathematics, a plane is a two-dimensional surface with no definite beginning or end, extending infinitely in all directions. The properties of a plane, such as the loss of the usual 1/² dependence, are abstract and not physically tangible. Examples of motion, like an airplane passenger's movement or the effect of wind on a plane's trajectory, can help visualize concepts related to planes.
Explanation:When considering the concept of a plane in mathematics, it is important to understand its properties. A plane is a flat, two-dimensional surface that extends infinitely in all directions. It does not have a definite beginning or end, meaning there is no bounded border that marks where it starts or stops. This idea can be difficult to conceptualize because it is abstract and not something we encounter in the physical world. In terms of geometry, we often approach problems involving planes by considering a portion of the plane that is relevant to the problem. For example, the concept of an infinite plane becomes intriguing as it affects the mathematical properties, such as the loss of the usual 1/² dependence encountered in finite plane calculations. To illustrate motion in a plane, one might analyze the average velocity of an object, such as an airplane passenger moving from the front to the back of an airplane or the influence of wind on a plane's trajectory relative to the ground. These scenarios involve physical planes and motions, but they help to visualize the movements within the mathematical context of planes.
solve the exponential equation 9^8x = 27
Answer:
[tex]x=\frac{3}{16}[/tex]
Step-by-step explanation:
Given : Exponential function [tex]9^{8x}=27[/tex]
We have to solve the given exponential equation.
Consider the given exponential function [tex]9^{8x}=27[/tex]
[tex]\mathrm{Convert\:}9^{8x}\mathrm{\:to\:base\:}3[/tex]
[tex]9^{8x}=\left(3^2\right)^{8x}[/tex]
Function becomes,
[tex]\left(3^2\right)^{8x}=27[/tex]
Convert 27 to base 3, we have,
[tex]\left(3^2\right)^{8x}=3^3[/tex]
Apply exponent rule, [tex]\left(a^b\right)^c=a^{bc}[/tex]
We have, [tex]3^{2\cdot \:8x}=3^3[/tex]
[tex]\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g\left(x\right)[/tex]
We have,
[tex]2\cdot \:8x=3[/tex]
Simplify, we have,
[tex]16x=3[/tex]
Thus, [tex]x=\frac{3}{16}[/tex]
find two consecutive odd integers whose sum is -88
Round this number 15,680
Arrange the following polynomial into descending order for x, then interpret the degree of the 2nd term.
7x3y3 + 4 − 11x5y2 − 3x2y
Answer:
Always double check first but I am pretty sure that it is 6
Your poor health causes you to miss one work day every two weeks. You do not get paid when you are out sick. You normally work 8 hours a day and get paid $9.29 per hour. How much pay are you losing each year
The annual loss of income due to missing one work day every two weeks at $9.29 per hour, working 8 hours per missed day, is $1,932.32.
Explanation:To calculate the amount of pay being lost each year due to missing one work day every two weeks, we need to consider the weekly work schedule and hourly wage.
Step-by-Step CalculationThe annual loss of income due to missing one day of work every two weeks at an hourly wage of $9.29 is $1,932.32.
Which pair of variables has a clear causal link between the two named variables?
the number of hats sold and the number of mittens sold in a city
the amount of butter and the amount of bread consumed by a family
the number of notebooks sold and the number of pens sold in a stationery store
the number of air conditioners sold per day in a city and the daily temperature
the number of hours a person can swim and the depth of the pool
NextReset
Answer: The number of air conditioners sold per day in a city and the daily temperature
Step-by-step explanation:
We know that if there is a causal relationship between two variables then one variable is responsible for causing the other variable.
the number of hats sold and the number of mittens sold in a city.there is no causal relationship between the variables since both are independent variables.
the amount of butter and the amount of bread consumed by a family .there is no causal relationship between the variables since both are independent variables.
the number of notebooks sold and the number of pens sold in a stationery store .there is no causal relationship between the variables since both are independent variables.
the number of air conditioners sold per day in a city and the daily temperature .there can be causal relationship between the variables since by increasing or decreasing temperature the the number of air conditioners sold per day in a city can be increased or decreased respectively.
the number of hours a person can swim and the depth of the pool.there is no causal relationship between the variables since both are independent variables.
which of the following represents the most accurate estimation if 75-33?
NEED YOUR HELP!! I WILL UPVOTE!
Combining Like Terms:
Solve the equations by combining like terms. Show all the steps.
Then write two of your own problems where you combine like terms. Show all steps, as well as your solution.
1. 16x − 4x = -48
The border line of the linear inequality 4x-2y<1 is solid.
true or false?
34 - 2(x + 17) = 23x - 15 - 3x what is x.
you have a full job that pays 2400 per month you decide to take a part time job delivering newspapers that pay 200 per week if 15% is withheld for taxes from both jobs how much would you make in a year after taxes
The sales tax rate in jans town is 7.5.if she buys 3 lamps for $23.59 each and a sofa for $769.99 , how much sales tax does she own ?
A, 4, D, H, 16, M, 25, _, _ What are the next two in the sequence?
The sequence alternates between letters and squares of integers. The letters seem to follow a particular positional increment pattern, and the numbers are squares of consecutive positive integers. The missing elements in the sequence are R and 36.
The given sequence is: A, 4, D, H, 16, M, 25, _, _. This sequence appears to have two separate patterns interleaved. One pattern is a sequence of letters and the other is a sequence of numbers. For the letters part, A (1st letter), D (4th letter), H (8th letter), M (13th letter), so the next letters might follow an increasing pattern with the position of the letters in the alphabet. For the numbers, we have 4, 16, 25 which are squares of 2, 4, and 5 respectively. To solve for the next elements in the pattern, we would have to decipher the rule that connects the letters with their positions and the next squares of numbers.
The numbers are squares of consecutive positive integers: 2², 4², 5². The next number is 6² which is 36. Following the pattern in letters, after M (the 13th letter), the next letter should be the letter that is five positions ahead because the interval between the previous letters increased by 3 each time (D is 3 letters after A, H is 4 letters after D, M is 5 letters after H), so the next letter should be R (the 18th letter, which is 5 letters after M).
Therefore, the sequence should continue with R, 36.
What is y=5/6x-3 in standard form
isabella bought 1.1 kilograms of top quality hamburger meat at $5.00 per kilogram. how much did it cost?
The cost of 1.1 kilograms of hamburger meat at $5.00 per kilogram is $5.50
Multiply the weight of the meat (1.1 kg) by the price per kilogram ($5.00):
1.1 kg x $5.00/kg = $5.50.
Therefore, it cost Isabella $5.50 to buy 1.1 kilograms of top-quality hamburger meat.
What is the expression in radical form?
(5x4y3)^2/5
Enter your answer, in simplest form, in the box.
Damion found a new game system he wanted to buy. the price of the system was reduced from $250 to $200. by what percentage was the price reduced?
multiplicative inverse of -3.4
Factor completely: 2x2 + 6x − 80
(2x − 5)(x + 8)
(2x − 10)(x + 8)
2(x − 5)(x + 8)
2(x − 10)(x + 8)
...?
Quadratic functions are functions that has a degree of 2. The factored form of the function is (2x-10)(x+8)
Factorization of functionsQuadratic functions are functions that has a degree of 2. Given the function below;
2x^2 + 6x - 80
Factorize
2x^2+16x - 10x - 80
Group
(2x^2+16x)-(10x+80)
Factor out the GCF
2x(x + 8)-10(x+8)
(2x-10)(x+8)
Hence the factored form of the function is (2x-10)(x+8)
Learn more on factoring here: https://brainly.com/question/25829061
#SPJ5
The perimeter of dawna's new flat screen television is 70 inches. the ration from length to width is 4:3. write and solve an algebraic equation to determine the dimensions of the television
What are the least common multiples of 7 and 11
What is the range of the function h(x) = -8x?
The range of the function h(x) = -8x is all real numbers, as there are no restrictions on the output the function can produce. This is typical of a linear function.
Explanation:The range of a function refers to the possible outputs it can produce. In the case of the function h(x) = -8x, it is a linear function, and there are no restrictions on the values that x can take, meaning x can be any real number between -∞ and +∞. The output, h(x), therefore, can be any real number, also between -∞ and +∞, given that it will be the result of -8 multiplied by x. Therefore, the range of the function h(x) = -8x is all real numbers from -∞ to +∞.
Learn more about range of a function here:https://brainly.com/question/29145252
#SPJ12
Alex has 520 yards of fencing to enclose a rectangular area.
A retangle that maximises the enclosed area has a length of _ yards and a width of _ yards.
The maxium area is _____ yards
The first thing we are going to do for this case is define variables.
We have then:
w: width
l: length
The perimeter is given by:
[tex] 2w + 2l = 520
[/tex]
The area is given by:
[tex] A = w * l
[/tex]
The area as a function of a variable is:
[tex] A (w) = w * (260-w)
[/tex]
Rewriting we have:
[tex] A (w) = -w ^ 2 + 260w
[/tex]
To obtain the maximum area, we derive:
[tex] A '(w) = -2w + 260
[/tex]
We equal zero and clear the value of w:
[tex] -2w + 260 = 0
2w = 260
[/tex]
[tex] w = \frac{260}{2}
w = 130
[/tex]
Then, the length is given by:
[tex] l = 260 - w
l = 260 - 130
l = 130
[/tex]
Finally, the maximum area obtained is:
[tex] A = w * l
A = 130 * 130
A = 16900
[/tex]
Answer:
A retangle that maximizes the enclosed area has a length of 130 yards and a width of 130 yards.
The maxium area is 16900 square yards
Please help !!
Answer correct for a brainliest and also a thanks ! Don't answer if you don't know it .
If your teacher tells you to do questions 28 through 41 in your math book for homework, how many questions is that?
(Do not include units in your answer.)
Answer:
14 questions.
Step-by-step explanation:
We have been given that your teacher tells you to do questions 28 through 41 in your math book for homework. We are asked to find he total number of questions.
Since we need to solve questions 28 through 41, this means we have to solve question number 28 and 41 as well.
We know that 28-37 would be 10 questions and 38-41 would be 4 questions.
[tex]\text{Total questions}=10+4[/tex]
[tex]\text{Total questions}=14[/tex]
Therefore, you need to solve 14 questions to complete the homework.
PLEASE HELP
A line has slope -5/3. Through which two points could this line pass?
A. (12,13), (17,10)
B. (16,15), (13,10)
C. (0,7), (3,10)
D. (11,13), (8,18)
Antarctica comprises about 10.5% of the total land area on Earth. Antarctica has a surface area of about 5,400,000 square miles. What is the total land area on Earth?
Integrate sin^-1(x) dx
please explain how to do it aswell ...?
. SOMEONE PLEASE HELP ME?!?!
5. This is the Reed family budget. How much discretionary income does the family have each month?
Housing $800.00
Groceries $425.00
Utilities $285.00
Miscellaneous $120.00
Transportation $150.00
Insurance $286.00
Savings $200.00
Healthcare $60.00
Clothing $50.00
Total Expenses $2,376.00
Net income $2,850.00
$______
8. Paula created a monthly budget. A pie graph shows a clear picture of where her money is spent. How much of the circle would be shaded for the total of housing, utilities, food, and insurance?
Housing $500.00
Insurance $283.00
Food $225.00
Utilities $174.00
Miscellaneous $75.00
Transportation $64.00
Clothing $50.00
Medical $25.00
Savings $20.00
10. You are making a pie graph of the expenses in the Reed family budget. How much of the pie graph would be used to represent the amount spent on housing?
Housing $800.00
Utilities $285.00
Groceries $425.00
Miscellaneous $120.00
Transportation $150.00
Insurance $286.00
Savings $200.00
Healthcare $60.00
Clothing $50.00
Total Expenses $2,376.00
Net income $2,850.00
A. half of the circle
B. less than half
C. over 75% of the circle
D. 50% to 75%
Total Expenses $1,416.00
A. half of the circle
B. less than half
C. over 75% of the circle
D. 50% to 75%
Abcd is a rectangle. Find the length of each diagonal. .AC= 3y/5 BD=3y-4
Answer:
AC = BD = 1 unit
Step-by-step explanation:
Given : length of diagonal of rectangle ABCD [tex]AC=\frac{3y}{5}[/tex] and [tex]BD=3y-4[/tex]
We have to find the length of diagonal.
We know In rectangle diagonal are of equal lengths.
Therefore, for rectangle ABCD diagonals AC= BD
Substitute the values, we get,
[tex]\frac{3y}{5}=3y-4[/tex]
Cross multiply , we get
[tex]3y=5(3y-4)[/tex]
On simplyfy , we get
[tex]3y=15y-20[/tex]
Solve for y , we get
[tex]15y-3y=20[/tex]
[tex]12y=20[/tex]
Divide both side by 12, we get,
[tex]y=\frac{20}{12}=\frac{10}{6}[/tex]
Thus, put the values of y in AC and BD to find the length of diagonals , we get,
[tex]AC=\frac{3y}{5}=\frac{3}{5}\times\frac{10}{6}=1[/tex]
Similarly for BC, we get,
[tex]BD=3y-4=3(\frac{10}{6})-4=5-4=1[/tex]
Thus, AC = BD = 1 unit