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Algebra
The use of letters to substitute unknown numbers to form an equation. Solve the equation to get the unknown number using different methods such as simultaneous equations and more.
227,579 Questions
Does a right triangle have rotational symmetry?
The modern answer is that if the shape only fits once onto the original when rotated 360o it has no rotational symmetry.
A right triangle only fits once when rotated 360o so it has no rotational symmetry.
How do you write 1.26 as a fraction in lowest terms?
To write 1.26 as a fraction in lowest terms, we first note that 1.26 is equivalent to 126/100 (since 1.26 = 1 + 26/100 = 1 + 26/10^2 = 1 + 26/100). To simplify this fraction, we divide the numerator and denominator by their greatest common divisor, which is 2. This gives us 63/50 as the fraction in lowest terms.
What is the length and width of 1000 square meters?
Well, darling, if we're talking about a square, the length and width of 1000 square meters would be the square root of 1000, which is approximately 31.62 meters. So, the length and width would both be around 31.62 meters. Hope that clears things up for you, sugar!
How many combinations of 2 numbers are there in 5 numbers?
It depends on whether the number order can or cannot be identical. Also whether you can use the same number twice. There are 10 unique pairs possible (i.e. 1 and 5 is the same as 5 and 1), but 20 sequential pairs where the order of the pair makes them different, and 25 if you can use the same number in a pair.
10 = 1-2, 1-3, 1-4, 1-5, 2-3, 2-4, 2-5, 3-4, 3-5, 4-5
20 = (include the reverse of those)
25 = (include 1-1, 2-2, 3-3, 4-4, 5-5)
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A combination is a selection of a number of items from a group without regard to order (i.e. AB = BA). Since order is not important, then the number of combinations is given by the formula: n!/(n - r)! r!
where n = the total number of items. r = the number of items chosen from n
(recall that n!, pronounced n factorial, means the continued product of successive natural numbers from 1 to n. So 5!= 5x4x3x2x1, for example)
Let the 5 numbers be 1, 2, 3, 4, and 5. Possible combinations are: 1 and 2, 1 and 3, 1 and 4, 1 and 5, 2 and 3, 2 and 4, 2 and 5, 3 and 4, 3 and 5, 4 and 5.
(Note how '2 and 1' is not listed because '2 and 1' is the same as '1 and 2' when using combinations).
So there are 10 combinations of 2 numbers taken from 5 numbers.
Using the formula there are 5!/3!2!=10 ways to pick 2 items from 5 where the order does not matter. We also assume we are not replacing an item after we pick it.
When we pick r items from n with replacement, we must use a different method or another formula. We often use a method known as bars and stars. Alternatively, we can use the formula (n+r-1)! / r! (n - 1)!. When we put the items back, we can pick more than n items. So it would make sense to talk about how many ways to pick 7 items from 5, whereas without replacement this is impossible.
Can common ratio be 1 in geometric progression?
if a number is multiplied by 1, then it does not change, it is Still the same number. A ratio of 1 is impossible . The ratio between two quantities must always be greater than 1 otherwise there is no difference between them.
What is the perimeter of a square with an area of 25m2?
Well, darling, if the area of the square is 25m², then each side must be the square root of 25, which is 5m. Since a square has four equal sides, the perimeter would be 4 times the length of one side, giving us a sassy perimeter of 20m. Voilà!
What is the least common multiple of x and 3x?
The least common multiple (LCM) of two numbers is the smallest multiple that is divisible by both numbers. In this case, the LCM of x and 3x is the smallest multiple that can be divided evenly by both x and 3x. Since 3x is a multiple of x (3 times x), the LCM of x and 3x would simply be 3x.
The common misconseption: divide 5.75 by 2. What you should do is multiply 5.75 by 2, because if you divide something by half it must double, for example when you divide 1 by 0.5, you get 2, this is because there are 2 halves in each 1, which is the concept of division.
What is 29.15 as a mixed number in simplest form?
Sure thing, honey. 29.15 as a mixed number in simplest form is 29 3/20. Just divide the decimal part by 0.15 by 0.05 to get 3, then simplify it to 3/20. Voilà, you got yourself a nice and tidy mixed number.
What are the 7 steps in problem solving?
1) Finding the right problem to solve
- Too often our approach to problem solving is reactive; we wait for the problems to arise. Firstly in our seven step problem solving process, we advocate taking a proactive approach, go and find problems to solve; important and valuable problems. The real starting point then for any problem solving process is to find the right problem to solve.
2) Defining the problem
- It is very tempting to gloss over this step and move to analysis and solutions. However, like the first step, it is one of the secrets of effective problem solving. Combining problems that are valuable to solve, with defining exactly what you are trying to solve, can dramatically improve the effectiveness of the problem solving process. The secret to defining the problem is really about attitude. Try to see every problem as an opportunity.
3) Analyzing the problem
- Analysis is a process of discovery of the facts, finding out what you know about the situation. The problem solving activity question checklist leads you through a set of questions to identify the nature of the problem and to analyze what it is and what it isn't. One of the most important aspects of analyzing any situation is involving the right people.
4) Developing possibilities
- The previous steps will have already revealed plenty of possibilities for solving the problem and realizing the opportunities. At this stage it is important to give time and space for creative solutions. Placing a high value on the ideas of others is a crucial leadership concept and facilitator skill when generating ideas to solve problems.
5) Selecting the best solution
- There will be constraints restricting what you can do, issues about whether solutions fit within what is currently done, and various stakeholders views to consider. Solutions therefore need to be evaluated.
6) Implementing
- Carefully defined the problem and the desired outcome, analyzed the problem at length, collected every available item of information about it, explored all possible avenues, and generated every conceivable option & chosen the best alternative after considerable deliberation.
7) Evaluating and learning
- It would be all too easy to forget them in rushing to solve the next problem, or to implement the solution. You should evaluate at least two areas:
1) How you carried out the seven step problem solving process 2) The effectiveness of the solution you implemented. Did it deliver the outcomes you expected?
- You should also ask what you are now able to do, or what you could do next, now that you have improved things by solving the problem. What further opportunities can you now realize that you weren't able to before?
How many rectangles are in a 5 by 4 grid?
In a grid of A x B squares, the formula to find how many unique rectangles there are (and all squares are considered to be rectangles) is:
A * (A+1) * B * ((B+1)/4)
A and B are interchangeable.
So in a 5 x 4 grid, there are
5 * (5+1) * 4 * ((4+1)/4)
Or 5 * 6 * 4 * (5/4)
Or 150 unique rectangles.
Now if we switch A and B, the equation reads:
4 * (4+1) * 5 * ((5+1)/4)
Or 4 * 5 * 5 * (6/4)
Again 150 unique rectangles.
What does 'Cu' mean in mathematics?
In mathematics, 'Cu' typically stands for the symbol of the element copper on the periodic table. Copper is a transition metal with the atomic number 29 and the chemical symbol Cu. It is commonly used in various mathematical equations and formulas, particularly in chemistry and physics.
What is the ratio for 12 and 15 as a fraction in simplest form?
12 and 15 as fraction is 12/15 . then turn it into simplest form you divide top number ( 12 ) and the bottom number ( 15 ) by the biggest number that fits into both of them which in this case is 3 . now you divide the top number and bottom number by the biggest number that fit into both of them which is 3 . so 12 divided 3 is 4 and 15 divided by 3 is 5 so your final answer is 4/5 .
REMEMBER - when simplify fraction , the top and bottom number is always divided
by the same number which is the biggest number that fits into both of them .
Are y-5x 9 and 5x y-21 parallel or perpendicular?
Honey, those two lines are perpendicular. How do I know? Well, if the slopes are negative reciprocals of each other, they're like two peas in a pod - perpendicular! So, in this case, the slope of the first line is 5, and the slope of the second line is -1/5. Case closed!
How many squares are in a 4x5 grid?
Oh, what a delightful question! In a 4x5 grid, you have a total of 20 squares. You see, each row has 3 squares, and there are 4 rows in total. Remember, it's all about finding the beauty in the simplicity of numbers.
What is the HCF of 7 8 and 10?
The highest common factor (HCF) of 7, 8, and 10 is 1. This is because the only factor that these three numbers share is 1, as 7, 8, and 10 do not have any other common factors. Therefore, the HCF of 7, 8, and 10 is 1.
Oh honey, let me break it down for you. Non-examples of a formula are basically anything that doesn't fit the criteria of a formula. It's like trying to fit a square peg into a round hole - it just ain't gonna work. So, if it doesn't follow the rules and structure of a formula, then it's a non-example. Simple as that.
How many times can you get 6 sets of numbers from 1 to 28 what are these sets of numbers?
There are 376740 such sets and you must think me crazy if you think I will list them all!
A rectangle has a perimeter of 67.8 cm What migh the dimentions be?
Oh, dude, I mean, like, if you wanna get technical and all, you could say the dimensions of that rectangle might be like 15 cm by 18.9 cm. But hey, who's really measuring, am I right? Just go with it and call it a day.
What is the units' digit of 3 to the 333?
To find the units' digit of 3 to the power of 333, we need to look for a pattern. The units' digit of powers of 3 cycles in a pattern: 3, 9, 7, 1. Since 333 divided by 4 leaves a remainder of 1, the units' digit of 3 to the power of 333 will be the first digit in the pattern, which is 3.
In the expression v x 5x, the variable v is being multiplied by the product of 5 and x. This can be simplified as 5v x. The commutative property of multiplication allows us to rearrange the terms as v x 5 x, which is equivalent to 5v x.
