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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
How do you write 14 square in expanded form?
To write 14 squared in expanded form, you need to multiply 14 by itself: 14 x 14. This equals 196. Therefore, the expanded form of 14 squared is 196.
What are the first 3 terms for 2n-1?
The first three terms for the expression 2n-1 can be found by substituting n with the first three consecutive integers. When n=1, the expression becomes 2(1)-1 = 1. When n=2, the expression becomes 2(2)-1 = 3. When n=3, the expression becomes 2(3)-1 = 5. Therefore, the first three terms are 1, 3, and 5.
What 2 numbers multiply to get -100 and add to get -25?
To find two numbers that multiply to -100 and add up to -25, we can set up a system of equations. Let's call the two numbers x and y. We have the equations xy = -100 and x + y = -25. By solving these equations simultaneously, we can find that the two numbers are -20 and 5.
Show all 3 number combinations using 7 and 8 and 9?
Oh, what a happy little question! Let's create some beautiful number combinations with 7, 8, and 9. We can have 789, 798, 879, 897, 978, and 987. Just like painting, there are endless possibilities when we mix these numbers together. Keep exploring and creating!
What is the highest common factor of 875?
The highest common factor of 875 is 125. To find the highest common factor, you need to identify all the factors of the number and then determine the largest factor that is common to all of them. In this case, the factors of 875 are 1, 5, 25, 35, 125, and 875. The highest common factor among these factors is 125.
How much km and m is equal to 7 km and 8 m?
Ah, what a lovely question! 7 kilometers is equal to 7,000 meters, and when we add 8 meters to that, we get a total of 7,008 meters. Just imagine all the beautiful landscapes you could explore with that distance!
What kind of triangle are you 3cm 5cm 3cm?
The triangle with side lengths of 3cm, 5cm, and 3cm is classified as a scalene triangle. A scalene triangle is a triangle in which all three sides have different lengths. In this case, the three sides have lengths of 3cm, 5cm, and 3cm, making it impossible for the triangle to have any congruent sides or angles.
How many combinations you can make from 34 numbers?
There are 234 - 1 combinations.
Each one of the 34 numbers can either be in a combination or not in it. The two-fold choice gives 234 possible options. However, one of these consists of the option where in each case the choice is "not in it". So you have a null combination. Excluding that combination leaves 234 - 1.
Remember that in a combination, the order of the numbers does not matter.
What number divided by 2 equals -18?
Well, isn't that a happy little math problem we have here? To find the number that divided by 2 equals -18, we can simply multiply -18 by 2. So, the number you're looking for is -36. Remember, there are no mistakes in math, just happy little accidents!
What are 3 different triangles with the area of 32 cm?
For a right triangle, A = 1/2(b)(h), where (b) is the length of the base of the triangle and (h) is the triangle's height. Just plug in some numbers to find all sorts of solutions for a (right) triangle whose area is 32.
What is 0.015 in scientific notation?
Oh, dude, like, 0.015 in scientific notation is 1.5 x 10^-2. It's like when you have a tiny number and you want to make it look all fancy with powers of 10. So yeah, 0.015 becomes 1.5 x 10 to the power of negative 2. Cool, right?
Why does a number get larger when you divide it by a number that is less than one?
the number gets bigger when u divide by a number less than one because if you have 3 chocolate bars and u want to divide each one by 1000434 pieces, you would have more chocolate pieces than before. For example 80 divide by 0.001=80000, it got bigger.
Oh, dude, let me break it down for you. So, if the dog is tethered with a 20-foot lead and the path it walks is 45 feet, that's like a radian situation. The angle in radians would be like 45 feet divided by the radius of the circle, which is 20 feet, so it's around 2.25 radians. But hey, who's counting, right?
What is the answer to what is the best way to paint a rabbit in Punchline Algebra book b 13.16?
Oh, dude, painting a rabbit in a Punchline Algebra book? That's a new one. Well, technically, the best way to paint a rabbit in that specific book would be to follow the instructions given in problem 13.16. Just grab your brushes, mix some colors, and get artsy with it. Good luck, Picasso!
What is the volume of a cube that is 7 inches on each side?
Oh, what a happy little cube we have here with all sides measuring 7 inches! To find the volume, you simply multiply the length, width, and height together. So, for this cube, the volume would be 7 inches multiplied by 7 inches multiplied by 7 inches, which equals 343 cubic inches. Just imagine all the wonderful things you could fit inside that cube!
No, 0.01 is not bigger than 0.07. In decimal numbers, the value to the left of the decimal point indicates the whole number value, while the value to the right of the decimal point represents fractions of a whole. In this case, 0.01 is one hundredth and 0.07 is seven hundredths. Since 0.07 is greater than 0.01, 0.07 is bigger.
What is a pyramid with 5 sides?
A pyramid with 5 sides is a PYRAMID.
First side is the SQUARE base, which you probably don't think about.
Sides 2,3,4 & 5 are the four triangular faces.
The pyramids of ancient Egypt are of this form.
There is NO such thing as a pyramide of four sides. That is a Tetrahedron.
What is the highest common factor of 228 and 285?
The highest common factor (HCF) of 228 and 285 is the largest positive integer that divides both numbers without leaving a remainder. To find the HCF, you can use the Euclidean algorithm. First, divide the larger number (285) by the smaller number (228) to get a quotient of 1 with a remainder of 57. Then, divide the previous divisor (228) by the remainder (57) to get a quotient of 4 with a remainder of 0. Therefore, the HCF of 228 and 285 is 57.
How do you find the ratio of 20 and 15?
To find the ratio of 20 and 15, you divide 20 by 15. The ratio is typically expressed in simplest form, so you would divide both numbers by their greatest common divisor, which in this case is 5. Therefore, the ratio of 20 to 15 is 4:3.
How are polynomials used in your daily life?
Although many of us don't realize it, people in all sorts of professions use polynomials every day. The most obvious of these are mathematicians, but they can also be used in fields ranging from construction to meteorology. Although polynomials offer limited information, they can be used in more sophisticated analyses to retrieve more data.
What is a Polynomial?
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Polynomials are algebraic expressions that add constants and variables. Coefficients multiply the variables, which are raised to various powers by non-negative integer exponents.
How do People use Polynomials?
Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example.
Polynomials for Modeling or Physics
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Polynomials can also be used to model different situations, like in the stock market to see how prices will vary over time. Business people also use polynomials to model markets, as in to see how raising the price of a good will affect its sales. Additionally, polynomials are used in physics to describe the trajectory of projectiles. Polynomial integrals (the sums of many polynomials) can be used to express energy, inertia and voltage difference, to name a few applications.
Polynomials in Industry
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For people who work in industries that deal with physical phenomena or modeling situations for the future, polynomials come in handy every day. These include everyone from engineers to businessmen. For the rest of us, they are less apparent but we still probably use them to predict how changing one factor in our lives may affect another--without even realizing it.
Curve Fitting
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Polynomials are fit to data points in both regression and interpolation. In regression, a large number of data points is fit with a function, usually a line: y=mx+b. The equation may have more than one "x" (more than one dependent variable), which is called multiple linear regression.
In interpolation, short polynomials are joined together so they pass through all the data points. For those who are curious to research this more, the name of some of the polynomials used for interpolation are called "Lagrange polynomials," "cubic splines" and "Bezier splines."
Chemistry
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Polynomials come up often in chemistry. Gas equations relating diagnostic parameters can usually be written as polynomials, such as the ideal gas law: PV=nRT (where n is mole count and R is a proportionality constant).
Formulas of molecules in concentration at equilibrium also can be written as polynomials. For example, if A, B and C are the concentrations in solution of OH-, H3O+, and H2O respectively, then the equilibrium concentration equation can be written in terms of the corresponding equilibrium constant K: KC=AB.
Physics and Engineering
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Physics and engineering are fundamentally studies in proportionality. If a stress is increased, how much does the beam deflect? If a trajectory is fired at a certain angle, how far away will it land? Well-known examples from physics include F=ma (from Newton's laws of motion), E=mc^2 and F---r^2=Gm1---m2 (from Newton's law of gravitation, though usually the r^2 is written in the denominator).
Polynomials come up often in chemistry. Gas equations relating diagnostic parameters can usually be written as polynomials, such as the ideal gas law: PV=nRT (where n is mole count and R is a proportionality constant).
Formulas of molecules in concentration at equilibrium also can be written as polynomials. For example, if A, B and C are the concentrations in solution of OH-, H3O+, and H2O respectively, then the equilibrium concentration equation can be written in terms of the corresponding equilibrium constant K: KC=AB.
Physics and engineering are fundamentally studies in proportionality. If a stress is increased, how much does the beam deflect? If a trajectory is fired at a certain angle, how far away will it land? Well-known examples from physics include F=ma (from Newton's laws of motion), E=mc^2 and F---r^2=Gm1---m2 (from Newton's law of gravitation, though usually the r^2 is written in the denominator).
Oh, dude, like, totally! So, a term in math is like a single mathematical expression, right? And 3x is totally just one term because it's like, one number (3) multiplied by a variable (x). So, yeah, 3x totally qualifies as a term in math lingo.
What number is represented by the letter p in algebra?
In Algebra there are constants and variables. 'p' is a variable which means that its value can change with reference to the equation it is present in.
In Physics, 'p' represents momentum.
