Algebra

Oh, what a happy little question! When you have y squared plus y squared, you simply add them together to get 2y squared. It's just like painting a beautiful landscape, each part coming together to create something wonderful. Just remember, there are no mistakes in math, only happy little accidents!

Well, darling, the Least Common Multiple (LCM) of 4, 9, and 2 is 36. It's the smallest multiple that all three numbers can divide into without leaving a pesky remainder. So, there you have it, 36 is the magic number that keeps these three amigos happy.

Well, darling, the highest common factor of 78, 91, and 156 is 13. It's like finding the perfect pair of shoes that goes with every outfit - simple and essential. So, there you have it, 13 is the magic number that can divide all three of those numbers without a fuss.

Oh, dude, it's like super easy. You just type in the numbers and symbols for the algebraic expression you want to solve, hit the equal sign, and voilà, the calculator does the magic for you. It's like having a tiny math wizard in your pocket, but without the cool hat.

To find the square footage of a rectangular area, you need to multiply the length by the width. In this case, the length is 27 inches and the width is 14 inches. So, the square footage would be 27 inches x 14 inches = 378 square inches. To convert square inches to square feet, you would divide by 144 (since 1 square foot is equal to 144 square inches). Therefore, the square footage of a 14-inch by 27-inch area is 2.625 square feet.

1252 days * ( 1 year / 365 days) = 3.43 years

0.43 years * ( 12 months / 1 year) = 5.16 months

SO: 3 years 5.16 months.

Nope, honey, that's not gonna work. A scalene triangle has three sides of different lengths, so having two sides that are the same length ain't gonna cut it. You need three different side lengths to make that scalene magic happen.

Well, honey, to find the side length of a square with an area of 400 cm², you take the square root of the area. So, the square root of 400 is 20. Therefore, the side length of the square is 20 cm. Hope that clears things up for ya!

There are six sixths in a whole. In terms of numbers, 6/6 = 1.

Ah, what a lovely question! One of my favorite ways to show the relationship between two variables is by using a scatter plot. It's like planting little seeds of data on a canvas, showing how they relate to each other in a beautiful and visual way. Just remember to add some labels and a title to your plot, so others can appreciate the beauty of your data garden too.

Put a flat layer of hearts on the bottom and count them. Estimate how many layers can fit into the jar and multiply.

Well, darling, factorization is just a fancy term for breaking down an expression into its simplest parts. In this case, we have 8x + 26x - 7. Combine like terms to get 34x - 7. So, the factorization of 8x + 26x - 7 is simply 34x - 7. Easy peasy lemon squeezy!

The simplest way to describe this action is to demonstrate using a simple truth table. This is not intended to be an in depth study of the theorms but a simple demonstration of how a trivial equation can be demorganized. Given a simple boolean equation !A+!B=1. One could show in a truth table. !A !B !A+!B (fully inhibited OR function)

0 0 1

0 1 1

1 0 1

1 1 0 Demorganizing (hypersimplified method)

1) NOT all variables

2) NOT the equation

3) Invert the function (AND to OR or OR to AND)

Iterative steps yeilds

!A becomes !!A which is the same as A

(!!A + !B) = (A+!B)

!B becomes !!B which is the same as B

(A +!!B) = A+B OR function becomes AND

(A+B) = (AB)

NOT the full equation !(AB) = !A+!B Truth table for the new equation (which happens to be a NAND function) A B AB !AB !A+!B

0 0 0 1 1

0 1 0 1 1

1 0 0 1 1

1 1 1 0 0

Algebraically this would be writtwen as '5+y'

The square root of 1742400 is 1320. To work this out, you can factorize 1742400 into its prime factors, which are 2^6 * 3 * 5^2 * 7^2. Then, you can take the square root of each prime factor and multiply them together to get the final result of 1320.

Oh, dude, ordinal points are like those fancy little numbers that show the position or order of something, you know? It's like saying "first," "second," "third," but in a more official and proper way. So, if you're ever in a super serious situation where you need to sound all sophisticated, just throw in some ordinal points and you'll be golden.

8

Oh, dude, we're diving into some math here! So, when you have -2x minus -2, you can simplify it by adding the opposite of that second negative, which is like adding a positive. So, it becomes -2x + 2. Math can be a trip, man!

A relation is an expression that is not a function. A function is defined as only having one domain per range, meaning that when graphed, a function will have no two points on the same vertical line. If your expression is graphed and two points do appear on the same vertical line, it is a relation, not a function.

30

Oh, what a happy little question! You see, a square meter is a unit of area, like the size of a small painting. A metric ton, on the other hand, is a unit of weight, like the amount of paint on your palette. So, they're like apples and oranges, each special in their own way and not quite the same. Just remember, it's important to use the right unit for the right job, and everything will come out just fine.

59

To calculate the speed of one mile in ten seconds, we need to convert the time to hours. There are 3,600 seconds in an hour, so 10 seconds is equivalent to 10/3,600 hours. To find the speed, we divide the distance (1 mile) by the time (10/3,600 hours), which equals 360 miles per hour. Therefore, one mile in ten seconds is equivalent to a speed of 360 miles per hour.

First you convert the inches to feet by dividing by 12 inches per foot. This gives

(24/12) x (16/12) = 2 x 4/3

Then you multiply out

2 x 4/3 = 8/3 = 2 and 2/3 square feet.

Or, conversely, multiply 24 x 16 = 384, and divide by 144 (sq. inches in a square foot),

with the same answer : 2 and 2/3 or 2.66 square feet.

One example of a square-based pyramid in a home could be a roof with a square base and four triangular sides sloping upwards. Another example could be a decorative piece like a crystal or glass ornament with a square base that tapers to a point at the top. A third example could be a stack of square-based boxes arranged in a pyramid shape for storage or display purposes.