could someone please help me with this two part question? I can not understand it. I need to hand in my homework by tomorrow. Thanks
A thousandths grid is completely coloured in when three different decimals are shown. One decimal is double one of the others.
a) what could the three decimals be?
b) how do you know there are many answers to part a)?
how do you do do 2 step algebra
The three decimals could be
0.1 , 0.2 and 0.7
0.2 , 0.4 and 0.4
0.3 , 0.6 and 0.1
There are many solution to part a). As long as the three number added up to 1 (i.e. a gird is completely coloured) and one number is double the other number.
In algerba, first decimal is x, the second decimal is 2x and third decimal is y. Add them all up we have 3x + y = 1
Sure, I can help you with that. Let's break it down step-by-step.
a) To find the possible three decimals, we need to understand what a thousandths grid is and how it relates to the decimals being double of each other.
A thousandths grid is a grid divided into a thousand equal parts, usually represented as a 10x10 grid with 100 squares in total. Each square would represent 0.01 or one hundredth.
So, let's say we have three decimals: x, y, and z.
We know that one decimal is double another. Let's assume x is the decimal that is double of y. In this case, we can express x as 2y.
To represent these decimals in terms of thousandths, we need to convert them. Since there are 1000 thousandths in one whole, we can write:
x = 2000 thousandths
y = 1000 thousandths
z = ?
We can also determine the value of z by subtracting the sum of x and y from 1000 thousandths because the three decimals should completely fill the thousandths grid:
z = 1000 thousandths - (x + y)
Substituting the values of x and y, we get:
z = 1000 thousandths - (2000 thousandths + 1000 thousandths)
Simplifying the expression:
z = 1000 thousandths - 3000 thousandths
z = -2000 thousandths
Now, to make sure the decimals are different, we need to convert them back to decimals.
x = 2000 thousandths = 0.200
y = 1000 thousandths = 0.100
z = -2000 thousandths = -0.200
So, the three possible decimals are 0.200, 0.100, and -0.200.
b) There are multiple answers to part a) because there are different ways to choose which decimal is double of another. In the above example, we assumed x is double y, but we could have assumed y is double x, leading to different decimal values. Therefore, there can be many answers based on the different combinations of doubling one decimal over another.
Sure, I'd be happy to help you with your two-part question.
a) To find the possible three decimals, let's start by understanding what a "thousandths grid" means. A thousandths grid is a grid that represents numbers in increments of one-thousandth (0.001). It can be visualized as a square grid divided into 10 equal columns and 10 equal rows, giving us 100 cells.
Now, we need to find three different decimals that can completely color in this grid. One decimal should be double one of the others. Let's go through the options:
- We could have 0.001, 0.002, and 0.004. Here, 0.004 is double 0.002.
- We could also have 0.002, 0.004, and 0.008. In this case, 0.008 is double 0.004.
- More generally, one possible pattern is to choose any decimal (let's call it "x"), and the other two decimals can be "2x" and "4x." For example, if x = 0.001, then the three decimals would be 0.001, 0.002, and 0.004.
b) There are many answers to part a) because we can choose any decimal "x" and construct the other two decimals by doubling and quadrupling "x." As long as "x" is a valid decimal, we will have a valid answer for the three decimals that meet the given condition. Since there are infinite possibilities for "x," there are also infinite possibilities for the three decimals.
Therefore, there are many answers to part a) because the decimals can vary depending on the chosen value for "x."