Order the numbers from greatest to least - use the number line to help you visualize correct placement: Biggest number at the top of the list, smallest number at the bottom
√15
-√45
7/3
-0.0123456
3√27
0
-√45
√15
3√27
7/3
0
-0.0123456
how do you know this is the correct order
To determine the correct order of the numbers, we can compare them on a number line. Here's how we can do it:
1. Start by plotting the numbers on the number line.
-√45 is approximately -6.7 (to compare, √16 is 4 and √49 is 7, so it's between -4 and -7)
√15 is approximately 3.9 (to compare, √9 is 3 and √16 is 4, so it's between 3 and 4)
3√27 is 9 (since √27 is 3 and multiplying by 3 gives 9)
7/3 is approximately 2.33 (fraction between 2 and 3)
0 is right at the center of the number line
-0.0123456 is a very small negative number, to visualize it let's round it to -0.01 (a little to the left of 0)
2. Now, observe the positions of the numbers on the number line.
From greatest to least:
-√45 is the farthest left (smallest) on the number line
√15 is next, further right than -√45
3√27 is greater than √15, closer to the right end of the number line
7/3 is greater than 3√27, closer to the right end of the number line
0 is right at the center of the number line
-0.0123456 is a little left of 0, smaller than 0 but still to the right of the other numbers.
Therefore, the correct order from greatest to least is:
-√45, √15, 3√27, 7/3, 0, -0.0123456
If I wanted to estimate 59−−√
, the first step would be to find the two Response area squares that 59 lies Response area on the number line. The closest perfect square less than 59 is Response area. The closest perfect square greater than 59 is Response area. I could then think about the number 59 and how close it is to the smaller perfect square and the larger perfect square. I could then take the Response area root of the perfect squares to see how I would estimate 59−−√
. The 59−−√
is closest to
If you want to estimate √59, the first step is to find the two perfect squares that 59 lies between on the number line. The closest perfect square less than 59 is 49 (7^2). The closest perfect square greater than 59 is 64 (8^2).
To estimate √59, you can think about how close 59 is to the smaller perfect square (49) and the larger perfect square (64). Since 59 is closer to 64, you can take the square root of the larger perfect square (8) to estimate the square root of 59.
Therefore, the estimate for √59 would be approximately 8.
Look at the steps for solving the equation and choose a true statement.
3x−9x+1=2(−3x+1)−1
−6x+1=−6x+2−1
−6x+1=−6x+1
(1 point)
Responses
The only solution to the equation is –6.
There is no way to know if there is a solution to this equation.
There are no solutions to the equation.
The only solution to the equation is 1.
There are infinitely many solutions to the equation.
The correct statement is: The only solution to the equation is 1.
how do you know that is the correct answer
We can determine that the only solution to the equation is 1 by solving the equation step by step:
1. Start with the equation: 3x - 9x + 1 = 2(-3x + 1) - 1
2. Simplify both sides of the equation:
-6x + 1 = -6x + 2 - 1
3. Combine like terms on the right side:
-6x + 1 = -6x + 1
4. We can see that the variables (-6x) cancel out on both sides of the equation, leaving:
1 = 1
5. Since 1 is equal to 1, this means that the equation is true for any value of x. Therefore, there are infinite solutions to the equation.
Apologies for the previous incorrect response. The correct statement is: There are infinitely many solutions to the equation.