<h3>
Answer: -√46 is between -7 and -6</h3>
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Explanation:
List out the perfect squares
- 1^2 = 1
- 2^2 = 4
- 3^3 = 9
- 4^2 = 16
- 5^2 = 25
- 6^2 = 36
- 7^2 = 49
- 8^2 = 64
and so on. We can see that 46 is between 6^2 = 36 and 7^2 = 49.
We can say 6^2 < 46 < 7^2
Applying the square root to all three sides leads us to 6 < sqrt(46) < 7
Now multiply all three sides by -1. This will flip the inequality signs
We go from
6 < sqrt(46) < 7
to
-6 > -sqrt(46) > -7
It might help to order things from smallest to largest to get this
-7 < -sqrt(46) < -6
This means -sqrt(46) is between -7 and -6 on the number line
See the diagram below.
Answer:
If 3 + 4 ≠ 6, then 2 · 5 = 10.
Step-by-step explanation:
To form the contrapositive of the conditional statement, interchange the hypothesis and the conclusion of the inverse statement. The contrapositive of "If it rains, then they cancel school" is "If they do not cancel school, then it does not rain." If p , then q .
When we distribute, we multiply the number outside of the parenthesis to every number inside the parenthesis.
So we have:
![\sf-6(8+12)](https://tex.z-dn.net/?f=%5Csf-6%288%2B12%29)
Answer:
b= 2x²; c = 4; 3 = 3 ; g = 6x
Step-by-step explanation:
![\textbf{(1)}\\\sqrt{50{x}^{2} } = \sqrt{25\times2x^{2}} = 5\times \mathbf{\sqrt{2x^{2}}}\\\textbf{b = 2x}^{2}\\\\\textbf{(2)}\\\sqrt{32x} = \sqrt{16 \times 2x} = \mathbf{4}\times \sqrt{2x}\\\textbf{c = 4}\\\\\textbf{(3)}\\\sqrt{18n} = \sqrt{9 \times 2n} = \mathbf{3}\times \sqrt{2n}\\\textbf{e = 3}\\\\\textbf{(4)}\\\sqrt{72x^{2}} = \sqrt{36 \times 2x^{2}} = 6\times \sqrt{2} \times x\\= \mathbf{6x}\sqrt{2}\\\textbf{g = 6x}](https://tex.z-dn.net/?f=%5Ctextbf%7B%281%29%7D%5C%5C%5Csqrt%7B50%7Bx%7D%5E%7B2%7D%20%7D%20%3D%20%5Csqrt%7B25%5Ctimes2x%5E%7B2%7D%7D%20%3D%205%5Ctimes%20%5Cmathbf%7B%5Csqrt%7B2x%5E%7B2%7D%7D%7D%5C%5C%5Ctextbf%7Bb%20%3D%202x%7D%5E%7B2%7D%5C%5C%5C%5C%5Ctextbf%7B%282%29%7D%5C%5C%5Csqrt%7B32x%7D%20%3D%20%5Csqrt%7B16%20%5Ctimes%202x%7D%20%3D%20%5Cmathbf%7B4%7D%5Ctimes%20%5Csqrt%7B2x%7D%5C%5C%5Ctextbf%7Bc%20%3D%204%7D%5C%5C%5C%5C%5Ctextbf%7B%283%29%7D%5C%5C%5Csqrt%7B18n%7D%20%3D%20%5Csqrt%7B9%20%5Ctimes%202n%7D%20%3D%20%5Cmathbf%7B3%7D%5Ctimes%20%5Csqrt%7B2n%7D%5C%5C%5Ctextbf%7Be%20%3D%203%7D%5C%5C%5C%5C%5Ctextbf%7B%284%29%7D%5C%5C%5Csqrt%7B72x%5E%7B2%7D%7D%20%3D%20%5Csqrt%7B36%20%5Ctimes%202x%5E%7B2%7D%7D%20%3D%206%5Ctimes%20%5Csqrt%7B2%7D%20%5Ctimes%20x%5C%5C%3D%20%5Cmathbf%7B6x%7D%5Csqrt%7B2%7D%5C%5C%5Ctextbf%7Bg%20%3D%206x%7D)
#2. 32 3/4 - 12 1/2 =
= 32 3/4 - 12 2/4 =
= 20 1/4
#3. 517 37/ 50 + 312 3/100 =
= 517 74/100 + 312 3/100 =
= 829 77/100
#4. 632 16/25 + 32 3/10 =
= 632 32/50 + 32 15/50 =
= 664 47/50
#5. 421 3/50 - 212 9/10 =
= 421 3/50 - 212 45/50 =
= 208 4/25