Answer:
(25x9x4)(x)
Step-by-step explanation:
They both equal 900x
Answer:
18
Step-by-step explanation:
24 ÷ 4 = 6 6 × 3 =18
So I got 10 bows he can make
7 1/2 = 15/2 = 7.5
3/4 = .75
1) 7.50-.75=6.75
2) 6.75-.75=6.00
3) 6.00-.75=5.25
4) 5.25-.75=4.50
5) 4.50-.75=3.75
6) 3.75-.75=3.00
7) 3.00-.75=2.25
8) 2.25-.75=1.50
9) 1.50-.75=.75
10) .75-.75=0
10 times total
Problem 6
It's not clear what the instructions are, but I'm assuming your teacher wants you to rationalize the denominator.
If so, then we could have these steps
![\sqrt{\frac{3\text{x}}{7}}\\\\\frac{\sqrt{3\text{x}}}{\sqrt{7}}\\\\\frac{\sqrt{3\text{x}}*\sqrt{7}}{\sqrt{7}*\sqrt{7}}\\\\\frac{\sqrt{3\text{x}*7}}{(\sqrt{7})^2}\\\\\frac{\sqrt{21\text{x}}}{7}\\\\](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B3%5Ctext%7Bx%7D%7D%7B7%7D%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B3%5Ctext%7Bx%7D%7D%7D%7B%5Csqrt%7B7%7D%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B3%5Ctext%7Bx%7D%7D%2A%5Csqrt%7B7%7D%7D%7B%5Csqrt%7B7%7D%2A%5Csqrt%7B7%7D%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B3%5Ctext%7Bx%7D%2A7%7D%7D%7B%28%5Csqrt%7B7%7D%29%5E2%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B21%5Ctext%7Bx%7D%7D%7D%7B7%7D%5C%5C%5C%5C)
In the third step, I multiplied top and bottom by
so that the denominator can get rid of the square root.
<h3>Answer:
![\frac{\sqrt{21\text{x}}}{7}\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B21%5Ctext%7Bx%7D%7D%7D%7B7%7D%5C%5C%5C%5C)
</h3>
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Problem 7
We'll follow the same idea for this problem.
![\sqrt{\frac{5m^2}{2}}\\\\\frac{\sqrt{5m^2}}{\sqrt{2}}\\\\\frac{\sqrt{5m^2}*\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\\frac{\sqrt{5m^2*2}}{(\sqrt{2})^2}\\\\\frac{\sqrt{10m^2}}{2}\\\\\frac{\sqrt{10}*\sqrt{m^2}}{2}\\\\\frac{m\sqrt{10}}{2}\\\\](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B5m%5E2%7D%7B2%7D%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B5m%5E2%7D%7D%7B%5Csqrt%7B2%7D%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B5m%5E2%7D%2A%5Csqrt%7B2%7D%7D%7B%5Csqrt%7B2%7D%2A%5Csqrt%7B2%7D%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B5m%5E2%2A2%7D%7D%7B%28%5Csqrt%7B2%7D%29%5E2%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B10m%5E2%7D%7D%7B2%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B10%7D%2A%5Csqrt%7Bm%5E2%7D%7D%7B2%7D%5C%5C%5C%5C%5Cfrac%7Bm%5Csqrt%7B10%7D%7D%7B2%7D%5C%5C%5C%5C)
Where m is nonnegative.
In the second to last step, I split up the root so I could use the rule ![\sqrt{x^2} = x \text{ when } x \ge 0](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%7D%20%3D%20x%20%5Ctext%7B%20when%20%7D%20x%20%5Cge%200)
<h3>Answer:
![\frac{m\sqrt{10}}{2}\\\\](https://tex.z-dn.net/?f=%5Cfrac%7Bm%5Csqrt%7B10%7D%7D%7B2%7D%5C%5C%5C%5C)
</h3>
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Problem 8
![\sqrt{\frac{12\text{x}^3}{5}}\\\\\frac{\sqrt{12\text{x}^3}}{\sqrt{5}}\\\\\frac{\sqrt{12\text{x}^3}*\sqrt{5}}{\sqrt{5}*\sqrt{5}}\\\\\frac{\sqrt{12\text{x}^3*5}}{(\sqrt{5})^2}\\\\\frac{\sqrt{60\text{x}^3}}{5}\\\\\frac{\sqrt{4\text{x}^2*15\text{x}}}{5}\\\\\frac{\sqrt{4\text{x}^2}*\sqrt{15\text{x}}}{5}\\\\\frac{\sqrt{(2\text{x})^2}*\sqrt{15\text{x}}}{5}\\\\\frac{2x\sqrt{15\text{x}}}{5}\\\\](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B12%5Ctext%7Bx%7D%5E3%7D%7B5%7D%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B12%5Ctext%7Bx%7D%5E3%7D%7D%7B%5Csqrt%7B5%7D%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B12%5Ctext%7Bx%7D%5E3%7D%2A%5Csqrt%7B5%7D%7D%7B%5Csqrt%7B5%7D%2A%5Csqrt%7B5%7D%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B12%5Ctext%7Bx%7D%5E3%2A5%7D%7D%7B%28%5Csqrt%7B5%7D%29%5E2%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B60%5Ctext%7Bx%7D%5E3%7D%7D%7B5%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B4%5Ctext%7Bx%7D%5E2%2A15%5Ctext%7Bx%7D%7D%7D%7B5%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B4%5Ctext%7Bx%7D%5E2%7D%2A%5Csqrt%7B15%5Ctext%7Bx%7D%7D%7D%7B5%7D%5C%5C%5C%5C%5Cfrac%7B%5Csqrt%7B%282%5Ctext%7Bx%7D%29%5E2%7D%2A%5Csqrt%7B15%5Ctext%7Bx%7D%7D%7D%7B5%7D%5C%5C%5C%5C%5Cfrac%7B2x%5Csqrt%7B15%5Ctext%7Bx%7D%7D%7D%7B5%7D%5C%5C%5C%5C)
where x is nonnegative.
<h3>Answer:
![\frac{2x\sqrt{15\text{x}}}{5}\\\\](https://tex.z-dn.net/?f=%5Cfrac%7B2x%5Csqrt%7B15%5Ctext%7Bx%7D%7D%7D%7B5%7D%5C%5C%5C%5C)
</h3>
Answer:
48 percent!
Step-by-step explanation: