Answer:
5![\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B6%7D)
Step-by-step explanation:
Using the rule of radicals
×
⇔ ![\sqrt{ab}](https://tex.z-dn.net/?f=%5Csqrt%7Bab%7D)
Given
![\sqrt{150}](https://tex.z-dn.net/?f=%5Csqrt%7B150%7D)
= ![\sqrt{25(6)}](https://tex.z-dn.net/?f=%5Csqrt%7B25%286%29%7D)
=
× ![\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B6%7D)
= 5![\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B6%7D)
<h3>2) Rationalize the denominator:</h3>
![\sf \sqrt{\dfrac{15}{2} } = \dfrac{\sqrt{15} }{\sqrt{2} }](https://tex.z-dn.net/?f=%5Csf%20%20%5Csqrt%7B%5Cdfrac%7B15%7D%7B2%7D%20%7D%20%20%3D%20%5Cdfrac%7B%5Csqrt%7B15%7D%20%7D%7B%5Csqrt%7B2%7D%20%7D)
[ apply radical rule: √a × √b = √ab ]
[multiply the integers] [note: √2 × √2 is 2]
<h3>3) Solve by taking the square root:</h3>
![\sf x^2 -4 = 0 \\\\\sqrt{x^2-4} = 0\\ \\x^2 - 2^2 = 0^2 \ \quad \quad \quad \leftarrow third \ step \ should \ be \ this\\\\ (x-2)(x + 2) = 0 \\\\x = 2, x = -2 \\ \\ x = \pm 2](https://tex.z-dn.net/?f=%5Csf%20%20%20x%5E2%20-4%20%3D%200%20%5C%5C%5C%5C%5Csqrt%7Bx%5E2-4%7D%20%20%3D%200%5C%5C%20%5C%5Cx%5E2%20-%202%5E2%20%3D%200%5E2%20%20%20%5C%20%5Cquad%20%5Cquad%20%5Cquad%20%20%5Cleftarrow%20%20third%20%5C%20step%20%20%5C%20should%20%5C%20be%20%5C%20this%5C%5C%5C%5C%20%28x-2%29%28x%20%2B%202%29%20%3D%200%20%5C%5C%5C%5Cx%20%3D%202%2C%20x%20%3D%20-2%20%5C%5C%20%5C%5C%20x%20%3D%20%5Cpm%202)
Answer:
$2 640
Step-by-step explanation:
Principal = $16 500; Time = 2 years Rate = 8%
Simple Interest = P × R × T/100
= $16 500 × 8 × 2/100
=$264 000/100
Simple Interest = $2 640
Micas conclusion is incorrect. There were 30 high school students surveyed and 15 of them said that they could drive, and out of the 60 college students half of them also said they could drive. In both situations, half of the groups were able to drive which shows that his conclusion of knowing that a person is in college means they are more likely to drive is incorrect.
Answer:
y = 4
Step-by-step explanation:
In this situation, because all the angles have the same arc mark, they must have the same measure which means that the triangle is equiangular. Therefore, you can use the definition of an equilateral triangle which states that if the triangle is equiangular, it must be equilateral which means that all sides are the same. This is because x + x + x = 180 → 3x = 180 → x = 60. When you learn trigonometry, you will realize that the proportion of sides corresponds to the angles. Or you could experiment and you may realise that if the angles of the triangles are all 60° then you can only form a triangle where the sides are all equal. If all sides are the same, then 9y - 3 = 7y + 5
So if 9y - 3 = 7y + 5, then
9y - 3 = 7y + 5 →
[subtract 7y from both sides]
9y - 7y - 3 = 7y - 7y + 5 →
2y - 3 = 5 →
[add 3 to both sides]
2y - 3 + 3 → 5 + 3 → 2y = 8 →
[divide both sides by 2]
y = 4