Answer:
Step-by-step explanation:
12a)To rationalize the denominator, multiply the denominator and numerator by √5.
![\frac{15}{\sqrt{5}}=\frac{15*\sqrt{5}}{\sqrt{5}*\sqrt{5}}\\\\=\frac{15\sqrt{5}}{5}\\\\=3\sqrt{5}](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B%5Csqrt%7B5%7D%7D%3D%5Cfrac%7B15%2A%5Csqrt%7B5%7D%7D%7B%5Csqrt%7B5%7D%2A%5Csqrt%7B5%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B15%5Csqrt%7B5%7D%7D%7B5%7D%5C%5C%5C%5C%3D3%5Csqrt%7B5%7D)
b) (a+b)² = a² + 2ab + b²
(1 +√3)² = 1² + 2*1*√3 + (√3)²
= 1 + 2√3 + 3
= 4 + 2√3
a = 4 ; b =2
13) (a + b)(a - b) = a² - b²
![\frac{(6-\sqrt{5})(6+\sqrt{5})}{\sqrt{31}}=\frac{6^{2}-(\sqrt{5})^{2}}{\sqrt{31}}\\\\ =\frac{36-5}{\sqrt{31}}\\\\=\frac{31}{\sqrt{31}}\\\\=\frac{31*\sqrt{31}}{\sqrt{31}*\sqrt{31}}\\\\=\frac{31\sqrt{31}}{31}\\\\=\sqrt{31}](https://tex.z-dn.net/?f=%5Cfrac%7B%286-%5Csqrt%7B5%7D%29%286%2B%5Csqrt%7B5%7D%29%7D%7B%5Csqrt%7B31%7D%7D%3D%5Cfrac%7B6%5E%7B2%7D-%28%5Csqrt%7B5%7D%29%5E%7B2%7D%7D%7B%5Csqrt%7B31%7D%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B36-5%7D%7B%5Csqrt%7B31%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B31%7D%7B%5Csqrt%7B31%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B31%2A%5Csqrt%7B31%7D%7D%7B%5Csqrt%7B31%7D%2A%5Csqrt%7B31%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B31%5Csqrt%7B31%7D%7D%7B31%7D%5C%5C%5C%5C%3D%5Csqrt%7B31%7D)
Answer:
10
Step-by-step explanation:
Answer:
2.6 and 2.7
Step-by-step explanation:
The actual square root of 7 is 2.64 and that is between 2.6 and 2.7.
2x + 3y = 6
3y = - 2x + 6
y = -2/3x + 2....slope here is -2/3
A parallel line will have the same slope
y = mx + b
slope(m) = - 2/3
(-2,3)...x = -2 and y = 3
now we sub, we r looking for b, the y intercept
3 = -2/3(-2) + b
3 = 4/3 + b
3 - 4/3 = b
9/3 - 4/3 = b
5/3 = b
ur equation is : y = -2/3x + 5/3 (slope intercept form)
y = -2/3x + 5/3
2/3x + y = 5/3
2x + 3y = 5 (standard form)