Answer:
1st: 3*root6 + 5
2nd: 35*root2 + 115
3rd: 24*root2 - 20*root6 + 15*root3 - 18
4th: 17*root6 - 38
5th: 13*root10 - 42
Step-by-step explanation:
To simplify these expressions we need to use the distributive property:
(a + b) * (c + d) = ac + ad + bc + bd
So simplifying each expression, we have:
1st.
(2 root 2 + root 3 ) ( 2 root 3 - root 2)
= 4*root6 - 2*2 + 2*3 - root6
= 3*root6 - 4 + 9
= 3*root6 + 5
2nd.
(root 5 + 2 root 10) (3 root 5 + root 10)
= 3 * 5 + root50 + 6*root50 + 2*10
= 15 + 5*root2 + 30*root2 + 100
= 35*root2 + 115
3rd.
(4 root 6 - 3 root 3) (2 root 3 - 5)
= 8*root18 - 20*root6 - 6*3 + 15root3
= 24*root2 - 20*root6 + 15*root3 - 18
4rd.
(6 root 3 - 5 root 2 ) (2 root 2 - root 3)
= 12*root6 - 6*3 - 10*2 + 5*root6
= 17*root6 - 18 - 20
= 17*root6 - 38
5th.
(root 10 - 3 ) ( 4 - 3 root 10)
= 4*root10 - 3*10 - 12 + 9*root10
= 13*root10 - 30 - 12
= 13*root10 - 42
This may be one of those questions that could take
more paper to ask than to answer.
Line-1 goes through (-4, 8) and (4,6) .
Its slope is (difference in 'y') / (difference in 'x')
Dif in 'y' = (6 - 8) = 2
Dif in 'x' = (4 - -4) = 8
Slope of Line-1 = 2/8 or 1/4
Line-2 goes through (-1, 1) and (3, 5)
Its slope is (difference in 'y') / (difference in 'x')
Dif in 'y' = (5 - 1) = 4
Dif in 'x' = (3 - -1) = 4
Slope of Line-2 = 4/4 = 1
Slope of Line-1 = 1/4
Slope of Line-2 = 4
The slopes of the lines are different.
They can't be parallel, and they can't be the same line.
They must intersect in one point, and only one point.
That means the pair of equations has exactly one (1) solution.
Answer:
Domain: x=(0,∞)
Range: f(x)=(-∞,∞)
Step-by-step explanation:
For the domain:
The square root of a number is defined in real numbers only for positive numbers.
For the range:
The square root of a number could be positive or negative with any restriction. For example, 
could be 5 or -5.
Answer:
375
Step-by-step explanation:
