Answer:
Option A for part A and $79 for part B
Step-by-step explanation:
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
Answer:
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Step-by-step explanation:
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Let's say "n" is a natural number. {1,2,3,4,..} To ensure we have an even number we will multiply "n" by 2. Two times any number will make an even number.
consecutive even numbers are like; 2, 4, 6, 8, 10 .. etc. Add +2 to the previous number to get the next consecutive.
1st even number = 2n
2nd even number = 2n + 2
3rd even number = 2n + 4
twice the first number (2n) is 20 more then the second (2n + 2).
2(2n) = 2n + 2 + 20
4n = 2n + 22
4n - 2n = 22
2n = 22
n = 11
Now use n = 11 to find the 3 consecutive even numbers.
1st even number = 2(11) = 22
2nd even number = 2(11) + 2 = 24
3rd even number = 2(11) + 4 = 26
22, 24, 26
