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
If you're looking for the number of dogs (I'm assuming, you didn't specify), all you'd have to do is divide the number by two, then round down to find the number of dogs, then check your answer by adding that number and that number plus 5.
For example, yours would look like 125/6=62.5, and rounding down to 60.
Then check your answer by adding 60 and 65, the number of cats. 60+65=125.
There are 60 dogs inside the kennel.
Answer:
7, 8, 9, 10
Step-by-step explanation:
If Zoe worked 4 hours of babysitting at $7 per hour, she earned $28. Therefore, she must earn another $102 to earn at least $130. At $15 per hour, she must work a minimum of 7 hours clearing tables to make at least $102. This is fine since she can work another 10 hours before reaching her maximum of 14 total hours. Therefore, all possible values for the number of whole hours clearing tables that she must work to meet her requirements are 7, 8, 9, 10.
X = -4
y = 0
8x-12y+32 = 24
