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
<u>Picture 1:</u>
To figure this out, notice the pattern happening on x. It's simply counting to four, so the first blank is 1 and the next is 2.
The y coordinates seem to be going up by 9. 27 plus 9 is 36, so the answer to the fourth box is 36.
Another way to see how this is correct is to notice that the x is multiplying by 9 to get y. It works out as you look at it and plug it in!
<u>Picture 2:</u>
Yes, this is a proportional relationship. Since Dennis is adding 3 logs every hour, it is keeping a consistent pattern.
<u>Picture 3:</u>
If Jane is driving 60 miles per hour, the first hour she would've gone 60 miles. After a second hour, she would've gone 120 miles. Multiply 60 to your x coordinates to figure this out. You should get 60, 120, 180, and 240 for each box.
Answer:
18 lawns
Step-by-step explanation:
Expected sum = $515
Bonus for 1 day = $15
Bonus for 5 days = $15 × 5 = $75
Amount to be earned from mowing lawns in 5 days = $515 - $75 = $440
$25 ≡ 1 lawn
$440 ≡ 440 ÷ 25 = 17.6
The minimum number of lawns is 18.
<em>(Note that we take the minimum integer greater than 17.6. If he mows 17 lawns, his earning from 17 lawns = $425 + $75 = $500)</em>
Answer:
1816 feet below sea level
Step-by-step explanation:
The deeper the submarine goes or descends, the higher its height below sea level.
The ascending of the submarine will be taken as negative while the descending will be taken as positive
So, 671-218+1363 = 1816ft below sea level
Answer:
A
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original
scale factor = 
= 
= 3 → A
