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
The answer to your equation: 2/7 x 42 = 12
12 is the correct answer
Answer:
Let the height of the larger box = h
and length and width of the larger box = l and w , repectively
Now , Let find the volume of the larger box
Volume = length * width * height
So Volume of the larger box = l*w*h = lwh
Now the question says
the height of the smaller box is 80% of the height of the larger box
It means
Height of the smaller box = 80% of h = 0.80*h = 0.80h
and the other two dimensions are same so it means length and width of the smaller box = l and w
so, Volume of the smaller box = l*w*0.80h = 0.80lwh
So the Difference in the volume of the two boxes = Volume of larger box - Volume of smaller box
therefore , Difference in the Volume of two boxes = lwh - 0.80 lwh = 0.20lwh
Step-by-step explanation:
N+15=M N+M=-47 -47-15=-62 -62/2=-31 -31+-16=-47, therefore the answer is N=-31 and M=-16
Answer:
g= 6
j = 2
r= 4
Step-by-step explanation:
Gummy bears = $1.50 per pound
Jelly beans = $1.00 per pound
Runt = $1.00 per pound
Total cost of the mixture = $15.00
Let
g = quantity of gummy bears
j = quantity of jelly beans
r = quantity of runts
g + j + r=12 (1)
1.5g + 1.0j + 1.0r = 15 (2)
three times as many gummy bears as jelly beans.
g=3j
Substitute g=3j into 1
g + j + r = 12
3j + j + r =12
4j + r =12 (3)
Substitute g=3j into 2
1.5g + 1.0j + 1.0r = 15
1.5(3j) + 1.0j + 1.0r =15
4.5j + 1.0j + 1.0r = 15
5.5j + 1.0r =15 (4)
4j + r =12 (3)
5.5j + 1.0r =15 (4)
Subtract (3) from (4)
5.5j - 4j = 15-12
1.5j = 3
Divide both sides by 1.5
j = 3/1.5
= 2
j = 2
Substitute j = 2 into (3)
4j + r =12
4(2) + r =12
8 + r = 12
r= 12-8
r= 4
Substitute j=2 and r= 4 into (1)
g + j + r=12
g + 2 + 4 = 12
g + 6 = 12
g = 12-6
=6
g=6
g= 6
j = 2
r= 4
