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masha68 [24]
3 years ago
9

Bill ate 1/4 pound of trail mix on his first break during a hiking trip. On his second break, he ate 1/6 pound. How many pounds

of trail mix did he eat during both breaks? Explain.
Mathematics
2 answers:
dybincka [34]3 years ago
8 0
He ate 5/12 in all because 1/4 and 1/6 are equal to 3/12 and 2/12 and the sum of those two is 5/12
tino4ka555 [31]3 years ago
7 0
Since we know that he ate 1/4 pound one time, and 1/6 another time, we have to add up the fractions. 

1/4+1/6

LCM of 4 and 6 = 12

3/12 + 2/12 

Add the numerators: 

5/12

So, he ate 5/12 of a pound of bars in both breaks. 

Hope this helps!
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2x-5y+5z=-10<br> 5x-4y+3z=-19<br> X-y+5z=17
yarga [219]

Answer:

x = -125/71 , y = 448/71 , z = 356/71

Step-by-step explanation:

Solve the following system:

{2 x - 5 y + 5 z = -10 | (equation 1)

5 x - 4 y + 3 z = -19 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Swap equation 1 with equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

2 x - 5 y + 5 z = -10 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Subtract 2/5 × (equation 1) from equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - (17 y)/5 + (19 z)/5 = (-12)/5 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Multiply equation 2 by 5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

x - y + 5 z = 17 | (equation 3)

Subtract 1/5 × (equation 1) from equation 3:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x - y/5 + (22 z)/5 = 104/5 | (equation 3)

Multiply equation 3 by 5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x - y + 22 z = 104 | (equation 3)

Subtract 1/17 × (equation 2) from equation 3:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+(355 z)/17 = 1780/17 | (equation 3)

Multiply equation 3 by 17/5:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+71 z = 356 | (equation 3)

Divide equation 3 by 71:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y + 19 z = -12 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Subtract 19 × (equation 3) from equation 2:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x - 17 y+0 z = (-7616)/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Divide equation 2 by -17:

{5 x - 4 y + 3 z = -19 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Add 4 × (equation 2) to equation 1:

{5 x + 0 y+3 z = 443/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Subtract 3 × (equation 3) from equation 1:

{5 x+0 y+0 z = (-625)/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Divide equation 1 by 5:

{x+0 y+0 z = (-125)/71 | (equation 1)

0 x+y+0 z = 448/71 | (equation 2)

0 x+0 y+z = 356/71 | (equation 3)

Collect results:

Answer: {x = -125/71 , y = 448/71 , z = 356/71

5 0
3 years ago
Aubrey's coach asks her to bring 5 liters of water to practice.
fenix001 [56]

Answer:

C

Step-by-step explanation:

This is because a liter is 1000 milliliters, so multiplying the amount of liters to the milliliters you would get 5000, you would then divide that by 500  since a bottle would contain that much, giving you 10 bottles

8 0
2 years ago
Solve for x<br> 10 + 4x = 5(z - 6) + 33
gogolik [260]

Answer:

Step-by-step explanation:

X=5/4z - 7/4

5 0
3 years ago
Read 2 more answers
Express the product in simplest form.
Romashka [77]
\frac{8}{2x+8} *  \frac{ x^{2}-16 }{4}

1. Cross cancel
\frac{4}{2x+8}* \frac{ x^{2} -16}{1}

2. Multiply numerators
4*x²-16 = 4x²-64

3. Multiply denominators
2x+8*1 = 2x+8

\frac{4 x^{2} -64}{2x+8}

4. Divide
\frac{4 x^{2} -64}{2x+8} = 2x-8

5. Simplify
2(x-4)

Answer is 2(x - 4)
4 0
3 years ago
HELP PLZ!!!i cant figure this out and dont worry about what else im typin it wont let me continue without having 20 word typed s
morpeh [17]

Answer:

The length is 42 inches and the width is 14 inches

Step-by-step explanation:

You know the width is 1/3 of the length, and the length is basically the longer side of a rectangle. The width is y-4, so multiply using distributive property to get 3y-12.

You now know that the 2y+6 is equal to 3y-12, so you add 12 to both sides using additive property of addition to get 2y+18=3y.

Then you subtract 2y from both sides to get the unit value of y.

Y is equal to 18.

Then you can plug 18 into the y's to get

2(18)+6 which is 36+6 = 42

18-4   = 14

There you go.

The length is the longer side which is 42 inches and the width is 14 inches

Hope this helps!

6 0
3 years ago
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