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Reika [66]
2 years ago
14

16. Juice You bought 12 1-gallon bottles of apple and orange juice for a

Mathematics
1 answer:
const2013 [10]2 years ago
7 0

Answer:

Step-by-step explanation:

let x be apple juice and y be orange juice

12 = x + y

x = 12 - y


15 = 1x + 1.5y

x = 15 - 1.5y

set the equations as equal

12 - y = 15 - 1.5y

solve for y

12 + .5y = 15

.5y = 3

y = 6,  you bought 6 bottles of orange juice

so, 12 = x + 6 , x = 6 , you bought 6 bottles of apple juice

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1st. (2 root 2 + root 3 ) ( 2 root 3 - root 2)
satela [25.4K]

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

8 0
2 years ago
789/548x-89/887=688/8724 find x
Olin [163]

\frac{789}{548}x- \frac{89}{887}=\frac{688}{8724}

first we try to semplify as much as possible the fractions.

First we decompose the numbers

789 = 3 * 263

548 = 2 * 2 * 137 = 2^2

they have nothing in common, so the first fraction remains so

89 = 89 (prime number)

887 = 887 (prime number)

they have nothing in common, so the second one remains so

688 = 2 * 2 * 2 * 2 * 43 = 2^4 * 43

8724 = 2 * 2 * 3 * 727 = 2^2 * 3 * 727

they have 2^2 (=4) in common, so the numerator and the denominator can be devided by 4

\frac{688}{8724}= \frac{688:4}{8724:4}=\frac{172}{2181}

so:

\frac{789}{548}x- \frac{89}{887}=\frac{172}{2181}

now we calculate the common denominator

take the scomposition:

548 = 2^2 * 137

887 = 887

2181 = 3 * 727

take every number one time

so the common denominator is 2^2 * 137 * 887 * 727 * 3 = 1'060'131'756

now calculate every single numerator: first we divide each denominator by the common denominator, then we moltiply the result with each numerator

first fraction: 789/548

1060131756 / 548 = 1934547

1934547 * 789 = 1526357583

second fraction: 89/887

1060131756 / 887 = 1195188

1195188 * 89 = 106371732

third one: 172/2181

1060131756 / 2181 = 486076

486076 * 172 = 83605072

now we can delete the common denominator

1526357583x - 106371732 = 83605072

solve it

1526357583x = 83605072 + 106371732

1526357583x = 189976804

x = 1526357583 / 189976804

decompose

1526357583 = 887 * 3 * 3 * 727 * 263

189976804 = 137 * 2 * 2 * 211 * 53 * 31

nothing in common

x = 1526357583 / 189976804

8 0
3 years ago
Ms. Sublett's math class is putting three
givi [52]
Option 4 is your answer
4 0
2 years ago
What's the dot product of u = <-9, 4> and v = <1,3>? Thanks!
Leno4ka [110]
\langle-9,4\rangle\cdot\langle1,3\rangle=(-9)(1)+(4)(3)=-9-12=-21
8 0
3 years ago
A cinema has three screens.
lidiya [134]

Answer:

200 are on screen 1

125 are on screen 2

175 went to screen 3

Step-by-step explanation:

10% is 50 so 50 x 4 =200

25% of 500 is 12, divide 500 by 4

35% is 25% + 10% = 125 + 50 = 175

7 0
2 years ago
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