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iogann1982 [59]
3 years ago
10

A recipe calls for 1/2 cup of celery,2 1/3 of water and 3/4 cups of carrots. What the combined amont of these three ingredients?

​
Mathematics
1 answer:
lys-0071 [83]3 years ago
7 0

Answer:

43/12

Step-by-step explanation:

First we must find a common denominator for all 3 fractions, 1/2 cup, 2 1/3 cup, and 3/4 cup all share 12 as a common denominator.

However, let's convert 2 1/3 cup into an improper fraction: there are 2 (3/3 cups) here multiply (3/3) and (2/1) you get 6/3. Finally, add the remaining 1/3 to 6/3 and you get 7/3.

Now, to get all these fractions to have the same common denominator.

(1/2) ×(6/6)=(6/12)

(7/3)×(4/4)=(28/12)

(3/4)×(3/3)=(9/12)

Add them all together and your answer is: (43/12)

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Solve the simultaneous equation 2p - 3q = 4, 3p + 2q = 9. <br>b. if 223= 87 find x<br>​
wolverine [178]

Answer:

Step-by-step explanation:

Given the simultaneous equation 2p - 3q = 4 and 3p + 2q = 9, to get the value of p and q we will use elimination method.

2p - 3q = 4 ...................... 1 * 3

3p + 2q = 9 ..................... 2 * 2

Multiplying equation 1 by 3 and 3 by 2:

6p - 9q = 12

6p + 4q = 18

Subtracting both equation

-9q-4q = 12-18

-13q = -6

q = -6/-13

q = 6/13

Substituting q = 6/13 into equation 2

2p - 3(6/13) = 4

2p - 18/13 = 4

2p = 4+18/13

2p = (52+18)/13

2p = 70/13

p = 70/26

p = 35/13

<em>Hence p = 35/13 and q = 6/13</em>

<em></em>

<em>b) </em>If if 223ₓ = 87 find x

Using the number base system and converting 223ₓ  to base 2 will give us;

223ₓ = 2*x² + 2*x¹ + 3*x⁰

223ₓ  = 2x²+2x+3

​

Substituting back into the equation, 2x²+2x+3 = 87

2x²+2x+3-87 = 0

2x²+2x-84 = 0

x²+x-42 = 0

On factorizing:

(x²+6x)-(7x-42) = 0

x(x+6)-7(x+6) = 0

(x+6)(x-7) = 0

x+6 = 0 and x-7 = 0

x = -6 and 7

<em>Hence the value of x is 7 (neglecting the negative value)</em>

5 0
3 years ago
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