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jasenka [17]
3 years ago
13

Which expression shows the result of applying the distributive property to 3(1/2x - 1/7)

Mathematics
1 answer:
AveGali [126]3 years ago
8 0
The answer is 3/2x - 3/7
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Question 1: Classify the system of equations and identify the number of solutions. 7x + 3y = 10 3y = 9 − 7x Answers: consistent,
Vladimir [108]

Answer:

1. The equations is inconsistent and has no solution

2. The equations is consistent and has no solution

3. A pen costs $1.50 and a notebook costs $2.00

Step-by-step explanation:

Solving 7x + 3y = 10 and 3y = 9 - 7x

7x + 3y = 10 --- Equation 1

3y = 9 - 7x --- Equation 2

Add 7x to both sides in equation 2

7x + 3y = 9 - 7x + 7x

7x + 3y = 9  --- Equation 3

Subtract equation 3 from 1

(7x + 3y = 10) - (7x + 3y = 9)

7x - 7x + 3y - 3y = 10 - 9

0 + 0 = 1

0 \neq 1

The equations is inconsistent and has no solution

Solving 3x + y = 4 and  12x + 4y = 16

3x + y = 4 -- Equation 1

12x + 4y = 16 ---- Equation 2

Make y the subject of formula in equation 1

y = 4 - 3x

Substitute 4 - 3x for y in equation 2

12x + 4(4 - 3x) = 16

12x + 16 - 12x = 16

Collect Like Terms

12x - 12x = 16 - 16

0 = 0

The equations is consistent and has no solution

3. Solving <em>John and Harry</em>

Given;

<em>Represent Pen with P and Notes with N</em>

John: 3P + 8N = 20.5

Harry: 4P + 5N = 16.00

Required

Find P and N

Make P the subject of formula in equation 2

4P = 16 - 5N

P = \frac{16 - 5N}{4}

Substitute P = \frac{16 - 5N}{4} in equation 1

3P + 8N = 20.5

3(\frac{16 - 5N}{4}) + 8N = 20.5

Open the bracket

\frac{48 - 15N}{4} + 8N = 20.5

Take LCM

\frac{48 - 15N + 32N}{4} = 20.5

\frac{48 + 17N}{4} = 20.5

Multiply both sides by 4

4 * \frac{48 + 17N}{4} = 20.5 * 4

48 + 17N = 82

Subtract 48 from both sides

48 - 48 + 17N = 82 - 48

17N = 82 - 48

17N = 34

Divide both sides by 17

17N/17 = 34/17

N = 34/17

N = 2

Substitute 2 for N in P = \frac{16 - 5N}{4}

P = \frac{16 - 5 * 2}{4}

P = \frac{16 - 10}{4}

P = \frac{6}{4}

P = 1.5

<em>Hence, a pen costs $1.50 and a notebook costs $2.00</em>

5 0
3 years ago
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