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svp [43]
3 years ago
5

Which equations have infinitely many solutions?

Mathematics
1 answer:
igomit [66]3 years ago
8 0

Answer:

4(x - 1) = 4x - 4

3x + 6 = 3(x + 2)

Step-by-step explanation:

The first equation is

5x - 1 = 5x + 1

We simplify to get;

- 1 = 1

This is not true, therefore this equation has no solution.

The second equation is

3x - 1 = 1 - 3x

Combine like terms:

3x + 3x = 1 + 1

6x = 2

x =  \frac{1}{3}

This has a unique solution.

The 3rd equation is

7x - 2 = 2x - 7

Group similar terms:

7x - 2x =  7 + 2 \\ 5x = 9 \\ x  =  \frac{9}{5}

The 4th equation is :

4(x - 1) = 4x - 4

4x - 4= 4x - 4 \\ x = x

This is always true. The equation has infinite solution.

The 5th equation is:

3x + 6 = 3(x + 2) \\ 3x + 6 = 3x + 6 \\ x = x

This also has infinite solution

The 6th equation is

3(x - 4) = 4(x - 3) \\ 3x - 12 = 4x - 12 \\ 3x - 4x =  - 12 + 12 \\ x = 0

It has a unique solution.

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Ms. Vicker is trying to save enough money to buy her wedding dress at the cost of $1,200. She has $600 saved from her summer sch
sattari [20]

Answer:

The inequality to determine how many hours Ms. Vicker must tutor to have enough money for the dress.

$600 + 10x ≥ $1200

Step-by-step explanation:

From the question, we are told that:

Ms. Vicker is trying to save enough money to buy her wedding dress at the cost of $1,200. She has $600 saved from her summer school job.

The amount to make up to complete her wedding dress = $1200 - $600

= $600

To make the rest of the money, Ms. Vicker plans to tutor for Sylvan at a cost of $10 per hour.

= Number of hours Ms vicker must tutor Sylvan to make $600 is calculated as:

$600/$10 = 60 hours

The inequality to determine how many hours Ms. Vicker must tutor to have enough money for the dress is written as

$600 + 10x ≥ $1200

4 0
3 years ago
Sahana sells two products for ₹. 8000 each gaining 8% on one and losing 6% on the other. Find her gain or loss percent in the wh
Margaret [11]

Based on the information given the gain or loss percent on the whole transaction​ is 1%.

<h3>Gain or loss percent: </h3>

First step is to calculate the profit on the whole transaction

Profit=(8%×8,000)-(6%×8,000)

Profit=$640-$480

Profit=$160

Now let calculate the gain or loss percentage on the whole transaction

Gain or loss percentage=160/(8000+8000)×100

Gain or loss percentage=160/16000×100

Gain or loss percentage=1%

Inconclusion the gain or loss percent on the whole transaction​ is 1%.

Learn more about gain or loss here:brainly.com/question/25278228

5 0
2 years ago
Find the value of x when <br> 2x = 64
Firlakuza [10]
64/2= 32

x=32

answer is 32


4 0
3 years ago
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Tran is solving the quadratic equation 2x2 – 4x – 3 = 0 by completing the square. His first four steps are shown in the table.
natulia [17]

The solution to the quadratic equation 2x² - 4x - 3 = 0 is x = 1 ± √2.5

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Solving the polynomial using completing the square:

2x² - 4x - 3 = 0

First divide through by 2:

x² - 2x - 3/2 = 0

add 3/2 to both sides:

x² - 2x - 3/2 + 3/2 = 0 + 3/2

x² - 2x = 3/2

add the square of half the coefficient x to both sides:

x² - 2x + 1 = 3/2 + 1

(x - 1)² = 2.5

taking square root:

x - 1 = ±√2.5

x = 1 ± √2.5

The solution to the quadratic equation 2x² - 4x - 3 = 0 is x = 1 ± √2.5

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7 0
2 years ago
A unit rate is a rate in which
LuckyWell [14K]

Answer:A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Step-by-step explanation:

7 0
3 years ago
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