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2 years ago

Solve for x: 7x-3/5x-2 = -2

Mathematics

1 answer:

VMariaS [17]2 years ago

4 0

Step-by-step explanation:

<h3>★ Solution:-</h3>

$\sf \leadsto \dfrac{7x - 3}{5x - 2} = -2$

$\sf \leadsto 7x - 3 = -2(5x - 2)$

$\sf \leadsto 7x - 3 = -10x + 4$

$\sf \leadsto 7x + 10x = 4 + 3$

$\sf \leadsto 17x = 7$

$\sf \leadsto x = \dfrac{7}{17}$

Hence the value of x is 7/17

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Please I’ve attached the question can you help me

Andreyy89

Answer:

1. n[(A U B) - C] = {23, 24, 27, 29, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 61, 63}

2. n[(A - B) U C] = n[A U C] = {6, 10, 12, 15, 20, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 60, 61}

3. D. I, II and III.

Step-by-step explanation:

U = {21, 22, 23, ..., 64}

A prime number is a number that can be divided only by 1 and itself.

A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

B = {24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63}

C = {6, 10, 12, 15, 20, 30, 60}

1. Find n[(A U B) - C]

n(A U B) = {23, 24, 27, 29, 30, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 60, 61, 63}

n[(A U B) - C] = {23, 24, 27, 29, 30, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 60, 61, 63} - {6, 10, 12, 15, 20, 30, 60}

Since only 30 and 60 are common to n(A U B) and C, we therefore remove them it and have:

n[(A U B) - C] = {23, 24, 27, 29, 33, 36, 37, 39, 41, 42, 43, 45, 47, 48, 51, 53, 54, 57, 59, 61, 63}

2. Find n[(A - B) U C]

To get n(A - B) we remove all the elements of B in A. Since there are no common elements between A and B, we therefore have:

A - B = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

C = {6, 10, 12, 15, 20, 30, 60}

Therefore, we have:

n[(A - B) U C] = n[A U C] = {6, 10, 12, 15, 20, 23, 29, 30, 31, 37, 41, 43, 47, 53, 59, 60, 61}

3. Which of the following is/are true?

I. A ∩ B = A ∩ C

A ∩ B = ∅

A ∩ C = ∅

Therefore, A ∩ B = A ∩ C is true.

II. A - B = A - C

A - B = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

A - C = A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

Therefore, A - B = A - C is true.

III. A ∩ (B ∪ C) = ∅

A = {23, 29, 31, 37, 41, 43, 47, 53, 59, 61}

B U C = {6, 10, 12, 15, 20, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63}

Therefore, A ∩ (B ∪ C) = ∅ is true.

Therefore, the correct option is D i.e. I, II and III are true.

4 0

3 years ago

The Big Telescope Company sells circular mirrors. Their largest mirrors have radii of 5 meters and their smallest mirrors have r

pogonyaev

Answer: 1:5

Step-by-step explanation:

Given: The cost of every mirror is proportional to the cube of the mirror's radius.

i.e. $\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{(\text{radii of smallest mirror}^3)}{\text{(radii of largest mirror)}^3}$

Their largest mirrors have radii of 5 meters and their smallest mirrors have radii of 1 meter.

Then,

$\dfrac{\text{Cost of smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{1^3}{(5)^3}=\dfrac{1}{125}$

The ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors will be:

$\dfrac{\text{Cost of 25 smallest mirror}}{\text{Cost of largest mirror}}=\dfrac{25\times 1}{125}=\dfrac{1}{5}$

Hence, the ratio of the total cost of 25 of the company's smallest mirrors to the cost of one of the company's largest mirrors = 1:5 .

5 0

2 years ago

Which form most quickly reveals the vertex?

Jet001 [13]

Answer:

Step-by-step explanation:

A will give you the roots (the x intercepts) just by reading the numbers and doing a small adjustment.

x + 1 = 0

x = - 1 So one of the roots is (-1,0)

x + 5= 0

x = - 5 The other root is (-5,0)

A is not the answer.

I have graphed B so that you can see that A is true. See below, Even so, B is in standard form and it is not the answer.

The answer is C. The vertex is at 2,27

x - 2 = 0

x = 2

The maximum value is located at 27 which is just read.

That point (2,27) is plotted on the graph.

6 0

2 years ago

Please show all work thanks

Luba_88 [7]

What grade r u in omg I would help but I don't understand I either

8 0

3 years ago

On a certain hot summer's day, 166 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for

Shalnov [3]

Answer:

134 children and 32 adults.

Step-by-step explanation:

This solution is based on guess and check, I don't know if you know this method but it's used all the time for questions like these.

Or the faster way called assumption, but it is much harder and might get careless easily.

So let's do guess and check.

Predict how much adults and children would be there.

Let's say 76 children and 90 adults.

76 x 1.50 = 114

90 x 2.00 = 180

Total for first attempt = 180 + 114 = 294

The total amount is too much, so let's lower the number of adults and increase the number of children.

Let's say 85 children and 81 adults.

85 x 1.50 = 127.5

81 x 2.00 = 162

162 + 127.5 = 289.5

Again it's too much.

Let's make it 120 children and 46 adults.

120 x 1.50 = 180

46 x 2.00 = 92

180 + 92 = 272

It's too much but almost there, let's make another one.

140 children and 32 adults.

140 x 1.50 = 210

32 x 2.00 = 64

Too much children, lower it down to 132 children and 34 adults.

132 x 1.50 = 198

34 x 2.00 = 68

198 + 68 = 266

As you can see we're quite close.

134 children and 32 adults.

134 x 1.50 = 201

32 x 2.00 = 64

201 + 64 = 265

So we finally got the answer.

7 0

2 years ago

Solve for x: 7x-3/5x-2 = -2​

Solve for x: 7x-3/5x-2 = -2