Mathematics High School

## Answers

**Answer 1**

**Answer:**

x = -23

**Step-by-step explanation:**

3.5(x+20) = 6 + .75(x + 1) Multiply the terms inside the parentheses on the left by 3.5 and the parentheses on the left by .75

(3.5)x +(3.5)(20) = 6 + (.75)x +(.75)(1)

3.5x + 70 = 6 + .75x + .75 Combine the 6 and .75 on the right side

3.5x + 70 = 6.75 + .75x Subtract .75x from both sides of the equation

2.75x + 70 = 6.75 Subtract 70 from both sides of the equation

2.75x = -63.25 Divide both sides by 2.75

x = -23

**Check**

3.5(-23+20) = 6 + .75(-23 + 1)

3.5(-3) = 6 +.75(-22)

-10.5 = 6 +(-16.5)

-10.5 = -10.5

**Answer 2**

Answer:

x = -23

Step-by-step explanation:

3.5(x+20)=6+.75(x+1)

3.5x + 70 = 6 + .75x + .75

3.5x+70=.75x+6.75

2.75x+70=6.75

2.75=−63.25

divide^

x = -23

## Related Questions

how do you write 4.93 as a percentage

### Answers

**Answer:**

493%

**Step-by-step explanation:**

To convert a decimal to percentage, muiltiply the decimal by **100**.

the function f(x) is shown. the function g(x)= 2x - 6 compare slopes

### Answers

**Answer: **The slope of **f(x)** is **less than** the slope of **g(x)** because the slope of f(x) is -3

**Step-by-step explanation:**

**Define slope?**

The **slope** of a line is the **ratio** of the amount that y **increases** as x increases some amount. **Slope** tells you how steep a line is, or how much **y** increases as** x **increases. The slope is **constant** (the same) anywhere on the line.

**We can write:**

**m**=(y2-y1) / (x2-x1)

If,** **

**g(x) **= 2x - 6

The slope of **g(x), **m = 2

**Let, **x1=0

y1=2

x2=-1

Y2=1

**So,** we take (x1, y1) and (x2, y2) Then **consider** (0, 2) and (-1, 1)

Solve it:

**Replace **with x1, y1 and x2, y2

**m **= [1-(-2)/(-1)**]**

m=[(1+2) /(-1) ]

m=3/(-1)

**m**=-3

Thus, the **slope** of f(x) is **less than** the **slope** of g(x) because the slope of f(x) is -3.

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calculate the median number of close friends females had. show your work

### Answers

**Proportion **of females who have less than 3 close friend working note

**What is the statistical median?**

The midway number in a set of data is known as the **median**. The data should first be arranged and ranked from smallest to greatest. Divide the total number of observations by two to get the midway value. The value in that location is the median if there are an odd number of observations; otherwise, round the number up.

(a) Mean =1.04

Median=1

assuming the number of close friends as a whole value, our mean is also 1.

the distribution is roughly symmetric. because mean is approximately equal to median.

The explanation is provided in the image attached above;

Answer (b)Median number of a close friend for females is 1.

The calculation for median is provided in the image.

Answer(c) According to the shape of the distribution as we have observed from the data we can say that the median calculated for close friends of females is the same as the mean number of close friends for men.

Here we are not assuming the number of close friends in decimal(because it is not a continous variable).

Answer (d) P(less than 3) = P(0) + P(1) + P(2)

= 0.353+0.368+0.191=0.912

Proportion of females who have less than 3 close friend

working note:

m= mean =1.04

probability = ( e-m x mr) / r

P(0) = (e-1.04 x 1.040 ) / 0 = 0.353

P(1) = (e-1.04 x 1.041 ) / 1 = 0.368

P(2) = (e-1.04 x 1.042 ) / 2 = 0.191

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The complete question is -

The following table reports counts of the number of "close friends" reported by a sample of men and a sample of women. Number of close friends 0 1 2. 3 4 Total Number of male respondents 20 12 10 5 N 49 Number of female respondents 25 13 9 6 2 2 55 a. Is the distribution corresponding to the number of female respondents roughly symmetric, skewed to the right, skewed to the left? Explain. b. Calculate the median number of close friends for females. Round your answer to two decimal places c. Based on the shape of the distribution (and only accounting for the number of close friends for females), do you expect the median calculated in part b. to be greater than the mean, smaller than the mean, or about the same as the mean number of close friends for men? Do not calculate the mean. d. What is the proportion of females who say they have less than 3 close friends? Give an exact answer.

Suppose a vector y is orthogonal to vectors u and v. show that y is orthogonal to the vector u v.

### Answers

**Using Dot product**

Two vectors x and y are said to be orthogonal if their dot product is zero

⇒ x.y = 0

This is because **orthogonal vectors** are make an angle of 90° with each other and therefore **θ** becomes **90°**

Dot product is given by :

**x.y = x*y*cosθ** = xycos90°

∵cos90° is zero , x.y=0 for orthogonal vectors.

Let u,v,y be vectors in R

y is orthogonal to u and v

⇒ y.u = 0 and y.v=0

Now, we have to prove that y is orthogonal to (u+v)

The dot product of these vectors is given by:

y.(u+v) = y.u + y.v (Dot product is distributive) = 0 + 0 = 0

∵The dot product is zero , vector y and (u+v) are orthogonal

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(-3,4), (2, y); m=5

### Answers

**Answer:**

I think y is 29

**Step-by-step explanation:**

It's what the results gave me

Subtract:

-2 - 6 =

Submit

A

### Answers

-2-6= -8

you can try to do it like me on the number line will be easier for you

after finishing the prep work, gilberta and maría start removing wallpaper at the same time. gilberta removes the paper at a constant rate of 4.3\,\text{m}^24.3m 2 4, point, 3, start text, m, end text, squared per hour, while maría removes 3.4\,\text{m}^23.4m 2 3, point, 4, start text, m, end text, squared of paper per hour. gilberta's room starts with 35\,\text{m}^235m 2 35, start text, m, end text, squared of paper, and maría's room starts with 30.5\,\text{m}^230.5m 2 30, point, 5, start text, m, end text, squared of paper.

### Answers

The **inequality** that depicts when Gilberta has much more wallpaper left throughout her room than Mara does in hers using **linear** **functions** is:

** t< 5.**

A linear function is :

A **linear** **function** has a **straight** **line** as its **graph**. The following is the form of a **linear** **function**. a + bx = y = f(x). One independent variable but one dependent variable make up a linear function. X and Y are the **independent** and **dependent** **variables**, respectively.

According to the given information:

Following t hours, the **quantities** Gilberta and Maria have remaining are determined by:

G(t) = 35 - 4.3t.

M(t) = 30.5 - 3.4t.

Gilberta has more papers when:

G(t) > M(t).

So,

35 - 4.3t > 30.5 - 3.4t

-0.9t < -4.5

Multiplying by -1:

0.9t < 4.5

t < 4.5/0.9

t < 5.

The inequality is:

t < 5.

The **inequality** that depicts when Gilberta has much more wallpaper left throughout her room than Mara does in hers using **linear functions** is:

t< 5.

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an exterior angle of a triangle is 105 degree and one of its interior opposite angle is 35 degree less than the other .calculate the measure of both interior angle

### Answers

The value of both the** interior angles** of the** triangle** is calculated as 70° and 35°.

What is the exterior angle property?

If a triangle side is formed, the exterior angle made is equal to the sum of a 2 interior opposite angles.

When an equivalent angle is chosen to take at each **vertex** of the triangle, this same exterior angles always add up to 360°.Each exterior angle equals 180° minus the interior angle. If the relating interior angle is given, this formula can be used. Exterior angle = Sum of opposite angles on the inside. When the exterior angle's distant interior opposite angles are given, this formula can be used to find it.

Now, as per the given question;

The exterior angle of a triangle is 105°.

Let one of the interior angle is 'x'.

Then, the other interior angle is 35 degree less; x - 35°.

By the** exterior angle **property.

Sum of interior angles = exterior angle

x + x - 35° = 105°

2x = 105° + 35°

2x = 140°

x = 70°

The other** interior angle** is; x - 35°

= 70° - 35°

= 35°

Therefore, the two interior angles of the **triangles** are estimated as 70° and 35°.

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$5660

R= 11%

T= 9 months

### Answers

**Answer:**

this is a finance and it is an

Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbl

Which number sentence tells the story of how many marbles he had left ?

### Answers

The number of **marbles** left in the pocket after losing is 29 { after narrating the story in numerical sentences}

Given that Tran bought 25 **marbles** and put them in his pocket with 10 other **marbles**. He had a hole in his pocket and lost 6 **marbles**. and asked to narrate the story in numerical form

Total number of **marbles** Tran bought=25 marbles

Total number of **marble** Tran has before buying new **marbles**=10 marbles

Total number of **marbles** after buying new marbles=35 marbles

Given that he lost 6 **marbles** because of the hole in his pocket

Therefore, the Total number of **marbles** left=35-6

The total number of **marbles** left=29 marbles.

Therefore, The number of **marbles** left in the pocket after losing is 29 { after narrating the story in numerical sentences}

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round 184329 to the nearest 100

### Answers

**Answer:**

184300

**Step-by-step explanation:**

When rounding to the nearest anything, you look at the place 1 unit smaller. Here, we'd look at the tens place.

1843**2**9

Anything 5 or greater increases the value of the place 1 unit bigger. Here, we have a 2 in the tens place. That doesn't increase the 3 in the hundreds place, so we round *down* to 184300.

Mark is purchasing new tiles for his bathrooms. The home improvement store charges $48 for each box of tiles when three or fewer boxes are purchased, $45 for each box when 4 to 8 boxes are purchased, $42 for each box when 9 to 19 boxes are purchased, and $38 for each box when more than nineteen boxes are purchased.

a. Write a piecewise function describing the cost of the boxes of tile.

### Answers

Answer:

f(x)=

1. 48x when x < or = 3,

2. 45x when 4 < or = x < or = 8

3. 42x when 9 < or = x < or = 19

4. 38x when x > 19

Step-by-step explanation:

3 boxes or less = Cost of tiles = $48

4 - 8 boxes ; cost = $45

9 - 19 boxes ; cost = $42

> 19 boxes ; cost = $38

Find the 9th term of the arithmetic sequence 4x+44x+4, 9x+119x+11, 14x+18, 14x+18,...

### Answers

**Answer:**

T9=60

**Step-by-step explanation:**

step 1: solve for x

it is an arithmetic pattern,so the 1st difference is the common difference (d)

therefore...9x+199x+11-(4x+44x+4)=14x+18-(9x+199x+11)

128x+11-48x-4=14x+18-128x-11

80x+7=-144x+7

80x+144x=7-7

224x=0

224x/224=0/224

X=0

step 2: substitute for x

4(0)+44(0)+4=4[1st term]

9(0)+119(0)+11=11(2nd term)

14(0)+18=18(3rd term)

step 3:find the common difference

d=3rd term- 2nd term, 2nd term-1st term

3rd term-2nd term

18-11=7

2nd term-1st term

11-4=7

therefore...d=7

step 4:find the general formula

we use the formula Tn=a+(n-1)d to find the general formula/ nth term

where: Tn is the nth term

a is the first term

n is the number of term

d is the common difference

Tn=a+(n-1)d

=4+(n-1)7

=4+7n-7

=7n-3

step 5:find the 9th term

Tn=a+(n-1)d

=7n-3

=7(9)-3

=60

Which equation represents a linear function? Iready- Understand functions, Level H.

### Answers

**Answer:**

y = 4x + 5

**Step-by-step explanation:**

y = 4x + 5 is the only one that graphs a straight line

-5(7x-9)-6=144 what is the answer.

### Answers

Answer: x= -3

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

First you must start by multiplying the parentheses by -5. Once you do that, your equation comes out to -35x+45-6=144. Then you must combine like terms which comes out to -35x+39=144. After that you must get x by itself, so to do that subtract 39 from 144 which comes out to 105. Then you must do the opposite of multiplication and divide 105 by -35 which comes out to x=-3. Hope this helps

Those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called?

### Answers

Those methods involving the **collection**, **presentation**, and **characterization** of a set of data in order to properly describe the various features of that set of data are called **descriptive statistics**.

**Descriptive statistics:-** Descriptive statistics helps to **describe**, **summarize** and **organize** the set of data **efficiently** and in an **informative** way, so that it'll be easier to make conclusion about the data in order to make **rational decisions**. This method describes the characteristics of a dataset.

Example:- The average test score for the students of a particular class, gives descriptive sense of the typical scores.

There are three types of descriptive statistics-

**Univariate statistics:-** It summarizes only one variable at a time.**Bivariate statistics:-** It compares between two variables.**Multivariate statistics:- **It compares between more than two variables.

Thus we can conclude that, those methods involving the collection, presentation, and characterization of a set of data in order to properly describe the various features of that set of data are called **descriptive statistics**.

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What is the constant term in the following expression?

4x - 2y + 3

### Answers

The **constant** term in the expression is** 3.**

The** expression is 4x ₋ 2y ₊ 3.**

Here in this equation we have** variables **and **constants.**

variables = x and y whose coefficients are 4 and ₋2 respectively.

A** variable** is anything whose value can change and is **not fixed. **Typically, the letters x, y, z, etc. are used to indicate variables.

The above equation is in the form **ax ₊ by ₊ c **

An **object** with a** fixed** value in a circ*mstance is said to be a **constant. **We are aware that the constant is fixed, even though we do not know its exact value. In general,** constants **are represented by the letters a, b, c, p, q, etc. if their values are unknown or not given, and by particular numerical values) if their values are **known.**

Hence we get the** constant term **as **3.**

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Find the equation of this line.

y = [? ]x + [ ]

Simplify your answer and enter as an integer.

### Answers

**Answer:**

y =x + 3

**Step-by-step explanation:**

i gotchu

simplify: 12.9 - 2.8 - 7.2 + 9.1

A. 17.6

B. -6.2

C. 26.4

D. 12

Step by step answer pls

### Answers

First, subtract 12.9 - 2.8, which gives you 10.1

Then, get 10.1 and subtract it by 7.2, which gives you 2.9

Lastly, get 2.9 and add it to 9.1, which will give you your final answer 12

**Answer:**

D

**Step-by-step explanation:**

the simplification of 12.9 - 2.8 - 7.2 + 9.1 is 12

Draw the graph of y = x² – 4x + 3. Identify the intercepts (x and y), the vertex, and the axis of symmetry.

### Answers

**Answer:**

y-intercept : 3

x-intercepts are 1 and 2

Vertex is at (2,-1)

Axis of symmetry is at x = 2

**Step-by-step explanation:**

See attached graph.

The equation y = x² – 4x + 3 represents a parabola

y-intercept at is at B(0,3); y-intercept is **3**

x-intercept points at C(1,0) and D(3,0) so x-intercepts are **1** and **3**

The vertex is the lowest point on this parabola** (2-1)**

Axis of symmetry is a line passing through the vertex and dividing the parabola into two equal halves. This is the vertical line **x = 2**

Find the general solution to the differential equation put the problem in standard form. find the integrating factor, . find . use c as the unknown constant.

### Answers

**y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x}** is the general solution to the **differential equation **put the problem in standard form.

**What is meant by integrating factor?**

A function called an **integrating factor** is used to solve differential equations in mathematics. It is a function that can be made integrable by multiplying it by an ordinary differential equation. Ordinary **differential equations** are typically solved using this method. This factor is also applicable to multivariable calculus.

x² + 2xy + x . dy/dx = 0

x dy/dx + 2xy = [tex]- x^{v}[/tex]

[tex]\frac{dy}{dx} =+ 2y = -x[/tex]

[tex]left u(x) = e^{\int\limits^_ {} } 2dx = e^{2x}[/tex]

integration factor p(x) = u(x) = [tex]e^{2x}[/tex]

Now ,multiply [tex]e^{2x}[/tex] both sides

[tex]e^{2x} ( \frac{dy}{dx} + 2y ) = -x . e^{2x}[/tex]

[tex]e^{2x} \frac{dy}{dx} + 2e^{2x} . y = -x e^{2x}[/tex]

[tex]\frac{d}{dx} (e^{2x} .y) = -x e^{2x}[/tex]

integrate both sides

∫ [tex]d .( e^{2x} .y )[/tex] = ∫[tex]-xe^{2x} .dx[/tex]

[tex]e^{2x} .y = -\frac{e^{2x}}{2} . x + \frac{e^{2x}}{4} + c[/tex]

[tex]y = \frac{-x}{2 } + \frac{1}{4} + ce^-{2x}[/tex]

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The complete question is -

Find the general solution to the differential equation 2 dy X+ + 2xy + x dx = 0 Put the problem in standard form. Find the integrating factor, p(x) = 2x - Find y(x) Use C as the unknown constant.

Please answer the question in the picture above.

### Answers

1/4n and n/4 are correct

Siobhan’s team is solving the following equation: . Amalia says there are no solutions. Brian says there is one solution, but it is imaginary. Cristina says there are two solutions! Help them out. Determine the solution(s) and justify your answer. You may want to refer to the Math Notes box in Lesson 2.2.2 for help.

### Answers

There is **no real solution** of given equation.

There is a special case that will tell us if a quadratic has **no real solution**: if b = 0 when a and c share the same sign (both positive or both negative), then there will be no real solution. The** quadratic formula** becomes much simpler when b = 0.

given equation [tex]x^{2} =-16[/tex]

[tex]x=\sqrt{-16},\:x=-\sqrt{-16}[/tex]

[tex]x=4i, x=-4i[/tex]

we get imaginary solutions of given equation

so, there is no real solution equation is exist.

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solve: 5-3|2x-5| ≤-1

### Answers

**Answer:**

[tex] \sf \large \: x≥ \frac{7}{2}orx≤ \frac{3}{2}[/tex]

**Step-by-step explanation:**

Let's solve your inequality step-by-step.

5−3(|2x−5|)≤−1

−3(|2x−5|)+5≤−1

Step 1: Add -5 to both sides.

−3(|2x−5|)+5+−5≤−1+−5

−3(|2x−5|)≤−6

Step 2: Divide both sides by -3.

−3(|2x−5|)/−3 ≤ −6/−3

|2x−5|≥2

Step 3: Solve Absolute Value.

|2x−5|≥2

We know either2x−5≥2or2x−5≤−2

2x−5≥2(Possibility 1)

2x−5+5≥2+5(Add 5 to both sides)

2x≥7

2x/2 ≥ 7/2

(Divide both sides by 2)

x≥7/2

2x−5≤−2(Possibility 2)

2x−5+5≤−2+5(Add 5 to both sides)

2x≤3

2x/2 ≤ 3/2

(Divide both sides by 2)

x≤ 3/2

What feature in excel allows you to begin with a 1 in a1 and a 2 in a2 and complete the sequence through the number 30 in a30 without having to type in the entire sequence?

### Answers

**Answer:**

type 1 in a1 type 2 in a2, (or whatever ur preferred no.s are),then heighlight both cells, then go to the bottom right corner of a2 and drag down or double click

**Step-by-step explanation:**

Drag **down** or double-click the **bottom** right corner of a2 to begin with a 1 in a1 and a 2 in a2 and **complete** the **sequence**.

What is excel?

**Excel **is a software in which we can **process** large amount of data and data handling **easily **and effectively, **Excel **can be used in **Data **analysis.

in a1 type 1 Type 2 in cell a2 (or whatever your chosen **numbers** are), highlight both cells, and then **drag **down or **double**-click the bottom right **corner **of a2.

Thus, drag **down** or double-click the **bottom** right corner of a2 to begin with a 1 in a1 and a 2 in a2 and **complete** the **sequence**.

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the lcm of (1/√2) + (1/√2)

### Answers

**Answer: **LCM would be [tex]\sqrt{2}[/tex]

**Step-by-step explanation:**

First we need to find number of which we need to find** lcm**

here we dont have any two number but operator (+) is present

so

first we need to solve this operation

=1/[tex]\sqrt{2}[/tex] + 1/[tex]\sqrt{2}[/tex]

=[tex]\sqrt{2}[/tex]

so lcm of [tex]\sqrt{2}[/tex] would be [tex]\sqrt{2}[/tex].

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Select the set of ordered pairs that does not satisfy the requirements of a function.

O {(1, 1), (2, 2), (3, 3), (4,4)}

O {(1,4), (2,4), (3, 4), (4,4)}

O {(1, 1), (1, 2), (1, 3), (1,4)}

O {(1, 2), (2, 3), (3, 4), (4,1)}

### Answers

Answer is {(1, 1), (1, 2), (1, 3), (1,4)}

The third choice

Step by step

{(1, 1), (1, 2), (1, 3), (1,4)} does not satisfy the requirements of a function because it has multiple x values of 1.

A function must have unique x values to pass the vertical line test. See attached picture showing the vertical line test.

These satisfy the requirements of a function.

O {(1, 1), (2, 2), (3, 3), (4,4)}

O {(1,4), (2,4), (3, 4), (4,4)}

O {(1, 2), (2, 3), (3, 4), (4,1)}

A **relation **will be only a **function **if and if only for **every single **value of x there **must **be only **one output **thus {(1,1),(1,2), (1,3), (1,4)} will not be a function, therefore, option (C) will be correct.

What is a function?

A certain kind of **relationship **called a function binds inputs to essentially one **output**.

A function can be regarded as a **computer**, which is **helpful**.

Given the **coordinates**,

In option (B) {(1,4),(2,4),(3,4),(4,4)} in this for y = 4 → x = 1,2,3,4 so it will be a **function **becuase for every **single x **value there is a **single y **value but for a single y value, there could be two x.

In option (D) {(1,1),(1,2), (1,3), (1,4)} for x = 1 → y = 1,2,3,4 so it will **not **a **function**.

Hence "{(1,1),(1,2), (1,3), (1,4)} will **not **be a **function**".

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Ella's bait and tackle shop sold 128,107 live worms in april and 102,278 live worms in may to the nearest thousand how many worms did ella's bait and tackle shop sell in april and may together

### Answers

Ella's bait and tackle shop sells **230,385 in April and May.**

Based on the given conditions, formulate:

Bait and tackle sold in **128,278** live worms in **April**

Bait and tackle sold in** 102,278** live worms in **May**

So the total number of **Bait and tackles sold in April and May** =

=128,107+102,278

= 230,385

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19.6 is 24.5% of what number?

- For 11 points

### Answers

**Answer:**

**80**

**Step-by-step explanation:**

[tex]\frac{24.5}{100} *x = 19.6\\x = 19.6 *\frac{100}{24.5} \\x = 80[/tex]

19.6 is 24.5% of **80**

**Answer:**

24.5% of 80= 19.6

**Step-by-step explanation:**

**2****4****.****5****%** of what number is equal to **1****9****.****6**

**2****4****.****5**

**_****_****_****_**** **** **** ****x ****=**** ****1****9****.****6**

**1****0****0**** **** **** **** **** **** **** **** **** **** **** ****1****0****0**

**x ****=**** ****1****9****.****6**** ****x ****_****_****_****_**

** **** **** **** **** **** **** **** **** **** **** **** **** **** **** **** **** ****2****4****.****5**

**=**** ****x ****=****8****0**

**HOPE ****IT ****HELPS**

help meeeeeeeeeeeeee

### Answers

**Answer: Choice D **

======================================================

Explanation:

To find the inverse, we swap x and y, then solve for y.

y = 2x-3

x = 2y-3

x+3 = 2y

2y = x+3

y = (x+3)/2

y = x/2 + 3/2

y = (1/2)x + 3/2

This shows the original function y = 2x-3 leads to the inverse y = (1/2)x+3/2, and vice versa.

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Another approach:

Since we're given a list of multiple choice answers, we can rule out the non-answers.

Plug x = 0 into the first equation of choice A. It leads to y = 2

That output 2 is then plugged into the second equation for choice A. It leads to y = 13/2. We do not get the original input 0, which shows that the equations in choice A do not undo one another. They aren't inverses of each other.

This allows us to rule out choice A. Choices B and C are similar stories.

Notice that plugging x = 0 into the first equation of choice D leads to the output y = -3. Then plug this as the input into y = (1/2)x+3/2 and you should get y = 0 to get us back where we started. This partially helps confirm we have a pair of functions that are inverses of each other. I'll let you try other values.

**Answer:**

**Step-by-step explanation:**

Algorithm for deriving the formula of the inverse function

Step 1. In the formula for the original function, replace the notation of the argument and the value:

Step 2. From the resulting formula, express y(x).

Step 3. Take into account the constraints on the area of definition and the area of values of the original and/or inverse functions.

[tex]\displaystyle\\ y=\frac{1}{2}x+2\\\\ 1.\ x=\frac{1}{2}y+2\\ \Rightarrow\ x-2=\frac{1}{2}y \\2.\ Multiply\ both\ parts\ of\ the\ equation\ by\ 2:\\\\2(x-2)=y\\\\2x-4=y\\Thus,\\y=2x-4\neq 3x+\frac{1}{2} \\Answer:\ no\\\\2.\ y=5(x-2)\\\\1.\ x=5(y-2)\\\\2.\ Divide\ both\ parts\ of\ the\ equation \ by\ 5:\\\\\frac{x}{5} =y-2\\\\\Rightarrow\ \frac{x}{5}+2=y \\Thus,\\\\y=\frac{x}{5}+2 \neq \frac{1}{5}(x+2)\\ Answer:\ no[/tex]

[tex]y=2x-3\\1.\ x=2y-3\\\\2,\ x+3=2x\\\\Divide\ both\ parts\ of\ the \ equation\ by \ 2:\\\\\frac{1}{2}(x+3)=y\\\\ Thus,\\\\y=\frac{1}{2}x+\frac{3}{2} \equiv\frac{1}{2}x+\frac{3}{2} \\\\Answer:\ yes[/tex]