In triangle ABC, a = 3, b = 5, and c = 7. Find the approximate value of angle A. 22° 38° 142° 158°

Answer:

Step-by-step explanation:

f(x) - total cost in dollars, for renting a houseboat for x days.

f(15) → x = 15 - number of days

f(x) = 15 + 150x → f(15) = 15 + 150(15) = 2,265 - total cost in dollars for 15 days

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

f(x) = 15+150x

Here, x represents the number of days,

f(x) represents the total cost.

If we calculate f(15), we get that

[tex]f(15)=15+150\times 15\\\\f(15)=15+2250\\\\f(15)=2265[/tex]

$2265 is the cost for 15 days.

So, it shows the number of dollars it costs to rent the houseboat for 15 days.

Hence, Option 'c' is correct.

1. constant

2. -7 < x < -3

3. (-5,8)

Answer:

1.182

Step-by-step explanation:

z is inversely proportional to x:

z = k / x

When x is 4, z is 3.25:

3.25 = k / 4

k = 13

When x = 11:

z = 13 / 11

z ≈ 1.182

Answer:

So we have x+3 if -3<=x<=-1

and                5   if   -1<=x<=1

Step-by-step explanation:

The one piece from -1 to 1 is horizontal so the line is in the form of y=a number.  It goes through 5 on the y-axis so the equation there is y=5.

From -3 to -1, that is a line with positive slope (since that part is increasing).

Slope=rise/run

We see from the filled in dot to the unfilled in dot that the rise is 2 and the run is 2 so the slope is 2/2=1.

So if we did extend this line where we go at on the y-axis?  It would go through 3 because starting from the unfilled dot and rising 1 and running 1 will get us to the 3 on the y-axis.

The equation of a line in slope-intercept form is y=mx+b.

We have m=1 and b=3 so the equation is y=1x+3 or just y=x+3.

So we have x+3 if -3<=x<=-1

and                5   if   -1<=x<=1

Answer:

[tex]\large\boxed{f(x)=\left\{\begin{array}{ccc}x+3&,\ \text{if}\ -3\leq x<-1\\5&,\ \text{if}\ -1\leq x\leq1\end{array}\right}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

Read coordinates of the two points on the first piece:

(-3, 0) and (-2, 1).

Calculate the slope:

[tex]m=\dfrac{1-0}{-2-(-3)}=\dfrac{1}{1}=1[/tex]

Put it and coordinates of the point (-3, 0) to the equation of a line:

[tex]0=1(-3)+b[/tex]

[tex]0=-3+b[/tex]          add 3 to both sides

[tex]3=b\to b=3[/tex]

[tex]\boxed{y=x+3}[/tex]

Read coordinates of the two points on the second piece:

(-1, 5) and (1, 5) - second coordinates are the same.

It's a horizontal segment. Therefore the equation is [tex]y=5[/tex]

Answer:

6% ( to nearest percent )

Step-by-step explanation:

The percentage change is calculated as

[tex]\frac{change}{original}[/tex] × 100%

Change = 90 - 85 = 5, hence

percent change = [tex]\frac{5}{85}[/tex] × 100% = [tex]\frac{5(100)}{85}[/tex] = 6%

Answer:

Here, you have to calculate the percentage(%) of change.

To calculate this, you have to use this formula-:

[tex] { \bold{\mathfrak{\frac{change}{new} \times 100}}}[/tex]

Step-by-step explanation:

[tex] = \frac{5}{90} \times 100[/tex]

[tex] = \frac{50}{9 }[/tex]

[tex] = 5.55555[/tex]

Now, you have to round of this percentage to the nearest....

And that will be => 6%.

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[tex]\bf \begin{array}{ccll} CA(dollar)&US(dollar)\\ \cline{1-2} 1&0.74\\ x&518 \end{array}\implies \cfrac{1}{x}=\cfrac{0.74}{518}\implies 518=0.74x \\\\\\ \cfrac{518}{0.74}=x\implies 700=x[/tex]

Answer:

x = 2/3 , y = -23/12

Step-by-step explanation:

Solve the following system:

{-7.5 x - 1.2 y = -2.7

{1.2 y - 1.5 x = -3.3

In the first equation, look to solve for x:

{-7.5 x - 1.2 y = -2.7

{1.2 y - 1.5 x = -3.3

-7.5 x - 1.2 y = -(15 x)/2 - (6 y)/5 and -2.7 = -27/10:

{-(15 x)/2 - (6 y)/5 = -27/10

Add (6 y)/5 to both sides:

{-(15 x)/2 = 3/10 (4 y - 9)

{1.2 y - 1.5 x = -3.3

Multiply both sides by -2/15:

{x = 1/25 (9 - 4 y)

{1.2 y - 1.5 x = -3.3

Substitute x = 1/25 (9 - 4 y) into the second equation:

{x = 1/25 (9 - 4 y)

{1.2 y - 0.06 (9 - 4 y) = -3.3

1.2 y - 0.06 (9 - 4 y) = 1.2 y + (0.24 y - 0.54) = 1.44 y - 0.54:

{x = 1/25 (9 - 4 y)

{1.44 y - 0.54 = -3.3

In the second equation, look to solve for y:

{x = 1/25 (9 - 4 y)

{1.44 y - 0.54 = -3.3

1.44 y - 0.54 = (36 y)/25 - 27/50 and -3.3 = -33/10:

(36 y)/25 - 27/50 = -33/10

Add 27/50 to both sides:

{x = 1/25 (9 - 4 y)

{(36 y)/25 = -69/25

Multiply both sides by 25/36:

{x = 1/25 (9 - 4 y)

{y = -23/12

Substitute y = -23/12 into the first equation:

Answer: x = 2/3 , y = -23/12

Answer:

x = 2/3  y = -23/12

Step-by-step explanation:

- 7.5x - 1.2y = -2.7

- 1.5x + 1.2y = -3.3​

Add the equations together

- 7.5x - 1.2y = -2.7

- 1.5x + 1.2y = -3.3​

---------------------------

-9x                 = -6

Divide each side by -9

-9x/-9 =-6/-9

x =2/3

Now we need to find y

-1.5 (2/3) +1.2y = -3.3

-1 +1.2y = -3.3

Add 1 to each side

-1+1 +1.2y = -3.3+1

1.2y = -2.3

Divide by 1.2

1.2y/1.2 = -2.3/1.2

y =-23/12

Answer:

a

Step-by-step explanation:

Answer:

x = 19.4 units (answer rounded up to the nearest tenth)

Step-by-step explanation:

[tex]\frac{18}{x}[/tex] = cos 22

x = [tex]\frac{18}{cos 22}[/tex] = 19.41362537

x = 19.4 units (answer rounded up to the nearest tenth)

A. the product of the difference of x and 5 and the sum of x and 3.

Not really sure how I should explain this because the answer is just the expression in word form.

The expression (x - 5)(x + 3) correctly corresponds to 'the product of the difference of x and 5 and the sum of x and 3', matching option OA.

The expression (x - 5)(x + 3) is the product of two binomials: the first binomial is the difference of x and 5, and the second binomial is the sum of x and 3. Therefore, the correct description of the expression is 'the product of the difference of x and 5 and the sum of x and 3', which corresponds to option OA. This understanding illuminates how binomials are multiplied and underscores the significance of recognizing the individual terms within the expression to comprehend its meaning and structure effectively.

Answer: For part A, Yakob has 9 friends that like Maths best, 6 friends that like History the best, & 15 friends that prefer either English or Science the best.

Part B: There's a graph I made below.

Step-by-step explanation:

You have to use proportions to answer this question. The bar graph is 10 cm total, therefore it is proportional to the 30 friends that Yakob has in total. After that, you can make proportions out of the data in the chart. For example, History is 2 cm out of the 10 cm total. Think proportions! You had to multiply 3 to 10 to get 30, so you have to apply the same thing to the numerator. In this case, multiply 3 to 2 and you'll get 6. 2/10=6/30! I repeated that for the rest and put it into a graph. The prompt wanted you to combine English and Science, so I did that after separately making their proportions. Hope this helps!

Answer: 1/21 of the bag

Step-by-step explanation:

If only one person eats the meal they are consuming 1/3 of a bag of potatoes. However if more than one person is eating the potatoes we need to multiply 1/3 by the reciprocal of how many people are eating.

For example:

2 people 1/3*1/2=1/6

3 people 1/3*1/3=1/9

So then we apply this principle for seven people.

7 people 1/3*1/7=1/21

We can check our answer by working backwards

1/21*7=7/21=1/3

So each person got 1/21 of the bag.

Answer:

50.91

Step-by-step explanation:

Write a proportion:

1 kg / 2.2 lb = x kg / 112 lb

Cross multiply:

2.2 x = 112

Divide:

x = 50.91

50.91 kg equals 112 pounds.

ANSWER

a) Use the homogeneous property of the binomial expansion to find the missing exponent

b) Use the binomial theorem to find the coefficient

EXPLANATION

The given binomial expansion is:

[tex](x+y)^{12} [/tex]

When we compare this to

[tex](a + b) ^{n} [/tex]

We have

[tex]n = 12[/tex]

Therefore the of each term in the expansion must be 12.

[tex] \implies \: 7 + b = 12[/tex]

[tex]b = 12 - 7[/tex]

[tex]b = 5[/tex]

Since the coefficient of x and y are unity, we use the formula

[tex]^{n} C_r = \frac{n!}{(n - r)!r!} [/tex]

to find the coefficient.

Where n=12 and r=5(the exponent of the y-term).

Therefore the coefficient is

[tex]^{12} C_5= \frac{12!}{(12- 5)!5!} [/tex]

[tex]^{12} C_5= \frac{12!}{7!5!} [/tex]

[tex]^{12} C_5= \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{7! \times 5 \times 4 \times 3 \times 2 \times 1} [/tex]

When we simplify further we get:

[tex]^{12} C_5= 11 \times 9 \times 8 = 792[/tex]

Answer:

The volume of the stairway is

720 cubic inches

Step-by-step explanation:

we know that

The volume of the stairway is equal to the volume of two rectangular prism

The volume of the rectangular prism is equal to

[tex]V=LWH[/tex]

Find the volume of the larger rectangular prism

we have

[tex]L=6\ in[/tex]

[tex]W=10\ in[/tex]

[tex]H=4+4=8\ in[/tex]

substitute

[tex]V=(6)(10)(8)=480\ in^{3}[/tex]

Find the volume of the smaller rectangular prism

we have

[tex]L=6\ in[/tex]

[tex]W=10\ in[/tex]

[tex]H=4\ in[/tex]

substitute

[tex]V=(6)(10)(4)=240\ in^{3}[/tex]

Find the volume of the stairway

Adds the two volumes

[tex]V=480+240=720\ in^{3}[/tex]

Answer:

Option B

Step-by-step explanation:

We have to calculate the volume of concrete used to create the stairway given in the picture.

Volume of the stairway = volume of small stairway + volume of larger stairway

Dimensions of Large stairway = 10 in × 6 in × (4+4)in

                                                 = 10 in × 6 in × 8 in.

Therefore, volume of large stairway = 480 in³

Dimensions of small stairway = 10 in × 6 in × 4 in

                                                = 240 in³

Total volume = 480 + 240

                     = 720 in³

Option B is the answer.

Answer:

Step-by-step explanation:

first find one side:

18^2+10^2=c^2, so c=20.59

we need to find the length of one of the sides of the remaining triangle:

20.59^2+2^2=c^2

c=20.68 = the diagonal.

Answer:

2 square root 107

Step-by-step explanation:

Answer:

8

I made a couple of assumptions so you might want to make sure I made the right assumptions.

I assumed you meant square root of z; not source of z.

I also assumed you meant x=2 not x=z.

Step-by-step explanation:

y varies directly with means y=k times something where k is a constant.

Inversely means to divide by whatever it says it varies inversely with.

So we have:

[tex]y=k \cdot \frac{x}{\sqrt{z}}[/tex]

We are given y=4 and x=2 and z=4, which means:

[tex]4=k \cdot \frac{2}{\sqrt{4}}[/tex]

[tex]4=k \cdot \frac{2}{2}[/tex]

[tex]4=k(1)[/tex]

[tex]4=k[/tex]

So the constant is k which means the equation for any (x,y,z) is:

[tex]y=4 \cdot \frac{x}{\sqrt{z}}[/tex]

We want to know y when x=6 and y=9:

[tex]y=4 \cdot \frac{6}{\sqrt{9}}[/tex]

[tex]y=4 \cdot \frac{6}{3}[/tex]

[tex]y=4 \cdot 2[/tex]

[tex]y=8[/tex]

Answer:

im kinda sure the answer is 120 degrees

Step-by-step explanation:

but maybe not

Answer:

21 dogs

Step-by-step explanation:

In your question, we need to find how many dogs are in the store.

To find the answer to your question, we would need to use the information given in the question

Given Information:

Ratio of cats to dogs (respectively) is 2:3

There are 14 cats

With the information above, we can solve the question.

We know that there are 2 cats for every 3 dogs.

The question says that there are 14 cats.

We need to change the amount of cats there are in the ratio.

We would multiply 2 by 7 to fit the story, due to the fact that 2 times 7 makes 14.

Whatever you do to the left, you would do to the right. This means that you would multiply 3 by 7.

2   :   3

×7     ×7

14   :   21

When you multiply, you should get 21. This means that there are 21 dogs at the pet store when there are 14 cats.

There are 21 dogs at the pet store.

To find how many dogs are at the pet store, use the given ratio of cats to dogs and the number of cats. Apply the ratio to determine the number of dogs. There are 21 dogs at the pet store.

To find the number of dogs at the pet store, you can use the ratio of cats to dogs, which is 2:3.

Therefore, there are 21 dogs at the pet store.

Answer:

K 48 inches

Step-by-step explanation:

First lets determine how big of table cloth we need

The table is 3 ft in diameter which is 36 inches

That means the radius is d/2 = 36/2 = 18 inches

We need to add 5 inches to the radius to hang over the edge

18+5 = 23

We need to add the hem which is 1 inch

23+1 = 24

The radius is 24 inches

The diameter would be 2r = 2*24 = 48 inches

Answer:

Ten more than x x + 10

Step-by-step explanation:

Answer:

No.

10-x and x-10 are only the same when x=10.

They are not the same because subtraction is not commutative.

Step-by-step explanation:

A number less than 10 is 10-x .

The difference of a number and 10 means x-10.

10-x is not the same as x-10

We can find out when they are the same by solving:

10-x=x-10  

Add x on both sides:

10=2x-10

Add 10 on both sides:

20=2x

Divide both sides by 2:

10=x

So they are only the same when x=10.

It is mainly not an identity because subtraction isn't commutative.

central angle/360 = arc length/2pi•r

Let π = pi

Let A = length of intercepted arc

45/360 = A/2(20)π

1/8 = A/40π

8A = 40π

A = 40π/8

A = 5π

Did you follow?

Answer:

The length of the arc is 5π inches

Step-by-step explanation:

* Lets explain the relation between the central angle and its

 intercepted arc

- If the vertex of an angle is the center of the circle and the two sides

 of the angle are radii in the circle, then this angle is called  a

 central angle

- Each central angle subtended by the opposite arc, the name of the

 arc is the starting point and the ending point of the angle

- There is a relation between the central angle and its  subtended arc

 the measure of the central angle equals half the measure of its

 subtended arc

- The length of the subtended arc depends on the measure of its

 central angle and the length of the radius and the measure of the arc

- The measure of the circle is 360°

- The length of the circle is 2πr

- The length of the arc = central angle/360 × 2πr

* Now lets solve the problem

∵ The radius of the circle r = 20 inches

∵ The measure of the central angle is 45°

∵ The length of the arc = central angle/360 × 2πr

∴ The length of the arc = 45°/360° × 2 × π × 20 = 5π

* The length of the arc is 5π inches

Answer:

[tex]\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}[/tex]

Step-by-step explanation:

We need to sum the following two expressions:

[tex]\frac{x}{x+3} + \frac{x+2}{x+5}[/tex]

[tex]\frac{x(x+5) + (x+2)(x+3)}{(x+3)(x+5)}[/tex]

expanding the polynomial in the numerator:

[tex]\frac{2x^{2} + 10x + 6}{(x+3)(x+5)}[/tex]

[tex]\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}[/tex]

This is the most simplified form we can get:

[tex]\frac{2(x^{2} + 5x + 3)}{(x+3)(x+5)}[/tex]

Answer:

[tex]\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}[/tex]

Step-by-step explanation:

The given expression is [tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex]

We have to simplify the given expression

[tex]\frac{x}{x+3}+\frac{x+2}{x+5}[/tex]

= [tex]\frac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}[/tex]         [Distributive law]

= [tex]\frac{x^{2}+5x+x^{2}+3x+2x+6}{(x+3)(x+5)}[/tex]

= [tex]\frac{2x^{2}+10x+6}{(x+3)(x+5)}[/tex]

= [tex]\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}[/tex]

Finally the simplified form of the given expression is [tex]\frac{2(x^{2}+5x+3)}{(x+3)(x+5)}[/tex]

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$8000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, then fifty two} \end{array}\dotfill &52\\ t=years\dotfill &6 \end{cases}[/tex]

[tex]\bf A=8000\left(1+\frac{0.055}{52}\right)^{52\cdot 6}\implies A\approx 8000(1.00106)^{312}\implies A\approx 11133.81[/tex]

Mark's account balance after six years is $ 11126.

The term compound interest refers to the interest that accrues both on the principal and on the interest.

P = $8,000

r = 5.5% or 0.055

t = 6 years

n = 52 times

Hence;

A = 8,000(1 + 0.055/52)^(6 × 52)

A =$ 11126

Learn more about compound interest: https://brainly.com/question/731147?

Answer: Choice A

3 over 12 multiplied by 7 over 11

(3/12) * (7/11)

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

Explanation:

There are 3 yellow cars out of 2+7+3 = 12 total. The probability of selecting yellow is therefore 3/12. We can reduce this, but the answer choices decide not to, so we'll do the same.

After picking a yellow car, we have 12-1 = 11 left over. The amount of blue cars do not go down (because we haven't selected it yet). There are 7 blue cars out of the 11 total, so the probability of picking blue for this case is 7/11

Multiply the two fractions to get (3/12)*(7/11) which is a shorthand way of writing "3 over 12 multiplied by 7 over 11".

Answer:

the guy on top of me is correct give him brainliest and 5 star ratings because he is a freaking genius btw

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Using the trigonometric identities

• csc x = [tex]\frac{1}{sinx}[/tex]

• tan x = [tex]\frac{sinx}{cosx}[/tex]

cos x × [tex]\frac{1}{sinx}[/tex] × [tex]\frac{sinx}{cosx}[/tex]

Cancel sin x and cos x on the numerator/ denominator leaving

1

Answer:

1

Step-by-step explanation:

cscx=1/sinx

tanx=sinx/cosx

cosx*(1/sinx)*(sinx/cosx)

Cancel out common factors on top and bottom.

1

For this case we have that by definition, the area of a circle is given by:

[tex]A = \pi * r ^ 2[/tex]

Where:

r: It is the radius of the circle

How do we have to:

[tex]A = 64 \ ft ^ 2[/tex]

So:

[tex]64 = \pi * r ^ 2[/tex]

We take[tex]\pi = 3.14[/tex]

[tex]r ^ 2 = \frac {64} {3.14}[/tex]

We apply square root:

[tex]r = \pm \sqrt {\frac {64} {3.14}}[/tex]

We choose the positive value:

[tex]r = 4,515[/tex]

If we round we have that the radius is 4.5 feet.

Answer:

4.5 feet

Answer:

There were 35 gallons of gasoline and 500 gallons of kerosene.

Step-by-step explanation:

Step 1: Write data for equation 1

Let gallons of kerosene be x

Let gallons of gasoline be y

Total capacity of truck is 4000

Step 2: Form equation 1

x + y = 4000

Step 3: Write data for equation 2

Profit of total gallons of kerosene is 0.12x

Profit of total gallons of gasoline is 16y

Total profit is $620

Step 4: Form equation 2

0.12x + 16y = 620

Step 5: Find x in terms of y from equation 1

x + y = 4000

x = 4000 - y

Step 6: Substitute value of x in equation 2

0.12x + 16y = 620

0.12 (4000 - y) + 16y = 620

480 - 12y + 16y = 620

4y = 620 - 480

y = 140/4

y = 35

Step 7: Substitute value of y in equation 1 to find x

0.12x + 16y = 620

0.12x + 16 ( 35 ) = 620

0.12x = 60

x = 500

There were 35 gallons of gasoline and 500 gallons of kerosene.

!!

The owner loaded 3500 gallons of gasoline and 500 gallons of kerosene into the 4000-gal oil truck to achieve a profit of $620, by setting up a system of linear equations and solving for both variables.

To solve this problem, we can use a system of equations to find out how many gallons of gasoline and kerosene were loaded into the truck. Let's denote gasoline as G and kerosene as K. We know that the total volume of the truck is 4000 gallons, so:

G + K = 4000

Next, considering the profit per gallon, 16e represents 16 cents for gasoline and 12 cents for kerosene. If the total profit is $620, then:

0.16G + 0.12K = 620

To solve this system of equations, we can multiply the second equation by 100 to eliminate the decimals:

16G + 12K = 62000

Now solve one of the equations for a variable, for example:

K = 4000 - G

Substitute K in the profit equation:

16G + 12(4000 - G) = 62000

16G + 48000 - 12G = 62000

4G = 14000

G = 3500

So, we have 3500 gallons of gasoline. Substitute G back into the equation K = 4000 - G:

K = 4000 - 3500

K = 500

Therefore, there were 3500 gallons of gasoline and 500 gallons of kerosene.

The x is a placeholder for some currently unknown number. Let's say that number was 10. So we replace x with 10 to get 10-3 = 12. That statement is false because 10-3 is actually 7. What you can do is keep guessing until you get the right answer.

A much better approach is to undo what is happening to x. We have x and we subtract off 3 to get 12. Following this in reverse, we need to add 3 to both sides so that x is isolated.

x-3 = 12

x-3+3 = 12+3

x = 15

Let's replace x with 15 and see if the equation is true

x - 3 = 12

15 - 3 = 12

12 = 12

Sure enough we get the right answer.

The idea of adding 3 to both sides is possible through the additive property of equality (if a = b, then a+c = b+c)

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

In summary, I added 3 to both sides using the additive property of equality. Doing this isolated x to get x = 15.

Answer:

[tex]\large\boxed{a)\ y=\dfrac{5}{3}x+\dfrac{22}{3}}\\\boxed{b)\ 5x-3y=-22}[/tex]

Step-by-step explanation:

[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\m-slope\\b-y-intercept\\\\\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\=========================\\\\\text{We have the equation of a line in the standard form.}\\\text{Convert it to the slope-intercept form.}\\\\3x+5y=1\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\5y=-3x+1\qquad\text{divide both sides bvy 5}\\\\y=-\dfrac{3}{5}x+\dfrac{1}{5}\to m_1=-\dfrac{3}{5}[/tex]

[tex]a)\\\\y=m_2x+b\\\\m_1=-\dfrac{3}{5}\to m_2=-\dfrac{1}{-\frac{3}{5}}=\dfrac{5}{3}\\\\\text{Put the value of slope and the coordinates of the given point (1, 9)}\\\text{to the equation of a line:}\\\\9=\dfrac{5}{3}(1)+b\\\\9=\dfrac{5}{3}+b\qquad\text{subtract}\ \dfrac{5}{3}\ \text{from both sides}\\\\\dfrac{27}{3}-\dfrac{5}{3}=b\\\\\dfrac{22}{3}=b\\\\\text{Finally:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}[/tex]

[tex]b)\\\\\text{The standard form of an equation of a line:}\\\\Ax+By=C\\\\\text{Convert the equation}\ y=\dfrac{5}{3}x+\dfrac{22}{3}\ \text{to the standard form:}\\\\y=\dfrac{5}{3}x+\dfrac{22}{3}\qquad\text{multiply both sides by 3}\\\\3y=5x+22\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-5x+3y=22\qquad\text{change the signs}\\\\5x-3y=-22[/tex]