Kim is cutting construction paper into rectangles for a project. She needs one rectangle that is 9”x13 1/3”. She needs to cut another rectangle that is 10 1/4” x 10 1/3”. How many total square inches of construction paper does Kim need for her project?

Answer:

0.066

Step-by-step explanation:

462/7000= 0.066

Answer:

0.66

Step-by-step explanation:

To find the additional cost incurred when production is increased from 2 units to 13 units, we need to calculate the difference between the total cost of producing 13 units and the total cost of producing 2 units.

The total cost of producing x units is given by the antiderivative of the marginal cost function:

C(x) = ∫ C′(t) dt = 0.04t^3 - 2t^2 + 80t + C

where C is an arbitrary constant of integration.

To find the value of C, we can use the fact that the total cost of producing 2 units is known:

C(2) = 0.04(2)^3 - 2(2)^2 + 80(2) + C = 162 + C

We know from the problem statement that the total cost of producing 2 units is $162, so we can solve for C:

162 + C = C(2) = 0.12(2)^2 - 4(2) + 80 = 68

C = -94

Now we can find the total cost of producing 13 units:

C(13) = 0.04(13)^3 - 2(13)^2 + 80(13) - 94 = 1956

The additional cost incurred when production is increased from 2 units to 13 units is:

C(13) - C(2) = 1956 - 162 = $1794

Therefore, the additional cost incurred in dollars when production is increased from 2 units to 13 units is $1794.

The inverse of the function f(x) = k/x is the expressed derived as; f⁻¹(x) = k/x

A function is said to have an inverse if it is both one-to-one and onto

we replace the function f(x) with y and make x the subject to arrive at the inverse f⁻¹(x) as follows;

Given f(x)= k/x

y = k/x

y × x = k/x × x {multiply both sides by x}

xy = k

xy/y = k/y {divide through by y}

x = k/y

f⁻¹(x) = k/y.

Therefore, the inverse of the function f(x) = k/x is the expressed derived as; f⁻¹(x) = k/x.

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The equations that can be used to solve for y, the length of the room, are: y(y + 5) = 750, y² – 5y = 750, and y(y – 5) + 750 = 0.

It states that when multiplying a number by a group of numbers added together, you can multiply the number by each individual number in the group and add the products together to get the same answer.

In order to find the length of the room, we need to solve for y in each of the equations given.

First, let's solve for y in the equation y(y + 5) = 750. We can use the distributive property to expand the equation to y² + 5y = 750.

Then, we can subtract 750 from both sides of the equation to get y² + 5y - 750 = 0.

To solve the equation, we need to factor it. We can use the difference of squares formula to factor the equation, yielding (y + 25)(y - 30) = 0. Therefore, one solution for y is y = -25, and the other solution is y = 30.

Second, let's solve for y in the equation y² – 5y = 750.

To solve this equation, we can add 5y to both sides to get y² = 5y + 750. Then, we can divide both sides by y to get y = 5y + 750.

We can then subtract 5y from both sides to get y - 5y = 750. Finally, we can divide both sides by 5 to get y = 150.

Third, let's solve for y in the equation y(y – 5) + 750 = 0.

To solve this equation, we can use the distributive property to expand the equation to y² – 5y + 750 = 0.

Then, we can subtract 750 from both sides to get y² – 5y = -750.

To solve the equation, we need to factor it. We can use the difference of squares formula to factor the equation, yielding (y + 25)(y - 30) = 0. Therefore, one solution for y is y = -25, and the other solution is y = 30.

In conclusion, the equations that can be used to solve for y, the length of the room, are y(y + 5) = 750, y2 – 5y = 750, and y(y – 5) + 750 = 0. The solutions for y are y = -25 and y = 30.

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[tex]\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{1}{2}nR^2\sin\left( \frac{360}{n} \right) ~~ \begin{cases} R=\stackrel{\textit{radius of}}{circumcircle}\\ n=\stackrel{\textit{number of}}{sides}\\[-0.5em] \hrulefill\\ n=8\\ R=6 \end{cases}\implies A=\cfrac{1}{2}(8)(6)^2\sin\left( \frac{360}{8} \right) \\\\\\ A=144\sin(45^o)\implies A=144\cdot \cfrac{\sqrt{2}}{2}\implies A=72\sqrt{2}\implies A\approx 101.8[/tex]

The depth by which the gardener must increase the depth of his garden to double the area is: 8 m

We have the area of the trapezoid is 60m squared and depth is 8m.

We will let the front width be x so that the back width will be 2x

Here, we will apply the formula of trapezium.

A = ¹/₂(a + b)*h

Plugging in the relevant values, we have:

A = ¹/₂(x + 2x)8

60 = ¹/₂(x + 2x)8

60 = 4(x + 2x)

60/4 = 3x

15 = 3x

x = 15/3

x = 5

We get the front width that is 5 so the back width would be 2 * 5 = 10 m

Now, we will double the area to find the new depth:

120 = ¹/₂(5 + 10)h

240/15 = h

h = 16 m

Thus we have to increase the depth by:

16 - 8 = 8 m

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Here is the answer to the function

f(5) = 35

g(-2) = 7

h(6) = 1

Explain function

A function is a rule that assigns a unique output value to each input value in a set. It is often represented as f(x), where x is the input variable and f(x) is the output value. Functions can be used to describe relationships between variables, model real-world phenomena, and solve equations. They are fundamental to many branches of mathematics and have wide-ranging applications in science and engineering.

According to the given information

To find f(5), we use the function F(x)=5|x-12| and substitute x=5. We get:

F(5) = 5|5-12| = 5|-7| = 5*7 = 35

Therefore, f(5) = 35.

To find g(-2), we use the function G(x)=10-3x²/x² and substitute x=-2. We get:

G(-2) = 10-3(-2)²/(-2)² = 10-3(4)/4 = 10-3 = 7

Therefore, g(-2) = 7.

To find h(6), we use the function H(x)=-2+√(3+x) and substitute x=6. We get:

H(6) = -2+√(3+6) = -2+√(9) = -2+3 = 1

Therefore, h(6) = 1.

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1   2/35 miles you run down the slope.

You run 8 2/5 miles in total, and you run 1/2 of that distance on a hill, so you run (1/2) x 8 2/5 = 4 1/5 miles on the hill.

You run down the slope for the last 2/7 of the hill.

To find how many miles that is, we can multiply the total distance on the hill by 2/7:

(2/7) x 4 1/5 = 1  2/35

Therefore, you run down the slope for 1  2/35 miles of your run.

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The lengths of the segments in the drawing, obtained using Thales Theorem are;

1) [AD] = 33.5 cm

2) a) OM ║ AB, therefore, OMAB is a trapezium

b) Thales Theorem indicates that point L is the midpoint of [DE]

c) Rectangle

3) JO ║ IL and IJ ║ OL, therefore, IJOL is a parallelogram

b) [JA] ≅ [AI], therefore; {OD] ≅ [DF] and point D is the midpoint of [OF]

IF = 5.25 cm

5) 1) the point C, which is the point of intersection of the medians is the center of gravity of BJD

2) The parallel sides of the parallelogram ABCD, and Thales Theorem indicates that M and N are the midpoints [BJ], and [DI]

Thales Theorem indicates that MN = DI = IB

Thales Theorem states that a line drawn parallel to one side of a triangle such that it intersects the other two sides, then the line divides the other two sides of the triangle in the same proportion.

1) The the diagonals of a rectangle bisect each other, therefore;

The length of [AD] = Length of [AB] = BE/2

The length of [AD] = 7 cm/2 = 3.5 cm

2) a) Whereby the point M is the midpoint of [AD], then according to the midsegment theorem, [OM] is parallel to [AB], therefore; OMAB is a trapezium, by the definition of a trapezium

b) Whereby [OM] is parallel to [AB], we get;

[OM] is parallel to [BE], therefore;

[OL] is parallel to [DE]

According to the triangle proportionality theorem, which is also known as Thales Theorem, the segment [OL] that divides [BD] in two also divides DE in two, therefore, point L is the midpoint of [DE].

c) Whereby the points A and L are the midpoints of [BE] and [DE], and the point O is the midpoint of [BD], we get;

[AO] is parallel to [DL], and [AL] is parallel to [OD]

[DL] is perpendicular to [BD], by definition of rectangle HBDE, therefore, [AO] is perpendicular to [BD]

Similarly, [AL] is perpendicular to [DE], and the quadrilateral ALDO is a rectangle

3) a) [OL] is parallel to [IJ]

The midsegment theorem indicates that AD is parallel to JO and segment AD is parallel to IL, therefore;

JO is parallel to IL and IJOL is a parallelogram

b) Whereby BD is extended to the point F, and IL cuts BD in F, we get;

JO, AD, and IF cut segment OAI into parts JA and AI of the same length, therefore;

JO, AD, and IF cut segment ODF into parts OD, and DF of the same lengths, therefore, point D is the midpoint of OF

AB = AD = 3.5

FA = 3.5/2 = 1.75

BF = 3.5 + 1.75 = 5.25

IF/5.25 = 3.5/3.5

Therefore, IF = 5.25 cm

5) The center of gravity of a triangle is the point of intersection of the three medians of the triangle

Whereby point J is the symmetric of A with respect to C, we get;

AC = CJ

The parallel sides BA and CD, and the midsegment theorem indicates;

BM = MJ, therefore;

Point M is the midpoint of BJ, and DM is a median of the triangle BJD

Similarly, BN is a median of the triangle BJD

The diagonals of a parallelogram bisect each other, therefore, the point of intersection of the diagonals, I is the midpoint of BD, and JI is a median of the triangle BJD, therefore, the point C is the center of gravity of the triangle BJD

2) The segments AC and CJ are congruent, and the segments CD and BA are parallel. According to the triangle proportionality theorem, segment BM is congruent to segment MJ, and the point M is the midpoint of BJ

Similarly, BC is parallel to AD, therefore, DN is congruent to NJ, and the point N is the midpoint of DJ

The Thales Theorem or midsegment theorem indicates MN = (1/2) × BD, therefore;

MN = DI = BD

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without too much fuss, Check the picture below.

so we have roots at -5 and 1, and a point, incidentally the vertex, at (-2 , 9)

[tex]\begin{cases} x = -5 &\implies x +5=0\\ x = 1 &\implies x -1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +5 )( x -1 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=-2\\ y=9 \end{cases} \\\\\\ a ( -2 +5 )( -2 -1 ) = 9\implies -9a=9\implies a=\cfrac{9}{-9}\implies a=-1 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} -( x +5 )( x -1 ) =y \end{array}}~\hfill[/tex]

The similar rectangle with the dimensions is 4 feet by 8 feet

Given data ,

A rectangle with the dimensions of 2ft by 8ft is similar to a rectangle with the dimensions given by

The scale factor of the rectangle is 2

So , the new dimensions of the rectangle are 4 feet by 8 feet

Hence , the rectangle is having a dimension of 4 feet by 8 feet

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The complete question is attached below :

A rectangle with the dimensions of 2ft by 8ft is similar to a rectangle with the dimensions of?

Answer:

1156

Step-by-step explanation:

[tex]\sqrt{x} =34[/tex]

Square both sides. This cancels the square root on the left side.

[tex](\sqrt{x} )^2 = 34^2[/tex]

The x is now free. Square 34 by multiplying it by itself.

x = 1156

The amount invested each rate is $2704 and $5599.

What is simple interest?

The cost of borrowing money is known as simple interest because compounding effects are not taken into consideration. Simply said, simple interest solely affects the principal sum. When money is borrowed for a specific period of time at a specific rate, a tiny sum of money known as simple interest is levied. Simple interest can be calculated using the formula SI = P R T.

Here let us take the money invested at 5% is $x.

Then Money invested at 12% = $2x+191

Now using Total interest after one year = $807.08

Now using simple interest formula I = PNR/100

=> [tex]\frac{x\times1\times5}{100}+\frac{(2x+191)\times1\times12}{100}=807.08[/tex]

=> 5x + 24x+2292 = 807.08*100

=> 29x + 2292 = 80708

=> 29x  = 80708 - 2292 = 78416

=> x= 78416/29 = $2704

Then 2x+191 = $5599.

Hence the amount invested each rate is $2704 and $5599.

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Julie's total time for the race could be any time t < 48.72.

Given that,

Connor finished race at 48.72.

Julie finishes the race before Connor.

We have to find the total time taken by Julie to finish the race.

Julie could finish the race at any time before Connor.

Already we have,

Time that Connor finished race = 48.72

So time that Julie finished the race could be any time t < 48.72.

Hence the time required to finish the race by Julie could be any time t < 48.72.

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Answer:where graph

Step-by-step explanation:

The value of the constants a, b and c. are a = 0.145, b = 0.21 and c = 0.645

Given that

X : 0,1,2

P(X = x) : a,b,c

E(X) = 1.5 and Var(X) = 0.54

The formula of expected value is

E(x) = ∑x P(x)

So, we have

0 * a + 1 * b + 2 * c = 1.5

b + 2c = 1.5

The variance of a discrete random variable is

Var(x) = E(x²) - E(x)

Where

E(x²) = ∑x² P(x)

So, we have

E(x²) = 0² * a + 1² * b + 2² * c

E(x²) = b + 4c

Next, we have

Var(x) = E(x²) - E(x)²

b + 4c - (b + 2c)² = 0.54

Evaluate

b + 4c - (b² + 4cb + 4c²) = 0.54

So, we have

b + 4c - (b² + 4cb + 4c²) = 0.54

b + 2c = 1.5

Solve by graphing, we have

b = 0.21 and c = 0.645

The sum of the probabilities is 1

So, we have

a + b + c = 1

This gives

a + 0.21 + 0.645 = 1

Evaluate

a = 0.145

Hence, the value of constant a is 0.145

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Answer:

Step-by-step explanation:

The answer is 4 because 8 times 4 is 32

Answer: 8·[tex]x[/tex]=32 or 8·4=32

Step-by-step explanation:

The one-step equation 8·[tex]x[/tex]=32 shows how Nina can sort 32 cards into 8 equal groups. To solve, divide 32 by 8. You should get 4. Therefore, an equation to show how Nina can sort 32 cards into 8 equal groups is 8·4=32.

Answer:

[tex]\large\boxed{\tt x \approx 7.61.}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem we are asked to find the measure of x.}[/tex]

[tex]\textsf{Note that we are given a Right Triangle, which means that we can use one}[/tex]

[tex]\textsf{\underline{Trigonometric Identity} to find the value of x.}[/tex]

[tex]\textsf{These Trigonometric Identities are Sine, Cosine, and Tangent.}[/tex]

[tex]\boxed{\begin{minipage}{20 em} \\ \underline{\textsf{\large Trigonometric Identities;}} \\ \\ \textsf{Trigonometric Identities are trigonometric ratios determined with what's given in order to find a missing value. For a Right Triangle, the Trigonometric Identities are Sine, Cosine, and Tangent. These are used to find missing sides.} \\ \\ \tt Sine = \tt $ \tt \frac{Opposite}{Hypotenuse} \\ \\ Cosine = \frac{Adjacent}{Hypotenuse} \\ \\ Tangent = \frac{Opposite}{Adjacent} \end{minipage}}[/tex]

[tex]\textsf{Because we are focused on the 65}^{\circ} \ \textsf{angle, we will use Cosine. Remember that the}[/tex]

[tex]\textsf{Hypotenuse is the longest side, and the side opposite from the right angle. The}[/tex]

[tex]\textsf{Adjacent Side is the side that the angle is nearest to, or touches. Due to what's}[/tex]

[tex]\textsf{given, we have to find x by using cosine.}[/tex]

[tex]\large\underline{\textsf{Solving for x;}}[/tex]

[tex]\textsf{Let's use cosine to solve for x.}[/tex]

[tex]\tt \cos(65^{\circ}) = \frac{x}{18}[/tex]

[tex]\textsf{Cancel out the fraction by using the \underline{Multiplication Property of Equality}, which}[/tex]

[tex]\textsf{states that expressions are still equal if they're multiplied by the same term.}[/tex]

[tex]\tt 18 \times \cos(65^{\circ}) = \frac{\not{18}x}{\not{18}}[/tex]

[tex]\tt 18\cos(65^{\circ}) = x[/tex]

[tex]\underline{\textsf{Evaluate;}}[/tex]

[tex]\large\boxed{\tt x \approx 7.61.}[/tex]

Answer:

The standard deviation of the sampling distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:

standard error = standard deviation / square root of sample size

In this case, the standard deviation of the population is 1.1 years, and the sample size is 35. Substituting these values into the formula, we get:

standard error = 1.1 / sqrt(35) ≈ 0.186

Rounding to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.19 years.

give thanks, your welcome <3

Step-by-step explanation:

The expression, in terms of y, for the perimeter of the rectangle is 4 + 4y

From the question, we have the following parameters that can be used in our computation:

Dimensions = y + 2 and y

The perimeter of the rectangle is represented as

P = 2 * (LEngth + Width)

So, we have

P = 2 * (y + 2 + y)

Evaluate

P = 4 + 4y

Hence, the permeter expression is 4 + 4y

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Answer:

Mikas is Saltier

Step-by-step explanation:

Brainliest please.


Jack used 1 tsp to 3 tsp of water Thats a fraction of 1/3

Mika Used 4 tsp to 9 tsp of water which its 4/9

4/9 is greater than 1/3

So, there is approximately an 85.02% probability that the sample mean will be between 50 and 54.

We'll use the Central Limit Theorem which states that the sampling distribution of the sample mean will be approximately normally distributed if the sample size is large enough (n ≥ 30).

In this case, the sample size is 42, so we can apply the Central Limit Theorem.

First, we'll calculate the standard deviation of the sampling distribution (also known as the standard error) using the formula:

Standard error (SE) = population standard deviation / √sample size

SE = 9 / √42 ≈ 1.387

Next, we'll calculate the Z-scores for the lower and upper bounds of the range (50 and 54) using the following formula:

Z = (sample mean - population mean) / standard error

For the lower bound (50):

Z1 = (50 - 52) / 1.387 ≈ -1.44

For the upper bound (54):

Z2 = (54 - 52) / 1.387 ≈ 1.44

Now, we'll use a Z-table or calculator to find the probability that the sample mean lies between these Z-scores. We need to find the area between Z1 and Z2.

P(-1.44 < Z < 1.44) = P(Z < 1.44) - P(Z < -1.44)

Using a Z-table or calculator:

P(Z < 1.44) ≈ 0.9251

P(Z < -1.44) ≈ 0.0749

Now subtract:

P(-1.44 < Z < 1.44) = 0.9251 - 0.0749 = 0.8502

So, there is approximately an 85.02% probability that the sample mean will be between 50 and 54.

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Given a sample of size 42 drawn from a population with a mean of 52 and a standard deviation of 9, what is the probability that the sample mean is between 50 and 54?

a.  the equation with n as the subject is  [tex]n = y/z[/tex] . b.the equation with z as the subject is [tex]z = y/n.[/tex]

a) Making n the subject:

Starting with the equation y = zn, where y, z, and n are variables, we want to rearrange the equation to isolate n on one side of the equation.

Step 1: Divide both sides by z to eliminate z from the right-hand side:

y/z = n

Step 2: Swap the sides to get n on the left-hand side:

n = y/z

So, the equation with n as the subject is n = y/z.

Explanation: In this rearrangement, we used the inverse operation of division to isolate n on one side of the equation. By dividing both sides of the equation by z, we eliminated z from the right-hand side, leaving n alone on the left-hand side.

b) Making z the subject:

Starting with the equation y = zn, we want to rearrange the equation to isolate z on one side of the equation.

Step 1: Divide both sides by n to eliminate n from the right-hand side:

y/n = z

Step 2: Swap the sides to get z on the left-hand side:

z = y/n

Therefore,  a.  the equation with n as the subject is  [tex]n = y/z[/tex] . b.the equation with z as the subject is [tex]z = y/n.[/tex]

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In the given problem, solving systematically, the company will pay $3,000 if they purchase 8 computers. (Option C).

To solve this problem, we can use the following steps:

Therefore, the company will pay $3,000 if they purchase 8 computers.

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The maximum that the couple can spend on the meal is $40.63

Let's say that the couple spends a total of X.

Then we know that we need to add a tax of 7%, then we need to add a factor of (1.07) to the total cost.

And we also know that they want to pay a tip of 15%, then we need to add a factor of (1.15) to the total cost.

Then the total cost for the meal will be:

C = x*(1.15)*(1.07)

The maximum that the spend is 50, then let's solve this for C = 50

50 = X*(1.15)*(1.07)

50/(1.15)*(1.07) = X

40.63 = X

The maximum that they can spend is $40.63

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By answering the presented question, we may conclude that As a result, equation if Quigley Inc. converts from Plan A to Plan B, the ROE will increase by 8.6%.

A mathematical equation is a formula that links two statements and uses the equals sign (=) to indicate equality. In algebra, an equation is a statement that demonstrates the equality of two mathematical expressions. The equal sign divides the variables 3x + 5 and 14 in the equation 3x + 5 = 14, for instance.

TIE is an abbreviation for operating income minus interest expense.

3.2 x $35,000 = $35,000 / Interest cost

Interest cost = $35,000 divided by 3.2 is $10,937.50.

The greatest amount of debt that will cover this interest expense is:

Debt = $10,937.50 / 8.8% = $124,488.64

$200,000 - $124,488.64 = $75,511.36 equity

Debt = $124,488.64

Interest paid = $10,937.50

$35,000 in operating income

$35,000 / $10,937.50 = 3.20 TIE ratio (which meets the 3.2 requirement)

EBT = $35,000 - $10,937.50 = $24,062.50

Taxes = 25% * $24,062.50 = $6,015.63

Net profit = $24,062.50 minus $6,015.63 = $18,046.87

ROE = $18,046.87 / $75,511.36 = 0.239 or 23.9%

The difference in ROE between Plan B and Plan A is as follows:

ROE change = ROE (Plan B) - ROE (Plan A)

ROE change = 0.239 - 0.153 = 0.086 or 8.6%

As a result, if Quigley Inc. converts from Plan A to Plan B, the ROE will increase by 8.6%.

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The graph of the given exponential function is as shown in the attached file.

An exponential function is defined as a function with the general form:

y = a(b)^x

where:

a ≠ 0

b is a positive real number and b ≠ 1.

In an exponential function, the base b is a constant. The exponent x is the independent variable where the domain is the set of real numbers.

The given exponential function is:

f(x) = 1(¹/₅)ˣ

The vertical intercept will be the point where x = 0. Thus:

f(0) = 1(¹/₅)⁰

f(0) = 1

Using this value and others, we have the graph as shown in the attached file.

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The range is 33.  The interquartile range is 18. The variance is 187.7143 and the standard deviation is 13.69.

The mean deviation is 7.75. The median deviation is 7.38.

Range = maximum value - minimum value

Maximum value = 40

Minimum value = 7

Range = 40 - 7 = 33

The median of the lower half is (7 + 9 + 18 + 22)/4 = 14

The median of the entire set is (7 + 9 + 18 + 22 + 27 + 29 + 32 + 40)/8 = 24.5

The median of the upper half is (27 + 29 + 32 + 40)/4 = 32.

So, Q1 = 14 and Q3 = 32.

Interquartile range (IQR) = Q3 - Q1 = 32 - 14 = 18

Mean (μ) = (7 + 9 + 18 + 22 + 27 + 29 + 32 + 40)/8 = 23

Variance (σ^2) = Σ(xi - μ)^2 / (n-1)

= ((7-23)^2 + (9-23)^2 + (18-23)^2 + (22-23)^2 + (27-23)^2 + (29-23)^2 + (32-23)^2 + (40-23)^2) / (8-1)

= 187.7143

Standard deviation (σ) = √(σ^2) = √(187.7143) = 13.69

Mean deviation (MD) = Σ|xi - μ| / n

= (|7-23| + |9-23| + |18-23| + |22-23| + |27-23| + |29-23| + |32-23| + |40-23|) / 8

= 62 / 8

= 7.75

Median deviation = Σ|xi - M| / n

where M is the median.

M = (22 + 27) / 2 = 24.5

Median deviation = (|7-24.5| + |9-24.5| + |18-24.5| + |22-24.5| + |27-24.5| + |29-24.5| + |32-24.5| + |40-24.5|) / 8

= 59 / 8

= 7.38

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4 is the answer

Step-by-step explanation:

You will first expand the bracket that will be

2u +6u-30=2

grouping of like terms

2u+6u =2+30

8u =32

dividing both sides by the coefficient u

u =4