Solving exponential functions

Answer:

$ 154

Step-by-step explanation

Let the value of suitcase=x

x × 4.5% = 6.93 (converted the question into equation)

x × [tex]\frac{4.5}{100}[/tex] = 6.93 (converted the percentage into fraction)

x = 6.93 x [tex]\frac{100}{4.5}[/tex] (took reciprocal of 4.5/100 after moving it to the other side of the equation)

x = [tex]\frac{693}{4.5}[/tex] (multiplied the values)

x = 154 $ (simplified the fraction)

make it the brainliest and get 20 years of luck : )

Answer:

We also know that the cost for the tax is 6.93 and we can set up the following proportion rule:

[tex]\frac{x}{100} =\frac{6.93}{4.5}[/tex]

And for this case the value of x represent the cost of the suitcase and solving we got:

[tex]x= 100 \frac{6.93}{4.5}= 154[/tex]

Step-by-step explanation:

Let x the original cost and we also knwo that the tax is 4.5%.

We also know that the cost for the tax is 6.93 and we can set up the following proportion rule:

[tex]\frac{x}{100} =\frac{6.93}{4.5}[/tex]

And for this case the value of x represent the cost of the suitcase and solving we got:

[tex]x= 100 \frac{6.93}{4.5}= 154[/tex]

Answer:

[tex]\boxed{x^3+6x^2+9x}[/tex]

Step-by-step explanation:

[tex]x(x+3)(x+3)[/tex]

Resolving the first parenthesis

[tex](x^2+3x) (x+3)[/tex]

Using FOIL

[tex]x^3+3x^2+3x^2+9x[/tex]

Adding like terms

[tex]x^3+6x^2+9x[/tex]

[tex]\text{If } \: a\cdot b \cdot c = 0 \text{ then } a=0 \text{ or } b =0 \text{ or } c=0 \text{ or all of them are equal to zero.}[/tex]

[tex]x(x+3)(x+3) =0[/tex]

[tex]\boxed{x_1 =0}[/tex]

[tex]x_2+3 =0[/tex]

[tex]\boxed{x_2 = -3}[/tex]

[tex]x_3+3 =0[/tex]

[tex]\boxed{x_3 = -3}[/tex]

Answer: A) 15

Step-by-step explanation:

Because of Pythagorean Theorem, 9^2+12^2=BC^2.  Thus, 81+144=BC^2.  Thus, 225=BC^2.  Thus, 15=BC.

Hope it helps, and ask if you want further clarification <3

Answer:

On a coordinate plane, a curve is level at y = -1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2).

Step-by-step explanation:

y = -2 ^x -1

On a coordinate plane, a curve is level at y = – 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2). Option C is correct.

The Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure can be drawn. A location is assigned to each point on a Cartesian plane.

On a coordinate plane, a curve is level at y = – 1 in quadrant 3 and then decreases rapidly into quadrant 4. It crosses the y-axis at (0, -2).

Hence, option C is correct.

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Answer:

(A)

[tex]N = -b = -(-13) = 13\\\\[/tex]

[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]

[tex]M = 2a = 2(6) = 12[/tex]

(B)

[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]

Step-by-step explanation:

The given equation is

[tex]6x^2 - 13x + 5 = 0[/tex]

The solution is of the form as given by

[tex]$x=\frac{N\pm\sqrt{D}}{M}$[/tex]

(A) Use the quadratic formula to solve this equation and find the appropriate integer values of N, M and D. Do not worry about simplifying the VD yet in this part of the problem.

The quadratic formula is given by

[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

The equations of N, M and D are

[tex]N = -b[/tex]

[tex]D =b^2 -4ac[/tex]

[tex]M = 2a[/tex]

The values of a, b and c are

[tex]a = 6 \\\\b = -13 \\\\c = 5[/tex]

So,

[tex]N = -b = -(-13) = 13\\\\[/tex]

[tex]D =b^2 -4ac = (-13)^2 - 4(6)(5) = 169- 120 = 49[/tex]

[tex]M = 2a = 2(6) = 12[/tex]

(B) Now simplify the radical and the resulting solutions. Enter your answers as a list of integers or reduced fractions, separated with commas. Example: -5/2-3/4

N = 13

D = 49

M = 12

[tex]$x=\frac{13\pm\sqrt{49}}{12}$[/tex]

[tex]$x=\frac{13\pm7}{12}$[/tex]

[tex]$ x=\frac{13+7}{12} $[/tex]  and [tex]$ x=\frac{13-7}{12} $[/tex]

[tex]$ x=\frac{20}{12} $[/tex]  and [tex]$ x=\frac{6}{12} $[/tex]

[tex]$ x=\frac{5}{3} $[/tex]  and [tex]$ x=\frac{1}{2} $[/tex]

[tex]$ x = (\frac{5}{3} , \: \frac{1}{2}) $[/tex]

Answer:

A. This statement A is false.

B. This statement A is false.

C. This statement is true .

Step-by-step explanation:

Determine which of the following statements is true.

From the statements we are being given , we are to determine if the statements are valid to be true or invalid to be false.

SO;

A: If V is a 6-dimensional vector space, then any set of exactly 6 elements in V is automatically a basis for V

This statement A is false.

This is because any set of exactly 6 elements in V is linearly independent vectors of V . Hence, it can't be automatically a basis for V

B. If there exists a set that spans V, then dim V = 3

The statement B is false.

If there exists a set , let say [tex]v_1 ...v_3[/tex], then any set of n vector (i.e number of elements forms the basis of V)  spans V. ∴ dim V < 3

C. If H is a subspace of a finite-dimensional vector space V  then dim H ≤ dim V is a correct option.

This statement is true .

We all know that in a given vector space there is always a basis, it is equally important to understand that there is a cardinality for every basis that exist ,hence the dimension of a vector space is uniquely defined.

SO,

If  H is a subspace of a finite-dimensional vector space V  then dim H ≤ dim V is a correct option.

Answer: a) 0.8708, b) 5714, c) 0.000, d) 0.3830

Step-by-step explanation:

(a)

To find P(Z>-1.13):

Since Z is negative, it lies on left hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.3708

So,

P(Z>-1.13) = 0.5 + 0.3708 = 0.8708

(b)

To find P(Z<0.18):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.0714

So,

P(Z<0.18) = 0.5 + 0.0714 = 0.5714

(c)

To find P(Z>8):

Since Z is positive, it lies on right hand side of mid value.

Table of Area Under the Standard Normal Curve gives area = 0.5 nearly

So,

P(Z>8) = 0.5 - 0.5 nearly = 0.0000  

(d)

To find P(| Z | < 0.5)

that is

To find P(-0.5 < Z < 0.5):

Case 1: For Z from - 0.5 to mid value:

Table of Area Under the Standard Normal Curve gives area = 0.1915

Case 2: For Z from mid value to 0.5:

Table of Area Under the Standard Normal Curve gives area = 0.1915

So,

P(| Z | < 0.5) = 2 * 0.1915 = 0.3830

The Probability can be determine using z-Table. The z- table use to determine the area under the standard normal curve for any value between the mean (zero) and any z-score.

(a) The value of [tex]P(z>-1.13)=0.8708[/tex].

(b) The value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c) The value of [tex]P(Z > 8) = 0.0000[/tex].

(d) The value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Given:

The given condition is [tex]Z\sim N(\mu= 0,\sigma = 1).[/tex]

(a)

Find the value for [tex]P(Z > -1.13)[/tex].

Here Z is less than 1 that means Z is negative. So it will lies it lies on left hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.3708[/tex].

Now,

[tex]P(Z > -1.13)=0.5 + 0.3708 = 0.8708[/tex]

Thus, the value of [tex]P(z>-1.13)=0.8708[/tex].

(b)

Find the value for [tex]P(Z < 0.18)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area = 0.0714[/tex].

Now,

[tex]P(Z <0.18)=0.5 + 0.0714 = 0.5714[/tex]

Thus, the value of  [tex]P(Z < 0.18) = 0.5714[/tex].

(c)

Find the value for [tex]P(Z >8)[/tex].

Here Z is positive. So it will lies it lies on right hand side of mid value.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area \approx 0.5[/tex].

Now,

[tex]P(Z >8)\approx0.5 - 0.5 = 0.0000[/tex]

Thus, the value of [tex]P(Z > 8) = 0.0000[/tex].

(d)

Find the value for [tex]P(|Z| <0.05)[/tex].

Here Z is mod of Z, it may be positive or negative. Consider the negative value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Consider the positive  value of Z.

Refer the table of Area Under the Standard Normal Curve.

[tex]\rm Area =0.1915[/tex].

Now,

[tex]P(|Z| <0.5)=2\times 0.1915 = 0.3830[/tex]

Thus, the value of [tex]P(| Z | < 0.5) =0.3830[/tex].

Learn more about z-table here:

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Answer:

Measure of angle W + measure of angle Z = 180°

Step-by-step explanation:

The reason is that angles in a straight line add up to 180° and angles at a point add up to 360° (i.e the sum of measure of angles W, X, Y, Z is 360°)

Answer:

D is your answer

Step-by-step explanation:

I have no explanation

Answer:

[tex]\boxed{3}[/tex]

Step-by-step explanation:

We can use ratios to solve since the sides are proportional.

[tex]\frac{18}{x} =\frac{48}{8}[/tex]

Cross multiply.

[tex]48x=18 \times 8[/tex]

Divide both sides by 48.

[tex]\frac{48x}{48} = \frac{18 \times 8}{48}[/tex]

[tex]x=3[/tex]

The value of x in the given triangle is 3.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Given are two similar triangles,

Therefore, they have the same ratio of corresponding sides

18/48 = x/8

x = 3

Hence, The value of x in the given triangle is 3.

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Answer:

The option are incorrect because as its slope is only 5/7 the answer will never come like that.

Step-by-step explanation:

Here,

Given,

The dlope of a line is 5/7 and (6,2) is a point.

By one point formulae,

(y-y1)= m (x-x1).

or, (y-2)=5/7(x-1)

or, y = 5/7x -5/7+2

taking lcm of -5/7 and 2. we get,

or, y= 5/7 x -5+7/7

Therefore, the equation is y = 5/7 x -2/7.

Hope it helps..

do not know because my brain cant focus on this sorry :/

Answer:

O B. Positive integers only

Step-by-step explanation:

You have that the temperature of a plate is measured respect to the number of hours that the plate has been left in the sun.

In this case you have that the independent variable is the number of hours and the dependent variable is the temperature.

Due to James would like to know how is changing the temperature of the plate, per hour, the best domain for the function, that is, the best available values for the time on which the temperature of the plate is measured, are the positive integers only.

O B. Positive integers only

Answer:

(2x - y)³ = 8x³ - 12x²y + 6xy² - y³

Step-by-step explanation:

Pascal's Theorem uses a set of already known and easily obtainable numbers in the expansion of expressions. The numbers serve as the coefficients of the terms in the expanded expression.

For the expansion of

(a + b)ⁿ

As long as n is positive real integer, we can obtain the coefficients of the terms of the expansion using the Pascal's triangle.

The coefficient of terms are obtained starting from 1 for n = 0.

- For the next coefficients of terms are 1, 1 for n = 1.

- For n = 2, it is 1, 2, 1

- For n = 3, it is 1, 3, 3, 1

The next terms are obtained from the previous one by writing 1 and summing the terms one by one and ending with 1.

So, for n = 4, we have 1, 1+3, 3+3, 3+1, 1 = 1, 4, 6, 4, 1.

The Pascal's triangle is

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

The terms can also be obtained from using the binomial theorem and writing the terms from ⁿC₀ all through to ⁿCₙ

So, for n = 3, the coefficients are 1, 3, 3, 1

Then the terms are written such that the sum of the powers of the terms is 3 with one of the terms having the powers reducing from n all through to 0, and the other having its powers go from 0 all through to n

So,

(2x - y)³ = [(1)(2x)³(-y)⁰] + [(3)(2x)²(-y)¹] + [(3)(2x)¹(-y)²] + [(1)(2x)⁰(-y)³]

= (1×8x³×1) + (3×4x²×-y) + (3×2x×y²) + (1×1×-y³)

= 8x³ - 12x²y + 6xy² - y³

Hope this Helps!!!

Answer:

the perimeter of the square is just "(5+2x)(2)+(7+2x)(2)

Step-by-step explanation:

Answer:

2 × 10 + 2 × 14

Step-by-step explanation:

The frame is given to have measurements 2 times that of the photograph's measurements. We also know that the photograph is given by dimensions being 5 inch by 7 inch. Therefore the measurements of the frame should be 5 [tex]*[/tex] 2, which = 10 inches, by 7 [tex]*[/tex] 2 = 14 inches.

So the dimensions of the frame are 10 inch × 14 inch. As the frame is present as a rectangle, the perimeter is given by two times both dimensions together. That would be represented by the expression " 2 × 10 inch + 2 × 14 inch. " In other words you can say that the expression is 2 × 10 + 2 × 14 - the expression that represents the perimeter of the frame.

Answer/Step-by-step Explanation:

To create a stem-and-leaf plot for the GPAs of the 20 students that were listed in the above question, take the following steps:

Step 1: for easy plotting, write down the GPAs in an ordered manner, that is, from the smallest value to the largest.

0.5, 0.5, 0.9, 1.1, 1.6, 1.6, 1.7, 1.8, 1.9, 1.9, 2.1, 2.3, 2.4, 2.9, 3.3, 3.4, 3.6, 4.0,  4.0,  4.0

Step 2: divide each set of data into a stem and a leaf. For example, for a GPA, 0.5, 0 would be the stem, while 5 would be the leaf.

For a GPA listed, 2.9, 2 is the stem, 9 is the leaf. Same applies to all the other GPAs.

Step 3: All stems should be written in ascending order, vertically, from the smallest to the largest. From the listed GPAs, you would observe that the highest stem value would be 4, while the lowest would be 0.

Therefore, write down your stems vertically, in ascending order as shown below:

0 |

1 |

2 |

3 |

4 |

Step 4: All leaves should be written also in ascending order to their corresponding stem, from the smallest to the largest, as shown below:

Stem | Leaf

0 | 5 5 9

1 | 1 6 6 7 8 9 9

2 | 1 3 4 9

3 | 3 4 6

4 | 0 0 0

Thus,

0 | 5 5 9 represents => 0.5, 0.5, 0.9

*See attachment below for the stem-and-leaf plot.

Answer:

We can assume that the decline in the population is an exponential decay.

An exponential decay can be written as:

P(t) = A*b^t

Where A is the initial population, b is the base and t is the variable, in this case, number of hours.

We know that: A = 800,000.

P(t) = 800,000*b^t

And we know that after 6 hours, the popuation was 500,000:

p(6h) = 500,000 = 800,000*b^6

then we have that:

b^6 = 500,000/800,000 = 5/8

b = (5/8)^(1/6) = 0.925

Then our equation is:

P(t) = 800,000*0.925^t

Now, the population after 24 hours will be:

P(24) = 800,000*0.925^24 = 123,166

Answer:

122,070 bacteria.

Step-by-step explanation:AA0ktA=500,000=800,000=?=6hours=A0ekt

Substitute the values in the formula.

500,000=800,000ek⋅6

Solve for k. Divide each side by 800,000.

58=e6k

Take the natural log of each side.

ln58=lne6k

Use the power property.

ln58=6klne

Simplify.

ln58=6k

Divide each side by 6.

ln586=k

Approximate the answer.

k≈−0.078

We use this rate of growth to predict the number of bacteria there will be in 24 hours.

AA0ktA=?=800,000=ln586=24hours=A0ekt

Substitute in the values.

A=800,000eln586⋅24

Evaluate.

A≈122,070.31

At this rate of decay, researchers can expect 122,070 bacteria.

Answer:

9 and 18

Step-by-step explanation:

2x and x are the numbers

1/x-1/2x=1/18

2/2x-1/2x=1/18

1/2x=1/18

2x=18X=9,

2x=18

The two integers are 9 and 18

Answer:

All real numbers except for 5.

Step-by-step explanation:

[tex]f(x)=\frac{x}{x-5}[/tex]

The domain of rational functions is determined by the denominator. The denominator cannot equal zero since if they do, the function will be undefined.

Thus, we need to find the zero(s) of the denominator to determine the domain.

[tex]x-5=0[/tex]

[tex]x=5[/tex]

Therefore, the domain of the rational function is all real numbers except for 5.

In set builder notation, this is:

[tex]\{x|x\in \mathbb{R}, x\neq 5\}[/tex]

Answer:

A ) i) X control chart : upper limit = 50.475, lower limit = 49.825

    ii) R control chart : upper limit =  1.191, lower limit = 0

Step-by-step explanation:

A) Finding the control limits

grand sample mean = 1253.75 / 25 = 50.15

mean range = 14.08 / 25 = 0.5632

Based on  X control CHART

The upper control limit ( UCL ) =

grand sample mean + A2* mean range ) = 50.15 + 0.577(0.5632) = 50.475

The lower control limit (LCL)=

grand sample mean - A2 *  mean range = 50.15 - 0.577(0.5632) = 49.825

Based on  R control charts

The upper limit = D4 * mean range = 2.114 * 0.5632 = 1.191

The lower control limit = D3 * mean range = 0 * 0.5632 = 0  

B) estimate the process mean and standard deviation

estimated process mean = 50.15 = grand sample mean

standard deviation = mean range / d2  = 0.5632 / 2.326 = 0.2421

note d2 is obtained from control table

Answer:

c ≤ -9

Step-by-step explanation:

c / -3 ≥ 3

c ≤ -9

Remember, we flip the sign of the inequality by multiplying / dividing by a negative number.

Answer:

c ≤ -9

Step-by-step explanation:

c / -3 ≥ 3

c ≤ -9

Answer:

Let E be the event that the first marble selected is green. Let F be the event that the second marble selected is green. A box contains 20 blue marbles, 16 green marbles and 14 red marbles P(F/E)=15/49 because if the first marble selected is green there are 49 in total and 15 are green. I think this is it.

Step-by-step explanation:

Answer: It will  take you about 61 years for you to reach your goal.

Step-by-step explanation:

We will represent this situation by an exponential function. So if you earn 5% yearly then we could represent it by 1.05.So in exponential function we need to find the initial value and the common difference and in this case the common difference is 1.05 and the initial value or amount is 50,000 dollars.

We could represent the whole situation by the equation.

y= [tex]50,000(1.05)^{x}[/tex]  where x is the number of years. so if you aspire to have 1,000,000 in some years then we will put in 1 million dollars for y and solve for x.

1,000,000 = 50,000(1.05)^x   divide both sides by 50,000

20 = (1.05)^x

x= 61.40

Answer:

The volume of the solid is: [tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]

Step-by-step explanation:

GIven that :

[tex]y = 2 + sec \ x , -\dfrac{\pi}{3} \leq x \leq \dfrac{\pi}{3} \\ \\ y = 4\\ \\ about \ y \ = 2[/tex]

This implies that the distance between the x-axis and the axis of the rotation = 2 units

The distance between the x-axis and the inner ring is r = (2+sec x) -2

Let R be the outer radius and r be the inner radius

By integration; the volume of the of the solid  can be calculated as follows:

[tex]V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(4-2)^2 - (2+ sec \ x -2)^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [(2)^2 - (sec \ x )^2]dx \\ \\ \\ V = \pi \int\limits^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} [4 - sec^2 \ x ]dx[/tex]

[tex]V = \pi [4x - tan \ x]^{\dfrac{\pi}{3}}_{\dfrac{-\pi}{3}} \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) - 4(-\dfrac{\pi}{3})+ tan (-\dfrac{\pi}{3})] \\ \\ \\ V = \pi [4(\dfrac{\pi}{3}) - tan (\dfrac{\pi}{3}) + 4(\dfrac{\pi}{3})- tan (\dfrac{\pi}{3})] \\ \\ \\ V = \pi [8(\dfrac{\pi}{3}) - 2 \ tan (\dfrac{\pi}{3}) ][/tex]

[tex]\mathbf{V = \pi [ \dfrac{8 \pi}{3} - 2\sqrt{3}]}[/tex]

Answer:

75

Step-by-step explanation:

In this case, you just need to use the distance formula of AC and DB.

Using the distance formula, we find that AC= 15, and DB=10

Therefore, area= 150/2=75

Answer:

x = -1

y =2

Step-by-step explanation:

3x+ 5y = 7

9x+ 11y = 13

Multiply the first equation by -3 so we can eliminate x

-3 (3x+ 5y = 7)

-9x -15y = -21

Add this to the second equation

-9x -15y = -21

9x+ 11y = 13

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

   - 4y = -8

Divide by -4

-4y/-4 = -8/-4

y=2

Now solve for x

3x+5y = 7

3x+5(2) = 7

3x+10 = 7

Subtract 10

3x = 7-10

3x = -3

Divide by 3

3x/3 = -3/3

x = -1

Answer:

-1, 2

Step-by-step explanation:

Although you already have the answer, here's another method of doing it that may or may not help you someday. First, we solve the top equation for x. We get:

[tex]x = \frac{7}{3} - \frac{5}{3}y\\9x + 11y = 13[/tex]

Now that we know what x is, we can plug it into the bottom equation to solve for y.

[tex]9(\frac{7}{3} - \frac{5}{3}y) + 11y = 13[/tex]

Simplify everything out, and you'll see that y = 2. We can now plug it into our equation to solve for x.

x = 7/3 - 5/3 x 2; x = -1

Answer:

-3/2

Step-by-step explanation:

Hey there!

Well to find the slope of a line with 2 points we use the following formula,

y2 - y1 / x2 - x1

5 - 2 = 3

-6 - -4 = -2

Slope = -3/2

Hope this helps :)

Answer:

[tex]Slope = -\frac{3}{2}[/tex]

Step-by-step explanation:

[tex](-4, 2) \:(-6,5).\\\\m =\frac{y_2-y_1}{x_2-x_1} \\\\x_1 = -4\\y_1 =2\\x_2 = -6\\y_2 =5\\\\m = \frac{5 -2}{-6-(-4)}\\ m = \frac{3}{-6+4}\\ m = \frac{3}{-2}\\ \\Slope = -\frac{3}{2}[/tex]

Answer:

36y² - 1

Factorize

We have the final answer as

[tex](y - \frac{1}{6} )(36y + 6)[/tex]

Hope this helps you

Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Expand brackets or use distributive law.

1/2(x) + 1/2(6) = 18

1/2x + 6/2 = 18

1/2x + 3 = 18

Subtract 3 on both sides.

1/2x + 3 - 3 = 18 - 3

1/2x = 15

Multiply both sides by 2.

(2)1/2x = (2)15

x = 30

Answer:

30

Step-by-step explanation: