The graph of the function y= x^2 is shown. How will the graph change if the equation is changed to y = (1/4) x^2

The linear equation that represents the cost of visiting the gym x times is: y = 2x + 25

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, and division) that are used to represent quantities and their relationships.

The cost of joining a gym includes an initial fee of $25 and then $2 per visit. Let y be the total cost of visiting the gym x times.

To find the equation that represents this relationship, we need to determine the slope and the y-intercept.

The slope represents the rate of change of the cost with respect to the number of visits, which is the cost per visit. Since the cost per visit is $2, the slope is 2.

The y-intercept represents the initial cost of joining the gym, which is $25.

Therefore, the linear equation that represents the cost of visiting the gym x times is: y = 2x + 25

In this equation, x represents the number of visits to the gym, and y represents the total cost of those visits.

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The statement can be linked to a theorem in geometry known as the "double angle rotation theorem". According to this theorem, if a geometric figure has symmetry about a straight line, and that line intersects another straight line at a point, then the symmetry of the figure about the second line is equivalent to a rotation of twice the angle from the first line to the second line, that is about the point of intersection.

In simple terms, the double angle rotation theorem means that if we can have a geometric figure that is symmetric about a line L1, and L2 is another line that intersects L1 at a point P, then we can rotate the figure about point P by twice the angle formed between L1 and L2 to get the same symmetry about the line L2.

The application of this theorem applies to various aspects of geometry that include transformational geometry and symmetry.

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Answer:

To find the distance between two points, we use the distance formula: distance = square root of [(x2 - x1)^2 + (y2 - y1)^2] In this case, our points are (4, -3) and (-7, -3), so we can plug in the values: distance = square root of [(-7 - 4)^2 + (-3 - (-3))^2] distance = square root of [(-11)^2 + (0)^2] distance = square root of (121) distance = 11 Therefore, the distance between the points (4, -3) and (-7, -3) is 11 units.

Based on the given information, the measure of angle Y is 30 degrees.

A transformation is a process or operation that changes the position, shape, or orientation of a geometric figure or an object in space.

There are several types of transformations, including:

Rotation: A transformation that rotates a figure around a fixed point, called the center of rotation, by a certain angle.

Reflection: A transformation that produces a mirror image of a figure across a line, called the line of reflection.

To start, let's first find the vertices of triangle XYZ after the given transformations:

Rotation of 90 degrees counterclockwise about the origin:

The rotation of point (x, y) by 90 degrees counterclockwise about the origin gives us the point (-y, x). So we can apply this transformation to each vertex of triangle ABC to get the vertices of triangle XYZ after rotation:

A = (cos(45), sin(45)) = (√2/2, √2/2) → A' = (-√2/2, √2/2)

B = (cos(55), sin(55)) → B' = (-sin(55), cos(55))

C = (cos(80), sin(80)) → C' = (-sin(80), cos(80))

Reflection across the line y=x:

To reflect a point (x, y) across the line y=x, we simply swap the x and y coordinates to get (y, x). So we can apply this transformation to each vertex of triangle XYZ to get the final vertices:

A'' = (√2/2, -√2/2)

B'' = (cos(55), -sin(55))

C'' = (cos(80), -sin(80))

Now we can use the law of cosines to find the measure of angle Y:

cos(Y) = [B''C''² + A''C''² - A''B''²] / [2 * B''C'' * A''C'']

= [cos(55)² + cos(80)² - (√2/2)²] / [2 * cos(55) * cos(80)]

≈ 0.866

So we have cos(Y) = 0.866, which means Y ≈ 30 degrees. Therefore, the measure of angle Y is approximately 30 degrees.

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We can use the quadratic formula to solve for x, and the system of equations to solve for y. We have two possible solutions for x: x = 4 + [tex]\sqrt{28}[/tex] ≈ 8.29, and y = 7 - x ≈ -0.29.

A system of linear equations can be solved using the substitution approach. In this procedure, one variable in one of the equations is solved in terms of the other, and that expression is then replaced into the other equation. This yields an equation with a single variable that can be solved. Once one variable has been identified, it may be swapped into one of the original equations to determine the second variable.

We can use the first equation to solve for one of the variables in terms of the other, and then substitute that expression into the second equation to get an equation in just one variable. Let's solve the first equation for y:

x + y = 7

y = 7 - x

Now we can substitute this expression for y into the second equation:

[tex]y = x^2 - 9x - 5[/tex]

[tex]7 - x = x^2 - 9x - 5[/tex]

Rearranging terms, we get:

[tex]x^2 - 8x - 12 = 0[/tex]

Now we can use the quadratic formula to solve for x:

x = (-b ± [tex]\sqrt{(b^2 - 4ac)}[/tex]) / 2a

where a = 1, b = -8, and c = -12. Plugging these values in, we get:

x = (-(-8) ± [tex]\sqrt{(-8)^2 - 4(1)(-12))}[/tex]) / 2(1)

Simplifying:

x = (8 ± [tex]\sqrt{(64 + 48)}[/tex]) / 2

x = (8 ± [tex]\sqrt{(112)}[/tex]) / 2

x = 4 ± [tex]\sqrt{(28)}[/tex]

So we have two possible solutions for x:

x = 4 + [tex]\sqrt{(28)}[/tex] ≈ 8.29

x = 4 - [tex]\sqrt{(28) }[/tex]≈ -0.29

Now we can use either equation to solve for y. Let's use y = 7 - x:

When x = 4 + [tex]\sqrt{(28)}[/tex], we have:

y = 7 - (4 + [tex]\sqrt{(28)}[/tex]) = 3 - [tex]\sqrt{(28)}[/tex]

When x = 4 - [tex]\sqrt{(28)}[/tex], we have:

y = 7 - (4 - [tex]\sqrt{(28)}[/tex]) = 3 + [tex]\sqrt{(28)}[/tex]

So the two solutions to the system of equations are:

x = 4 + [tex]\sqrt{(28)}[/tex], y = 3 - [tex]\sqrt{(28)}[/tex]

x = 4 - [tex]\sqrt{(28)}[/tex], y = 3 + [tex]\sqrt{(28)}[/tex]

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The length of OI is 6.5 units. The solution has been obtained by using the Pythagoras theorem.

What is Pythagoras theorem?

Pythagoras' Theorem states that the square of a right-angled triangle's hypotenuse side is equal to the sum of the squares of its other two sides.

We are given a circle with two tangents drawn from a external point and the radius perpendicular to the tangent measures 3.9 units.

We know that the tangents when drawn from a external point are equal in length.

So,

IK = IJ = 5.2 units

Now, in triangle OJI, using the Pythagoras theorem, we get

⇒ [tex]OI^{2}[/tex] = [tex]OJ^{2}[/tex] + [tex]IJ^{2}[/tex]

⇒ [tex]OI^{2}[/tex] = [tex]3.9^{2}[/tex] + [tex]5.2^{2}[/tex]

⇒ [tex]OI^{2}[/tex] = 15.21 + 27.04

⇒ [tex]OI^{2}[/tex] = 42.25

⇒ OI = 6.5 units

Hence, the length of OI is 6.5 units.

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Answer:

(a) 7

(b) 7

(c) 27

The property of addition used in all three equations is the associative property, which allows us to regroup the numbers being added without changing their sum.

This test is left-tailed and the test statistic is -1.53

Since the alternative hypothesis is that less than 10% of treated subjects experienced headaches, and this is a lower bound, the test is left-tailed.

To find the test statistic, we first need to calculate the expected number of subjects who would experience headaches if the null hypothesis were true (i.e., if the true proportion were 10%). This is found by multiplying the total number of treated subjects by the hypothesized proportion:

Expected number of subjects with headaches = 0.10 * 288 = 28.8

We then use the formula for the z-score of a sample proportion:

z = (p - P) / √(P(1 - P) / n)

where p is the sample proportion (21/288), P is the hypothesized proportion (0.10), and n is the sample size (288).

Plugging in the values, we get:

z = (0.073 - 0.10) / √(0.10 * 0.90 / 288) = -1.53

Therefore, the test statistic is z = -1.53.

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The measurement of angle EFG is 42.

The central angle is an angle with two arms and a vertex in the middle of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle. An excellent illustration of a central angle is a pizza slice. A pie chart is made up of several sectors and is useful for representing various amounts.

A straightforward illustration of a sector with a center angle of 180o is a protractor. The angle created by a circle's arc at its center is another way to describe the term "central angle."

We have a circle with center H and the central angle is 84 degrees

The central angle of the circle is double of circumference angle.

Then the measurement of angle EFG is 42.

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The terrarium has 594 cm³ volume of dirt.

What is volume?

Given the dimensions of the terrarium as h=12cm, l=22cm, and b=9cm, we can calculate the volume of the terrarium as follows:

Volume of terrarium = length x width x height

= 22 cm x 9 cm x 12 cm

= 2,376 cm³

Since the terrarium is filled 1/4 of the way with dirt, the volume of dirt is:

Volume of dirt = (1/4) x Volume of terrarium

= (1/4) x 2,376 cubic cm

= 594  cm³

Therefore, the terrarium has 594 cubic centimeters of dirt.

what is terrarium?

A terrarium is a sealed or partially enclosed glass container used to grow and display plants or small animals. It is typically made of clear glass or plastic and is designed to mimic a miniature ecosystem, providing a controlled environment for plants to grow and thrive. Terrariums are popular for indoor gardening and can be used to create a variety of landscapes, from tropical rainforests to desert landscapes. They require minimal maintenance and are an excellent way to bring a touch of nature into your home or office.

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Complete question is: A terrarium is filled 1/4 of the way with dirt. the  terrarium have 594 cubic centimeters of dirt.

the volume of one scoop of ice cream is 523.6 cc. The cup can hold a volume of 942.5 cc, which is more than one scoop of ice cream. Therefore, Moses's cup can hold one scoop of ice cream without overflowing or spilling.

let's break down the problem step by step.

First, we need to calculate the volume of one scoop of ice cream. Since each scoop is a perfect sphere with a radius of 5 cm, we can use the formula for the volume of a sphere, which is:

V = (4/3)πr³

where V is the volume and r are the radius. Substituting r = 5 cm, we get:

V = (4/3)π(5³) = 523.6 cubic centimeters (cc)

So, the volume of one scoop of ice cream is 523.6 cc.

Next, we need to calculate the volume of the cup and the cone. Since both have the same radius as the scoop of ice cream, we can use the formula for the volume of a cylinder and a cone, respectively, with height 12 cm and radius 5 cm:

For the cup:

[tex]V_{cup}[/tex]= πr²h = π(5²) (12) = 942.5 cc

For the cone:

[tex]V_{cone}[/tex] = (1/3)πr²h = (1/3)π(5²)(12) = 314.2 cc

So, the volume of the cup is 942.5 cc, and the volume of the cone is 314.2 cc.

Now, we can determine how much ice cream each container can hold. Since each person gets one scoop of ice cream, we need to compare the volume of one scoop of ice cream to the volume of each container.

For Gaby's cone:

We know that the volume of one scoop of ice cream is 523.6 cc. The cone can hold a volume of 314.2 cc, which is less than one scoop of ice cream. Therefore, Gaby's cone can only hold one scoop of ice cream.

For Moses's cup:

Again, the volume of one scoop of ice cream is 523.6 cc. The cup can hold a volume of 942.5 cc, which is more than one scoop of ice cream. Therefore, Moses's cup can hold one scoop of ice cream without overflowing or spilling.

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The complete question: What is the volume of ice cream in each scoop and what is the total volume of ice cream that Mr. Woods needs to buy for Moses and Gaby? Also, what is the total surface area of the ice cream exposed to the air in each container (cone and cup)?

The maximum value of Q was found to be 26.49 subject to the cost constraint K+4L=16.2, and the optimal value of Q decreased by approximately 9.39 when the cost constraint was changed to K+4L=17.

To find the maximum value of Q subject to the cost constraint, we can use the method of Lagrange multipliers. We first define the Lagrangian function:

L(K, L, λ) = 10√(KL) + λ(K + 4L - 16.2)

where λ is the Lagrange multiplier.

∂L/∂K = 5√(L/K) + λ = 0

∂L/∂L = 5√(K/L) + 4λ = 0

∂L/∂λ = K + 4L - 16.2 = 0

K = 3.24, L = 2.16, λ = -2.5

Therefore, the maximum value of Q is:

Q = 10√(3.24*2.16) = 10√7.0224 ≈ 26.49

If the cost constraint is changed to K+4L=17, we can repeat the same process with the new constraint to get:

K = 4.25, L = 0.6875, λ = -2.5

Therefore, the new maximum value of Q is:

Q = 10√(4.25*0.6875) = 10√2.9297 ≈ 17.10

The change in the optimal value of Q is then:

17.10 - 26.49 ≈ -9.39

The optimal value of Q decreases by approximately 9.39 when the cost constraint is changed from K+4L=16.2 to K+4L=17. This indicates that the optimal value of Q is sensitive to changes in the cost constraint.

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Find the maximum value of Q = 10√/KL subject to the cost constraint K+4L=16.

Estimate the change in the optimal value of Q if the cost constraint is changed to K+4L =17. Interpret the meaning of Lagrange multiplier.

Answer:

AB = 9

Step-by-step explanation:

Since triangle ACE and BCD are congruent, they have the same angles, you can figure out the fraction to get from ACE to BCD, then reverse it. So since CE is 12 + 4 = 16 and CD is 4, we can see that ACE is 4 times greater than BCD because 16/4 = 4.

So to get AB, find AC by multiplying BC by 4, which gives 12, then subtract AC by BC to get AB: 12 - 3 = 9

Plotting the equation shows that the graph crosses the

The value of h is 8

To find the value of y when x is 3, we need to substitute 3 for x in the given equation -x^2 - x + 20:

y = -x^2 - x + 20 (substitute x = 3)

y = -(3)^2 - 3 + 20

y = -9 - 3 + 20

y = 8

Therefore, when x is 3, y is 8.

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Answer:

It will take them 9756 minutes

Step-by-step explanation:

10 students take 813

How do you get from 10 to 120?

times 10 by 12

Now times 813 by 12

9756

Answer: What is minor arc and major arc?

Image result for 1. Name a minor arc. 2. Name a major arc. 3. Name a point of tangency. 4. Name a radius.

Every pair of endpoints defines two arcs. An arc whose measure is less than 180 degrees is called a minor arc. An arc whose measure is greater than 180 degrees is called a major arc. An arc whose measure equals 180 degrees is called a semicircle, since it divides the circle in two.

Step-by-step explanation:

The estimated yield of wheat when the average amount of fertilizer is applied is 68.65 units.

To estimate the yield of wheat when the average amount of fertilizer is applied, we first need to calculate the average amount of fertilizer from the given data.

Use a linear regression tool to fit a line to the data points.

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

where y is the yield of wheat, x is the amount of fertilizer, m is the slope of the line, and b is the y-intercept.

Using this method, we can estimate the yield of wheat when no fertilizer is applied.

To estimate the yield of wheat when the average amount of fertilizer is applied, we first need to calculate the average amount of fertilizer from the given data.

[tex](50 + 80 + 100 + 122 + 150 + 180 + 200) / 7 = 120[/tex]

Therefore, the average amount of fertilizer applied is 120.

[tex]y = m(120) + b[/tex]

To get the values of m and b, we can perform a linear regression analysis on the given data points.

[tex]m = 0.3903[/tex]

b = 21.754

Substituting these values into the equation above, we get:

[tex]y = 0.3903(120) + 21.754 = 68.65[/tex]

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Answer:

32°

Step-by-step explanation:

2x + 1 + x - 7 = 90

3x + 1 - 7 = 90

3x - 6 = 90

3x = 96

x = 32

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Answer:

Step-by-step explanation:

Value of x:-

[tex]\mathrm{(2x+1)+(x-7)=90^o}[/tex]

[tex]\mathrm{2x+1+x-7=90}[/tex]

[tex]\mathrm{(2x+x)+(1-7)=90}[/tex]

** [tex]\mathrm{2x+x=\bf 3x}[/tex]

** [tex]\mathrm{1-7=\bf -6}[/tex]

[tex]\mathrm{3x-6=90}[/tex]

[tex]\mathrm{3x-6+6=90+6}[/tex]

[tex]\mathrm{3x=96}[/tex]

[tex]\mathrm{\cfrac{3x}{3}=\cfrac{96}{3}}[/tex]

[tex]\mathrm{x=32}[/tex]

Therefore, the value of x is 32°.

____________________

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The area of the regular polygon and rounded  to the nearest hundredth is 200 sq. units.

How to find the area of any polygon?

Area of Regular Polygon Formula = [tex]\frac{l^2n}{4tan\left(\frac{180}{n}\right)}[/tex] Square units

Length of side of the regular polygon is 5.2 and have n= 9 sides

Let's say, Area is A for the polygon,

[tex]A = \frac{(5.2)^2 \times 9}{4 tan\left(\frac{180}{9}\right)}\\\\A= 167.16\ sq.\ units\\A= 200\ sq.\ units\ (round-off\ to\ nearest\ hundred)[/tex]

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area is approximately 158.72 square centimeters

To find the area of a regular octagon with a given side length and apothem, we can use the formula:

Area = (1/2) × Perimeter × Apothem

where Perimeter is the total length of all the sides of the octagon.

We are given that the side length of the octagon is 5.2 cm and the apothem is 7.6 cm.

To find the perimeter of the octagon, we can use the fact that the octagon is a regular polygon and has eight equal sides. Thus:

Perimeter = 8 × side length = 8 × 5.2 cm = 41.6 cm

Now we can substitute the values we have into the formula to get:

Area = (1/2) × Perimeter × Apothem

Area = (1/2) × 41.6 cm × 7.6 cm

Area = 158.72 cm²

Therefore, the area of the regular octagon with a side length of 5.2 cm and an apothem of 7.6 cm is approximately 158.72 square centimeters.

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Answer:

You can start by changing 12 3/4 into a decimal, which would be 12.75.

The formula for perimeter of a rectangle is (l + w) x 2, so you could write it like this:

(12.75 + 6.4) x 2

Then solve the question in the parenthesis...

19.15 x 2 = 38.30

Now, the question says to write the perimeter into simplest fraction form.

38.30 = 38 3/10.

So, there you have it!

38 3/10 meters

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If 88% of the stamps were foreign, then the remaining 12% must be domestic stamps.

To find out how many domestic stamps Blake collected, we can start by calculating what 12% of 275 is:

12% of 275 = 0.12 x 275 = 33

The remaining stamps are foreign stamps.

Therefore, Blake collected 33 domestic stamps.

The required solution of the given inequality is {m | 6 ≤ m < 9}.

In mathematics, inequality is a statement of an order relationship between two numbers or algebraic expressions that is greater than, greater than or equal to, less than, or less than or equal to.

According to question:

We can solve the inequality as follows:

3 + m ≥ 9 or 1 + 2m < 19

Subtracting 3 from both sides of the first inequality, we get:

m ≥ 6

Subtracting 1 from both sides of the second inequality and then dividing by 2, we get:

m < 9

Putting these two inequalities together, we get:

6 ≤ m < 9

This is the solution in interval notation. To write it in set-builder notation, we can use the following notation:

{m | 6 ≤ m < 9}

This means the set of all values of m such that m is greater than or equal to 6, and less than 9.

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The rectangular prism, which has sides measuring 12 feet, 14 feet, and 20 feet, has a surface area of 1376feet².

The space a two-dimensional flat surface occupies is the area. Its unit of measurement is the square. A three-dimensional object's surface area is the area occupied by its exterior surface. It is also measured in units².

We must first determine the surface area of each face of a rectangular prism with sides measuring 12 feet, 14 feet, and 20 feet before adding them all up.

Let's first determine the area of the top and bottom faces, which are both rectangles measuring 12 feet by 20 feet each:

480feet² is equal to 2 x (12 ft x 20 ft) for the top and bottom faces.

The front and back faces, which are both rectangles with measurements of 12 feet by 14 feet, can now be calculated as follows:

2 x (12 ft) x (12 ft) x (12 ft) = 336feet² is the area of the front and back faces.

Let's finally determine the area of the rectangles that make up the left and right faces, both of which measure 14 feet by 20 feet:

2 x (14 ft x 20 ft) = 560feet² is the area of the left and right faces.

We add up the areas of all six faces to determine the total surface area:

Overall surface area equals the sum of the areas on the top, bottom, front, and back, as well as the left and right faces.

Overall surface area equals 480feet² + 336feet² + 560feet² =1376 feet².

As a result, the rectangular prism with measurements of 12 feet, 14 feet, and 20 feet has a surface area of 1376 feet².

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The complete question is:

what is the surface area of 12 ft 16 ft 14 ft 20 ft

Answer:

Step-by-step explanation:

To simplify 5(y+2) +5(y-1), we distribute the 5 to each term inside the parentheses, and then combine like terms as follows:

5(y+2) +5(y-1)

= 5y + 10 + 5y - 5 // Distribute the 5

= 10y + 5 // Combine like terms

Therefore, 5(y+2) +5(y-1) simplifies to 10y + 5.

Credit card issuers use credit scores to determine the consumer's eligibility for credit and to set pricing for credit lines. (Options C and E).

A credit card is a type of payment card that allows the cardholder to borrow money from a financial institution or issuer to purchase goods or services. The cardholder can use the card to make purchases up to a certain credit limit set by the issuer, and they are required to pay back the borrowed amount, usually with interest, within a specified period of time.

Credit cards typically offer a range of benefits, such as rewards programs, cash back, and fraud protection, and they are widely used for online and in-person transactions. However, if not used responsibly, credit cards can lead to debt and financial problems.

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The fraction for 6 and 10 is 6/10, which can be simplified to 3/5 by dividing both the numerator and denominator by their greatest common factor, which in this case is 2.

So 6/10 is equivalent to 3/5.

By dividing the numerator and denominator by their 3 greatest common factor, the resultant fraction is 8/21 .

To express a portion of a whole or the division of a quantity, use a fraction. It consists of a horizontal or slant line separating the two integers that make up the numerator and denominator. The total quantity of components in the whole is represented by the denominator, while the numerator is the number of equal parts that are being taken into account. As an illustration, the numerator and denominator of the fraction 3/4 are 3 and 4, respectively. Parts of a set, chunks of a pie, and ratios between quantities can all be represented using fractions. Using particular guidelines and algorithms, they can be multiplied, divided, added, or subtracted. To make calculations and comparisons simpler, fractions can be changed to decimals or percentages.

given

We combine the numerators and denominators together to multiply two fractions. So:

(4/9) x (6/7) = (4 x 6) / (9 x 7) = 24/63

By dividing the numerator and denominator by their 3 greatest common factor, the resultant fraction can be made simpler:

24/63 = (3 x 8) / (3 x 21) = 8/21

Because of this, 4/9 x 6/7 Equals 8/21.

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Answer:After layla adds a tip, the price of the item is $16.20. The percent of the tip is 10 %

Step-by-step explanation:

What is a tip?

A tip is a gift or a sum of money placed or given for a service performed or anticipated, by extension, a form of gratuity. Even if the service is poor, it's recommended you leave at least 10 percent.

How to calculate a tip?

There are four ways of calculating a tip:

Method 1: Move over the decimal in the bill total and then double that number.

Method 2: Multiply the tax of the bill by two.

Method 3: Double the pretax bill and then move the decimal over one space.

Method 4: Determine 10% of the bill and add half