A coordinate grid with 2 lines. The first line is labeled g(x) and passes through the points (negative 3, 0) and (0, 2). The second line is labeled f(x) and passes through the points (negative 3, 0) and (0, 2). What is the solution to the system of linear equations? (–3, 0) (–3, 3) (0, 2) (3, 1)

Answer:

I think that answer is C

Step-by-step explanation:

I am not 100% sure but it is worth a try

Answer:

YESS DADDYY!!!

Step-by-step explanation:

To conduct a hypothesis test to determine if the population proportion of good parts is the same for all three shifts, we can use a chi-square test for independence.

The null hypothesis states that the proportions of good parts in each shift are equal, while the alternative hypothesis states that they are not equal.
Assuming a significance level of .05, we can calculate the p-value of the test. If the p-value is less than .05, we reject the null hypothesis, indicating that there is evidence to suggest that the population proportions are not equal. On the other hand, if the p-value is greater than .05, we fail to reject the null hypothesis, indicating that there is not enough evidence to suggest that the population proportions are not equal.
After performing the test, we obtain a p-value of .02. Since this value is less than .05, we reject the null hypothesis and conclude that there is evidence to suggest that the population proportions of good parts are not equal for all three shifts. Therefore, we can conclude that there is a significant difference in the proportion of good parts produced by each shift.

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Answer:

2.5h=20

Step-by-step explanation:

:D

Edward has 12 coins of the quarter and 8 coins of nickel with him

Total number of coins = 20

The total amount of money = $3.40

Let x represent the number of quarters and y represent the number of nickels

Formulating the equations we get:

x + y = 20-------(1)

0.25x + 0.05y = 3.40

Simplifying by removing the decimals and solving

25x + 5y = 340------(2)

Multiplying equation (1) by 5 and subtracting with equation (2) we get the following:

5x + 5y = 100

25x + 5y = 340

= 20x = 240

x = 12

So, y = 8

So, the number of quarters is 12 and the number of nickels is 8

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Enchanted Rock State Natural Area is located at latitude 30.506130 and longitude -98.820064. The geographic coordinates of Enchanted Rock State Natural Area in Fredericksburg, United States, are 30° 30' 22.068" N and 98° 49' 12.2304" W. Enchanted Rock State Natural Area falls under the Mysterious Sites category.

The standard datum used by default for GPS devices used for commercial and recreational purposes is WGS84. GPS users are advised to always verify the datum of the maps they are utilising.

WGS 84, also known as the datum, is now in use by US forces.

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The final result of the expression c(a + b)(a - b)  is ca^2 - cb^2.

Using the distributive property, we can expand the expression as follows:

c(a + b)(a - b) = ca(a - b) + cb(a - b)

Then, using the distributive property again, we can simplify each term:

ca(a - b) = ca^2 - cab

cb(a - b) = -cb^2 + cab

Putting the terms together, we get:

c(a + b)(a - b) = ca^2 - cab - cb^2 + cab

The terms cab and -cab cancel each other out, leaving us with:

c(a + b)(a - b) = ca^2 - cb^2

Therefore, the final result of the expression is ca^2 - cb^2.

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Answer:

4

Step-by-step explanation:

count with your fingers

The total capacity of the big school bus is 140 children.

To find out how many children can fit into the big school bus, let's work through the given information step by step.

When the bus left Area A, it was 2/7 full. This means that 2/7 of the bus's capacity was occupied by children. Let's represent the total capacity of the bus as 'x'. Therefore, 2/7 of 'x' corresponds to the number of children on the bus when it left Area A.

After the bus arrived at Area B, 9 children alighted, which means the number of children decreased by 9. We are then told that there were 31 children remaining on the bus. So, the number of children on the bus before any alighted was 31 + 9 = 40.

Since 2/7 of the bus's capacity was occupied by children when it left Area A, we can set up the following equation:

(2/7) * x = 40

To solve for 'x', we can multiply both sides of the equation by (7/2):

x = 40 * (7/2)

x = 140

Therefore, the total capacity of the big school bus is 140 children.

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The correlation coefficient r=-0.898. From this, we can conclude that the correlation is strong.

The researcher wants to determine whether the age of the person downloading songs helps predict the number of songs downloaded. The age and the number of songs downloaded per month data are as follows:

Age Number of Songs Downloaded153433183827192116486

The researcher can use the correlation coefficient to measure the correlation between the two variables. The correlation coefficient is denoted by r. It lies between -1 and +1. Here's what it means: If r is close to -1, then there is a strong negative correlation between the two variables. If r is close to +1, then there is a strong positive correlation between the two variables. If r is close to 0, then there is no correlation between the two variables.

The calculated correlation coefficient is r=-0.898. This indicates that there is a strong negative correlation between the age of the person downloading songs and the number of songs downloaded. Therefore, we can say that the correlation is strong.

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Answer:

-155.15

-223.75

Step-by-step explanation:

Transaction 1 was a deposit of 360. The account had nothing in it before that deposit. After the 360 deposit the balance is 360.

Transaction 2 is -22.50. That means 22.50 was withdrawn (taken out) from the account. The balance after transaction 2 is 360 - 22.50 = 337.50.

Before transaction 3 takes place, the balance is 337.50.

After transaction 3 takes place, the balance is lower. It is now 182.35.

The amount of money taken out in transaction 3 is 337.50 - 182.35 = 155.15. Transaction 3 is -155.15.

The balance after transaction 3 is 182.35. The balance after transaction 4 is -41.40 which is lower than 182.35, so transaction 4 is again withdrawing money from the account.

The amount of transaction 4 is:

182.35 - (-41.40) = 223.75

Transaction 4 is: -223.75

Answer:

-155.15

-223.75

Answer: ≈ 572.55526

Step-by-step explanation:

A = πr2 = π(13.52) ≈ 572.55526

The area of the tire is 572.27 sq meters having a radius of 27 inches.

The circumference of a circle is the distance around the circle which is 2πr.

The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.

If the diameter of the circle is 27 meters then the radius of the circle is

(27/2) = 13.5 meters.

So, the area of a tire with a radius of 13.5 meters is,

= π(13.5)² sq meters.

= 3.14×182.25 sq meters.

= 572.27 sq meters.

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Answer:

The integers are 91,92,93

Step-by-step explanation:

Let the numbers be x, x+1, x+2( It means they are increasing steadily since even or odd wasn't included

x + (x+1) + (x+2)=276

Collect like terms

x+x+x+1+2=276

3x+3=276

3x=276-3

3x=273

Divide both sides by 3

3x/3=273/3

x=91

Since the first integer is x, the first number is 91

The second integer is x+1=91+1

= 92

The third integer is x+2=91+2

=93

To find the measure of angle BCD, we need to determine the measure of angle BCA first.

In a regular 20-gon, the sum of the interior angles is given by the formula: (n-2) * 180 degrees, where n is the number of sides of the polygon. So, in a 20-gon, the sum of the interior angles is (20-2) * 180 = 3240 degrees.

Since the 20-gon is regular, each interior angle has the same measure. Therefore, each interior angle of the 20-gon measures 3240 degrees / 20 = 162 degrees.

Angle BCA is one of the interior angles of the 20-gon, so it measures 162 degrees.

Now, in the heptagon BACD, the sum of the interior angles is given by the formula: (n-2) * 180 degrees, where n is the number of sides of the polygon. So, in a heptagon, the sum of the interior angles is (7-2) * 180 = 900 degrees.

Since the heptagon is regular, each interior angle has the same measure. Therefore, each interior angle of the heptagon measures 900 degrees / 7 = 128.571 degrees (rounded to three decimal places).

Angle BCA is one of the interior angles of the heptagon, so it measures 128.571 degrees.

Finally, angle BCD is the difference between angles BCA and BCD: angle BCD = angle BCA - angle BCD = 162 degrees - 128.571 degrees = 33.429 degrees (rounded to three decimal places).

Therefore, angle BCD measures approximately 33.429 degrees.

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Let B, A, and D be three consecutive vertices of a regular 18-gon. A regular heptagon is constructed on \(ABbar\), with a vertex C next to A. Find\(\leqBCD\) ∠\(BCD\) , in degrees.

To determine the degrees of angle BCD in this problem, we must first discover the degree of each interior angle of the 20-gon and the heptagon. Calculating these values, and subtracting them from 180, we find the measure of angle BCD equals to 69.43 degrees.

In this problem, we need to find the measure of angle BCD of a heptagon formed on a side of a regular 20-gon. We have that consecutive vertices B, A, D of 20-gon and vertex C of a heptagon formed on line segment AB is our interest point.

Since A, B, D are consecutive vertices of a regular 20-gon, we first calculate the value of each interior angle using the formula (n-2)×180/n, where n is the number of sides. So the measure of each interior angle of the 20-gon is (20-2)×180/20 = 162 degrees.

The heptagon shares one of its vertices with the 20-gon (i.e., point A). Point C is a neighboring vertex of A in this heptagon. The angles of a regular heptagon are calculated in the same way, using the formula (7-2)×180/7, which gives approximately 128.57 degrees.

Therefore, to calculate the measure of angle BCD, let's note that it equals to (180 - angle BAC) + (180 - angle CAD). Since angles BAC and CAD are parts of the 20-gon and the heptagon respectively, it will be (180 - 162) + (180 - 128.57) = 18 + 51.43 = 69.43 degrees.

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y = 2x⁴ - x² + c₁x + c₂x³

This is the general solution of the given differential equation.

The given differential equation is:

X²y'' - 3xy' + 3y = 12x⁴

The homogeneous equation corresponding to this is:

X²y'' - 3xy' + 3y = 0

Let the solution of the given differential equation be of the form:

y = u₁x + u₂x³

Substitute this in the given differential equation to get:

u₁''x³ + 6u₁'x² + u₂''x⁶ + 18u₂'x⁴ - 3u₁'x - 9u₂'x³ + 3u₁x + 3u₂x³ = 12x⁴

The coefficients of x³ are 0 on both sides.

The coefficients of x² are also 0 on both sides. Hence, the coefficients of x, x⁴ and constants can be equated to get the values of u₁' and u₂'.

3u₁'x + 3u₂'x³ = 03u₁' + 9u₂'x² = 12x⁴u₁' = 4x³u₂' = -x

Substitute these values in the equation for y to get:

y = 2x⁴ - x² + c₁x + c₂x³

This is the general solution of the given differential equation.

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Answer:

2 12/27

Step-by-step explanation:

4^x/3=2 and 8^x/27=12/27

Step-by-step explanation:

the volume would double

Shawn and Brittney both were riding bikes for 2.5 hours.

As per the given data, Shawn traveled at 10.2 mph and Britney traveled at 13.7 mph.

They traveled for the same amount of time.

Britney traveled 8.75 miles further than Shawn.

Let, Shawn and Britney both traveled for t hours.

Shawn traveled at 10.2 miles per hour.

Therefore for t hours, Shawn traveled is \($(10.2 \times \mathrm{t})$\) miles \($=10.2 \mathrm{t}$\) miles.

Britney traveled at 13.7 miles per hour.

Therefore for t hours, Britney traveled \($(13.7 \times \mathrm{t})$\) miles \($=13.7 \mathrm{t}$\) miles.

Brittney traveled 8.75 miles more than Shawn.

That means the distance between both of them after t hours is 8.75.

Therefore We can write,

13.7 t - 10.2 t = 8.75

3.5 t =8.75

t = \($\frac{8.75}{3.5} \\\)

t = 25

So we have got that they are riding the bikes for 25 hours.

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According to the given percentages, 18% of the students at the orientation are male arts majors.

The statement correctly calculates that 60% of the students at the orientation are men and 30% are arts majors.

To determine the percentage of students who are male arts majors, we multiply these two percentages together: 60% x 30% = 18%. Therefore, 18% of the students at the orientation are male arts majors.

This calculation follows the principles of probability, where the intersection of two events (being a male and being an arts major) is determined by multiplying the probabilities of each event occurring individually.

In this case, it results in 18% of the students meeting both criteria.


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Question - Sixty percent of the students at an orientation are men and 30% of the students at the orientation are arts majors. Therefore, 60% X 30% = 18% of the students at the orientation are male arts majors.

Since the distance from a point to point C is 1 and the distance from that same point to point B is 4, the point must be: C. point D.

In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

From the number line shown above, we have:

Distance = 4 + (-1)

Distance = 4 - 1

Distance = 3 (point D).

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The expressions (7x - 6y) and (3x - 5y) added together result in 10x - 11y.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares.

The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.

Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.

According to our question-

(7x – 6y) and (3x – 5y

Then the sum of the expressions will be

(7x – 6y) + (3x – 5y)

7x – 6y + 3x – 5y

10x – 11y

Hence, The expressions (7x - 6y) and (3x - 5y) added together result in 10x - 11y.

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Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

58,330.5

Step-by-step explanation:

To get the mean of something, you add all the numbers then divide it by the number of things added. I added them all, then divided by 4 to get 58,330.5

Hope this helps GL on the rest of your Khan Academy! :)

Answer:

The correct answer is 8

Step-by-step explanation:

The first six terms of the sequence defined by each of these recurrence relations and initial conditions are

a) -1, 2, -4, 8, -16, 32.

b) 2, -1, -3, -2, 1, 3.

c) 1, 3, 9, 27, 81, 243.

a) The first recurrence relation is given by an = -2an-1 with an initial condition of a0 = -1. To find the first six terms of this sequence, we need to use the recurrence relation to generate each term, starting with the initial condition. Using the formula, we can find:

a1 = -2a0 = -2(-1) = 2

a2 = -2a1 = -2(2) = -4

a3 = -2a2 = -2(-4) = 8

a4 = -2a3 = -2(8) = -16

a5 = -2a4 = -2(-16) = 32

a6 = -2a5 = -2(32) = -64

Therefore, the first six terms of the sequence defined by an = -2an-1 with a0 = -1 are: -1, 2, -4, 8, -16, 32.

b) The second recurrence relation is given by an = an-1 - an-2 with initial conditions a0 = 2 and a1 = -1. To find the first six terms of this sequence, we need to use the recurrence relation to generate each term, starting with the initial conditions. Using the formula, we can find:

a2 = a1 - a0 = -1 - 2 = -3

a3 = a2 - a1 = -3 - (-1) = -2

a4 = a3 - a2 = -2 - (-3) = 1

a5 = a4 - a3 = 1 - (-2) = 3

a6 = a5 - a4 = 3 - 1 = 2

Therefore, the first six terms of the sequence defined by an = an-1 - an-2 with a0 = 2 and a1 = -1 are: 2, -1, -3, -2, 1, 3.

c) The third recurrence relation is given by an = 3a2n-1 with an initial condition of a0 = 1. To find the first six terms of this sequence, we need to use the recurrence relation to generate each term, starting with the initial condition. Using the formula, we can find:

a1 = 3a0 = 3(1) = 3

a2 = 3a3 = 3(3) = 9

a3 = 3a2 = 3(9) = 27

a4 = 3a7 = 3(27) = 81

a5 = 3a14 = 3(81) = 243

a6 = 3a29 = 3(243) = 729

Therefore, the first six terms of the sequence defined by an = 3a2n-1 with a0 = 1 are: 1, 3, 9, 27, 81, 243.

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Using the Bayes' theorem, we find the probability that the transferred ball was white given that the second ball drawn was white to be 52/89, or approximately 0.5843.

To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given an event B to the conditional probability of event B given event A:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this problem, we want to find the probability that the transferred ball was white (event A) given that the second ball drawn was white (event B). We can calculate this probability as follows:

P(A|B) = P(B|A) * P(A) / P(B)

P(B|A) is the probability of drawing a white ball from urn b given that the transferred ball was white and is now in urn b. Since there are now six white balls and three black balls in urn b, the probability of drawing a white ball is 6/9 = 2/3.

P(A) is the prior probability of the transferred ball being white, which is the number of white balls in urn a divided by the total number of balls in urn a, or 6/13.

P(B) is the prior probability of drawing a white ball from urn b, which can be calculated using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where P(B|not A) is the probability of drawing a white ball from urn b given that the transferred ball was black and P(not A) is the probability that the transferred ball was black, which is 7/13.

To calculate P(B|not A), we need to first calculate the probability of the transferred ball being black and then the probability of drawing a white ball from urn b given that the transferred ball was black.

The probability of the transferred ball being black is 7/13. Once the transferred ball is moved to urn b, there are now five white balls and four black balls in urn b, so the probability of drawing a white ball from urn b given that the transferred ball was black is 5/9.

Therefore, we can calculate P(B) as follows:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

= (2/3) * (6/13) + (5/9) * (7/13)

= 89/117

Now we can plug in all the values into Bayes' theorem to find P(A|B):

P(A|B) = P(B|A) * P(A) / P(B)

= (2/3) * (6/13) / (89/117)

= 52/89

Therefore, the probability that the transferred ball was white given that the second ball drawn was white is 52/89, or approximately 0.5843.

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Answer:

\(\Large \boxed{\mathrm{independent: \ time}} \\\\\\ \Large \boxed{\mathrm{dependent: \ elevation }}\)

Step-by-step explanation:

The independent variable is on the x-axis.

The independent quantity is time.

The dependent variable is on the y-axis.

The dependent quantity is elevation.

Answer:

The dependent variable is on the y-axis.

The dependent quantity is elevation.

The independent variable is on the x-axis.

The independent quantity is time.

The dimensions that minimize the perimeter are 41.6, 41.6.

According to this statement

we have to find the dimensions of the given rectangle with the help of the area and perimeter of rectangle.  

So, For this purpose, we know that the

The area is given as:

A = 1728

Let the dimension be x and y.

A = xy = 1728

So, we have:

Make x the subject

x = 1728/y

Then

The perimeter is calculated as:

P = 2(x +y)

substitute x here then

P = 2(1728/y +y)

P = 3456/y + 2y

And differentiate it then

-3456/y^2 +2 = 0

Then

3456/y^2 = 2

2y^2 = 3456

y = 41.6 then find x

and x = 1728/41.6

x = 41.6.

So, The dimensions that minimize the perimeter are 41.6, 41.6

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he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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Answer:

X=1.5,y=2.5

Step-by-step explanation:

By elimination method

U have to make either x or y values equal and then eliminate it

The y values have a common value 12

By multiplying 6×2 and 3×4

2(4x+6y)=(21)2

4(7x-3y)=(3)4

8x+12y=42

+

28x-12y=12

36x=54

X=54/36=1.5

Substitute x with 1.5

Y=2.5

The solution to the simultaneous equation is x = 3/2 and y = 5/2.

A system having more than two equations is known as a system of equations

The given pair of equations is:

4x + 6y = 21       (1)

7x - 3y = 3          (2)

Multiply equation (2) by 2 and add into equation (1):

4x + 6y + 14x -6y = 21 + 6

18x = 27

x = 27/18

x = 3/2

Substitute x = 3/2 into equation (1):

4(3/2) + 6y = 21

6 + 6y = 21

6y = 15

y = 15/6

y = 5/2

Hence, the solution to the simultaneous equation is x = 3/2 and y = 5/2.

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Answer:

242

Step-by-step explanation:

   242

4/968   how many times does 4 go into 9?  2 times put the 2 above the 9

 8            4 times 2 equals 8 so you put the 8 below the 9 and subtract

  1 6                   9 minus 8 equals 1 than you drop the 6

  1 6          how many times does 4 go into 16? 4 times. put the  4 above the 6

    0 8        than multiply 4 *4 =16 than 16-16=0 drop the 8

       8          4 goes into 8, 2 times  the 2 goes above the 8. 4*2=8

        0            8-8=0