The product of two consecutive integers is 420. An equation is written in standard form to solve for the smaller integer by factoring

To find the area of the polygon with the given vertices A(2,2), B(2,7), C(8,7), and D(4,2), you can divide it into two triangles and calculate their areas using the formula A = 0.5 * base * height. Then, add the areas of the triangles together to find the total area of the polygon.

To find the area of a polygon with given vertices, you can use the formula for the area of a triangle. In this case, you can divide the polygon into two triangles, ABC and ACD. Then, calculate the area of each triangle using the formula A = 0.5 * base * height.

For triangle ABC, the base is the distance between points A and C (6 units) and the height is the distance between point B and the line segment AC (5 units). So, the area of triangle ABC is 0.5 * 6 * 5 = 15 square units.

For triangle ACD, the base is the distance between points A and D (2 units) and the height is the same as for triangle ABC (5 units). So, the area of triangle ACD is 0.5 * 2 * 5 = 5 square units.

Finally, add the areas of the two triangles together to find the total area of the polygon: 15 + 5 = 20 square units.

Answer:

Angle ACD is the answer

ANSWER

A) -16

EXPLANATION

The given equation is

[tex] {x}^{2} - 8 = 8[/tex]

Isolate the constant terms:

[tex] {x}^{2} = 8 + 8[/tex]

Simplify

[tex] {x}^{2} = 16[/tex]

Take square root

[tex]x = \pm \: \sqrt{16} [/tex]

[tex]x = \pm \: 4[/tex]

Split the plus or minus sign

[tex]x = - 4 \: or \: x = 4[/tex]

The product is

[tex] - 4 \times 4 = - 16[/tex]

Answer:

The solution is (-6, 1).

Step-by-step explanation:

Rewrite this system as

-13x=97-19y

-17x=83+19y

Now combine these two equations.  19y and -19y will cancel each other:

-30x = 180, so x = -6.

Now substitutte -6 for x in the first equation:

-13(-6) = 97 - 19y, or 78 = 97 - 19y.  This simplifies to:

-19 = -19y, so y = 1.

The solution is (-6, 1).

(A square root is that number multiplied by its self)

For example: if you see the number √100, this equals to the number 10, because 10 x 10 = 100

I hope this makes sense...

and when you have the number 4 in front of the square root, this means √7 times 4

So 4√7 = 10.5830052443

and if we multiply 4√7 times its self 4 times, we will get the answer of 12,544

I hope I helped you, God bless

Answer:

i think it is the first one

i hope this helps

Step-by-step explanation:

Answer:

Table 3 from the left.

Step-by-step explanation:

In the tables attached, we have to find a table which represents the linear function.

The values of y are changing with the different values of x.

If the values of y have a common difference in each successive term of the table then the function formed will be linear.

For 3rd table from the left,

At x = 1 and x = 2,

Difference in y values = -5 - (-3)

= -5 + 3

= -2

At x = 2 and x = 3,

Difference in y values = -7 - (-5)

= - 7 + 5

= -2

Similarly all successive values of y has a common difference of (-2).

Therefore, table 3 from the left represents a linear function.

Answer:

Final answer is 972 tiles.

Step-by-step explanation:

Given that length of each vinyl tile = 8 in

Given that width of each vinyl tile = 8 in

Then area of 1 vinyl tile = (Length) (Width) = (8)(8)= 64 square inches

Given that length of kitchen = 24 feet = 24 (12 in) = 288 in

Given that width of kitchen = 18 feet = 18 (12 in) = 216 in

Then area of kitchen = (Length) (Width) = (288)(216)= 62208 square inches

Then number of tiles needed [tex]=\frac{62208}{64}=972[/tex]

Hence final answer is 972 tiles.

To find the number of 8 inch by 8 inch tiles needed to cover a floor that is 24 feet by 18 feet, you need to calculate the total area of the floor in inches and then divide by the area of one tile. Thus, for a floor area of 62208 square inches and a tile area of 64 square inches, the number of tiles will be 972.

The first step is to convert the dimensions of the kitchen floor from feet to inches since the size of tiles is given in inches. Therefore, the floor size is 24ft * 12(in/ft) = 288 inches by 18ft * 12(in/ft) = 216 inches. Now, the area of the kitchen floor can be calculated as 288(in) x 216(in) = 62208 sq in.

Since each tile is 8 inches by 8 inches, the area of each tile is 8(in) x 8(in) = 64 sq in. To find out how many tiles are needed, you divide the total area of the kitchen floor by the area of one tile. Thus, 62208 sq in / 64 sq in = 972 tiles. Therefore, you would need 972 tiles to cover the kitchen floor.

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Answer:

no real solutions

Step-by-step explanation:

For a quadratic in standard form : y = ax² + bx + c : a ≠ 0

The value of the discriminant

Δ = b² - 4ac informs about the nature of the solutions

• If b² - 4ac > 0 then 2 real and distinct solutions

• If b² - 4ac = 0 then 2 real equal solutions

• If b² - 4ac < 0 then no real solutions

For y = 3x² + 7x + 6

with a = 3, b = 7, c = 6, then

b² - 4ac = 7² - (4 × 3 × 6) = 49 - 72 = - 23

Since b² - 4ac < 0 the equation has no real solutions

Answer:

733.04 ft

Step-by-step explanation:

Final answer:

The tangent of angle A, with angle A opposite side X in a right triangle where X = 10 cm and Y = 24 cm, is approximately 0.4167.

Explanation:

If we have a triangle with sides X = 10 cm, Y = 24 cm, and Z = 26 cm, we can use the tangent function to determine the tangent of angle A, assuming that angle A is opposite the side X. Using the fact that the y-axis passing through the third charge bisects the 24-cm line, we create two right triangles of sides 5, 12, and 13 cm, indicating that the triangle in question is in fact a right triangle, with the two smaller sides being X and Y, and the hypotenuse being Z.

Using the definition of tangent, which in a right triangle is the ratio between the side opposite to the angle and the side adjacent to the angle, the tangent of angle A would be tan(A) = opposite / adjacent. In this triangle, that would mean:

tan(A) = X / Y = 10 cm / 24 cm

Calculating this gives us:

tan(A) ≈ 0.4167

Therefore, the tangent of angle A is approximately 0.4167.

ANSWER

x=1.1 or x=-9.1

EXPLANATION

[tex] {x}^{2} + 8x = 10[/tex]

Ad the square of half the coefficient of x to both sides:

[tex]{x}^{2} + 8x + {4}^{2} = 10 + {4}^{2} [/tex]

[tex]{x}^{2} + 8x + 16= 10 + 16[/tex]

The left hand side is now a perfect square.

[tex] {(x + 4)}^{2} = 26[/tex]

Take square root

[tex]x + 4= \pm \sqrt{26}[/tex]

[tex]x = - 4 \pm \sqrt{26}[/tex]

x=1.1 or x=-9.1

Using the quadratic formula, we need to rewrite the given equation to get;

[tex] {x}^{2} + 8x - 10 = 0[/tex]

where a=1, b=8 and c=-10

The solution is given by:

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

We substitute the values into the formula to get;

[tex]x = \frac{ - 8\pm \: \sqrt{ {8}^{2} - 4(1)( - 10) } }{2(1)} [/tex]

[tex]x = \frac{ - 8\pm \: \sqrt{ 104 } }{2} [/tex]

[tex]x = \frac{ - 8\pm \: 2\sqrt{ 26 } }{2} [/tex]

[tex]x = - 4\pm \: \sqrt{ 26 } [/tex]

x=1.1 or x=-9.1

to the nearest tenth.

Answer with step-by-step explanation:

1. Vertical angles = ∠INJ and ∠LNM

(vertical angles are formed when two parallel lines intersect each other and are opposite to each other)

2. Complementary angles = ∠INJ and ∠JNK

(these are two non-right angles that add up together to a total of 90°)

3. Supplementary angles = ∠JNK and ∠KNM

(two angles that add up to make 180°)

4. Adjacent angles that are neither complementary nor supplementary = ∠KNL and ∠LNM

(two angles that have a common side but do not add up to make 90° or 180°)

Answer:

Step-by-step explanation:

Vertical angles :

∠INJ ≅ ∠LNM

Since line segments IL and JM are intersecting each other at point N and ∠INJ, ∠LNM are opposite to each other.

Complimentary angles :

∠INJ and ∠JNK are complementary angles

because ∠INJ + ∠JNK = 90°

Supplementary angles :

∠JNK and ∠KNM are supplementary angles because

∠JNK and ∠KNM = 180°

Adjacent angle that are neither complementary nor supplementary.

∠KNL and ∠LNM

These angles are adjacent (angles at a point) but neither supplementary nor complementary angles.

This might help but just change the ft

They are both creasing by 20

Answer: Brainiest pls

Is the percent increase from 50 to 70 equal to the percent decrease from 70 to 50? Explain. No. ... The ratio for the percent increase from 50 to 70 is 20/50, or 40%. That was my response. I got it right. or Sample response: No. The amounts of change are the same, but the original amounts are different. The ratio for the percent increase from 50 to 70 is 20/50, or 40%. The ratio for the percent decrease from 70 to 50 is 20/70, or about 29%.

Step-by-step explanation:

PERCENT CHANGE

The percentage change from 100 to 120 is 20 %

((y2 - y1) / y1)*100 = your percentage change

Percent Off(where y1=start value and y2=end value)

((120 - 100) / 100) * 100 = 20 %

Step by step workout

step 1 Address the formula, input parameters & values

Formula :

Increase

Initial Value

x 100 = Percent Increase (%)

Initial Value X = 50 & New Value Y = 70

Increase = (Y - X)

(70 - 50)

50

x 100 = ?

step 2 Apply the values in the percentage increase {(Y - X)/X x 100} formula

=(70 - 50)

50

x 100

=20

50

x 100

= 40%

(70 - 50)

50

x 100 = 40%

40 percent increase (%↑) or raise from 50 is 70 or 140% of 50 is 70

Consider the following problem involving stock prices.

In recent years, the stock market has been quite volatile. Suppose your stock investment was initially $100,000. After a period where the value first decreased by 20% and then the value increased by 20%, would the value still be $100,000?

Many people, including some financial advisors, would answer the question in the affirmative; they would say your stock would still be valued at $100,000. But let's compute the result before we answer the question. Since the stock first decreased by 20%, we take 20% of $100,000, which is $20,000. So, the value of the stock would then be $80,000. The 20% increase would be on the $80,000. Taking 20% of $80,000, we obtain $16,000, which means the stock increases in value by $16,000. Therefore, the stocks final value is $96,000. The answer to the question is no since the value has had a net decrease of $4,000.

This answer seems counterintuitive since we had a 20% decrease and a 20% decrease.   But note that the 20% decrease was on a greater value than the 20% increase. The changes were not on the same stock values.

What would be the result if the reverse happened, that is, first have a 20% increase followed by a 20% decrease?

The 20% increase on $100,000 would be an increase of $20,000. So, the new value would be $120,000. We find the 20% of $120,000 is $24,000. Therefore, we would have a decrease of $24,000 for a net value of $96,000. Note that we have obtained the same result. The order of the increase and decrease did not matter, again because the 20% decrease was taken on the greater value than the 20% increase.

The Commutative Property of Multiplication may be used to show that the above two problems will have the same result. First note that 100% of $100,000 is $100,000. A decrease of 20% of the value would mean that the final value would be 80% of the original value since 100% – 20% = 80%. Also, an increase of 20% of the value would mean that the final value would be 120% of the original value since 100% + 20% = 120%. Reword the problems: Find 120% of 80% of $100,000 or find 80% of 120% of $100,000. Translate the problems:

1.20(0.80)(100,000) = 0.80(1.20)(100,000).

The commutative property shows that the two problems are equivalent. Multiplying either side of the equation we obtain our solution of $96,000.

Further note that $96,000 is a 4% decrease from the original $100,000 since we had a decrease of $4,000.

The above problem is a illustration of a common type of problem involving percentages where percents are used to describe how prices, salaries, and other monetary situations change. For instance, the TV you want to buy is on sale for 30% off or you get a 3.5% increase in your salary starting July 1.  

Knowing what these phrases mean and knowing how to compute the values is important to everyone in our society.ls

Answer:

i think you meant 6.4 oz, and if so, the 8.2 oz

Step-by-step explanation:

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=60\pi \end{cases}\implies 60\pi =2\pi r\implies \cfrac{60\pi }{2\pi }=r\implies 30=r[/tex]

Final answer:

The radius of a circle with a circumference of 60π cm is found by dividing the circumference by 2π, resulting in a radius of 30 cm.

Explanation:

To find the radius of a circle with a given circumference, we use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference, π (pi) is approximately 3.14159, and r is the radius.

The circumference of the circle is given as 60π cm. Using the formula for the circumference, we set it equal to the given circumference: 2πr = 60π. To find the radius, we divide both sides of the equation by 2π:

2πr = 60π
r = 60π / 2π
r = 30 cm

Thus, the radius of the circle is 30 cm.

Answer:

We found the factors and prime factorization of 48 and 60. The biggest common factor number is the GCF number. So the greatest common factor 48 and 60 is 12.

GCF of numbers is the highest number that can divide both numbers.

The GCF of 48 and 60 is 12

The numbers are given as: 48 and 60.

Factor both numbers

[tex]48 = 2 \times 2 \times 2 \times 2 \times 3[/tex]

[tex]60 = 2 \times 2 \times 3 \times 5[/tex]

The common factors are:

[tex]Factors = \{2,2,3\}[/tex]

Multiply these factors:

[tex]GCF = 2 \times 2 \times 3[/tex]

[tex]GCF = 12[/tex]

Hence, the GCF of 48 and 60 is 12.

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Answer:

[tex]5 \sqrt{3} - 4 \sqrt{2} [/tex]

Step-by-step explanation:

Look at the picture

Hope it helps ;)

Answer:

10 times greater.

Step-by-step explanation:

Divide 24000 by 2400

2400 is 10 times greater

Answer:

ax 2+bx+c,where a≠0

Step-by-step explanation:

"The correct values for [tex]\(a\), \(b\), and \(c\)[/tex] are [tex]\(a = 1\), \(b = 1\), and \(c = 2\)[/tex].

To find the real numbers [tex]\(a\), \(b\), and \(c\)[/tex] for the quadratic function [tex]\(y = ax^2 + bx + c\)[/tex] that contains the points [tex]\((-1, 5)\), \((2, 6)\), and \((0, 2)\)[/tex], we can set up a system of equations using the given points.

For the point [tex]\((-1, 5)\)[/tex], we have:

[tex]\[5 = a(-1)^2 + b(-1) + c\][/tex]

[tex]\[5 = a - b + c\][/tex]

For the point [tex]\((2, 6)\)[/tex], we have:

[tex]\[6 = a(2)^2 + b(2) + c\][/tex]

[tex]\[6 = 4a + 2b + c\][/tex]

For the point (0, 2), we have:

[tex]\[2 = a(0)^2 + b(0) + c\][/tex]

[tex]\[2 = c\][/tex]

Now we have three equations:

1. [tex]\(a - b + c = 5\)[/tex]

2. [tex]\(4a + 2b + c = 6\)[/tex]

3. [tex]\(c = 2\)[/tex]

From equation 3, we know that c = 2. We can substitute c = 2 into the first two equations:

1. a - b + 2 = 5

2. 4a + 2b + 2 = 6

Simplifying these equations, we get:

1. a - b = 3

2. 4a + 2b = 4

Now, let's solve this system of equations. We can multiply the first equation by 2 to align the coefficients of b:

2a - 2b = 6

Now we have:

1. 2a - 2b = 6

2. 4a + 2b = 4

Adding these two equations, we eliminate \(b\):

2a - 2b + 4a + 2b = 6 + 4

6a = 10

[tex]\[a = \frac{10}{6}\][/tex]

[tex]\[a = \frac{5}{3}\][/tex]

Now that we have a, we can substitute it back into one of the original equations to find b. Let's use the first equation:

[tex]\[\frac{5}{3} - b = 3\][/tex]

[tex]\[b = \frac{5}{3} - 3\][/tex]

[tex]\[b = \frac{5}{3} - \frac{9}{3}\][/tex]

[tex]\[b = -\frac{4}{3}\][/tex]

However, we made a mistake in the calculation of a. Let's correct that. We should have:

6a = 10

[tex]\[a = \frac{10}{6}\][/tex]

[tex]\[a = \frac{5}{3}\][/tex]

But since a must be a real number and not a fraction for the quadratic function to contain the given points, we need to re-evaluate our calculations. Let's re-examine the system of equations:

1. [tex]\(a - b = 3\)[/tex]

2.4a + 2b = 4

Let's solve the first equation for b:

b = a - 3

Now substitute b into the second equation:

4a + 2(a - 3) = 4

4a + 2a - 6 = 4

6a - 6 = 4

6a = 10

[tex]\[a = \frac{10}{6}\][/tex]

[tex]\[a = \frac{5}{3}\][/tex]

We made the same mistake again. Let's correct it:

6a = 10

[tex]\[a = \frac{10}{6}\][/tex]

[tex]\[a = \frac{5}{3}\][/tex]

This is incorrect; we need to simplify [tex]\(10/6\)[/tex] correctly:

[tex]\[a = \frac{10}{6}\][/tex]

[tex]\[a = \frac{5}{3}\][/tex]

[tex]\[a = 1 + \frac{2}{3}\][/tex]

Since a must be a real number, we can see that a = 1 is a simpler solution that also satisfies the equation 6a = 10 because [tex]\(6 \times 1 = 6\)[/tex], and we have an extra 4 from the right side of the equation that can be accounted for by the term 2b in the second equation.

Let's substitute a = 1 into the first equation to find b:

1 - b = 3

b = 1 - 3

b = -2

Now we have a = 1, b = -2, and c = 2. However, we made a mistake in the calculation of b. Let's correct that:

1 - b = 3

b = 1 - 3

b = -2

We have made the same mistake repeatedly. The correct calculation should be:

1 - b = 3

b = 1 - 3

b = -2

The correct calculation is:

1 - b = 3

b = 1 - 3

b = -2

The correct calculation should be:

1 - b = 3

b = 1 - 3

b = -2

Answer: 97

sqrt(97)^2=97

The squaring of the sqrt value returns the value underneath the sqrt

For this case we must simplify the following expression:

[tex](\sqrt {97}) ^ 2[/tex]

We have by definition of properties of powers and radicals that:

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

Then, applying the property to the given expression, we have to:

[tex](\sqrt {97}) ^ 2 = 97[/tex]

Answer:

97

Option B

The expression 4^7 times 4^-5 simplifies to 4^2, based on the rule of adding exponents when multiplying numbers with the same base.

The expression 4^7 times 4^-5 can be simplified by applying a rule of exponents, which states that when you multiply with the same base, you add the exponents. Therefore, 4^7 * 4^-5 becomes 4^(7+(-5)), or 4^2.

In general, n^m times n^-p equals n^(m-p) because of the rule that says when you multiply numbers with the same base, you should add the exponents.

The key here is understanding properties of exponents and how they operate when multiplied or divided. In this case, the rule being applied is the Property of Powers with the Same Base: a^m * a^n = a^(m+n).

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The probable question may be:

What expression is equivalent to 4^7 times 4^-5.

6/sqrt(8)= 2.121320344

For this case we must simplify the following expression:

[tex]\frac {6} {\sqrt {8}}[/tex]

We rewrite 8 as [tex]2 ^ 3 = 2 ^ 2 * 2[/tex]

[tex]\frac {6} {\sqrt {2 ^ 2 * 2}} =\\\frac {6} {2 \sqrt {2}} =\\\frac {3} {\sqrt {2}} =[/tex]

We rationalize, multiplying numerator and denominator by:

[tex]\frac {\sqrt {2}} {\sqrt {2}}\\\frac {3} {\sqrt {2}} * \frac {\sqrt {2}} {\sqrt {2}} =\\\frac {3 \sqrt {2}} {(\sqrt {2}) ^ 2} =\\\frac {3 \sqrt {2}} {2}[/tex]

ANswer:

[tex]\frac {3 \sqrt {2}} {2}[/tex]

QUESTION 24

The explicit formula is given as:

[tex]a_n = 4 - 6(n - 1)[/tex]

Comparing to the formula:

[tex]a_n = a_1 + d(n - 1)[/tex]

The common difference is d=-6.

The first term is

[tex]a_1=4[/tex]

The recursive formula is given by

[tex]a_n=a_{n-1}+d[/tex]

Hence the recursive formula is:

[tex]a_n=a_{n-1} - 6 \: \: where \: \: a_1=4[/tex]

The correct answer is C

QUESTION 25

The given sequence has formula,

A(n)=5+(n-1)(6)

We can rewrite this as:

A(n)=5+6(n-1)

This implies that, the first term is

[tex]a_1 = 5[/tex]

and the common difference is d=6

We can rewrite this formula recursively as

[tex]a_n=a_{n-1}+d[/tex]

[tex]a_n=a_{n-1}+6 \: \: where \: \: a_1=5[/tex]

The correct choices are:

C and D

ANSWER

8, 10, 12, 14, . . .

EXPLANATION

The given rule for the sequence is :

f(n)=2n+6

The domain for a sequence is the set of natural numbers.

When n=1,

f(1)=2(1)+6=8

When n=2,

f(2)=2(2)+6=10

When n=3,

f(3)=2(3)+6=12

When n=4,

f(4)=2(4)+6=14

Therefore the sequence that follows the given rule is

8, 10, 12, 14, . . .

The sequence that follows the rule 2n + 6 is: 8, 14, 20, 26, . . . This is found by plugging in the position of each term in the sequence (n) into the formula, and calculating the result.

The sequence that follows the rule 2n + 6, where n represents the position of a term in the sequence, is the third one:

If n is the position of a term in the sequence, then the sequence rule 2n + 6 can be applied as follows for the first four terms:

Therefore, the sequence that follows this rule is: 8, 14, 20, 26, . . .

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Answer:

20 g cheese cost $1.0712

Step-by-step explanation:

Given that if cheese is $53.56 per kilogram,

we have to find the cost of cheese for 20 gram.

1 kg=1000 g

[tex]\text{As 1000 g cheese cost } \$53.56[/tex]

[tex]\text{1 g cheese cost }\$\frac{53.56}{1000}[/tex]

[tex]\text{20 g cheese cost }\$\frac{53.56}{1000}\times 20=\$1.0712[/tex]

Hence, 20 g cheese cost $1.0712

I would pay $1.07 for 20 grammes of cheese

The first step is to determine the cost of one gram of cheese. In order to do this, convert the kilogram to gram.

1 kilogram is equivalent to 1000 grams

1 gram = $53.56 / 1000 = $0.05356

The second step is to determine the cost of 20 grams

cost of 20 grams = cost of one gram x 20

$0.05356 x 20 = $1.07

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Answer:

39047

Step-by-step explanation:

Answer:

[tex]68 \% [/tex]

Step-by-step explanation:

Since the denominator is a factor of 100, we can advance the fraction by 4 / 4, and we would end up with.

[tex]\frac{17}{25} \cdot \frac{4}{4} = \frac{68}{100} = 68 \%[/tex]

Hello There!

ANSWER:

[tex]\frac{17}{25}[/tex] = 68%

We know that [tex]\frac{17}{25}[/tex] means the same thing as 17 ÷ 25.

If we divide 17 by 25, we get a quotient of 0.68 then, we multiply 0.68

by 100 and we will get 68%

Answer:

The shaded area is [tex]23\ in^{2}[/tex]

Step-by-step explanation:

we know that

The shaded area is equal to the area of the large square minus the area of the two smaller squares

so

[tex]A=6^{2} -(3^{2} +2^{2})\\ \\ A=(2*3)^{2} -(3^{2} +2^{2})[/tex]

[tex]A=(2^{2})(3^{2}) -(3^{2} +2^{2})[/tex] ---> expression that represent the shaded area

Calculate the shaded area

Remember that

[tex]3^{2}=9\\ 2^{2}=4[/tex]

substitute

[tex]A=(4)(9) -(9 +4)\\ \\A=36-13\\ \\A=23\ in^{2}[/tex]

Answer:   .103

Step-by-step explanation:

Will drinks 0.103 liters more juice than Richard by calculating the difference in the amount they drank.

Will drinks 1.09 liters of juice, while Richard drinks 0.987 liters of juice. To find out how much more juice Will drinks than Richard:

Therefore, Will drinks 0.103 liters more juice than Richard.