Question 3 Of 39The Graph Below Represents The Average Monthly Rainfall (y), Ininches, In Miami, FL During (2024)

The volume of the cardboard box is approximately 13197.402 cubic inches.

The volume of a cardboard box is 216 dm³, we can convert it to the English system of measurements.

1 dm (cubic decimeter) is equivalent to 1 liter.

To convert dm³ to cubic inches, we can use the following conversion factors:

1 dm³ = 61.0237 cubic inches

Using this conversion factor, we can calculate the volume of the box in cubic inches:

The cube carton volume is 216 dm3 and the cube edge value is 6 dm.

The volume of the cube is calculated by dividing the edge values. In other words, volume = edge 3.

To find the edge (side) value, you can solve for the volume formula as follows:

edge 3 = volume.

edge = ∛ volume,

Where ∛ is the cube root.

Applying this formula to the given problem gives edge = ∛(216 dm³).

Edge = 6dm. Therefore, the side (edge) value of the cube is 6dm.

Volume (cubic inches) = 216 dm³ * 61.0237 cubic inches/dm³

= 13197.402 cubic inches

Question :- If the volume of a cubic cardboard box is 216 dm³

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In fraction form, the answer is 1/4, which represents the simplified probability of the given event occurring.

To find the probability of picking a prime number and then picking another prime number, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

Given the four numbers: 5, 6, 7, and 8, we can see that there are two prime numbers (5 and 7) and two non-prime numbers (6 and 8).

The total number of possible outcomes is 4 since there are four cards to choose from.

Now, let's consider the favorable outcomes, which are picking a prime number and then picking another prime number.

The probability of picking a prime number on the first draw is 2/4, as there are two prime numbers out of the four total cards.

Since we replace the card before the second draw, the probability of picking a prime number on the second draw is also 2/4.

To find the probability of both events occurring, we multiply the individual probabilities:

(2/4) * (2/4) = 4/16 = 1/4

Therefore, the probability of picking a prime number and then picking another prime number is 1/4.

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The combined weight of the boat and its trailer is approximately 4000 pounds.

To determine the combined weight of the boat and its trailer, we need to consider the forces acting on the ramp.

When an object is on an inclined plane, the force acting parallel to the incline can be calculated using the formula: Force = Weight * sin(θ), where θ is the angle of inclination.

Given that the force required to hold the boat and its trailer in place is 700 pounds, and the angle of inclination is 10 degrees, we can rearrange the formula to solve for the weight:

Weight = Force / sin(θ)

Weight = 700 / sin(10°)

Weight ≈ 4000 pounds

It's important to note that this calculation assumes ideal conditions and does not consider other factors such as friction or additional forces.

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Answer:

Step-by-step explanation: 1/4 is 0.25 as a decimal so the answer is 0.75>1/4

h( a + 3) = 4a² - 4a + 13

Given,

h(x) = 4x² - 2x + 1

∴ h(a+3) = 4(a+3)² - 2(a+3) + 1

Now, calculating the three terms individually,

4(a-3)² = 4(a² + 3²- 2×a×3) {∵ (a-b)² = a² + b² - 2ab}

= 4(a² + 9 - 6a)

= 4a² - 6a + 9

and, 2(a + 3) = 2a + 3

Adding the calculated terms, we get,

h(a+3) = 4( a + 3 )² - 2( a + 3 ) + 1

⇒ h( a + 3 ) = 4a² - 6a + 9 + 2a + 3 + 1

⇒ h( a + 3 ) = 4a² - 6a + 2a + 9 + 3 + 1

⇒ h( a + 3 ) = 4a² - 4a + 13

Hence, h( a + 3) = 4a² - 4a + 13.

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The magician's sampling method involves using a survey to collect responses from people who attended her shows. The sample is self-selected and may not be representative of the general population. The survey asks respondents to rank their favorite tricks, allowing the magician to determine the most popular trick based on the rankings provided by the respondents.

Based on the given information, we can identify the following true statements about the sampling method used by the magician to determine the popularity of her magic tricks:

1. The magician uses a survey method: The magician emails a survey to people who previously attended her shows. This method involves collecting responses from individuals through a questionnaire or survey.

2. The sample consists of people who attended the magician's shows: The survey is sent to individuals who have attended the magician's shows in the past. This ensures that the sample includes people who have direct experience with her tricks.

3. The sample is self-selected: The individuals who respond to the survey are self-selecting. They choose to participate voluntarily, potentially leading to a biased sample. Those who were more interested or had stronger opinions may be more likely to respond.

4. The survey involves ranking favorite tricks: The survey asks respondents to rank their three favorite tricks. This ranking approach allows the magician to determine the most popular trick based on the preferences expressed by the respondents.

5. The sample may not be representative of the general population: Since the sample consists only of individuals who attended the magician's shows in the past, it may not be representative of the general population's preferences. Those who have not attended the shows may have different opinions.

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Answer:

I think its C

Step-by-step explanation:

Answer:

Refer below:

Step-by-step explanation:

To form a frequency distribution table for the number of runs scored by a batsman in 20 matches, we can use class intervals of 20 runs.

The given scores are 16, 41, 13, 39, 45, 28, 48, 51, 67, 12, 89, 30, 0, 28, 35, 27, 38, 32, 64, and 70.

Let's create the frequency distribution table:

Class IntervalFrequency

0-19 1

20-39 6

40-59 4

60-79 5

80-99 2

In the table, the class intervals represent ranges of scores, and the frequency represents the number of scores falling within each interval.

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The values of x and y are 35° and 20 ft

What is Pythagoras theorem?

Pythagoras theorem staes that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

This means if a and b are the two legs of the triangle and c is the hypotenuse then,

c² = a² + b²

Since triangle DEC and ABC are congruent triangles, then line DC is equal to line AC

therefore DC = 15 ft

Using Pythagorean theorem

25² = 15² + y²

y² = 25² -15²

y² = 400

y = √400

y = 20 ft

Since angle C = 45°

therefore;

100+45 +x = 180

x = 180 -145

x = 35°

Therefore the values of x and y are 35° and 20ft respectively.

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(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

[tex]y^{2} - 9y + 8.[/tex]

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step [tex]"22x + 49(2) = 0,"[/tex] the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step [tex]"y^{2} - 9y + 8 = 0,"[/tex] the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be [tex](y - 8)(y - 1) = y^{2} - 9y + 8.[/tex]

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: [tex]22x + 4 - 9(2) = 0[/tex]

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

232cm=m887-jjj

Step-by-step explanation:

f(x) = x²

What is g(x)?

10

-5

f(x)

10%

g(x)

y

(2,8)

5

10

Both functions are quadratic functions, and their graphs are parabolas. The function of g(x) is -x² - 4.

We have,

Graph of f(x) = x²:

This is a simple quadratic function.

The graph of f(x) = x² is a parabola that opens upward.

As x moves away from 0 in either direction, the function value increases. The vertex of the parabola is at the origin (0, 0). The curve is symmetric with respect to the y-axis.

Graph of g(x) = -x² - 4:

This function is also a quadratic function but with a negative coefficient in front of the x² term.

The graph of g(x) = -x² - 4 is a parabola that opens downward.

As x moves away from 0 in either direction, the function value decreases.

The vertex of the parabola is at (0, -4). Like the previous function, this curve is also symmetric with respect to the y-axis.

Thus,

Both functions are quadratic functions, and their graphs are parabolas. that opens upward and downwards.

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The solution to the system of equations -3x - 5y = 45 and 2x - 2y = 2 using elimination is x = -9 and y = -6.

1. Start with the given system of equations:

-3x - 5y = 45 ...(1)

2x - 2y = 2 ...(2)

2. Multiply equation (2) by 3 to make the coefficients of x in both equations equal:

6x - 6y = 6 ...(3)

3. Add equation (1) and equation (3) together to eliminate x:

(-3x - 5y) + (6x - 6y) = 45 + 6

Simplify the equation:

3x - 11y = 51 ...(4)

4. Now we have two equations without the variable x:

3x - 11y = 51 ...(4)

-3x - 5y = 45 ...(1)

5. Multiply equation (1) by 3 to make the coefficients of x in both equations equal:

-9x - 15y = 135 ...(5)

6. Add equation (4) and equation (5) together to eliminate x:

(3x - 11y) + (-9x - 15y) = 51 + 135

Simplify the equation:

-26y = 186

7. Divide both sides of equation (6) by -26 to solve for y:

y = -186/26

Simplify the equation:

y = -93/13

8. Substitute the value of y back into equation (1) to solve for x:

-3x - 5(-93/13) = 45

Simplify the equation:

-3x + 465/13 = 45

Subtract 465/13 from both sides:

-3x = 45 - 465/13

Simplify the equation:

-3x = 585/13 - 465/13

-3x = 120/13

9. Divide both sides of equation (8) by -3 to solve for x:

x = (120/13) / -3

Simplify the equation:

x = -40/13

10. Therefore, the solution to the system of equations -3x - 5y = 45 and 2x - 2y = 2 is x = -40/13 and y = -93/13, which can be further simplified to x = -9 and y = -6.

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Answer: See below

Step-by-step explanation:

I'm assuming that A.P is a list...

The prime factorization of 15 is: 1, 3, 5, 15, which means that the first and last can only be 1 and 15, or 3 and 5.

However, If it were 1 and 15, this would mean that the sum of the other 3 numbers equals 4. Not sure if repetition is allowed.

Option 1: 1 and 15

Other numbers are 1, 1, and 2

Option 2: 3 and 5

Other numbers add up to 13

Only one number between 3 and 5 though, which is 4. Do you know if the list is numbered from least to greatest?

Call the 5 numbers x, x + y, x + 2y, x + 3y, x + 4y, where x is the value of the first number and y is the constant value difference.

Since their sum is 20, 5x + 10y = 20.

Since the product of the first and last number is 15, x^2 + 4xy = 15.

From 5x + 10y = 20, we can see that x + 2y = 4.

-> (x+2y)^2 = 16 -> x^2 + 4xy + 4y^2 = 16 -> 4y^2 = 1.

-> y = 1/2 or -1/2

Replace back into the original equation : 5x + 10.(1/2) = 20 or 5x + 10.(-1/2) = 20

-> 5x + 5 = 20 / 5x + (-5) = 20

-> x = 3 / x = 5.

From the 4 combinations of x and y, we see that (x;y) = (5; -1/2) and (3; 1/;2) would satisfy the second condition.

So, the five numbers that we need to find has 2 different combinations :

(5; 9/2; 4; 7/2; 3) or vice versa (sum = 20)

Given statement solution is :- The total number of bags distributed is 120 + 10 = 130.

To find the greatest number of bags required, we need to determine the common number of items that can be evenly distributed among the bags.

Let's assume the number of bags required is represented by 'x'.

The total number of hand sanitizer bottles, face shields, and masks distributed is 240 + 480 + 600 = 1320.

If 'x' is the number of bags required, then each bag would contain 240/x bottles of hand sanitizer, 480/x face shields, and 600/x masks.

Since we want an equal number of items in each bag, the values 240/x, 480/x, and 600/x should be integers.

To find the greatest number of bags, we need to find the greatest common divisor (GCD) of 240, 480, and 600. The GCD will represent the maximum number of bags that can be evenly packed.

The GCD of 240, 480, and 600 is 120.

Therefore, the greatest number of bags required to pack the items is 120.

Since 10 bags are empty, the total number of bags distributed is 120 + 10 = 130.

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The box plot for the given data set (35, 50, 50, 48, 48, 32, 38, 41, 48, 34, 29, 23, 41, 34, 43) is as follows:

| *

| *

| * * *

| * |

| * | *

| * * | *

| * | * * | *

|-------------

To create a box plot for the given dataset (35, 50, 50, 48, 48, 32, 38, 41, 48, 34, 29, 23, 41, 34, 43), we need to determine the five-number summary, which consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.

First, let's sort the data in ascending order: 23, 29, 32, 34, 34, 35, 38, 41, 41, 43, 48, 48, 48, 50, 50.

The five-number summary is as follows:

Minimum: 23

Q1: 34

Median: 41

Q3: 48

Maximum: 50

On a number line, we mark the minimum and maximum values (23 and 50) and draw a box with Q1, Q2 (median), and Q3 (34, 41, and 48). We connect the box with horizontal lines and indicate any outliers (values outside the minimum and maximum).

The box plot represents the distribution of the given dataset, with the box indicating the interquartile range and the median, and the whiskers showing the range of the data.

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The simplified expression of x(3x + 5)-5(2x - 1) is 3x² - 5x + 5

How to expand and simplify the expression

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

x(3x + 5)-5(2x - 1)

Open the brackets

So, we have

3x² + 5x - 10x + 5

Evaluate the like terms

So, we have

3x² - 5x + 5

Hence, the simplified expression is 3x² - 5x + 5

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The value of m in the ratio 3:7 is 9.

What is a ratio?

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.

Given the problem above, we need to find the value of m for 3:7 = m:21.

We can use proportionality in order to find m.

So,

[tex]\dfrac{3}{7} =\dfrac{\text{m}}{21}[/tex]

[tex]\rightarrow\text{m}=\dfrac{21\times3}{7}[/tex]

[tex]\rightarrow\text{m}=\dfrac{63}{7}[/tex]

[tex]\rightarrow\bold{m=9}[/tex]

Therefore, the value of m is 9.

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a.) The equation for the problem is 3X + 4 = 27. Solving it, we find X = 7.67 (rounded).

b.) The solution for X in the equation "Four more than three times a number is equal to 27" is approximately X = 7.67. This satisfies the statement, as when we multiply 7.67 by 3 and add 4, we get 27.

a.) Let's write the equation for this problem using X as the variable. The problem states that "Four more than three times a number is equal to 27." We can translate this into an equation as follows:

3X + 4 = 27

To solve this equation for X, we need to isolate X on one side of the equation. We can do this by subtracting 4 from both sides:

3X = 27 - 4

3X = 23

Next, we can divide both sides of the equation by 3 to solve for X:

X = 23/3

Therefore, the solution for X is X = 7.67 (rounded to two decimal places).

b.) Findings Statement: The solution for X in the equation "Four more than three times a number is equal to 27" is X = 7.67. This means that if we take the number 7.67, multiply it by 3, and add 4, we will obtain 27. Thus, the original statement is satisfied when the unknown number is approximately 7.67.

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Answer:

Step-by-step explanation:

between 18 & 24

The two-column proof should be completed as follows;

Statements Reasons__________

1. m∠A ≅ m∠D, 1. given

m∠B ≅ m∠E

2. ∠A ≅ ∠D, ∠B ≅ ∠E 2. Definition of congruence

3. m∠A + m∠B + m∠C = 180° 3. Triangle Sum Theorem

4. m∠D + m∠E + m∠F = 180° 4. Triangle Sum Theorem

5. m∠A + m∠B + m∠C ≅ 5. Definition of congruence

m∠D + m∠E + m∠F

6. m∠A + m∠B + m∠C ≅ 6. Substitution Property of

m∠A + m∠B + m∠F Equality

7. m∠C ≅ m∠F 7. Subtraction Property of

Equality

8. ∠C ≅ ∠F 8. Definition of congruence

What are the properties of similar triangles?

In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the angle, angle (AA) similarity theorem, we can logically deduce the following congruent triangles:

ΔABC ≅ ΔDEF

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The elements in numerical and alphabetical order.

N = {5N, 7N},

Q = {4Q, 6Q, 7Q, 8Q, 9Q},

S = {4D, 4N, 4Q}.

N = {5N, 7N}

Q = {4Q, 6Q, 7Q, 8Q, 9Q}

S = {4D, 4N, 4Q}

To clarify, the sets are written in numerical and alphabetical order, as follows:

N = {5N, 7N}

Q = {4Q, 6Q, 7Q, 8Q, 9Q}

S = {4D, 4N, 4Q}

In set N, we have the elements 5N and 7N, representing the 1965 nickel and 1967 nickel, respectively.

In set Q, we have the elements 4Q, 6Q, 7Q, 8Q, and 9Q, representing the 1964 quarter, 1966 quarter, 1967 quarter, 1968 quarter, and 1969 quarter, respectively.

In set S, we have the elements 4D, 4N, and 4Q, representing the 1964 dime, 1964 nickel, and 1964 quarter, respectively.

It is important to note that the remaining sets (P, D, H, W, X, Y, Z, T, and V) are not explicitly listed in this exercise.

However, based on the information given, each of these sets would contain the corresponding coins from the given years.

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The value of x is 76°, which satisfies the equation cos(x) = sin(14°) within the given range.

To find the value of x for which cos(x) = sin(14°), we need to determine the angle whose cosine is equal to the sine of 14°.

In the given range, 0° < x < 90°, we know that the sine function is positive, and the cosine function is also positive.

Since cos(x) = sin(90° - x), we can rewrite the equation as cos(x) = sin(90° - x) = sin(14°).

So, we have cos(x) = sin(90° - x) = sin(14°).

Using the identity sin(a) = cos(90° - a), we can write the equation as sin(90° - x) = sin(14°).

To find the angle whose sine is equal to sin(14°), we can set the angles inside the sine functions equal to each other:

90° - x = 14°

Simplifying the equation:

90° - 14° = x

76° = x

Therefore, the value of x for which cos(x) = sin(14°), within the given range of 0° < x < 90°, is x = 76°.

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Answer:

The simplified expression is,

[tex]2a^2 +12a +1[/tex]

Step-by-step explanation:

[tex]3a^2 + 8a+5-a^2+4a-4\\3a^2-a^2+8a+4a+5-4\\2a^2 +12a +1[/tex]

The length of the x-component of the vector is 3, the correct option is A.

How to find the length of the x-component?

To find the length of the x-component, count the number of units between the start of the vector (the origin in this case) and the point.

Here we can see that the point is 3 units to the right of the start of the vector, which means that the x-vomponent of the vector is 3.

(and we can see that the y-component is 4) then the vector is <3, 4>

finally we can see that the correct option is A.

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The solutions to the simultaneous equations are approximately (2.18, -2.45) and (-0.18, 3.45).

To solve the simultaneous equations:

Begin by rearranging the second equation to solve for one variable in terms of the other. In this case, we'll solve for y:

5x + 2y = 6

2y = 6 - 5x

y = (6 - 5x)/2

Substitute the expression for y in terms of x into the first equation:

[tex]2x^2 + y^2 = 12[/tex]

[tex]2x^2 + ((6 - 5x)/2)^2 = 12[/tex]

Simplify the equation by expanding and combining like terms:

[tex]2x^2 + (6 - 5x)^2/4 = 12[/tex]

[tex]2x^2 + (36 - 60x + 25x^2)/4 = 12[/tex]

Multiply through by 4 to eliminate the fraction:

[tex]8x^2 + 36 - 60x + 25x^2 = 48[/tex]

Rearrange the equation to form a quadratic equation:

[tex]33x^2 - 60x - 12 = 0[/tex]

Solve the quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula here:

[tex]x = (-b ± √(b^2 - 4ac)) / (2a)[/tex]

Plugging in the values from the quadratic equation, we have:

[tex]x = (-(-60) ± √((-60)^2 - 4 * 33 * -12)) / (2 * 33)[/tex]

x = (60 ± √(3600 + 1584)) / 66

x = (60 ± √5184) / 66

x = (60 ± 72) / 66

Calculate the values of x:

For x = (60 + 72) / 66: x ≈ 2.18

For x = (60 - 72) / 66: x ≈ -0.18

Substitute the x values back into the second equation to find the corresponding y values:

For x ≈ 2.18:

5(2.18) + 2y = 6

10.9 + 2y = 6

2y = 6 - 10.9

2y ≈ -4.9

y ≈ -2.45

For x ≈ -0.18:

5(-0.18) + 2y = 6

-0.9 + 2y = 6

2y = 6 + 0.9

2y ≈ 6.9

y ≈ 3.45

Therefore, the solutions to the simultaneous equations are approximately (2.18, -2.45) and (-0.18, 3.45).

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Answer:

((1+2)x3) + (4x5) = 29

Step-by-step explanation:

Since 4x5 = 20 and 3x3 = 9, and 9 + 20 = 29, we put parenthesis around 1+2,

we get,

((1+2)x3) + (4x5) = 29

This is true because,

(3x3) + (4x5) = 29

(9) + (20) = 29

29 = 29

The true statement about infinite geometric series​ is (b) [tex]\sum\limits^{\infty}_{i=0} {7(\frac{1}{10})^n}[/tex] is not convergent

How to determine what is true about infinite geometric series​

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

The geometric series​

Where, we have

[tex]\sum\limits^{\infty}_{i=0} {7(\frac{1}{10})^n}[/tex]

From the above geometric series​, we have

First term, a = 7

Common ratio, r = 1/10 = 0.1

So, the sum of the series is

Sum = a/(1 - r)

This gives

Sum = 7/(1 - 0.1)

Evaluate

Sum = 7.78

From the list of options, we can see that (a), (c) and (d) are not true

Hence, the true statement about infinite geometric series​ is (b) [tex]\sum\limits^{\infty}_{i=0} {7(\frac{1}{10})^n}[/tex] is not convergent

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Answer:

slope = - 8

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 10) and (x₂, y₂ ) = (4, 2) ← 2 points on the line

m = [tex]\frac{2-10}{4-3}[/tex] = [tex]\frac{-8}{1}[/tex] = - 8