1. List five different vocabulary words that could be used to describe each given expression.
a-d+c

The equation has an imaginary root when (b) c = d

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

2(c^2+d^2)x^2+(c-d)x+9=0

At the point of imaginary root, we have

b^2 < 4ac

This means that

(c - d)^2 < 4 * 2(c^2+d^2) * 9

So, we have

c^2 + d^2 - 2cd < 72c^2 + 72d^2

Evaluate the like terms

71c^2 + 71d^2 + 2cd > 0

Using a graphing calculator, we have

c = d

Hence, the solution is (b) c = d

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The 4-th term in the sequence  d(n) = d(n - 1) × (-6) is -2592

Consider the mentioned recursive function of a sequence :

d(n) = d(n - 1) × (-6) and d(1) = 12

To find the fourth term of the sequence i.e., when n = 4,

Since the sequence is a recursive sequence, in order to find d(4) first we need to find d(2) and d(3)

For  n = 2,

⇒ d(2) = d(2 - 1) × (-6)

⇒ d(2) = d(1) × (-6)

⇒ d(2) = 12 × (-6)

⇒ d(2) = -72

For  n = 3,

⇒ d(3) = d(3 - 1) × (-6)

⇒ d(3) = d(2) × (-6)

⇒ d(3) = (-72) × (-6)

⇒ d(3) = 432

For  n = 4,

⇒ d(4) = d(4 - 1) × (-6)

⇒ d(4) = d(3) × (-6)

⇒ d(4) = 432 × (-6)

⇒ d(4) = -2592

Thus, the fourth term is -2592.

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The complete question is:

d(1) = 12,  

d(n) = d(n - 1) . (-6) ​

What is the 4-th term in the sequence?

The explanatory and response variables for each set of data:

a.  number of hours spent reading is response variable and page number on which you are reading is explanatory variable.

b. calories burned is response variable and number of minutes of exercising is explanatory variable.

c. amount paid as income tax is response variable and the amount of a paycheck is explanatory variable.

d. pounds of hamburger used to make a meatloaf is response variable and number of people that can be fed from the meatloaf is explanatory variable.

A variable in mathematics is a symbol that represents a mathematical object. A variable can be a number, a vector, a matrix, a function, its argument, a set, or an element of a set.

Here,

For each set of data, the explanatory and response variables are as follows:

a. the number of hours spent reading is the response variable, and the page number on which you are reading is the explanatory variable.

b. The response variable is calories burned, and the explanatory variable is the number of minutes spent exercising.

c. the amount of income tax paid is the response variable, and the amount of a paycheck is the explanatory variable.

The response variable is the number of pounds of hamburger used to make a meatloaf, and the explanatory variable is the number of people who can be fed from the meatloaf.

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Answer:

h = 11cm

Step-by-step explanation:

Rectangular pyramid formula:

[tex] \frac{lwh}{3} [/tex]

therefore

[tex]\frac{7 \times 9 \times h}{3} = 231[/tex]

simplify 7x9=63, then multiply the equation by 3

[tex]63h = 693[/tex]

now divide by 63

[tex]h = 11cm[/tex]

h=11cm

Answer: To find the direction and magnitude of the resultant of these three forces, we will use the law of cosines and law of sines.

First, we will find the horizontal and vertical components of each force using trigonometry:

F1x = 80 * cos(30) = 69.28 pounds

F1y = 80 * sin(30) = 40 pounds

F2x = 95 * cos(45) = 67.08 pounds

F2y = 95 * sin(45) = 67.08 pounds

F3x = 125 * cos(120) = -62.5 pounds

F3y = 125 * sin(120) = -106.57 pounds

Next, we will add the horizontal and vertical components of each force together to find the overall horizontal and vertical components of the resultant force:

Rx = F1x + F2x + F3x = 69.28 + 67.08 + (-62.5) = 72.86 pounds

Ry = F1y + F2y + F3y = 40 + 67.08 + (-106.57) = 0.51 pounds

Finally, we can use the law of cosines to find the magnitude of the resultant force, and the law of sines to find the direction of the resultant force:

R = sqrt(Rx^2 + Ry^2) = sqrt(72.86^2 + 0.51^2) ≈ 114.66 pounds

theta = atan(Ry/Rx) = atan(0.51/72.86) = 0.0068 radians ≈ 0.39 degrees

So, the direction of the resultant force is 0.39 degrees counter-clockwise from the positive x-axis, and the magnitude of the resultant force is 114.66 pounds.

Note: Keep in mind that angle given in the question is in degree and the trigonometric functions in most programming languages accept the angle in radians, so you have to convert the angle to radians before using the trigonometric functions.

Step-by-step explanation:

The population is all students in accounting class. 3.29 is sample statistic, not population parameter.

What is average ?

An average, also known as a mean, is a measure of central tendency that represents the typical value of a set of data. To calculate the average of a set of numbers, you add them up and then divide by the number of items in the set.

a. The statement "the population is all students enrolled in the accounting class" is true.

The population in this case refers to all the students who are currently enrolled in the accounting class and from which the sample is taken from.

b. The value 3.29 represents the sample statistic.

The sample statistic is a value that is calculated from a sample of data taken from the population. In this case, the average GPA of 3.29 is calculated using a sample of students enrolled in the accounting class, which is a subset of the population of all students enrolled in the accounting class. This value is used to make inferences about the population parameter, which is the true mean GPA of all students enrolled in the accounting class.

The population is all students in accounting class. 3.29 is sample statistic, not population parameter.

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f(x) = -1/x is not a linear function.

Option (B) is correct,

What is a function?

A function is a mathematical relationship between two sets of quantities, called the domain and the range. In other words, a function is a rule that assigns to each element of a set (called the domain) exactly one element of another set (called the range). The most common way to represent a function is using an equation of form f(x) = y, where x is the input variable (or independent variable) and y is the output variable (or dependent variable).

A linear function is a function whose graph is a straight line. A linear function can be represented by an equation of the form f(x) = mx + b, where m and b are constants.

Out of the given options, the function which is not linear is B) f(x) = -1/x

This function is not linear because it's graph is not a straight line.

All the other options are linear functions, option A) f(x) = x/4 is a function with a slope of 1/4, option C) f(x) = 2x + 1 is a function with a slope of 2, and option D) f(x) = -3 is a constant function with a slope of 0.

Hence, f(x) = -1/x is not a linear function.

Option (B) is correct.

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Answer:

767 mph

Step-by-step explanation:

At 20 °C (68 °F), the speed of sound in air is about 343 metres per second (1,125 ft/s; 1,235 km/h; 767 mph; 667 kn), or one kilometre in 2.91 s or one mile in 4.69 s. It depends strongly on temperature as well as the medium through which a sound wave is propagating.

The completely factored form of 12x³-60x² + 4x - 20 can be expreesed as  4(3x² - 1)(x - 5).

The concept that will be used here is factorization. The process of breaking or decomposing an entity (like a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number or matrix is known as factorization or factoring.

To solve this problem then we need to take out all the common ratios :

12x³ - 60x² + 4x - 20

The we can factor 4 out as;

=[ 4(3x³ - 15x² + x - 5)]

The we can factorize the inner brackets  as:

[3x³ - 15x² + x - 5]

The we will have this

= [3x²(x - 5) + (x - 5)]

Then we can now express as

= (3x² + 1)(x - 5)

Therefore, option A is correct.

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The equation of line is calculated and the value of y = 2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line QR be represented as A

Let the equation of line ST be represented as B

Now , the lines QR is perpendicular to the line ST

And , the product of slopes of lines will be -1

Now , the coordinates of point Q ( 1 , -5 )

The coordinates of point R is R ( 4 , -6 )

The slope of the line QR m₁ = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m₁ = ( -6 - ( -5 ) ) / ( 4 - 1 )

Slope m₁ = -1/3

Now , the coordinates of point S ( -6 , 5 )

The coordinates of point T is T ( -7 , y )

The slope of the line ST m₂ = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope m₂ = ( y - 5 ) / ( -7 - ( - 6 ) )

Slope m₂ = ( y - 5 ) / -1

Slope m₂ = ( 5 - y )

Now , the product of slopes = -1

m₁ x m₂ = -1

Substituting the values in the equation , we get

( -1/3 ) x ( 5 - y ) = -1

On simplifying the equation , we get

Multiply by 3 on both sides of the equation , we get

- ( 5 - y ) = -3

Multiply by -1 on both sides of the equation , we get

5 - y = 3

Adding y on both sides of the equation , we get

y + 3 = 5

Subtracting 3 on both sides of the equation , we get

y = 2

Hence , the value of y is 2

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Answer:

0.7901

Step-by-step explanation:

Answer:

Step-by-step explanation:

The greatest integer is ten.

An integer is a number that does not contain a decimal or fractional element and can be positive or negative, including zero.

Let’s call the three integers a,b, and c.

Because the sums of each distinct pair of numbers are 6, 8, and 18,

A + b = 6 (1) (1)

B + c = 8 (2) (2)

C + a = 18 (3) (3)

Subtraction of equation (1) and equation (2):

C – a = 2

Add the preceding equation to equation (3):

2c = 20

C = 10

In equation (3), substitute c = 10:

10 + a = 18

A = 8

In equation (1), substitute a = 8:

8 + b = 6

B = -2

As a result, the three integers are 8, -2, and 10.

As a result, the greatest integer is 10.

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The table using this function rule is:

 x      y

-1     -9

 0     1

 1      11

 5     51    

When the specified input values are applied, the function rule y = 2x+4 produces the output values displayed in the table. As of right now, the output numbers are denoted by and the input values are denoted by and. The function rule y = 3 x + 1 can therefore alternatively be represented as f (x) = 3 x + 1.

The connection between the input or domain and the output or range is called a function rule. When there is exactly one value in the range for each domain value, a relation is a function.

y = 10x+1

x = -1→y=10(-1)+1=-10+1→y=-9

x = 0→y=10(0)+1=0+1→y=1

x = 1→y=10(1)+1=10+1→y=11

x = 5→y=10(5)+1=50+1→y=51

x      y

-1     -9

0     1

1      11

5     51    

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The complete question is,

Use this function rule to complete the table's fields.

y = 10x + 1.      

The value of x will be 6, while the value of y will be 3 in the given pair of the ordered equation.

As we have,

The pair of equations as:

2x + 8y = 36 -----------------(i)

5x − 4y = 18 -----------------(ii)

From above,

We can see that in the first equation the coefficient of x is 2 while in the second one, the coefficient of x is 5.

So, for solving the given sets of equation we need to first equalise the co-efficient of x in both the equations.

So, to make the coefficient equal we will multiply the first equation by 5 and the second equation by 2.

Thus we will get the set of equations as:

10x+40y=180--------(iii)

10x-8y=36------------(iv)

From (iii) and (iv), Now subtracting the (iv) from (iii),

We will get it as:

48y = 144

y = (144/48) = 3

Now for getting the value of x, we will put the value of y in the first equation.

Thus, we will get it as:

2x+24=36

=>2x=12

=>x = (12/2)=6

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The inequalities that include 7 in the solution set are;

D) -3 - x < -9

E) ¹/₂(x + 3) ≥ 2

A) -6 + x ≤ 5

Add 6 to both sides using addition property of equality to get;

x ≤ 11

B) 11 - x ≥ 7

Add x - 7 to both sides to get;

4 ≥ x

C) 3(2x - 9) > 15

Expand the bracket to get;

6x - 27 > 15

Add 27 to both sides to get;

6x > 42

Divide both sides by 6 to get;

x >  7

D) -3 - x < -9

Add 9 + x to both sides to get;

6 < x

E) ¹/₂(x + 3) ≥ 2

Multiply both sides by 2 to get;

x + 3 ≥ 4

Subtract 3 from both sides to get;

x ≥ 1

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Answer: Undefined

Step-by-step explanation:

[tex]\displaystyle\\x=-3\ \ \ \ \Rightarrow\\\\f(x)=\frac{3x+9}{x^3+4x^2+x-6} \\\\\\f(-3)=\frac{3(-3)+9}{(-3)^3+4(-3)^2+(-3)-6}\\\\\\f(-3)=\frac{-9+9}{-27+4(9)-3-6} \\\\\\f(-3)=\frac{0}{-36+36} \\\\\\f(-3)=\frac{0}{0}\\\\\\\\[/tex]

Answer:

x [tex]\geq[/tex] -2

Step-by-step explanation:

The domain is all the possible numbers that x can be.

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.

Given that the slope of the line is -2/5 and the y-intercept is -2/5. We can substitute these values into the equation:

y = -2/5x + -2/5

y = -2/5x - 2/5

The equation in slope-intercept form is y = -2/5x - 2/5.

The domain of function is ( 2 , -4 ) and range of function is ( 4 , -8 ) . The term "range" refers to the set of numbers that the function assumes.

The term "parameters" refers to the set of values that can be entered into the domain of a function. This collection (x) contains the x values for a function like f. The term "range" refers to the set of numbers that the function assumes.

The collection of all y-coordinates with values of 2, 3, and so on is called the range. There are two parts to functions: their range and their domain. A function's domain is the collection of all its input values, while its range is its potential output.

A domain function is range. If f is a function: There is a state known as A B in which each element in A is mapped to one in B. A is the domain, and B is the co-domain. The set of photos is the range of the function if (a,b) R, and then "b" provides the image of element "a" within relation "R."

The following are the domain and range of a function in this general notation: Range(f) = f(x) and domain(f) = x R: domain(x) (f). The domain and range of this function are denoted by D = x N and R = (y): y and x are the same.

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The final number is 176

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

7.Given;

Original price = $275

Resell price = $660

660-275=385

Percent markup= 385*100/275

=140%

9.Given;

The number 200 is increased by 20%

The result is then decreased by 20%

So, 20% increase of 200= 220

Now,20% less of 220=220-44

=176

Therefore, 20 percent decreased number will be 176

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Answer:  P= mgh

Step-by-step explanation: Gravitational potential energy is the energy possessed or acquired by an object due to a change in its position when it is present in a gravitational field. It can be said that gravitational potential energy is an energy that is related to gravitational force or to gravity.

Therefore P= mgh

where m is the mass of an object

g is the acceleration due to gravity

h is the height of an object

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A) One of the factors of the given function would be (x + 2).

B) The factored form of the function would be f(x) = (x+2)(x+1)(x-1).

C) The zeroes are -2, -1, and 1.

What is the cubic function?

A cubic function is a type of polynomial function with the highest degree of 3, meaning the highest power of the variable in the equation is 3. The general form of a cubic function is f(x) = ax³ + bx² + cx + d, where a, b, c, and d are real numbers and a is not equal to 0.

The given function f(x) = x³ + 9x² + 14x - 24
x     -2       -1       0      1       2
f(x)  -24     -30   -24   0     48

A) One factor of f(x) without using a calculator is (x+2) because, when x = -2, f(-2) = (-2)³ + 9(-2)² + 14(-2) - 24 = -24 and it's the same result as the table of values.

B) To completely factor f(x) without using a calculator we can use the rational root theorem. The rational root theorem states that if a polynomial function has rational roots, they must be of the form a/b, where a is a factor of the constant term (in this case -24) and b is a factor of the leading coefficient (in this case 1).

The factors of -24 are: -24, -12, -8, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 8, 12, 24

The factors of 1 are: 1,-1

So, using the rational root theorem, we can test the values of x that are in the form of a/b where a is a factor of -24 and b is a factor of 1.

By testing x=-2, x=-1, x=1, we find that f(x) = (x+2)(x+1)(x-1)

C) To determine the zeros of f(x) without using a calculator, we can use the fact that a zero of a polynomial function is a value of x that makes the function equal to zero. Since we already factorized the polynomial, we know that the zeros are -2, -1, and 1.

Hence,

A) One of the factors of the given function would be (x + 2).

B) The factored form of the function would be f(x) = (x+2)(x+1)(x-1).

C) The zeroes are -2, -1, and 1.

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Evan's earnings for the fuel he uses in the week are $1515.07597, which is more than $250. So Evan is correct that he will be paid more than $250 for the fuel he uses.

To convert miles to kilometers, we can use the conversion factor 1 mile = 1.609344 kilometers. Therefore, to convert the milometer readings to kilometers, we can multiply them by 1.609344:

Start of the week reading in kilometers: 120 miles * 1.609344 km/mile = 193.12128 km

End of the week reading in kilometers: 125465 miles * 1.609344 km/mile = 201788.50112 km

The distance Evan has traveled in the week can be calculated by subtracting the start of the week reading from the end of week reading:

Distance traveled in the week: 201788.50112 km - 193.12128 km = 7575.37984 km

Therefore, Evan has traveled 7575.37984 km in the week.

To calculate Evan's earnings for the fuel he uses, we can multiply the distance traveled in the week by the payment rate of 20 cents per kilometer:

Earnings for the week: 7575.37984 km * $0.20/km = $1515.07597

Therefore, Evan's earnings for the fuel he uses in the week are $1515.07597, which is more than $250. So Evan is correct that he will be paid more than $250 for the fuel he uses.

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Answer: 5040

Step-by-step explanation: The equation for the volume of a pyramid is v=lhw/3

Answer:

Answer: 5040

Step-by-step explanation:

The volume of a triangular pyramid can be found using the formula V = 1/3AH where A = area of the triangle base, and H = height of the pyramid or the distance from the pyramid's base to the apex.

The similarity between solving a compound inequality in a compact form and solving a simple inequality is that the same basic ways of resolving an algebra are followed in both cases. The difference is that any manipulation on one side of the equation must be repeated on all three sides of the compound inequality.

The similarity between solving a compound inequality and a simple one is that they both follow the same basic principles of solving an algebra.

However, there is a slight difference because any change that is applied in one part of the expression must be spread to other parts of the expression.  If we are dividing or multiplying in compound inequalities, the same must apply to all sides.

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Answer: -7

Step-by-step explanation:

Use this equation to help your answer

April lost 5 pounds. -5
She lost 3 pounds -3
She gained 2 pounds +2
She lost 1 pound

Now in a formula, this is -5-3+2-1 = x
To find x we have to simplify
X = -7
Make sure to include the negative since she lost weight

I hope this helps you :D

Answer:Over the fur weeks April lost 7 pounds

Step-by-step explanation:5+3-2+1=7

The height of 14 uch notebook placed one over the other is 420mm

Given that

Thickness of one notebook is 30 mm

To find the height of 14 such placed one over the other

For each  notebook's thickness is 30mm.

stacked notebooks equals fourteen

•°• 30×14=420mm

42 cm or 420 mm.

After placing 14 such notbooks one over the other we get the final Thickness  as 420 mm

This can we converted into 42 centimeters or 0.42 meters

So Therefore the final answer for the height of 14 such notebook placed one over the other is 420 mm or 42 cm

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