Find all the real and complex solutions of the polynomial equation. Be sure to show ALL work (4 points):

Solutions of a system of  an equations are given with the  values of the variables which  make all the equations true in which a solution of a system of given two linear equations is represented in  an ordered pair (x, y) as explained with example below:

An example of a system of two linear equations in an ordered pair , in order  to show the two equations that  are arranged  together to form a system of equations in an linear form .

let  , 2x + y = 7,

x- 2y = 6

A linear equation which consists of  two variables, as  2x + y = 7, has an infinite number of solutions. in which the  graph of a equation  is a line. we know that every point on the line is a required solution to the equation and every solution of an  equation is a point on the line.

To solve a system of two linear equations in an ordered pair , we want to find the values to particular  variables that are solutions to both  linear equations. In other words, we are expecting  for the ordered pairs (x, y) that make both equations valid . These type of equations are known as  solutions to a system of equations.

hence , the solutions of a system of equations are the values of the variables that make all the valid and obeyed equations are  true.  and solution of a system of two linear equations is represented always in an  ordered pair (x, y) .

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Answer:

1004 is the smallest four-digit palindrome that is divisible by 4.

The equation for dimensions of the rectangle is x(x - 3) = 10 and the width is 2 meters and the length is 5 meters.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

x(x-3)=10

x²-3x=10

x²-3x-10=0

x²-5x+2x-10=0

(x-5)(x+2)=0

x=-2,5

x=5 units

x-3=5-2

=2 units

The rectangle's dimensions are x(x - 3) = 10, with a width of 2 meters and a length of 5 meters.

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The diameter of Mars is 6825 kilometers.

First we quantify angular size a = 8. 0 arcseconds in radians.

a = ( 8/ 3600) × (π/180)

a = 0.000039 radians

also, the distance from Earth to Mars in kilometres is 175,000,000 km

So, r = 175,000,000 km

We use the formula S = r x a to find the diameter of Mars

Substitute r = 175,000,000 and a = 0.000039 in above formula

S = 175,000,000 × 0.000039

S = 6825 km

Therefore, the diameter is 6825 km

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The values of mean ,median, range and inter quartile range could be 23,23.5,22,14 respectively.

What is mean ?

mean can be defined as the ratio of sum of the total observations and the number of total observations.

Given set of data

11,13,17,20,22,25,27,31,31,33

Mean  =  11 +13+17+20+22+25+27+31+31+33/10

= 230/10

 =23

Hence  mean = 23

The (n/2)th term= the 5th term

                       =22

The  (n/2+1) term = The  6th term

= 25

The median = 22+25/2

                  =23.5

Range = Highest term - lowest term

          =33- 11

           =22

Here lower half {11,13,17,20,22}

The middle number of lower half is first quartile.

Q₁ = 17

And lower half is{25,27,31,31,33}

The middle number of upper half is third quartile.

Q₃=31

Interquartile Range =Q₃-Q₁

                               =31-17

                                =14

Hence, The values of mean ,median, range and inter quartile range could be 23,23.5,22,14 respectively.

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f(x) =2(3ˣ) is an exponential function which has an initial value of 2.

Another word for "involving an exponent" in mathematics is exponential. For instance, an exponential rise in a number occurs when you raise it to the tenth power.

A mathematical function with the formula f(x) = aˣ is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently seen. A variable is used as the exponent in exponential functions.

The exponential function that has an initial value of 2 is f(x) = 2ˣ.

f(x) = 2(3ˣ) can be written as f(x) = 2 × 3ˣ, so it starts at 2 × 3⁰ = 2 × 1 = 2.

f(x) = 3(2ˣ) can be written as f(x) = 3 × 2ˣ, so it starts at 3 × 2⁰ = 3 × 1 = 3

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Answer:

x=0

Step-by-step explanation:

Solving the equation:

10x+6-6=-9

10x=-9x

19x=0

x=0

The value of line GB is 6

From the diagram shown, we can see that AG, GB and AB form a triangle with two of its sides being equal.

Also, line AG = line GB

Where;

Then, we have;

Line AG = LIne GB

Substitute the expressions, we have;

5x - 24 = 3x - 12

Collect like terms

5x - 3x = - 12 + 24

Add or subtract like terms

2x = 12

Divide both sides by the coefficient of x

x = 12/ 2

x = 6

The, GB = 3(6) - 12 = 6

Hence, the value is 6

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The simplified form of 21b − 32 7b − 20b would be 8b - 32.

Reducing an equation is a technique for rewriting it in a more straightforward format. Although some mathematical equations are not in the form of linear equations, they can be converted into linear equations by applying certain mathematical operations to them. These equations can be easily solved after being reduced to linear form, and the value of the unknown can be determined.

21b – 32 + 7b – 20b

= 21b + 7b – 20b – 32

= 28b – 20b – 32 = 8b – 32

21b - 32 + 7b - 20b

= 21b + 7b - 20b -32

= 8b - 32

=8b - 32.

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Answer:

No

Step-by-step explanation:

Since [tex]2^2+3^2 \neq 5^2[/tex], the side lengths do not satisfy the Pythagorean theorem.

Answer:

1/2

Step-by-step explanation:

A line that is perpendicular to another has an opposite reciprocal slope. In this case, we can see that the slope of the given line is -2, so the perpendicular line would have a slope of 1/2.

Answer:

1/2

Step-by-step explanation:

The slope of a line perpendicular to any given line is the negative reciprocal of the given line's slope:

[tex]m_\perp = \dfrac{1}{m}[/tex]

In this problem, the slope of the given line is [tex]\dfrac{-2}{1}[/tex] (rise over run).

So, to find the slope of a line that is perpendicular to it, we simply flip the given line's slope and change its sign.

[tex]m_\perp = \dfrac{1}{2}[/tex]

So, a line which is perpendicular to the given line would have a slope of 1/2.

Let H be the number of hamburgers sold and C be the number of cheeseburgers sold.

The total number of hamburgers and cheeseburgers sold is given by the equation: H + C = 429

The number of cheeseburgers sold is given by the equation: C = 2H

Substituting the second equation into the first equation, we get: H + 2H = 429

Combining like terms, we get: 3H = 429

Dividing both sides by 3, we get: H = 143

On Thursday, 143 hamburgers were sold.

Answer:6 days

Step-by-step explanation:

62-26=36

36/6=

6

Answer: it is the 4 one which is 3(5-n)=2n+16

The third side of a triangle can be found using the Pythagorean Theorem.

This states that the sum of the squares of the two shorter sides of a triangle must equal the square of the longest side (the hypotenuse).

Let's say you have a triangle with sides a, b, and c, where c is the longest side. To find c, you can use the following formula:

c = √(a2 + b2)

For example, if you have a triangle with sides a = 4 and b = 5, then c = √(42 + 52) = √41 = 6.4. Therefore, the third side of the triangle is 6.4.

To calculate this using steps, you would first square the two shorter sides of the triangle:

a2 = 4 x 4 = 16

b2 = 5 x 5 = 25

Then, add the two squares together:

16 + 25 = 41

Finally, take the square root of the sum to find the length of the third side:

√41 = 6.4

Therefore, the third side of the triangle is 6.4.

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There are 4 cassette tapes.

Given that,

Let x be the number of compact discs

Then 5 times the number of CD's= 5x and 10 less than 5 times the number of CDs is 5x-10

Therefore the number of cassettes is 5x-10

Now we are told that the ratio of cassettes to CDs which is

((5x-10)/x) equals 5/2 so our equation to solve is:

(5x-10)/x=5/2 multiply both sides by 2x to get rid of the fractions and we get:

2(5x-10)=5x

Further solving this equation, we get:

10x-20=5x

5x=20

x= 4 (number of compact discs)

Thus, there are in total 4 cassette tapes.

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So,  a 72-month loan with a 2 annual simple interest rate is the loan choice that would need her to repay the least amount of money.

An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.

According to the information provided, a 72-month loan with a 2 annual simple interest rate is the loan choice that would require her to repay the least amount of money. This is because the amount she would have to pay will be the least compared to other loan options.

[tex]Loan = 72 months (2per cent of $6,000)\\Loan = 120 for 72 months\\Loan =$8,640\\[/tex]

a 72-month loan with a 2 yearly simple interest rate.

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The value of angle x in the triangle shown is 78°

An equation is an expression that shows the relationship between two or more numbers.

A triangle is a polygon that has three sides and three angles. The sum of angles in a triangle is 180 degrees. Types of triangles are isosceles, scalene, equilateral

In the large triangle let the missing angle by y, hence:

y + 87 + 36 = 180  (sum of angle in a triangle)

y = 57°

In the triangle containing the angle 45, let the missing angle be z, hence:

z + y + 45 = 180 (angle in a triangle)

z + 57 + 45 = 180

z = 78°

x = z (corresponding angles are equal)

x = 78°

The value of x is 78°

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Answer:

90 cups

Step-by-step explanation:

Number of cups needed = 30 / (1/3) cups

                                          = 90 cups

Thought process:

1 cup -> 1/3 ounce

3 cups -> 1 ounce

? cups -> 30 ounce

Hence, ? = 30 x 3

                = 90

Answer: , P = 2 +3g

Step-by-step explanation:

Answer:

a ≥ -5

Step-by-step explanation:

Think like this is a number line

--------------------------------------------------------------------------------------------------------

-6              -5           -4            -3        -2          -1       0         1        2         3   4

and all the inequality says is for it to be bigger than -6 so than is -5, -4, -3, -2 -1, 0,1 and so on. So the answer is a>-6 or a≥-5

The equation point slope is y - y1 = m(x - x1)

we got y - (-16)=3(x-7)

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The value of the length will be 17920cm.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

Since the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³.

The value of the length will be:

= 7 / (7 +5+2) × 35840

= 7/14 × 35840

= 17920cm

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the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³. Find the value of the length

The system of equations could be used to find the number of gallons of gas Chris bought at each station is,

B. x + y = 20 and 1.45x + 1.55y = 29.80.

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.

Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.

An example of a non-linear function is a quadratic function.

Given, Chris stopped for gas twice on a long car trip.

The price of gas at the first station was $1.45 per gallon, and the price of gas at the second station was $1.55 per gallon and filled a total of 20 gallons of gas and cost him a total of $29.80.

Therefore the system of linear equations that represents the context is,

x + y = 20 and 1.45x + 1.55y = 29.80.

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The range of a sample data collected by a researcher is 10 . So, correct answer is option (C).

Range of a sample data is calculated by using the formula to determine the difference between the highest and lowest value in sample set of values.

R = Highest Value (H) - Lowest Value (L)

Range Formula, R = H - L

Where, R --> range

H --> the highest value

L --> the lowest value

We have, a reaseacher collected a sample data .

Sample data values are following,

3 5 12 3 2

The mean of sample data = 5

Range of sample data = highest data value - lowest data value

There is highgest data value = 12

and lowest data value = 2

Range = 12 - 2 = 10

So, the required range of sample data is 10.

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Complete question:

A researcher has collected the following sample data. The mean of the sample is 5

"3 5 12 3 2"

Refer to Exhibit 1. The range is:

A)1

B)2

C)10

D) 12

Answer:

b

Step-by-step explanation:

The graph that shows the function h(x) = -x] which is a transformation of the absolute value parent function, f(x) = [x] is Option C.

The graph of the function h(x) = -x] is the reflection of the graph of f(x) = [x] about the x-axis. The graph of f(x) is piecewise defined as follows:

The graph of h(x) will have the same shape as f(x), but with all the y-values negated, so:

The graph of h(x) will thus be a downward-facing step function, with steps at x = 0, moving from -x to x as x moves from negative to non-negative values. Thus, Option C is correct.

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The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).

A line's steepness and direction are measured by the line's slope.

Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes.

The y coordinate's net change is y, and the x coordinate's net change is x.

Hence, The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).

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x = 448, which is the greatest of these integers.

Positive, negative, and zero are all examples of integers.

The Latin word "integer" signifies "whole" or "intact."

As a result, fractions and decimals are not included in integers.

All whole numbers and negative numbers are considered integers.

This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.

According to our question-

added together =1341

x +  x-1 + x-2 =1341

3x-3  = 1341

3x = 1344

x = 448

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On sectional charts, the graticules are the lines that separate each 30 minutes of latitude and each 30 minutes of longitude. One tick mark equals one minute of latitude or longitude. Moving northward increases latitude while moving westward increases longitude. The coordinates of the Garrison (Pvt) airport are 47° 40' 00" N and 101° 26' 00" W.

Direction is characterised as the course that something follows, the route that must be taken to get to a particular location, the direction in which something is beginning to take shape, or the direction you are facing. When you turn right instead of left, that is an illustration of direction.

Identifying whether a direction is clockwise or anticlockwise is a straightforward method for resolving direction problems. If we turn right, the direction will be entirely clockwise. Therefore, when starting from the correct point at North, every right movement will lead in the clockwise directions of East, South, and West.

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