How many real and complex roots exist for the polynomial
F(x)= x³ +2x² + 4x+8 ?
OA. 2 real roots and 1 complex root
OB. 1 real root and 2 complex roots
C. 3 real roots and 0 complex roots
D. 0 real roots and 3 complex roots

The new coordinates of the quadrilateral ABCD after the dilation is:

A' = (-6, 6)

B' = (-8, -4)

C' = (4, -8)

D' = (0, 0)

We have,

To find the coordinates of the new quadrilateral after a dilation with a scale factor of 2 centered at the origin, we multiply the x and y coordinates of each point by the scale factor.

Given the original coordinates of the quadrilateral ABCD:

A = (-3, 3)

B = (-4, -2)

C = (2, -4)

D = (0, 0)

To dilate the coordinates with a scale factor of 2, we multiply each coordinate by 2:

A' = 2 x (-3, 3) = (-6, 6)

B' = 2 x (-4, -2) = (-8, -4)

C' = 2 x (2, -4) = (4, -8)

D' = 2 x (0, 0) = (0, 0)

Thus,

The new coordinates of the quadrilateral ABCD after the dilation is:

A' = (-6, 6)

B' = (-8, -4)

C' = (4, -8)

D' = (0, 0)

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The radius of the cylinder is 2.25 feet.

To find the radius of the cylinder, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the volume V is 400 cubic feet and the height h is 25 feet, we can substitute these values into the formula and solve for the radius r.

400 = 3.14 r² x 25

Dividing both sides of the equation by (3.14 * 25) to isolate r^2, we have:

r² = 400 / (3.14 x 25)

r² ≈ 5.08

Taking the square root of both sides to solve for r, we get:

r ≈ √5.08

r ≈ 2.25

Therefore, the radius of the cylinder is 2.25 feet.

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Manuel received $187.50, and George received $562.50 for the job.

Let's break down the information provided:

The job paid a total of $750.

George received $3 for every $2 that Manuel received.

To determine the amounts George and Manuel received, we can set up a ratio based on their earnings.

Let's assume Manuel's earnings as the base amount:

George's earnings : Manuel's earnings = $3 : $2

We can set up the following equation to solve for Manuel's earnings:

(Manuel's earnings / Manuel's earnings) = ($2 / $2)

Since the ratio is equivalent, we can say:

George's earnings / Manuel's earnings = $3 / $2

To find the amount each person received, we'll assign a variable to Manuel's earnings. Let's call it "x."

Therefore, George's earnings can be represented as "3x."

According to the given information, their total earnings should sum up to $750:

x + 3x = $750

Combining like terms, we have:

4x = $750

To solve for x, we divide both sides by 4:

x = $750 / 4

x = $187.50

Now, we can determine the amounts each person received:

Manuel's earnings = x = $187.50

George's earnings = 3x = 3 * $187.50 = $562.50

Therefore, Manuel received $187.50, and George received $562.50 for the job.

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The calculated value of the price per cup is $1.16

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

A 3-quart jug of water costs $3.48

The price per cup is calculated as

Unit rate = Total cost/Size of the cup

Substitute the known values in the above equation, so, we have the following representation

Unit rate = 3.48/3

Evaluate

Unit rate = 1.16

Hence, the price per cup is $1.16

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The term 9b represents the cost to rent a bike.

We have,

               Rentals

Bike                            $9/h

Electric scooter          $10/h

Kayak                          $18/h

Canoe                         $20/h

Paddleboard               $22/h

Helmet                        Add $6

Here, the term 9b represents the cost to rent a bike.

In the provided rental options, the cost of renting a bike is $9 per hour.

The term "9b" indicates that the cost is calculated by multiplying the hourly rate of $9 with the number of hours (b) the bike is rented for.

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1) The dimensions of the 4 walls are:

Two walls are 20 feet long and 8 feet tall.

Two walls are 25 feet long and 8 feet tall.

2) Total area to be covered:

= 720 square feet.

3) You will need 1.8 gallons of paint to cover all four walls of the room.

Now, The dimensions of the 4 walls are:

Two walls are 20 feet long and 8 feet tall.

Two walls are 25 feet long and 8 feet tall.

And, The total area to be covered is:

For the two 20 feet long walls:

A = 20 feet x 8 feet

A = 160 square feet each.

And, For the two 25 feet long walls:

A = 25 feet x 8 feet

A = 200 square feet each.

Hence, Total area to be covered:

= (160 + 160 + 200 + 200) square feet

= 720 square feet.

For the number of gallons of paint needed, divide the total area to be covered by the area covered by one gallon of paint:

Number of gallons of paint needed = Total area to be covered / Area covered by one gallon of paint

Number of gallons of paint needed = 720 square feet / 400 square feet per gallon

Number of gallons of paint needed = 1.8 gallons

Therefore, you will need 1.8 gallons of paint to cover all four walls of the room.

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The equation that represents this situation is:

⇒ 60t = 0.0284091

where t is the time in minutes.

We have to given that,

The speed of the cheetah is 60 miles per hour

The distance timed was 50 yards

Now, We have to convert the distance to miles, because the speed is in miles per hour.

Since, 1 yard = 0.000568182 miles

Hence, 50 yards = 50 x 0.000568182 miles

50 yards = 0.0284091 miles

Now we can use the formula:

distance = speed x time

We know that,

The distance is 0.0284091 miles, and the speed is 60 miles per hour.

Hence, the time it took the cheetah to run the 50-yard distance.

So, the speed from miles per hour to miles per minute, since we want the time in minutes:

60 miles per hour = 1 mile per minute

Now we can plug in the values we know:

0.0284091 miles = (1 mile per minute) x time

Solving for time:

time = 0.0284091 / 1

time = 0.0284091 minutes

time = 0.0284091 minutes x 60 seconds per minute

time = 1.704546 seconds

Thus, the equation that represents this situation is:

⇒ 60t = 0.0284091

where t is the time in minutes.

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Answer:

900 kg

Step-by-step explanation:

Let's assume the cost price (C.P.) of sugar is Rs. x per kg.

The total quantity of sugar is 1500 kg.

Let the quantity of sugar sold at 8% profit be represented by y kg.

The quantity of sugar sold at 18% profit would then be (1500 - y) kg.

Using the rule of alligation, we can set up the following proportion:

(8% profit) y kg

-------------- = ------

(18% profit) (1500 - y) kg

Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).

The ratio of these differences is 2:3.

This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.

Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:

(2 kg) * (3/2) = 3 kg

Therefore, the quantity sold at 18% profit is 900 kg.

The value of x is 4.

To determine the value of x, we can use the concept of similarity between shapes.

Similar shapes have corresponding sides that are proportional to each other.

Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:

5/x = 30/24

To solve for x, we can cross-multiply:

30 · x = 5 · 24

30x = 120

Dividing both sides of the equation by 30:

x = 120 / 30

x = 4

Therefore, the value of x is 4.

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Answer: 14 ounces

Step-by-step explanation:

         To find the mean, we add up all the values and divide by the number of values.

[tex]\displaystyle \frac{12+14+15+15+14}{5} =\frac{70}{5} =14\;ounces[/tex]

The circumference of the circle is 62.8cm.

The Circumference of the circle is given by the formula,

Circumference = 2*[tex]\pi[/tex]*r cm.........equation 1

Given, r = 10cm

On substituting the radius value in equation 1

Circumference = 2*[tex]\pi[/tex]*10

Circumference = 62.8 cm

Therefore, the circumference of the circle is 62.8cm.

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An equation of the new graph is: A. y = ∣x - 4∣ - 9.

In Mathematics and Geometry, the translation of a graph to the right simply means a digit would be added to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph downward simply means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) + N

Since the parent function y = ∣x∣ was translated 4 units to the right and 9 units down in order to produce the graph of the image, we have:

y = ∣x - 4∣ - 9

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

There are a total of 3 forwards on the team.

A fraction represents a part of the whole or group of objects.In a fraction, numerator and denominator are separated by a horizontal bar known as the fractional bar

Given:

2/8 of the players are forwards.

Total number of players on the team = 12

We will determine the total number of forwards on the team by multiplying the total number of players by the fraction representing the forwards.

Fraction representing the forwards:

= 2/8

= 1/4

Total forwards on the team:

= 12 * (1/4)

= 3.

Translated question:

Of the 12 players on the team, 2/8 are forwards. What are the total forward in the team?

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Answer:

increasing exponential function.

Step-by-step explanation:

We can see from the table that the function is not increasing by the same amount as it goes up by 1 in x, so it is not linear.

It  must be exponential.

It is increasing at it increases in x, so it is an increasing exponential function.

Given statement Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.

To find (fg)(x), we need to first find the product of f(x) and g(x) and simplify the expression.

f(x) = 2x

g(x) = [tex]2x^2[/tex] + 3x

To find (fg)(x), we substitute g(x) into f(x):

(fg)(x) = f(g(x)) = f([tex]2x^2[/tex] + 3x)

Now we substitute f(x) = 2x into the expression above:

(fg)(x) = 2([tex]2x^2[/tex] + 3x)

Distribute the 2:

(fg)(x) = [tex]4x^2[/tex] + 6x

So, (fg)(x) = [tex]4x^2[/tex] + 6x.

Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.

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Given statement solution is :- The correct solutions to the quadratic equation  [tex]3(x-7)^2 = 27[/tex]  are x = 10 and x = 4.

Diego made an error in the step where he simplified [tex](x-7)^2 = 9 to x^2[/tex] - 72 = 9. The correct expansion of [tex](x-7)^2 is x^2 - 14x + 49[/tex], not [tex]x^2 - 72.[/tex]Therefore, his subsequent steps and solution are incorrect.

Mai made an error in the step where she simplified [tex](x-7)^2 = 9[/tex] to x - 7 = 9. The square root of 9 is ±3, so the correct equation should be x - 7 = ±3, not x - 7 = 9. Therefore, her solution is incorrect.

To solve the equation correctly, we start with the equation [tex]3(x-7)^2 = 27.[/tex]

Dividing both sides by 3, we have:

[tex](x-7)^2 = 9[/tex]

Taking the square root of both sides, we get:

x - 7 = ±3

Now, we need to solve for x by adding 7 to both sides:

x = 7 ± 3

This gives us two possible solutions:

x = 7 + 3 = 10

x = 7 - 3 = 4

So, the correct solutions to the quadratic equation [tex]3(x-7)^2 = 27[/tex] are x = 10 and x = 4.

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Among the mean, mode, and median, the unique one is the b. mode.

The mode is the data value that occurs many times more than other data values.

Unlike the mean that shows the average value of all the data values, the mode occurs more.  While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.

Similarly, the median can be computed when two values occur as the middle values.

Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.

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<1 and <2 are same-side interior angles. Option D

<1 and <5 are same-side interior angles. Option B

<6 and <8 are corresponding angles. Option C

To determine the angles, we need to know the following;

Now, from the information given, we have that;

1. <1 and <2 are same-side interior angles because they are found on the same side of the transversal

2. We can see that < 1 and <5 are also same-side interior angles because they are two angles found on the exact same side of the transversal

3. Since corresponding angles are angles on matching corners of a transversal, < 6 and < 8 are corresponding angles

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Answer:

Step-by-step explanation:

You have to use the quadratic formula

x = -b +/- [tex]\sqrt{(b^{2} -4ac)/2a[/tex]

and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2

you usually have to reject an answer but since there is no equal sign in the question, you should be fine

The probability that either event will occur is 0.67

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

Event A = 3

Event B = 1

Other Events = 2

Using the above as a guide, we have the following:

Total = A + B + C

So, we have

Total = 3 + 1 + 2

Evaluate

Total = 6

So, we have

P(A) = 3/6

P(B) = 1/6

For either events, we have

P(A or B) = 3/6 + 1/6 = 0.67

Hence, the probability that either event will occur is 0.67

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Answer:

18+x = -40

Step-by-step explanation:

The sum of 18 and a number x is translated to "18+x"
Equals means "="
Negative forty is "-40"
Put them all in order and you get 18+x = -40

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;

C² = a²+b²

Where:

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A graph of the linear equation y = 2x - 1 in slope-intercept form is shown in the image attached below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have the linear equation:

y = 2x - 1

Lastly, we would use an online graphing calculator to plot the given linear equation as shown in the graph attached below.

In conclusion, the slope of this linear equation is equal to 2 and it does not represent a proportional relationship.

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Complete Question:

Plot the linear equation on the coordinate axis shown on the right.

Answer:

118

Step-by-step explanation:

104+25+(-11)

129-11

118

Therefore, our answer is 118

Answer:

1,000 grams

noun. a unit of mass equal to 1,000 grams: the basic unit of mass in the International System of Units (SI). Up until 2019 the kilogram was defined as equal to the mass of an international prototype, a platinum-iridium cylinder kept in Sèvres, France.

The function notation of 9x + 3y = 12 is given as follows:

f(x) = 4 - 3x.

The function in the context of this problem is given as follows:

9x + 3y = 12.

The format for the function notation is given as follows:

Hence we must isolate the variable y, as follows:

3y = 12 - 9x

y = 4 - 3x (each term of the expression is divided by 3).

f(x) = 4 - 3x.

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