A cubic polynomial P(x) has real coefficients. If 3 - 2i and are roots of P(x) = 0 , what is one additional root?

A. 3 + 2i
B. -3-2i
C. - 3 + 2i
D. -5/2

The situations represented by 25/9 are "Melanie equally shares 25 meters of paper to create 9 banners" and "Joe makes 9 equal servings from a 25 ounce bag of peanuts".

Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.

We have the expression 25/9.

That means 25 divided in 9 equal parts.

Now the expression 1,

Melanie equally shares 25 meters of paper to create 9 banners.

We have to divide 25 meters of paper into 9 equal banners.

The above expression can be written as a mathematical term,

and that is 25/9.

Now the expression 2,

Quill gives away 9 baseball cards from a pack of 25.

In mathematical terms; 25 - 9.

Now the expression 3,

George invites 25 kids and 9 adults to his birthday party.

That means, the total 25 + 9 = 34 people

In mathematical terms : 25 + 9

Now the expression 4,

Becca creates 9 rows with 25 buttons each.

That means, each row has 25 buttons.

So the total 9 rows have 9 x 25 buttons.

In mathematical terms : 9 x 25

Now the expression 5,

Joe makes 9 equal servings from a 25 ounce bag of peanuts.

That means 25 ounce bag of peanuts equally divided into 9 parts.

In mathematical terms : 25/9

Therefore, expression 1 : Melanie equally shares 25 meters of paper to create 9 banners and expression 5: Joe makes 9 equal servings from a 25 ounce bag of peanuts, represented by 25/9.

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Answer:

the "^" symbol is called the exponent symbol

exponent is fast multiplication

in other words x^y means multiplying 'x' y times

Step-by-step explanation:

Answer:

your answer is -10

Step-by-step explanation:

HAPPY BIRTHDAY, wishing you luck!!

Answer:

1800

Step-by-step explanation:

suppose the initial cost to be x

it was increased by 6.5%

so, since the price increased is 117

117=6.5% of x

117=(6.5/100) . x

117 . 100=6.5 x

x=11700/6.5

x=1800

Answer: 4x

2x + 2x=4x

A gas station is open 365 day a year, 24 hours a day. If the gas station served 40,000 cups of coffee last year, then it served an average of 5 cups of coffee per hour.

The problem can be solved using the average value approach.

Average value = total amount or sum of data / number of data

In the given problem,

total amount = total coffee served last year

total amount = 40,000

number of data = number of hours in a year

number of data = 365 day/year x 24 hours/day = 8760 hours

Hence,

Average value = total amount or sum of data / number of data

                         = 40000 / 8760

                         = 4,6 ≈ 5 (round to the nearest whole cup)

Hence, the average coffee served is 5 cups per hour.

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Step-by-step explanation:

LHS = 5x+y =5(1)+2= 5+2= 7

RHS = 7

since LHS= RHS

LHS = 7x-2y =7(1)-2(2)=7-4=3

RHS = 3

since LHS=RHS

(1, 2) is a solution to the following system of equations.

True

Hi there!  

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I believe your answer is:  

A) True

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Here’s why:  

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Hope this helps you. I apologize if it’s incorrect.  

Answer:

x=9

Step-by-step explanation:

2.6 pounds based off what I did so I dont know

Answer:

- 18\(\sqrt{10}\)

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)

Given

(6\(\sqrt{2}\) )(- 3\(\sqrt{5}\) )

= 6 × - 3 × \(\sqrt{2}\) × \(\sqrt{5}\)

= - 18 × \(\sqrt{10}\)

= - 18\(\sqrt{10}\)

The variable change to turn the given differential equation into a homogeneous equation is y = vx.

To transform the given differential equation into a homogeneous equation, we can make a substitution y = vx. The derivative of y with respect to x can be expressed as:

y' = v + x(v')

Now, substituting y = vx and y' = v + x(v') into the given differential equation, we get:

v + x(v') = 2x + 3y + 22/(7x + 6y + 90)

Multiplying both sides by the denominator (7x + 6y + 90) and simplifying, we get:

(7x + 6y + 90)(v + x(v')) = 2x(7x + 6y + 90) + 3yx(7x + 6y + 90) + 22

Simplifying further, we get:

(7v + 6)x² + 90v'x + 6v = 2x(7x + 6y + 90) + 3yx(7x + 6y + 90) + 22

Now, we can divide both sides by x² and simplify:

7v' + (6/x)v = 2(7 + 6y/x + 90/x^2) + 3y/x

This equation is now in homogeneous form because the variables v and x appear only in the form of a quotient (v/x). Therefore, the variable change to turn the given differential equation into a homogeneous equation is y = vx.

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Answer:

b.   b=50√c

Step-by-step explanation:

The equation can be used to find other combinations of b and c will be b = 50√c. Then the correct option is B.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

The variable b varies directly as the square root of c.

b ∝ √c

If the proportionality sign is removed with the equal sign, then a constant (k) is introduced.

b = k√c

If b = 100 when c = 4.

Then the value of k will be

    100 = k√4

    100 = 2k

100 / 2 = k

        k = 50

Substitute the value of k in equation, then the equation will be

b = 50√c

The equation can be used to find other combinations of b and c will be b = 50√c.

Then the correct option is B.

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The study outlined above is an experiment. In the study, two firefly colonies are set up in a laboratory environment and are subjected to different conditions. Therefore, it is an experimental design as the researcher is actively manipulating the independent variable which is the exposure of fireflies to light.

An observational study would involve recording data on a subject without manipulating their environment or situation. An observational study would have a less controlled environment in which the researcher does not interfere with the study subjects. There is a control group and a treatment group. The control group is the colony that is exposed to normal daylight/darkness conditions. The treatment group is the colony that is exposed to continuous light. The control group is used to provide a baseline measure or standard of comparison for the experiment.

It provides a way to compare the difference between the treatment group and the control group. Thus, the control group is the normal light/darkness colony, and the treatment group is the continuous light colony.

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Answer:

0%

Step-by-step explanation:

the dots don't surpass 75% so 0% is the answer

The 3 × 3 matrix that translates a point in r 2 by (3, 1) then rotates the result 45 degrees about the origin is

M = | 1/√2    -1/√2    3/√2- 1/√2 |

      | 1/√2    1/√2     1/√2 + 1/√2 |

       | 0           0                1 |

To find the 3x3 matrix that translates a point in R^2 by (3, 1) and then rotates the result 45 degrees about the origin using homogeneous coordinates, we can follow these steps:

Translation Matrix:

The translation matrix for a 2D translation by (3, 1) is:

T = | 1 0 3 |

| 0 1 1 |

| 0 0 1 |

This matrix translates a point (x, y) by adding the translation vector (3, 1) to it.

Rotation Matrix:

The rotation matrix for a 2D rotation by 45 degrees counterclockwise is:

R = | cos(theta) -sin(theta) 0 |

| sin(theta) cos(theta) 0 |

| 0 0 1 |

Since we want to rotate by 45 degrees, theta = 45 degrees = π/4 radians. Therefore, the rotation matrix becomes:

R = | cos(π/4) -sin(π/4) 0 |

| sin(π/4) cos(π/4) 0 |

| 0 0 1 |

Simplifying, we have:

R = | 1/√2 -1/√2 0 |

| 1/√2 1/√2 0 |

| 0 0 1 |

Combine Translation and Rotation:

To obtain the combined transformation matrix, we multiply the translation matrix T by the rotation matrix R:

M = T * R

Performing the matrix multiplication:

M = | 1 0 3 | | 1/√2 -1/√2 0 |

| 0 1 1 | * | 1/√2 1/√2 0 |

| 0 0 1 | | 0 0 1 |

Simplifying, we have:

M = | 1/√2 -1/√2 3/√2 - 1/√2 |

| 1/√2 1/√2 1/√2 + 1/√2 |

| 0 0 1 |

This is the desired 3x3 matrix that translates a point in R^2 by (3, 1) and then rotates the result 45 degrees about the origin using homogeneous coordinates.

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Answer:

the answer is 126.46 I think

Step-by-step explanation:

It is true that the expressions 5y + 4 − 3y = 2y + 4 are equivalent

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

5y+4−3y = 2y+4

This equation can be rewritten as follows

So, we have the following representation

5y + 4 − 3y = 2y + 4

Collect the like terms in the above equation

This gives

5y − 3y + 4 = 2y + 4

Evaluate the like terms in the above equation

This gives

2y + 4 = 2y + 4

Both sides of the equation are the same

Hence, the expressions are equivalent

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Answer:

a. y=x^2

Step-by-step explanation:

desmos graphing calculator

The function f(x) = 2x³ - x² is an odd function.

An odd function satisfies the property f(-x) = -f(x) for all values of x. To determine if f(x) is odd, we substitute -x into the function and observe if it satisfies the given property.

Let's substitute -x into the function:

f(-x) = 2(-x)³ - (-x)²

      = -2x³ - x²

Now, let's compare this to the original function:

-f(x) = -[2x³ - x²]

      = -2x³ + x²

We can see that f(-x) = -2x³ - x² = -f(x), which confirms that the function satisfies the property for odd functions.

This means that when you reflect the graph of f(x) across the y-axis, it remains the same, but when you reflect it across the origin (the x-axis and the y-axis), it flips and changes its sign.

In summary, the function f(x) = 2x³ - x² is an odd function.

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The probable question may be:

Which answer describes the function f(x) = 2x³- x²,

A. even

B. neither

C. odd

The average daily cat cost for my family in six days is 485.5

You are aware that the average weekly expenditure is 485.5.

We must add the quantities for Monday, Tuesday, and Saturday.

505.3+615.40+489.30=1610

Now we need to estimate the three days that they ask us for on Wednesday, Thursday, and Friday.

And we have options; try the first option (a), and add the amounts as before.

404+589+310=1303

Now add the results of the two sums that were performed.

1610+1303=2913

The outcome of this operation must be divided into six parts because there are six days in total.

2913:6=485.5

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The full question

The average daily cat cost for my family in six days?

Answer:

5 years

Step-by-step explanation:

\(interest = \frac{prt}{100} \)

\(1080 = \frac{3600 \times 6 \times t}{100} \)

\( \frac{1080 \times 100}{3600 \times 6} = t\)

108000/21600 = t

time = 5 years

Answer:

This problem requires you to plug in the values to get an answer.

f(2)=1

f(-6)= 65

Step-by-step explanation:

You need to plug in each value in the equation.

\(f(2) = 2^{2} - 4(2) + 5\)

\(f(2) = 4 - 8 + 5\)

\(f(2) = - 4 + 5\)

\(f(2) = 1\)

For f(-6):

\(f( - 6) = ( - 6)^{2} - 4( - 6) + 5\)

\(f( - 6) = 36 + 24 + 5\)

\(f( - 6) = 65\)

The monthly payment for the loan is $1,013.16. After making 360 monthly payments, you will have paid a total of $364,137.64 to the bank. The total interest paid to the bank over the 360 months is $164,137.64.

To calculate the monthly payment, we can use the formula for calculating the monthly payment on a loan:

\(\[M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}\]\)

Where:

M is the monthly payment,

P is the principal loan amount,

r is the monthly interest rate, and

n is the total number of payments.

In this case, the principal loan amount is $200,000, the monthly interest rate is 0.35% (or 0.0035 as a decimal), and the total number of payments is 360. Plugging these values into the formula, we find that the monthly payment is $1,013.16.

To calculate the total amount paid to the bank over the 360 months, we simply multiply the monthly payment by the total number of payments: $1,013.16 * 360 = $364,137.64.

The total interest paid to the bank can be calculated by subtracting the principal loan amount from the total amount paid: $364,137.64 - $200,000 = $164,137.64.

Therefore, the monthly payment for the loan is $1,013.16, and after 360 monthly payments, the total payment to the bank is $364,137.64, with $164,137.64 being the total interest paid.

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The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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The obtained answers for the given piecewise function are:

(a) The cost of a call that is under six minutes is 0.70 (m < 6)

(b) The cost of a 14-minute call is 2.62 (m > 6; m is an integer)

(c) The cost of a 9 1/2 minute call is 1.66 (m > 6; m is not an integer)

A piecewise function is given by different functions at different intervals.

It is given that,

phone company set the following rate schedule for an m-minute call from any of its pay phones.

C(m) = 0. 70 when m ≤ 6

        = 0.70 + 0.24(m - 6) when m > 6 and m is an integer

        = 0.70 + 0.24([m - 6] + 1) when m > 6 and m is not an integer

(a) The cost of a call that is under six minutes:

Since m < 6, the cost is C(m) = 0.76

Thus, the cost of a call that is under six minutes is 0.76

(b) The cost of a 14-minute call:

Since 14 > 6, the cost is C(m) = 0.70 + 0.24(m - 6) when m > 6 and m is an integer.

C(14) = 0.70 + 0.24(14 - 6)

        = 0.70 + 0.24(8)

        = 0.70 + 1.92

        = 2.62

Thus, the cost of a 14-minute call is 2.62.

(c) The cost of a 9 1/2 minute call:

9 1/2 = 19/2 = 9.5

Since 9.5 > 6, the cost is C(m) = 0.70 + 0.24([m - 6] + 1) when m > 6 and m is not an integer.

C(9.5) = 0.70 + 0.24([9.5 - 6] + 1)

          = 0.70 + 0.24([3.5] + 1)

Since we know that if [x] is a function then its domain is R and the range is Z(integer)

So, [3.5] = 3(is an integer)

Then,

C(9.5) = 0.70 + 0.24(3 + 1)

          = 0.70 + 0.96

          = 1.66

Therefore, the cost of a 9 1/2 minute call is 1.66.

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Average score initially = 79, average score after 4 months is 57.47, after 24 months it is 35.09

Given: S(t)=79−14 ln(t+1),

(a) The average score when they initially took the test(i.e at t = 0)

S(0)= 79 − 14 ln (0+1) ⇒ S(0) = 79 - 14 ln(1) ⇒ S(0) = 79 - 14 (0) ⇒ S(0) = 79

Hence, the average score when they initially took the test was 79.

(b) The average score after 4 months (i.e at t = 4)

S(4) = 79 − 14 ln (4+1) ⇒ S(4) = 79 − 14 ln (5) ⇒ S(4) = 79 - 14(1.609) ⇒ S(4) = 57.47. Hence, the average score after 4 months was 57.47.

(c) The average score after 24 months (i.e at t = 24)

S(24) = 79 − 14 ln (24+1) ⇒ S(24) = 79 − 14 ln (25) ⇒ S(24) = 79 - 14(3.218) ⇒ S(24) = 35.09

Hence, the average score after 24 months was 35.09.

(d) Differentiating S(t) with respect to t, we get: S'(t) = dS(t)/dt= -14(1/(t+1))(1) ⇒ S'(t) = -14/(t+1)

Therefore, S'(t) = -14/(t+1).

(e) S'(4) = -14/(4+1) = -2.8 and S'(24) = -14/(24+1) = -0.5

The number S'(4) = -2.8 is interpreted as follows: If the students keep retaking the equivalent form of the test for every one more month after the first test (t=0), then on average, the score will drop by 2.8% after every one month. For example, if a student's score is initially 79 (in the first test) and keeps on taking the equivalent test every one month, then on average, their score after 1 month will be 76.2 (i.e 2.8% less than 79).

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