Which of the following relations are functions? Select all that apply.

A.
B.
C.
D.

The remaining roots of the given polynomial function are x=4+5i and x=4-5i.

The zeros of polynomial refer to the values of the variables present in the polynomial equation for which the polynomial equals 0.

The given polynomial function is p(x)=x³-3x²+x+205 and one of the root of the function x=-5.

Here, x+5=0

x+5|x³-3x²+x+205|x²-8x+41

   -(x³+5x²)
_______________

         -8x²+x+205

        -(-8x²-40x)
_______________
                 41x+205

               -(41x+205)
________________
                       0

Now, x²-8x+41

Using quadratic formula, we get

x = [-b ±√(b² - 4ac)]/2a

x= [8±√((-8)² - 4×1×41)]/2

=[8±√((-8)² - 4×1×41)]/2

=[8±√(-100)]/2

=[8±10i]/2

=4±5i

x=4+5i and x=4-5i

Therefore, the roots of polynomial function are x=4+5i and x=4-5i.

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Answer:

The possible values of the angle \alpha that satisfy the given equation are the angles in the range [0, 60] degrees or the angles in the range [300, 360] degrees. This is because we showed that the value of cos(\alpha) must be less than or equal to 1/\sqrt{3} in order for the equation to hold.

Step-by-step explanation:

It looks like you have entered some LaTeX code in your question, but it is not properly formatted. Here is the correct way to enter the equation:

cos(\alpha) + \frac{1}{\sqrt{3}} \cdot sin(\alpha) = 1

To solve this equation, we can use the identity cos^2(\alpha) + sin^2(\alpha) = 1. We can rewrite the left-hand side of the equation as follows:

cos^2(\alpha) + \frac{1}{3} \cdot sin^2(\alpha) = 1

Then, we can solve for sin^2(\alpha):

sin^2(\alpha) = 3 \cdot (1 - cos^2(\alpha))

Since sin^2(\alpha) is nonnegative, we know that cos^2(\alpha) must be less than or equal to 1/3. This means that cos(\alpha) must be less than or equal to 1/\sqrt{3}. Therefore, the possible values of \alpha that satisfy the given equation are the angles in the range [0, 60] degrees or the angles in the range [300, 360] degrees.

Note that this solution assumes that the angle \alpha is measured in degrees. If the angle is measured in radians, then the range of possible values for \alpha will be different.

Step-by-step explanation:

1 mile = 5280 ft

1 hour = 3600 seconds

65 miles / hour =

= 65 × 5280 ft / 3600 seconds = 65 × 528 ft / 360 s =

= 13 × 264 ft / 36 s = 13 × 66 ft / 9 s = 13 × 22 ft / 3 s =

= 13 × 11 ft / 1.5 s = 143 ft / 1.5 s

so, at 65 mph the driver travels 143 ft before the driver reacts (1.5 s) to an obstacle.

The values of the ED and DC are 12 and 18 respectively.

What is the centroid of the triangle?

The centroid of a triangle is formed when three medians of a triangle intersect. It is one of the four points of concurrencies of a triangle. The medians of a triangle are constructed when the vertices of a triangle are joined with the midpoint of the opposite sides of the triangle.

a) EC = 18

We have,

Point D is the centroid of ΔABC,

a) EC = 18

b) EC = 27

The centroid theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid-point of the sides.

Here, ΔABC is a triangle having a centroid D. F, G and E are the midpoints of the sides of the triangle BC, AC, and AB, respectively. Hence as per the theorem;

DE = 2/3 CE,

DG = 2/3 BG and

DF = 2/3 BF.

So,

a) EC = 18

ED = 2/3 EC,

ED = 2/3 * 18,

ED = 2 * 6,

ED = 12,

b) EC = 27

DC = 2/3 EC,

= 2/3 * 27,

= 2 * 9,

DC = 18,

Hence, the values of the ED and DC are 12 and 18 respectively.

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Answer:

10.  ED = 6  and  DC = 12

11.  ED = 9  and  DC = 18

Step-by-step explanation:

The centroid of a triangle is the point of intersection of its medians.

A median is a line that joins the vertex of a triangle to the midpoint of the opposite side.

Centroid Theorem

The centroid of the triangle is two-thirds of the distance from the vertex to the midpoint of the opposite side.

Given:

EC is a median that joins vertex C to midpoint E.

Therefore, DC is two-thirds of EC:

[tex]\implies \sf DC=\dfrac{2}{3}EC[/tex]

[tex]\implies \sf DC=\dfrac{2}{3} \cdot 18[/tex]

[tex]\implies \sf DC=\dfrac{36}{3}[/tex]

[tex]\implies \sf DC=12[/tex]

And ED is one-third of EC:

[tex]\implies \sf ED=\dfrac{1}{3}EC[/tex]

[tex]\implies \sf ED=\dfrac{1}{3}\cdot 18[/tex]

[tex]\implies \sf ED=\dfrac{18}{3}[/tex]

[tex]\implies \sf ED=6[/tex]

Given:

EC is a median that joins vertex C to midpoint E.

Therefore, DC is two-thirds of EC:

[tex]\implies \sf DC=\dfrac{2}{3}EC[/tex]

[tex]\implies \sf DC=\dfrac{2}{3} \cdot 27[/tex]

[tex]\implies \sf DC=\dfrac{54}{3}[/tex]

[tex]\implies \sf DC=18[/tex]

And ED is one-third of EC:

[tex]\implies \sf ED=\dfrac{1}{3}EC[/tex]

[tex]\implies \sf ED=\dfrac{1}{3}\cdot 27[/tex]

[tex]\implies \sf ED=\dfrac{27}{3}[/tex]

[tex]\implies \sf ED=9[/tex]

Answer:

If Sophie has $800 in a saving account that earns 5% interest per year and the interest is not compounded, then after one year she will have $840 in her account. This is because 5% of $800 is $40, and when we add this to the initial amount of $800, we get $840.

In general, if a saving account earns x% interest per year and the initial amount in the account is y dollars, then after one year the account will have y + (x/100) * y dollars. For example, if the interest rate is 5% and the initial amount is $800, then the final amount would be $800 + (5/100) * $800 = $840.

Step-by-step explanation:

With the application of numerical variable Line of best fit equation is
y = 0.28x + 6.

What is numerical variable?

A numerical variable is a type of data that is expressed as a number or numerical value. It is typically used to measure a quantitative value such as height, weight, age, income, distance, quantity, or speed. Examples of numerical variables include population size, test scores, stock prices, or sales figures. Numerical variables can also be discrete or continuous. Discrete numerical variables have a finite number of values, while continuous numerical variables can have an infinite number of values between any two numerical values.

Line of best fit equation is

y = 0.28x + 6

The slope point is ( 49, 19.8), ( 0,6 )

(19.8 - 6) / ( 49 - 0) = 13.8/ 49

= 0.28

After 58 weeks, The pound that alligator weigh

y = 0.28(58)+ 6

y = 22. 24 pounds

Therefore, After 58 weeks The pound that alligator weigh is 22. 24 pounds

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The 2 options that represent the coordinates that give a slope of -3/5 are;

Option A;(–8, 8) and (2, 2)

Option D;(–2, 1) and (3, –2)

What is slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

We are told that the slope of the line is -3/5.

Thus, m = -3/5

Formula for slope between two coordinates is;

m = (y₂ - y₁)/(x₂ - x₁)

A) At (–8, 8) and (2, 2);

m = (2 - 8)/(2 - (-8))

m = -6/10

m = -3/5

B) At (–5, –1) and (0, 2);

m = (2 - (-1))/(0 - (-5))

m = 3/5

C) At (–3, 6) and (6, –9);

m = (-9 - 6)/(6 - (-3))

m = -15/9

m = -5/3

D) At (–2, 1) and (3, –2);

m = (-2 - 1)/(3 - (-2))

m = -3/5

E) At (0, 2) and (5, 5);

m = (5 - 2)/(5 - 0)

m = 3/5

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Answer:

A;(–8, 8) and (2, 2)

D;(–2, 1) and (3, –2)

Step-by-step explanation:

If a pole has two wires attached to it, one on each side, forming two right triangles as shown, then the height of the pole is 29.6 feet

Consider the triangle on left hand side

The length of the base = 34 feet

The measure of angle = 41 degrees

Opposite side is the height of the pole

Here we have to use the trigonometric functions

sin θ = Opposite side / Hypotenuse

cos θ = Adjacent side / Hypotenuse

tan θ = Opposite side / Adjacent side

Here we have to use the equation of tan θ

Substitute the values in the equation

tan 41 = Opposite side / 34 feet

Opposite side = 34 × tan 41

= 29.6 feet

Therefore, the height of the pole is 29.6 feet

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Answer:

  -10

Step-by-step explanation:

You want to know the rate of descent in feet per second represented by a descent of 40 feet in 4 seconds.

The rate is the amount divided by the time:

  -40 ft/(4 s) = -10 ft/s

The relevant integer is -10.

A seismograph station in a particular city might not record any data about some earthquakes because the ground motion it produced might not be strong enough to be detected by the station.

Seismograph stations measure ground motion, and the farther an earthquake is from a station, the weaker the ground motion it produces. If an earthquake is too far away, the ground motion it produces may be too weak to be detected by the seismograph station.

Additionally, if the earthquake occurred in a direction that was not directly aligned with the seismograph station, the ground motion it produced might not be strong enough to be detected by the station.

Thus, a seismograph station in a particular city does not record any data about some earthquakes.

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Answer: -13.8  or -13 and 4/5

The number of times that -4 used as a factor in the expression (-4)5 is 5 times.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, in expression (-4)5, it can be seen that.-4 is used 5 times

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Answer:

A. r - s - t

Step-by-step explanation:

Observe the bounds of each integral. (Think of it as a number line if it's confusing.)
r is [1, 4]

s is [1, 2]

t is [3, 4]

Name the integral from [2, 3] = u.

s + t + u = r

u = r - s - t

If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between

2- 39$ and 41$.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A restaurant meal cost $35.50 and there was no tax.

Now the tax is more than 10% and less than 15% which is,

= (110/100)×35.50 and (115/100)×35.50.

= $39.05 and $40.825.

So, from the options, the total amount paid must have been between

39$ and 41$.

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Answer: Patrick invested €7,280 in the special savers bank account.

Step-by-step explanation:

If the money in the bank account earned 4% interest after one year, then the amount of interest earned is 4/100 * the amount invested. We can write this as an equation as follows:

4/100 * amount invested = €291.20

Solving for the amount invested, we get:

4/100 * amount invested = €291.20

amount invested = €291.20 / (4/100)

               = €291.20 / 0.04

               = €7,280

Therefore, Patrick invested €7,280 in the special savers bank account.

Answer:

The correct answer is "The APR on the unpaid balance".

Jerome should give importance to the APR on his unpaid balance, since he just applied for two more credit cards, while he already has three. If he plans to apply for two more, he should give attention to the unpaid balances, because the APR may increase due to his missed payments, which will also result in an increase in payments to his credit cards.

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

x = k/y         k = Konstant

when x = 5  and y = 50

   5  = k/50     shows proportionality constant to be k = 250

so    x = 250 / y       now when x =? and y = 250

  ? = 250 / 250  = 1           x = 1

Answer:

[tex]\ \ \ \ \ \ \: 1\\47 \overline{ \smash{)} \ 79}\\\textrm{ } \: \ \underline{-47}\\\textrm{ } \ \ \ \ 32[/tex]

Explanation:

47 goes into 79 once with remainder 32.

Answer:

check explanation

Step-by-step explanation:

To start I estimated.

47 x 2 = 94 and is too big of a number so instead, we use 47 x 1 = 47, because 47 is the closest to 79 in this case.

By doing this it changes to

       ___1__

47  |     79  

Next, you multiply 47 by 1 to get 47 (this goes below 79)

       ___1__

47  |     79  

         - 47

        =

Then subtract, this should get you 32

       ___1__

47  |     79  

         - 47

        = 32

because there are 'no more digits to move down from the dividend'* this means the problem is finished, and 32 is our remainder.

      ___1__

47  |     79  

         - 47

        = 32

           I

          V  

      ___1__ ( r 32 )

47  |     79  

The problem you have shows the remainder at the bottom as a way to show the steps.

your answer:

      ___1__

47  |     79  

         - 47

        = 32

quote:

" because there are no more digits to move down from the dividend the problem is finished."

Answer:

1

Step-by-step explanation:

to find slope we use y2-y1/x2-x1

8-6/3-1

2/2

1 is the slope

Hopes this helps please mark brainliest

Answer:11.6

Step-by-step explanation:

The price after discount will be $92.82

What does math's % mean?

Percentages are fundamentally fractions with 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

What is the formula's percentage?

The percentage can be calculated by dividing the value by the total value and multiplying the result by 100. (Value/Total Value)100% is the formula for calculating percentages.

given data

Price at launch: $123.75

10% off = 25%

Let's calculate the discount's amount.

= 25/100*123.75

= 0.25*123.75

=$30.93

Consequently, the shoe's price is

=123.75-30.93

=$92.82

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x+y=14

What is equation?

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

Let x = number of 5 ft long strings and 

y = number of 11 ft long strings

Consequently, 5x+11y=106,

because the whole string is 14,

x+y=14.

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We can write the negate of the conditional statement c⇒(a∧∼b) as : a∨(∼b).

We have the the following conditional statement -

c ⇒ (a∧∼b)

We can write the negate of this conditional statement as -

a∨(∼b)

Therefore, the negate of this conditional statement as : a∨(∼b).

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The value of children ticket is $7 and adults tickets is $10.

From the information, Two adult tickets and 4 child tickets cost $48. This will be:

2x + 4y = 48

Five adult tickets and 2 child tickets cost $64. This will be:

5x + 2y = 64

x = adult tickets

y = child tickets.

The two equations will be combined thus:

2x + 4y = 48

5x + 2y = 64

Multiply equation i by 5

Multiply equation ii by 2

10x + 20y = 240

10x + 4y = 128

Subtract the equations

16y = 112

Divide

y = 112/16

y = 7

Children tickets is $7

2x + 4y = 48

2x + 4(7) = 48

2x + 28 = 48

x = (48 - 28)/2

x = 10

Adult tickets cost $10.

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Answer: 4 hours

Step-by-step explanation:

in a bacteria growing experiment, a biologist will observe that the number of bacteria in a certain culture triples every 4 HOURS. After 12 hours, it is.

Answer:

Sine:O/H

cos:A/H

Tan:O/A

1-a

2-c

3-b

The power series expression for the following integral ∫x[tex]e^{2x^{3} }[/tex]dx is:

∫x[tex]e^{2x^{3} }[/tex]dx=(x²/2)+(2x⁵/5)+(x⁸/4)+(4x¹¹/33)+(x¹³/21)+......

A power series is an infinite series in mathematics where an is the coefficient of the nth component and c is a constant. Power series, which develop as Taylor series of indefinitely differentiable functions, are helpful in mathematical analysis.

For square matrices (for which the function is known as the matrix exponential), as well as more generally in any unital Banach algebra B, the exponential function's power series definition makes sense.

A power series is made up of terms with the generic form. Power series are functions because the selected x-value determines whether the series converges or diverges as well as the value it converges to.

Given integral is,

∫x[tex]e^{2x^{3} }[/tex]dx

We know that the Taylor series expansion for eˣ.

eˣ=1+x+(x₂/!)+(x₃/3!)+(x₄/4!).....∞

[tex]e^{2x^{3} }[/tex]=1+2x₃+((2x³)²/2!)+((2x³)³/3!)+((2x³)⁴/4!)+....

[tex]e^{2x^{3} }[/tex]=1+2x³+2x⁶+(4x⁹/3)+(2x¹²/3)+........

x[tex]e^{2x^{3} }[/tex]=x+2x⁴+2x⁷+(4x¹⁰/3)+(2x¹³/3)+......

Now, integral the power series expansion:

∫x[tex]e^{2x^{3} }[/tex]dx=∫(x+2x⁴+2x⁷+(4x¹⁰/3)+(2x¹³/3)+......)dx

∫x[tex]e^{2x^{3} }[/tex]dx=(x²/2)+(2x⁵/5)+(x⁸/4)+(4x¹¹/33)+(x¹³/21)+......

This is the required solution.

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Answer:

1

Step-by-step explanation:

7 can only go into 10 once because 2 7's is 14 and that's higher than 10.