Which polynomial function has a leading coefficient of 1 and roots (7 + i) and (5 – i) with multiplicity 1?
a. f(x) = (x + 7)(x – i)(x + 5)(x + i)
b. f(x) = (x – 7)(x – i)(x – 5)(x + i)
c. f(x) = (x – (7 – i))(x – (5 + i))(x – (7 + i))(x – (5 – i))
d. f(x) = (x + (7 – i))(x + (5 + i))(x + (7 + i))(x + (5 – i))

9514 1404 393

Answer:

Step-by-step explanation:

If y = f(x) then x = f^-1(y) is true if and only if f(x) is a one-to-one function.

__

1. False. Trig functions are periodic, so are not one-to-one.

2. True. The f(x) is specified as being one-to-one.

Answer:

1. True
2. True

Step-by-step explanation:

1. Since a capital letter (F) is used to show that the inverse equation is indeed a function, the question is true. If the inverse (second equation) was written as x=f-1(y), it would be false.

2. For one-to-one functions, all you need to do to reverse them is switch the x and y variables, and the [tex]f^-1[/tex] signifies that it is an inverse function.

Answer:

A. 12.4

Step-by-step explanation:

To find a, we'll use the Law of Sines that says:

[tex]\frac{a}{sin(A)} = \frac{c}{sin(C)}[/tex]

And we'll isolate a to get:

[tex]a = \frac{sin(A) * c}{sin(C)}[/tex]

We first need to find A, which is easy.  The sum of the interior angles of a triangle is 180 degrees... and we already have 2 of them, so:

A = 180 - 90 - 16.75 = 73.25

(converted 16°45' to 16.75)

Then we will plug-in the information we already have

[tex]c = \frac{sin(73.25) * 13}{sin(90)} = 12.45[/tex]

So, let's round it to 12.4 to match the answer A.

Answer:

The length of side marked a is 12.4 units.

Step-by-step explanation:

In ΔABC

∠B = 16°45’ = 16.75°

1 min arc = [tex]\frac{1}{60} degrees [/tex]

c = 13 units

a = ?

[tex]\cos \theta=\frac{Base}{Hypotenuse}[/tex]

[tex]\cos B=\frac{a}{13}[/tex]

[tex]0.95757=\frac{a}{13}[/tex]

[tex]a=0.95757\times 13=12.4484\approx 12.4 units[/tex]

The length of side marked a is 12.4 units.

Answer:

The area of the hexagon is [tex]96\sqrt{3}\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The area of the hexagon is equal to

[tex]A=\frac{1}{2}Pa[/tex]

where

P is the perimeter of the hexagon

a is the apothem

Find the Perimeter P

[tex]P=6(8)=48\ cm[/tex]

Find the apothem a

[tex]a=(8)sin(60\°)[/tex]

[tex]a=8(\frac{\sqrt{3}}{2})=4\sqrt{3}\ cm[/tex]

Find the area of the hexagon

[tex]A=\frac{1}{2}(48)(4\sqrt{3})=96\sqrt{3}\ cm^{2}[/tex]

Answer:

[tex]\boxed{ y = \frac{ 4}{ 9}x + \frac{4 }{3 }}[/tex]

Step-by-step explanation:

1. Calculate the slope of Line f

y - 3 = -⁹/₄(x – 6)

The coefficient of x is -⁹/₄, so

The slope m₁ = -⁹/₄.

2. Calculate the slope of the perpendicular line

m₂ = -1/m₁

m₂ =  ⁴/₉

3. Calculate the y-intercept of line g

y = mx + b

4 = 6(⁴/₉) + b

4 = ⁸/₃ + b

Subtract ⁸/₃ from each side:     b = 4 - ⁸/₃ = ⁴/₃

The y-intercept is b = ⁴/₃.

Step 4. Write the equation for line g

[tex]\boxed{ y = \frac{ 4}{ 9}x + \frac{4 }{3 }}[/tex]

The Figure below shows the graph of line f in red, and the graph of its perpendicular line g in black.

Answer:

  Most likely, 60% to 75% of the students in the town play video games.

Step-by-step explanation:

Of the 20 samples taken, ...

Most of the samples fall in the range 60%–75%, so we have to conclude that it is most likely that the fraction of students who play video games is in that range.

The diagonal (d) of the rectangular solid with dimensions l=8, w=4, h=2 is found using the Pythagorean theorem in three dimensions. Plugging in the values, d is approximately 9.17 units.

To find the diagonal (d) of a rectangular solid with length (l), width (w), and height (h), you can use the Pythagorean theorem in three dimensions. The formula for the diagonal of a rectangular solid is given by:

d = √(l² + w² + h²)

Given that l = 8, w = 4, and h = 2, we can substitute these values into the formula to find d:

d = √(8² + 4² + 2²) = √(64 + 16 + 4) = √84 ≈ 9.17

So the diagonal of the rectangular solid is approximately 9.17 units.

ANSWER

b=1, c=81, and d=9.

EXPLANATION

The given function is:

[tex]y={x}^{2}-18x[/tex]

This function is the same as:

[tex]y={(x - 9)}^{2}-81[/tex]

To find the inverse of this function, we interchange x and y.

[tex]x={(y-9)}^{2}-81[/tex]

Solve for y:

[tex]x+81={(y- 9)}^{2}[/tex]

Take square root of both sides:

[tex]\pm \sqrt{x + 81}=y-9[/tex]

[tex]y=\pm \sqrt{x + 81}+9[/tex]

Hence,

b=1, c=81, and d=9.

Answer: b=1, c=81, d=9

Step-by-step explanation:

Answer:

Part 1) The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.

[tex]x\leq 7.5\ pounds[/tex]

Part 2) [tex]m+n=(0.76x-0.28)[/tex]

Step-by-step explanation:

Part 1)

Let

x-----> the number of pounds of regular coffee

we know that

The inequality that represent the situation is

[tex]2x\leq 15[/tex]

Solve for x

Divide by 2 both sides

[tex]x\leq 15/2[/tex]

[tex]x\leq 7.5\ pounds[/tex]

The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.

The solution of the inequality is the interval ------> (-∞,7.5]

but the number of pounds cannot be a negative number

therefore

The solution is the interval -----> [0,7.5]

see the attached figure

Part 2) we have

[tex]m=0.56x-0.25[/tex]

[tex]m=0.20x-0.03[/tex]

Adds m and n

[tex]m+n=(0.56x-0.25)+(0.20x-0.03)[/tex]

Group terms that contain the same variable

[tex]m+n=(0.56x+0.20x)+(-0.25-0.03)[/tex]

Combine like terms

[tex]m+n=(0.76x-0.28)[/tex]

Answer:

a=25.km

Step-by-step explanation:

A traveler comes upon a fork in the road on the path to the travelers right a sign reads Mercer 24 km

The concluding part could be the following:

On the path to the traveler's left, a sign reads "Turtle Lake: 17km." The traveler also observes that the angle between the paths is 1.3 radians. Assuming both paths are perfectly straight, what is the distance between Mercer and Turtle Lake? km Round your answer to the nearest kilometer

since the angle between them is actually 1.3 rad

lets convert to degrees

74.48 degrees

using cosine of angle we can find the distance  between the two destinations

[tex]a^{2} =b^{2} +c^{2} -2bcCos\alpha[/tex]

[tex]\alpha[/tex]=74.48 deg

a^2=17^2+24^2-(2*17*24)cos74.48

a^2=646.65

find the square root of both sides

a=25.42km

approximately=25Km

(2x + 6x + 4) All you need to find is numbers that can all be divided by 2.

To write a trinomial with a GCF of 2, start by factoring out the GCF from each term. For example, the trinomial 4x^2 + 6xy + 8y^2 can be factored as 2(2x^2 + 3xy + 4y^2).

A trinomial is an algebraic expression with three terms. The greatest common factor (GCF) is the largest factor that all the terms share. To write a trinomial with a GCF of 2, we can start by factoring out the GCF from each term. Let's say the original trinomial is:

4x^2 + 6xy + 8y^2

The GCF of the trinomial can be found by listing the factors of each term and selecting the highest common factor. In this case, the factors of 4x^2 are 2 and 2x^2, the factors of 6xy are 2, 3, x, and y, and the factors of 8y^2 are 2^3 and y^2. The highest common factor is 2, so we can factor out 2 from each term:

2(2x^2 + 3xy + 4y^2)

This is a trinomial with a GCF of 2.

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Combined?? The sum of ?

Addends is the word in algebra that means something has been added​. Addition is an operation to solve the algebraic problems.

Algebra is a field of mathematics that solves problems by substituting letters for numbers.

Addends refer to the numbers that are being added in an addition issue. An addend is a group of numbers that are added together to generate a sum. 

Hence, addends is the word in algebra that means something has been added​.

To learn more about the algebra, refer to the link;l

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Answer:

13.86 units to the nearest hundredth.

Step-by-step explanation:

By Pythagoras:

16^2 = x^2 + 8^2

x^2 = 16^2 - 8^2

x^2  (16 + 8)(16 - 8) = 192

x = √192

= 13.86 (answer).

Answer:

x = 8[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Since the triangle is right use Pythagoras' theorem to solve for x

The square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides, thus

x² + 8² = 16²

x² + 64 = 256 ( subtract 64 from both sides )

x² = 192 ( take the square root of both sides )

x = [tex]\sqrt{192}[/tex] = [tex]\sqrt{64(3)}[/tex] = 8[tex]\sqrt{3}[/tex]

Answer:

im not sure what this means

Step-by-step explanation:

Answer:

5.6 kilometers  gradpoint

Step-by-step explanation:

i took the test

For this case we must find the product of the following expression:

[tex](y ^ 2 + 3y + 7) (8y ^ 2 + y + 1)[/tex]

We apply distributive property, which states that:

[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

So:[tex](y ^ 2 + 3y + 7) (8y ^ 2 + y + 1) =\\(y ^ 2) (8y ^ 2) + (y ^ 2) (y) + (y ^ 2) (1) + (3y) (8y ^ 2) + (3y) (y) + (3y) (1 ) + (7) (8y ^ 2) + (7) (y) + (7) (1) =\\8y ^ 4 + y ^ 3 + y ^ 2 + 24y ^ 3 + 3y ^ 2 + 3y + 56y ^ 2 + 7y + 7 =[/tex]

We add similar terms:

[tex]8y ^ 4 + 25y ^ 3 + 60y ^ 2 + 10y + 7[/tex]

Answer:

Option D

Answer:

7.5 weeks

Step-by-step explanation:

If you want to find out how long it take for the plant to reach a foot you set up the equation like so:

12=1.2w+3

and solve from there.

12=1.2w+3                       Subrtact 3 from both sides

9=1.2w                             Divide by 1.2 to isolate w

7.5=w                              Answer is 7.5 weeks

The [tex]7.5[/tex] weeks it will take the plant to reach one foot.

What is height?

In math, height is the vertical distance from the top to the base of the object and it is measured in cm, inches, meters, etc.

It is given that the height [tex]h[/tex] of the plant (in inches) [tex]w[/tex] weeks.

The equation is,

[tex]h=1.2w+3[/tex]

As we know that,

[tex]$12\,\text{inches}=1\,\text{foot}$[/tex]

The number of weeks that it will take the plant to reach one foot will be:

[tex]h=1.2w+3[/tex]

[tex]12=1.2w+3[/tex]

[tex]1.2w=12-3[/tex]

So,

[tex]w=\frac{9}{1.2}[/tex]

[tex]$\therefore w=7.5$[/tex]

Hence, it will take [tex]7.5[/tex] weeks.

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Answer:

5 times shorter

Step-by-step explanation:

The period is the time it takes for one cycle to complete, or in this case, one breath.  Since person A is breathing 5 times faster, the time per breath is 5 times shorter.

Answer:

16lb=30

22=88

Step-by-step explanation:

Answer:

16 lb = 64 cups

22 lb = 88 cups

Answer:

4.4

Step-by-step explanation:

The tenth place in this number is 4.432, so that should be the last digit.

Now, we need to know wether to round up or down. That is determined by the digit that comes after it. If that digit, here it is the hundredth, is 0-4, it rounds down, if it is 5-9, it rounds up. Our next digit is 3, which goes into the first category, so the number rounds down, so the tenth remains the same. That leaves us with 4.4.

Answer:

4.4

Step-by-step explanation:

The tenth decimal place is one to the left of the decimal. The hundreth decimal places is two digits to the right and so on an so forth. Knowing this, you apply the basic rules of rouding. If the digit to the left of the digit being rounded is greater than five, the digit is rounded up one and the others are discarded. In this case, the digit to the left of the digit in subject is less than five, 3. Therefore, the tenth decimal stays the same and the others are discarded.

Answer:

$438.66

Step-by-step explanation:

The total percent taken is:

6.2% + 1.45% = 7.65%

7.65% of the paycheck is taken.

The total paycheck is 100% of the paycheck. Since 7.65% of the paycheck is taken, and 100% - 7.65% = 92.35%, then 92.35% of the paycheck is left.

Now we find 92.35% of $475.

To find a percent of a number, multiply the percent by the number and divide by 100.

92.35 * $475/100 = $438.66

Answer: $438.66

$438.66 , because 6.2+1.45=7.65 and then 100-7.65=92.35 and then you turn that into a percentage which would be 92.35% in decimal form would be .9235 which is the portion you’ll receive from your paycheck so you multiply that by $475 and you will get your final answer of $438.66

Angle A= 60

You add angles A and D together and set them equal to 180 because opposite sides in a parallelagram =180. Then you solve for x and get 30 and you should then plug in 30 to angle A and get 60.

Answer:

The correct answer option is C. 0.

Step-by-step explanation:

We are given the following data set and we are to find its median value:

[tex] - 1 0 0 0 , - 9 9 9 , 1 9 9 8 , ... , -1 , 0 , 1 , ... , 9 9 8 , 9 9 9 , 1 0 0 0 [/tex]

Median is the middle value of a data set which divides it into to halves.

The data set we have starts from -1000 and goes till 1000 which means there are total 2001 elements in it.

Therefore, 0 will the middle value which is the median for this data set.

Answer:

C) 0

Step-by-step explanation:

Median is the middle value of a data set which divides it into to halves.

So then 0 will the middle value which is the median for this data set.

0 is the in the middle.

ANSWER

C(2,-6)

EXPLANATION

The solution set to given inequality is the shaded region.

The points are also located in the graph above.

The only point that falls in the solution region is C(2,-6)

The ordered pair that is in the solution set is C(2,-6)

The third option is correct.

the answer is c) 59.5

Answer:

D because 84 of 50 is 168...

solutions:

84:50*100 =

(84*100):50 =

8400:50 = 168

The video game costs $45. Look at the image to see what I did

The overall change in surface area when the height of a rectangular prism is increased by 0.2 cm can be calculated with the formula 0.4w + 0.4l.

In this question, we are looking at the surface area of a box that is a rectangular prism and how it will change if the height of the box is increased by 0.2 cm. The surface area of a prism is given by the formula 2lw + 2lh + 2wh, where l, w and h are the length, width and height respectively.

Now, if the height is increased by 0.2 cm, the difference in the surface area will be 2lw (because there are two ends with area lw that do not change) plus the change in the area of the sides. The sides' areas will increase by 2w x 0.2 and 2l x 0.2 respectively (since we have two opposing sides that both increase by 0.2 cm in height).

Therefore, the overall change in surface area when the height is increased by 0.2 cm is simply the sum of these two parts, which is 2w x 0.2 + 2l x 0.2. This can also be simplified to 0.4w + 0.4l.

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Answer:

$99.80

Step-by-step explanation:

499 * 0.20 = 99.8

499 / 0.20 = 99.8, then you would do this; 499 - 99.8 = 399.2... $399.20 is the sale price of the TV!

Answer:

33.333...

Step-by-step explanation:

First of all we put the 160/480 and further divide each of which to be simplified by the simplified version

Then we must find the decimal which is 33.333 recurring.

If require further assistance ask me.

Hope this helps and enlightens your day. Enjoy

33.33

hope i helped

have a good day

Answer:

x² + 9x + 8 = 0

Step-by-step explanation:

A quadratic equation is expressed this way: ax² + bx + c = 0

So, so find the quadratic equivalent of (x + 2)² + 5(x + 2) – 6 = 0, we just have to do the multiplications then simplify.

(x + 2)² + 5(x + 2) – 6 = (x² + 4x + 4) + (5x + 10) - 6

After merging the terms of same degree, we get:

x² + 9x + 8 = 0

Answer:

C

Step-by-step explanation:

u2 + 5u – 6 = 0 where u = (x + 2)

ED 2021

To find the volume, you need to do length times width times height

SO you have to do 5 times 5 times 6

The volume is 150 cubic feet

Since 150 cubic feet of this rectangular prism is 15 tons

you can do 15 divided by 150

so one cubic feet of this stone sculpture weight 0.1 tons

Btw, a pyramid is  a triangular structure, not rectangular

-5 cause it is 32-42 and the anserw is -5