Harvey is studying the polynomial f(x) = (4x – 3)(x – 3)(x2 +5) and determines that the polynomial has four real roots. Do you agree or disagree with Harvey’s statement? Explain your reasoning.
A.yes because there are 4 roots
B.yes because complex solutions do not matter
C.yes because when I solve he gets 4 x intercepts
D.no because there are two complex solutions

Answers

Answer 1

Yes because when I solve he gets 4 x-intercepts. The x-intercept is a point where the y value is zero.

The degree of a polynomial always determines the number of roots such polynomial function will have;

Given the polynomial function studied by Harvey as g(x) = (4x – 3)(x – 3)(x2 +5)

Taking the product of the leading variables

g(x) = (4x – 3)(x – 3)(x2 +5)

g(x) = 4x(x) (x^2)

g(x) = 4x^4

Since the degree of the polynomial is 4, hence the polynomial has four real roots.

Learn more here: https://brainly.com/question/16821812


Related Questions

GEOMETRY please help !

Answers

Step-by-step explanation:

A.

The incorrect statement in Triangle A is B

It is not a equilateral triangle. It is a isosceles triangle

B.

The incorrect statement in Triangle B is C

The missing angle is not 158. It is 68

C.

The incorrect statement in Triangle C is C

The missing angle is not 72 it is 36

Find the measure of the indicated angle.

Answers

Answer:

11) x = 21

12) x = 110

13) x = 85

14) x = 137

Step-by-step explanation:

Hope it helped <3

You have 20 quarters. You find 40% more in your room. Then you go to the store and spend 50% of them. How much money do you have left? please answer the question without a link

Answers

Answer:

14

Step-by-step explanation:

First fond 40% of 20

20×40/100 = 8

So now there is a total of 20+8 =28

At the store you spend exactly half

28×50/100 =14

So now you are left with 28-14 =14

18. Write the equation of the following line in function notation

Answers

Answer:

[tex]\LARGE\mathsf{f(x)\:=-\frac{3}{4}x\:+\:-\frac{5}{4}}[/tex]

Step-by-step explanation:

Slope:

Given the two points from the graph, (-3, 1) and (1, -2). Use these points to solve for the slope using the following formula:

[tex]\LARGE\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]

Let (x₁, y₁) = (-3, 1)

     (x₂, y₂) = (1, -2)

Substitute these points into the formula:

[tex]\LARGE\mathsf{m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex]

[tex]\LARGE\mathsf{m = \frac {-2\: -\: 1}{1\: -\: (-3)}\:=\:\frac {-2\: -\: 1}{1\: +\:3}\:=\frac{-3}{4}}[/tex]

m = -¾

Therefore, the slope of the given line is -¾.

Y-intercept:

Next, we need to determine the y-intercept, which is the point on the graph where it crosses the y-axis.  In order to solve for the y-intercept, we must use the slope, m = -¾, and one of the given points, (1, -2), and substitute these values into the slope-intercept form,  f(x) = mx + b:

f(x) = mx + b

-2 = -¾( 1 ) + b

-2 = -¾ + b

Add ¾ to both sides to solve for b:

-2 + ¾ = -¾ + ¾ + b

[tex]\LARGE\mathsf{y-intercept\:(b)\:=\:-\frac{5}{4} }[/tex]

Equation of the Line in Function Notation:

Given the slope, m = -¾, and y-intercept, b = [tex]\LARGE\mathsf{-\frac{5}{4}}[/tex], the equation of the line in function notation is:

[tex]\LARGE\mathsf{f(x)\:=-\frac{3}{4}x\:+\:-\frac{5}{4}}[/tex]

The sum of two consecutive even numbers is 54 find the answer

Answers

Answer:

26, 28

Step-by-step explanation:

2n , 2n + 2

2n + 2n + 2 = 54

4n + 2 = 54

4n = 52

n = 13

2n = 26

2n + 2 = 28

Answer:

26 and 28

Step-by-step explanation:

The sum of two consecutive even numbers is 54 find the answer

(54 - 2) : 2 = 26

26 + 2 = 28

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

check

26 + 28 = 54

Please help me solve this... I will mark you brainliest if it’s correct

Answers

(5 + 7x + 6)/2 = 3x + 9

7x + 11 = 6x + 18

7x - 6x = 7

x = 7

EF = 3x + 9

= 3(7) + 9

= 21 + 9

= 30

Mika is making a beaded necklace. Each bead is a14inch cube.If the necklace is 18 inches long, how many beads will Mika need?

Answers

Answer: The answer is 4

Step-by-step explanation:  2 ( g + 5 ) − 2 ( g + 3 ) = 2 ( g + 5 ) − 2 ( g + 3 )

= 2g + 10 - 2g - 6

= 2g -2g + 10 - 6

= 0 + 4

= 4

Hope this helps!

8i

−8

8i2

−8i
NO LINKS

Answers

Answer:

Step-by-step explanation:

x² = -64

   = -1 · 64

Using -1 = i²:

x² = 64 · i²

Using 64 = 8²:

x² = 8² · i²

   = (8·i)²

Taking the square root of both sides:

x = 8i

Factor the trinomial
10x^2+11X-6

Answers

Answer:

The expression is not factorable with rational numbers.

10x2+11X−6

Step-by-step explanation:

PLS Brainliest

Which of the binomials below is a factor of this trinomial?
x² + x -20
O A. X+ 2
O B. X+4
O C. X-4
O D. X-2

Answers

Answer:

C. X-4

Step-by-step explanation:

x^2+x-20

=(x-4)(x+5)

Answer:

C.

Step-by-step explanation:

Sorry I Can't explain because I'm busy right now

help help help help help

Answers

Answer:

2

Step-by-step explanation:

100 POINT!!!!! NEED HELP ASAP
Show that (a + bi)^2 = (a + b)(a − b) + 2abi

Answers

Answer:

Step-by-step explanation:

(a + bi)^2 = (a + b)(a − b) + 2abi

= a² + (bi)² + 2 * a * bi

= a² + b²i² + 2abi

= as i² = -1

= a² - b² + 2abi

= (a + b) (a - b) + 2abi

Answer: This is what I turned in and it was right :)

Step-by-step explanation:

(a + bi)^2 = (a + b)(a − b) + 2abi

= a² + (bi)² + 2 * a * bi

= a² + b²i² + 2abi

= as i² = -1

= a² - b² + 2abi

= (a + b) (a - b) + 2abi

Using this plot of annual peak discharge, what is the probability each year that a flood of 1,000 cubic meters per second will occur

Answers

Using the plot, it is found that there is a 10% probability each year that a flood of 1,000 cubic meters per second will occur.

The question is incomplete, but the plot can be found on the internet.On the x-axis, it is given the probability of a flood of of y cubic meters per second.

When y = 1,000, we have that x = 10%, hence, there is a 10% probability each year that a flood of 1,000 cubic meters per second will occur.

A similar problem is given at https://brainly.com/question/25757416

Can someone help:(( graph y=2x

Answers

Answer:

Look at the attached screenshot

Step-by-step explanation:

Slope is 2.

Since y-intercept is not given, we can assume that it is 0.

Answer:

Step-by-step explanation:

Make a table of points for y = 2x, and then plot these points, and finallyl draw a line through the points:

x   y

0   0

2   4

3   6 (and so on).

Plot this (0, 0) (it's the origin).  Next plot either (2, 4) or (3, 6) (or both).  Then draw a line through these points.  

(4 x 100,000) + (6 x 10.000) =

Answers

Answer:

answer is 400060

have a good day!!

If it's help pls give me Brainliest

tysm

Answer:

4000,060

answer explanation : when you add 4 times 100,000 ypu get 400,000 and now you get 400,000 and now you are going to muptiple 4,000,6 and 10.000 which is equal to 4,000,060


The seventh grade class is raising money to have a class trip at the end of the year. They began the year with $2,500. Now they have 54.750 in the account. What is the percent increase for the money the
dass has raised? The dass figured out that if there is a percent increase of 99% from the beginning of the year, they will have enough to pay for every student. How much money wil they need to pay for every student?
The percent increase is
They will need to pay for every student?

Answers

Answer:

21.6%

Step-by-step explanation:

Solve for bb.
42=42+9b

Answers

Answer:

0

Step-by-step explanation:

42=42+9b

We move all terms to the left:

42-(42+9b)=0

We add all the numbers together, and all the variables

-(9b+42)+42=0

We get rid of parentheses

-9b-42+42=0

We add all the numbers together, and all the variables

-9b=0

b=0/-9

b=0

write 3 example of quantities or things you know, or you have experienced within your community that show different types of variation.​

Answers

Answer:

Type of variation

1) Direct variation

Simple equation y=Kx

Y varies directly with x

Practical example-

Radius of the circle lit by a car's

Light decreases (y) as the distance away from the garage decreases (c)

2) Inverse variation

Simple equation y=k/x

Y inversely with c

Example- the brightness of a car's light increase (y) as the distance away from the garage decreases (x)

3) Joint variation

Simple equation y=kxz

Y varies jointly with x and z

Example-The heat lose through a glass window (y) varies jointly with the area of the window (x) and the temperature differences between inside and outside

Step-by-step explanation:

- You find a recipe for cookies. You want
to know how much sugar is in each cookie.
The recipe uses 3/4 cup of sugar and makes
one-dozen cookies. Find the amount of sugar
per cookie. Show unit rate work. Use fractions
not decimals.

Answers

Answer:

1/16

Step-by-step explanation:

3/4 ÷ 12

3/4 x 1/12

3/48 or 1/16

Hope this helps!

Answer:

1/16

Step-by-step explanation:

recipe uses 3/4 cup of sugar for one dozen cookies

3/4 cup ------ 12 cookies

x          -------  1 cookie

x * 12 = 3/4

x = 3/4 / 12

x = 3 / (4*12)

x = 1 / 4*4

x = 1/16

The circumference of a circle is increasing at a rate of pi over 2 m/h at a certain instant the circumference is 12 pi meters what is the rate of change of the area of the circle at that instant in square meters per hour

Answers

Answer: 3pi

Step-by-step explanation:

Guessed and it was right, sorry don’t have an explanation.

The rate of change of the area of the circle at that instant in square meters per hour will be 3π.

What is the rate of change?

The pace at which one quantity changes in relation to another is known as the rate of change function.

Given that the circumference of a circle is increasing at a rate of π / 2 m/h at a certain instant the circumference is 12 π meters.

The rate of change of circumference will be calculated as,

dc/dt = π/2

d (2πr)/ dt = π / 2

dr / dt = 1 / 4

The rate of change in the area,

A = πr²

dA / dt = ( 2πr )  dr / dt

dA/dt = 12π x ( 1 / 4)

dA/dt = 3π

Therefore, the rate of change of the area of the circle at that instant in square meters per hour will be 3π.

To know more about rate of change follow

https://brainly.com/question/14282291

#SPJ2

HELP ASAP PLEASE!!!!!!

Answers

Answer:

B

Step-by-step explanation:

In a function, every x-coordinate must be a different number.

If the same number appears more than once as an x-coordinate, it is not a function.

Answer: B

in the equation 3(x-1)=2x+c for what value of c will x=3? explain your reasoning.

Answers

Answer:

0

Step-by-step explanation:

if x is 3 then;

3(3-1)=2×3+c

c=0

so if c=0 then

x=3

What is the slope for this table?

Answers

Answer:   Slope = -3

=======================================================

Explanation:

Pick any two rows you want. I'll pick the middle two rows where every value is positive. So I'll pick these two rows:

x = 0 and y = 4x = 1 and y = 1

They lead to the points (0,4) and (1,1). Apply the slope formula for these rows.

m = (y2-y1)/(x2-x1)

m = (1-4)/(1-0)

m = -3/1

m = -3

The slope is -3

Answer:

is not proportional

Step-by-step explanation:

10/-2= -5

7/-1=-7

4/0=0

1/1=1

-2/2=-1

-5/3= -1 2/3

What is the slope of the line that passes through the points (-6, -8)and (-14, 4) ? Write your answer in simplest form.

Answers

Answer:

Slope = -3/2

Step-by-step explanation:

[tex]Slope = \frac{Change -in -y}{Change- in -x}\\\\\\\\Slope = \frac{-8 - 4}{-6 - (-14)}[/tex]

[tex]Slope = \frac{-12}{8}\\\\\\Slope = \frac{-3}{2}\\\\[/tex]

-Chetan K

Jon ate 1/3 of a bag of candies and Monica ate 1/4 of the bag. What fraction of the bag of candies did they eat?

Answers

Answer:

13 AND 14

Step-by-step explanation:

THERE IS NO PICTURE OR ANY ANSWERS

1/3+1/4=4/12+3/12
=7/12

Find the perimeter. Simplify the answer.

Answers

Answer:

34p-16

Step-by-step explanation:

Perimeter of parallelogram

= 2(9p-10)+2(8p+2)

= 18p-20+16p+4

= 34p-16

How to reduce decimals to fractions.

Answers

Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10. If needed, simplify the fraction.

Ivan put 500 000ISK (Icelandic Krona) and Blake put 700 000ISK into savings accounts
at different banks.
After 8 years, Ivan and Blake have the same amount of money in their accounts.
They both receive interest compounded quarterly and Blake has an annual interest rate
that is half of Ivan's annual interest rate.
Work out the annual interest rate that Blake receives.

Answers

Using compound interest, it is found that Blake receives an annual rate of 4.27%.

Compound interest:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

A(t) is the amount of money after t years.  P is the principal(the initial sum of money).  r is the interest rate(as a decimal value).  n is the number of times that interest is compounded per year.  t is the time in years for which the money is invested or borrowed.

Ivan's parameters are given by:

Put 500 000 ISK, hence [tex]P = 500000[/tex]8 years, hence [tex]t = 8[/tex]Quarterly compounding, hence [tex]n = 4[/tex]Interest rate of r.

Hence:

[tex]A_i(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A_i(t) = 500000\left(1 + \frac{r}{4}\right)^{32}[/tex]

[tex]A_i(t) = 500000(1 + 0.25r)^{32}[/tex]

Blake's parameters are given by:

Put 700 000 ISK, hence [tex]P = 700000[/tex]8 years, hence [tex]t = 8[/tex]Quarterly compounding, hence [tex]n = 4[/tex]Interest rate that is half of Ivan's, hence [tex]\frac{r}{2}[/tex]

Thus:

[tex]A_b(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A_b(t) = 700000(1 + 0.125r)^{32}[/tex]

These amounts are equal, hence:

[tex]A_i(t) = A_b(t)[/tex]

[tex]500000(1 + 0.25r)^{32} = 700000(1 + 0.125r)^{32}[/tex]

[tex]\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32} = \frac{700000}{500000}[/tex]

[tex]\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32} = \frac{7}{5}[/tex]

[tex]\sqrt[32]{\left(\frac{1 + 0.25r}{1 + 0.125r}\right)^{32}} = \sqrt[32]{\frac{7}{5}}[/tex]

[tex]\frac{1 + 0.25r}{1 + 0.125r} = \left(\frac{7}{5}\right)^{\frac{1}{32}}[/tex]

[tex]\frac{1 + 0.25r}{1 + 0.125r} = 1.01057023172 [/tex]

[tex]1 + 0.25r = 1.01057023172 + 0.12632127896r[/tex]

[tex]0.12367872103r = 0.01057023172 [/tex]

[tex]r = \frac{0.01057023172}{0.12367872103}[/tex]

[tex]r = 0.0854[/tex]

Blake's rate is:

[tex]\frac{r}{2} = \frac{0.0855}{2} = 0.0427[/tex]

Blake receives an annual rate of 4.27%.

A similar problem is given at https://brainly.com/question/24507395

Someone please solve and explain part a(i)

Answers

Step-by-step explanation:

the way I understand the description :

C is below B. they are on a kind of straight hill, and there is a straight "road" going up from C to B.

then, at B there is an antenna or other firm of mast going straight up.

therefore, this is not a right-angled triangle with 90 degrees at B (as it would be, if this would be in a flat plane).

but because it goes downhill from B to C the angle is 105 degree.

(a)(i)

now, imagine, there would be a horizontal plane either at B or at C. AB would have a true 90 degree angle with this plane. so, what is the angle of CB with this plane ?

this angle is the "excess" of the 90 degrees, as CB angles down from the horizontal plane at B, or angles up with the same angle from the horizontal plane at C.

what is the "excess" of 105 degrees vs. the standard 90 degrees ? 105 - 90 = 15 degrees.

(a)(ii)

the extended Pythagoras for not right-angled triangles :

c² = a² + b² - 2ab×cos(B)

B being the angle opposite of the Hypotenuse c.

so, we have

c² = 15² + 10² -2×15×10×cos(105) = 225 + 100 - 300×cos(105) =

= 325 - 300×cos(105) = 402.6457135...

c = 20.06603383... ≈ 20 m

Sub :- Linear Equations

Answers

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The value of x is 1 & y is 2 (a).

Steps are attached.

______

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