Mathematics High School

Find all the zeros of the equation. Need help finding the zeros.



-3 x^{4} } +27 x^{2} +1200=0

Answers

Answer 1
Given the expression
-3x^4+27x^2+1200=0
let x^2=a
we can re-write our expression as:
-3a^2+27a+1200=0
-3(a^2-9a-400)=0
a^2-9a-400=0
factorizing the above we have:
a^2+16a-25a-400=0
a(a+16)-25(a+16)=0
(a+16)(a-25)
thus replacing back x^2 we have:
(x^2+16)(x^2-25)
=(x^2+16)(x-5)(x+5)
factorizing (x^2+16) we get
x^2=+/-√-16
x=+/-4i
thus the zeros of the expression are:
x=-5, x=5 , x=-4i, x=4i

Answer 2

Final answer:

The zeros of the equation -3x^4 + 27x^2 + 1200 = 0 can be found by substituting y = x^2 to create a quadratic equation, solving for y using the quadratic formula, and then solving for x for each y value found.

Explanation:

To find all the zeros of the equation -3x^4 + 27x^2 + 1200 = 0, we can treat the equation as a quadratic in form by substituting y = x^2, which reduces the equation to -3y^2 + 27y + 1200 = 0. This is now a standard quadratic equation that can be solved using the quadratic formula, y = (-b ± sqrt(b^2 - 4ac))/(2a), where a = -3, b = 27, and c = 1200. Once we find the values for y, we substitute back x^2 = y to get the values of x which are the zeros we are looking for.

The quadratic equation would provide us with two values for y, say y1 and y2. For each y value found, we solve for x by taking the square root, resulting in two x values for each y, giving us a total of four zeros for the original quartic equation.

we can re-write our expression as:

-3a^2+27a+1200=0

-3(a^2-9a-400)=0

a^2-9a-400=0

factorizing the above we have:

a^2+16a-25a-400=0

a(a+16)-25(a+16)=0

(a+16)(a-25)

thus replacing back x^2 we have:

(x^2+16)(x^2-25)

=(x^2+16)(x-5)(x+5)

factorizing (x^2+16) we get

x^2=+/-√-16

x=+/-4i

thus the zeros of the expression are:

x=-5, x=5 , x=-4i, x=4i

Related Questions

Find the area of the regular pentagon if the apothem is 4.9 m and a side is 7.1 m. round to the nearest whole number. 62 m2 34 m2 87 m2 17 m2

Answers

we know that
[Area of the regular pentagon]=5*[side length * apothem] / 2
side length=7.1 m
apothem=4.9 m
then
Area=5*[7.1 * 4.9] / 2-----------> 86.975 m²----------> 87 m²

the answer is 87 m²

A rectangular field has a diagonal of 360 feet. One of the side of the field is 160 feet long. What is the perimeter of the field? Enter your answer, rounded to the nearest hundredth, in the box.

Answers

We need to calculate the other triangle side.
Using the Pythagorean Theorem,
3rd side^2 = 360^2 -160^2
3rd side^2 = 129,600 - 25,600
3rd side^2 = 104,000
3rd side = 322.49
Perimeter = 2 * (160 + 322.49)
Perimeter = 964.98 feet



Answer:

Perimeter of rectangle  rounded to the nearest hundredth is 964.98 feet.

Step-by-step explanation:

Given : A rectangular field has a diagonal of 360 feet. One of the side of the field is 160 feet long.

To find :  What is the perimeter of the field? Enter your answer, rounded to the nearest hundredth, in the box.

Formula used : perimeter =  2* length + 2√[tex]d^{2} -l^{2}[/tex].

Solution : We have diagonal of 360 feet and length = 60 feet .

plugging all the values of  d and , l in formula .

perimeter =  2* 160 + 2√[tex]360^{2} -160^{2}[/tex].

perimeter = 320 + 2√[129600 -25600].

perimeter =  964.98 feet = nearest hundredth = 964.98 feet.

Therefore, Perimeter of rectangle  rounded to the nearest hundredth is 964.98 feet.

Can someone help me and show me how to solve this?

In the figure, YX is a tangent to circle O at point X.

mXB = 52°
mXA = 104°

What is the measure of ∠XYA?


I can't remember how to solve questions like this since it's been a while. Thanks in advance.

Answers

XYA = (104 -52)/2

52 /2 = 26

the answer is 26 degrees
I think it is 26
but I'm not completely sure

Determine the measures of the apothem, the radius, and the perimeter of the regular octagon.
a. a = 14.4, r = 15.6, p = 96
b. a = 14.4, r = 15.6, p = 12
c. a = 15.6, r = 14.4, p = 96
d. a = 10, r = 15.6, p = 96

Answers

the complete question in the attached figure

we know that
A) a regular Octagon has all its eight sides congruent
B) all the eight interior angles are also congruent
C) the measure of each angle = 135º
therefore
see the attached figure

∠ alfa=135°/2--------> 67.5°
AP=12/2---------> 6 units
cos (alfa)=AP/AO----------> AO=AP/cos (alfa)
AO=6/cos(67.5)---------> 15.68 units

the radius= distance AO----------> 15.68 units
radius=15.68 units
the apothem=distance OP

sin(alfa)=OP/AO---------> OP=sin(alfa)*AO
OP=sin(67.5°)*15.68-------> 14.49 units
the apothem=14.49 units

perimeter=12*8--------> 96 units
perimeter=96 units

the answers Part A), B) and C) are
apothem=14.49 units
radius=15.68 units
perimeter=96 units

therefore the option is the a.) a = 14.4, r = 15.6, p = 96

Answer:

a.) a = 14.4, r = 15.6, p = 96

The graph represents the height y, in meters, above a lake of a rock x seconds after it is thrown from a ledge. Which statement is true? Select each correct answer.

Answers

Answer:

The graph represents the height y, in meters, above a lake of a rock x seconds after it is thrown from a ledge. Which statement is true? Select each correct answer.

EASY MEDAL !!!!!
Given the trinomial, what is the value of the coefficient 'B' in the factored form?

2x2 - 12xy - 32y2 = 2(x - 8y)(x + By)

B= ____________

Numerical Answers Expected!,

Answers

Let's start with the given polynomial:
2x² - 12xy - 32y²

As a first step, we want to regroup 2:
= 2(x² - 6xy - 16y²)

Now, we want to re-write the term -6xy in order to be able to perform a partial factoring. In this case, we can write:
-6xy = -8xy + 2xy
Therefore, the polynomial becomes:
= 2(x² - 8xy + 2xy - 16y²)

Now we factorize x within the first two terms and 2y within the last two:
= 2[x(x - 8y) + 2y(x - 8y)]

We can now regroup the common term:
=2(x - 8y)(x + 2y)

Your answer is hence B = 2

How can you divide 133 nickels into 8 bags so that there are the same number of nickels in each bag and the number in each bag is odd and there are none left over?

Answers

There is no way to divide them because 133 is odd, so 133 divided by 8 would be 16.625.


The rectangular room is given by the trinomial x^2+4x-12. What are the possible dimensions of the rectangle? Use factoring. (1 point) (x-6) and (x-2) (x+6) and (x+2) (x-6) and (x+2) (x+6) and (x-2) 17. What is the factored form of the following expression? X^2+2xy-48y^2 (1 point) a. (x+6y)(x-8y) b. (x-6y)(x-8y) c. (x+6y)(x+8y) d. (x-6y)(x+8y) 18. The area of a rectangular art studio is given by the trinomial 24x^2-4x-8. What are the possible dimensions of the studio? Use factoring. a. (3x-2) and (8x-4) b. (3x-2) and (8x+4) (3x-2) and (8x-4) (3x+2) and (8x-4)

Answers

Given that the rectangle is x²+4x-12, the possible sides will be given by:
a]
x²+4x-12
=x²+6x-2x-12
=x(x+6)-2(x+6)
=(x-2)(x+6)
thus the dimensions are (x-2) units (x+6) units

b]
x²+2xy-48y²
factorizing the above is:
x²+8xy-6xy-48y²
=x(x+8y)-6y(x+8y)
=(x+8y)(x-6y)

c] 
24x²-4x-8
factoring the above we get:
=4(6x²-x-2)
=4(6x²+3x-4x-2)
=4(3x(x+2)-2(x+2))
=4(3x-2)(x+2)
=(12x-8)(4x+8)




PLZ i need anwse ASAP

The figure is the net for a rectangular prism.

What is the surface area of the rectangular prism represented by the net?

Answers

Surface area is the sum of area of all the faces .

In the net diagram, we have 6 faces. So we have to find the area of each face and add them to find the surface area .

And since each face is rectangle in shape, so we will use the formula of area of rectangle, which is

[tex]Area= length*width[/tex]

So the required surface area is

[tex]A = (11*5)+(11*4)+(11*5) +(11*4)+(5*4)+(5*4)

\\

A = 55+44+55+44+20+20 =238 mm^2[/tex]

And that's the required surface area of the rectangular prism .

A hose dispenses 1,413 cm³ of water every minute into a cone with a radius of 60 cm and a height of 150 cm. How long will it take to fill the cone? Use 3.14 to approximate pi. Enter your answer in the box.

Answers

Hm. Have you ever dispensed water from a hose unto a cone? I know I haven’t, but math can give us a good idea of what it would be like — or at least, how long it would take.

We are told that the hose spills 1413 cm^3 of water every minute. We are also told the cone has a height of 150 cm and a radius of 60 cm. So far, so good.

First things first, we need to find out how much water can fit in the cone. That means volume. The volume of a cone is

π • r^2 • (h/3)

Let’s go ahead and plug in (remember we use 3.14 for π)

(3.14) • (60)^2 • (150/3)

The volume of the cone is 565,200 cm^3

Wait, I’m lost. What were we supposed to do again? Oh, right. We needed to find how long it would take for the hose to fill in the cone. Well, if we know the hose dispenses 1413 cm^3 per minute, and there is a total of 565,200 cm^3 the cone can take, we can divide the volume of the cone by the amount the hose dispenses per minute to get the number of minutes it’d take to fill it.

565200/1413

400 minutes. Wow, ok. I wouldn’t want to wait that long. That’s like watching 3 movies!

MATH HELP PLEASE WILL GIVE BRAINLIEST!
This figure shows circle Z with chords AB and RS .

mAR=55°
mRB=66°
AB=8 m
RS=8 m

What is ​ mRS​ ?

Enter your answer in the box.

Answers

Because AB=RS=8m, ArcRS=Arc AB=ArcAR+ArcRB=55+66=121

Jeanette purchased a concert ticket on a web site.The original price of the ticket was $75.She used a coupon code to receive a 20% discount.This website applied a 10% service fee to the discounted price.Jeanette ticket was less than the original price by what percent?

Answers

STEP 1:
Find discounted price.
Discounted $= original $ - (original $ * % discount)

Discounted $= $75 - ($75 * 20%)
Discounted $= 75 - 15
Discounted $= $60


STEP 2:
Find discounted $ plus service fee.
Price plus fee= discounted $ + (discounted $ * service fee %)

Price plus fee= $60 + ($60 * 10%)
Price plus fee= 60 + 6
Price plus fee= $66


STEP 3:
Find % change.
% change formula= (new # - original #) ÷ original # x 100

% change= (66-75)÷ 75 x 100
% change= -9 ÷ 75 x 100
% change= -0.12 x 100
% change= -12%

***the negative indicates a decrease


ANSWER: Her ticket was less than the original by 12%.

Hope this helps! :)

Evaluate log10 0.001

Answers

[tex]0.001=\dfrac1{1000}=10^{-3}[/tex]

[tex]\implies\log_{10}0.001=\log_{10}10^{-3}=-3\log_{10}10=-3[/tex]
Final answer:

The operation 'log10 0.001' means 'the power to which we must raise 10 in order to obtain 0.001'. The answer is -3 because 0.001 can be represented as 10^-3.

Explanation:

The question asks you to evaluate log10 0.001. To solve this, we examine the concept of 'logarithms'. In this case, the logarithm in question is base 10 (often written simply as 'log'), and we're being asked for the power to which we need to raise 10 to obtain 0.001.

We know that 0.001 can be written as 10^-3. Therefore, log10 0.001 = -3. This is because the logarithm indicates the exponent that the base number (10, in this case) must be raised to in order to obtain the specified number (0.001, here). So, when we say log10 0.001 = -3, we're saying '10 raised to power -3 gives us 0.001'.

Learn more about Logarithms here:

https://brainly.com/question/37287488

#SPJ12

The product of what number and 7 is less than 49?

Answers

Answer:

All real numbers less than 7

Step-by-step explanation:

Let

x ----> the number

we know that

The inequality that represent the situation is

[tex]7x < 49[/tex]

Solve for x

Divide by 7 both sides

[tex]x < 49/7[/tex]

[tex]x < 7[/tex]

The solution is the interval -----> (-∞, 7)

All real numbers less than 7

You want to make a scaled-down model of the statue of liberty that fits neatly on top of a pedestal with a 20 x 20 in horizontal surface. the actual statue of liberty is approximately 152 ft tall over a 40 x 40 ft base.
a.what is the scaling factor between the statue of liberty and your model? in other words, how many more times bigger is the statue of liberty than your model? show your work.
b.how tall should your model be, in inches? show your work.

Answers

a.what is the scaling factor between the statue of liberty and your model?

we know that
[scale factor[=[model]/[actual]
the pedestal model is 20 in*20 in
the pedestal actual is 40 ft* 40 ft
then
[scale factor]=[20 in]/[40 ft] ---------->[1 in]/[2 ft]-------> scale=1/2

the answer Part A) is 
the scale factor is [1 in]/[2 ft]

b.how tall should your model be, in inches? 
the actual statue of liberty is approximately 152 ft tall

[scale factor]=[model]/[actual]---------> [model]=[scale factor]*[actual]
[model]=[1/2]*[152]----------> 76 in

the answer part B) is 76 in tall

What is the value of n? Enter your answer in the box. n =

Answers

For two chords AB and PQ intersecting inside the circle, then AX × XB = PX × XQ.
In this case;
 5 × 7 = 4(n+8)
  35  = 4n + 32
      4n = 3
        n = 0.75 
Therefore; the value of x is 0.75

Answer:

6

Step-by-step explanation:

Please help me thank you.

Answers

The measure of a circle is 360°. The major arc is that portion of the circle that does not include the 50° minor arc. Hence the measure of the major arc is 310°. You designate the major arc by naming another point on it (in addition to the end points).

The 3rd selection is appropriate.

whats the surface area of a cylinder with a base of 12in and hieght of 40in

Answers

3920.71 so it wants like djehf ewfewvhe veiv

Luisa sells stuffed animals.she sells a stuffed elephant for $34.90, and the sale tax is 6% of the sale price.about how much is the sales tax on the elephant

Answers

To solve this problem you must follow the proccedure below:

 1. You have that Luisa sells a stuffed elephant for $34.90 and the sale tax is 6% of the sale price.

 2. Then, you only have to multiply $34.90 by the sale tax, as below:

 6/100=0.06

 Sales tax on the elephant=$34.90x0.06
 Sales tax on the elephant=$2.094

 About how much is the sales tax on the elephant?

 The answer is: $2.094

 

1. which two types of clouds indicate fair weather?
a) cirrus and cumulus
b) cirrus and stratus
c) cumulus and stratus
d) cumulus and nimbostratus,

Answers

The two types of clouds that indicate fair weather are cirrus and cumulus. Cirrus is a type of clouds that is compared and nicknamed sometimes as the hairs of an angel because it is so thin. Unlike cirrus that appears at high altitudes, cumulus generally are formed closer to the earth surface.

Answer:

a) cirrus and cumulus

Step-by-step explanation:

The two types of clouds that indicate fair weather are :

a) cirrus and cumulus clouds.

Cirrus clouds are usually white and predict fair to pleasant weather.

Cumulus clouds are also called fair weather clouds and look like floating cotton in the sky.

Suppose that c is the center of a circle with radius 13 in and a point p is at a distance of 32 in from
c. find an approximate value of the measure of the angle (in degrees) that is formed by the two tangent lines drawn to the circle from p. if needed, round your answer to three decimals

Answers

The sine of 1/2 the angle = 13 / 32

so this angle =  23.9695 degrees

Therefore the required angle = 2 * 23.9695  =  47.939  to 3 DP's. 

HOW DO YOU FIGURE OUT THE SLOPE OF A LINE ON A GRAPH?!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

To calculate the slope of a line you need only two points from that line, (x1, y1) and (x2, y2). The equation used to calculate the slope from two points is: On a graph, this can be represented as: There are three steps in calculating the slope of a straight line when you are not given its equation.

Answer:

There are different ways to find the slope of a line on a graph

Step-by-step explanation:

One way to find the slope of a line is by putting your line into the equation y=mx+b

In case you don't know m= the slope and b= the y-intercept

If you want to put your equation into y=mx+b; you will need to do rise/run

This means you count how much your line goes up on the y-axis so you rise however many and then you go to the right or left and count until you get to the point that is in line with the y and x axis'.

Also you can use the equation Y2-Y1/X2-X1  

You will do that by finding 2 points from the line and take the numbers and make it into Y2-Y1/X2-X1  

For Example if you had,

(4,3)(6,8) you would do

8-3/6-4= 5/2 so your m, or your slope would be 5/2

I hope this helps!

can somebody tell me the area of these figures:

Answers

1) A = bh = 16*15 = 240 . . . . square units

2) There are a number of ways to decompose the shaded area, or to construct the shaded area. We'll do the latter.

The shaded area is 1/2 of a 4x4 square plus a small triangle below the center of the "butterfly". The latter has a base of 2 and a height of 1, so an area of
.. (1/2)*2*1 = 1
The total area is 4^2/2 +1 = 9 . . . . square units

Draw a tree diagram to support the area model.
Draw a maze that fits her plan.
Find P(Y). Explain your reasoning.
Find P(N). Explain your reasoning.
Ms. Sweet predicts 50 people will enter the maze next year. Based on your findings, give Ms. Sweets a recommendation for the number of pumpkins to place in the maze.

Answers

As a tree diagram, I'd draw this with 2 branching levels. You obviously have a starting point, which branches into 3 levels for each row of the plan.

Then a second branch level off each of those 3 for the possible outcomes by the columns in that row. So the branch for the top row would have 4 further branches, the second row splits into 2 branches etc.

I'm assuming the probability is based off the area of each box, and that the splits are done equally each time.

As for drawing a maze, it's the same as the tree, just in a bit of a maze sort of shape (corners etc).

P(Y), P(N) and the number of pumpkins should come easily from the tree diagram.

Suzie drew the line of best fit on the scatter plot shown.



What is the approximate equation of this line of best fit in slope-intercept form?

y = 6 over 5x + 3
y = 3x + 6 over 5
y = 5 over 6x + 3
y = 3x + 5 over 6

Answers

Hey there!

Slope intercept form is defined as:

y = mx +b

In this form for lines, m is the slope, and b is the y intercept. Hence, slope intercept. That means that in order to write it in this form, we need to know both the slope and y intercept. We'll start with the former.

Slope is defined as ride over run, or up over right (you know it's negative when it goes left). In order to calculate this, we can take two points that lie directly on a coordinate and put them into a fraction as rise/run.

We have;

(0,3) and (5,9)

As we can see, the difference between the two points is that (5,9) is 5 more to the right, and is 6 higher.  We get 6/5. We can even see that in the coordinates, because they're written as (x, y). Additionally, you can use the slope given two points formula:

y2-y1/x2-x1 =

9-3/5-0 = 6/5

Notice how we get the same thing, because in both methods you're finding the difference between the two coordinates based off of rise/run. That's why it's y2 minus y1.


Now that we have our slope, we need the y intercept. The y intercept is simply where the line crosses the y axis. As we can see, it crosses at (0,3) - so the intercept is 3. Now we can create our equation

Slope = 6/5
Y intercept = 3

y = mx + b  --> y = 6/5x + 3

Your answer is A, the first option.

Hope this helps!

The drop that riders experience on Dr. Doom's Free Fall can be modeled by the quadratic function, h(t)9.8t2 5t 39 where h is height in meters and t is time in seconds. From what height are the riders dropped? What is the height of the riders after 1.5 seconds?

Answers

The correct answer is 53.55 meters.

To solve this problem, we need to analyze the given quadratic function h(t) = [tex]9.8t^2 - 5t + 39[/tex], where h is the height in meters and t is the time in seconds.

The given quadratic function: [tex]h(t) = 9.8t^2 - 5t + 39[/tex]

Part 1: From what height are the riders dropped?

[tex]h(0) = 9.8(0)^2 - 5(0) + 39[/tex]

[tex]h(0) = 39[/tex]

The riders are dropped from a height of 39 meters.

Part 2: What is the height of the riders after 1.5 seconds?

[tex]h(1.5) = 9.8(1.5)^2 - 5(1.5) + 39[/tex]

[tex]h(1.5) = 9.8(2.25) - 7.5 + 39[/tex]

[tex]h(1.5) = 22.05 - 7.5 + 39[/tex]

[tex]h(1.5) = 53.55[/tex]

The height of the riders after 1.5 seconds is 53.55 meters.

12-packs of skwunch apple juice cost $3.00 after a 40% discount.Which equation would allow you to find the original price of the 12-packs?

Answers

The answer is 8
Hope this help and plz give me points thank u :)

Answer:

The Iready Answer:

0.6x = 3

Math help please????

Answers

The y-intercept is 4. Divide by three to get y alone (12/3=4)
All you do is divide 3 on both sides, and it results to:

[tex]y = \frac{-4}{3} x + \frac{12}{3} [/tex]

The y intercept simplifies to 4

y-int = 4


PLEASE HELP ME!!!!!!! Estimate the correlation coefficient for each data set. Explain your reasoning.

Answers

The closer the set of data is to a line the closer the correlation coefficient is to 1

in a you can see somewhat of a line so you should pick a value between 0.5 and 0.7

in b you can see a line, the value you should estimate should be greater than 0.9

In c you kinda maybe imagine a line, but worse than a.  so you should pick a number between 0.2 and 0.4

If you were asked to find the 87th term in a sequence, which formula would you want to be given?
A) analog form
B) digital form
C) explicit form
D) recursive form,

Answers

If you were asked to find the 87th term in a sequence, the formula you would want to be given is the explicit form. The correct answer to your questions is letter C. It is a formula that allows direct computation of any term for a sequence a1, a2, a3..an

Answer:

C) explicit form

Step-by-step explanation:

Since the explicit form is written in terms of the number of the term, it would be the most useful to find the 87th term. To use the recursive form, you would have to know the 86th term.

Other Questions
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