Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.

Answers

Answer 1

Answer:

Step-by-step explanation:

We will make a substitution to make our work easier (when we get there). We also need to know that

[tex]i^2=-1[/tex]

We will use that as another substitution. First, let's make the job of factoring a bit easier. Here's the first substitution. We will let

[tex]x^4=u^2[/tex]

Therefore,

[tex]x^2=u[/tex]

Now we will write the polynomial in terms of u instead of x:

[tex]f(x)=u^2+21u-100[/tex]

Solve for the values of u by setting the polynomial equal to 0 and factoring. When you factor, you will get:

[tex](u+25)(u-4)[/tex]

But don't forget that

[tex]x^2=u[/tex]

so we have to put those back in now:

[tex](x^2+25)(x^2-4)=0[/tex]

By the Zero Product Property, either

[tex]x^2+25=0[/tex] or

[tex]x^2-4=0[/tex]

We will factor the first term. Solving for x-squared gives us:

[tex]x^2=-25[/tex] and

x = ±√-25

which simplifies down to

x = ±√-1 × 25

we can sub in an i-squared for the -1:

x = ±√[tex]i^2*25[/tex]

The square root of i-squared is "i" and the square root of 25 is 5, so

x = ±5i

The next one is a bit easier. If

[tex]x^2=4[/tex], then

x = ±2

You can see you have 4 solutions. But you knew that already, since this is a 4th degree polynomial. The types of solutions are: 2 real, 2 imaginary

Related Questions

Suppose that 24% of people own dogs. if you pick two people at random, what is the probability that they both own a dog?

Answers

To find the probability that both people randomly picked own a dog, we multiply the probability of one person owning a dog (24%) by itself, resulting in a 5.76% chance that both own a dog.

The question is asking us to calculate the probability that two randomly selected people both own a dog, given that 24% of people own dogs. Since the events (each person owning a dog) are independent, the probability of both events happening is the product of their individual probabilities.

Let's denote the probability of one person owning a dog as P(dog) = 0.24. Then, for two independent people, the probability that both own a dog is [tex]P(dog) \times\ P(dog) = 0.24 \times\ 0.24 = 0.0576.[/tex]

So, the probability that both people picked at random own a dog is 5.76%.

A product transformation _____.
multiplies coordinates to transform the image
combines the coordinates of multiple transformations
finds the result of combining multiple transformations
uses a scale factor to multiply coordinates of the image

Answers

The answer is 'D' because a transformation needs to have a pattern. Only A and D have a pattern to them and B and C don't because they are random every time. It's not A because it doesn't specify what you multiply the coordinates by.

Answer:

The answer is C

Step-by-step explanation:

4.Krissa drew a circle with a radius of 4 inches.

Fill in the blanks.

The area of the circle is _______ square inches and the circumference is _______ inches.

64π, 16π

16π, 8π

16π, 64π

8π, 16π

Answers

Answer: second option: 16π, 8π

Explanation:

1) To calculate the area use the formula:

Area = π (radius)^2

radius = 4 in => area = π (4 in)^2 = 16π in^2

2) To compute the circumference use the formula:

Circumference = 2π(radius)

=> Circumference = 2π (4 in) = 8π in.

To calculate the area of a circle, use the formula A = πr², where r is the radius. For this specific circle with a radius of 4 inches, the area is 16π square inches, and the circumference formula is C = 2πr, resulting in a circumference of 8π inches.

To find the area of a circle: A = πr². Substituting the given radius of 4 inches, we get Area = π(4)² = 16π square inches. The circumference of a circle is C = 2πr. Substituting the radius, we get C = 2π(4) = 8π inches.

Which is the best estimate for the product of 123.519 × 311,982.21?

A.
372,000,000

B.
37,200,000

C.
3,720,000

D.
372,000

Answers

B, these numbers are all the same, so in the end it's whichever Digit is the closes, but each gap is that changing by entire Tens of thousands.
The sum of those numbers has 8 digits, the only answer with 8 digits--

Consider the following pair of equations:

y = x + 4
y = −2x − 2

Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.

Answers

The pair of equations:
y = x + 4
y = -2x - 2

To solve the system of equation by substitution, you would substitute one variable for it's equivalent expression. Combining the pair of equations into one equation in only one variable. The easiest way to do this is by substituting out the variable y because it is already alone on one side of the equal sign. Substitute the y in the second equation for: x+4

x+4 = -2x - 2
solve for x
x + 2x = -2 -4
3x = -6
x = -2

now use the value for x to find y by putting into either equation.

y = x + 4
y = (-2) + 4
y = 2

solution is: (-2, 2)

What is the equation of the midline for the function y = 2sin(x - π) + 3

Answers

the maximum value of sin(x-π) is 1, the minimum is -1, so the maximum value for the function y = 2sin(x - π) + 3 is 2*1+3=5, the minimum is -2+3=1, half way between 5 and 1 is 3, so y=3 is the midline.

The equation of the midline for the function 2sin (x - π) + 3 is y = 3.

What is the Midline of a Function?

The midline of a function is the line horizontal to the minimum value and maximum value of the function.

Given function is 2sin (x - π) + 3.

We know the trigonometric formula,

sin (A - B) = sin A cos B - cos A sin B

sin (x - π) = sin x cos π - cos x sin π

= (sin x × -1) - (cos x × 0) [Since cos π = -1 and sin π = 0]

= -sin x

So, 2sin (x - π) + 3 = -2sinx + 3

Now, we know that,

-1 ≤ sin x ≤ 1

Multiplying whole sides by -2,

2 ≥ -2sin x ≥ -2

[since the inequality sign changes when negative is multiplied or divided]

Adding 3 throughout,

5 ≥ -2sin x + 3 ≥ 1

Maximum value is 5 and minimum value is 1.

Midline value = (5 + 1) / 2 = 3

So the equation of the midline is y = 3.

Hence the equation of midline is y = 3.

Learn more about Midlines of Functions here :

https://brainly.com/question/12685150

#SPJ3

Hey there

Could you plz help me id appreciate it so much: )
LIMITED TIME

Answers

The independent variable is known as 'x', and the dependent variable is known as 'y'. They just changed the variables here 'f(t)' or 'f(x)' is the same thing as 'y', and 't' is the same thing as 'x'.

So 't' is the independent variable, and 'f(t)' is the dependent variable.

The wording of the second option, the second to last, and the last is all correct. The questions says "let 't' be the time in years after 2000", so if 't' were say 5, this would mean 5 years after 2000 or 2005. The question also states "let f(t) be the amount of garbage", so the result must be the amount of garbage.

So now we just need to confirm if the calculations were done correctly.

Option 2:

[tex]\sf f(2)=1233[/tex]

This is the same thing as saying if you plug in 2 for 't', you will get 1233, let's try it:

[tex]\sf f(t)=1200\cdot (1.05)^t[/tex]

Plug in 2 for 't':

[tex]\sf f(2)=1200\cdot (1.05)^2[/tex]

Simplify the exponent:

[tex]\sf f(2)=1200\cdot (1.1025)[/tex]

Multiply:

[tex]\sf f(2)=1323[/tex]

So option 2 is incorrect, and we see also that option 6 is correct. Now for the last one:

Option 7:

[tex]\sf f(4)=1458.6[/tex]

This is the same thing as saying if you plug in 4 for 't', you will get 1458.6, let's try it:

[tex]\sf f(t)=1200\cdot (1.05)^t[/tex]

Plug in 4 for 't':

[tex]\sf f(4)=1200\cdot (1.05)^4[/tex]

Simplify the exponent:

[tex]\sf f(4)=1200\cdot (1.21550625)[/tex]

Multiply:

[tex]\sf f(4)\approx 1458.6[/tex]

So the last option is also correct.

So your answers are options 3, 4, 6 and 7.

PLEASE HELP ME ON THIS!!!!

Answers

The last two choices are appropriate.

Both give you f(1) = 7, f(2) = 9.50, f(3) = 12.00, ... as they should.

14. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,3) E (8,3) and F(1,-5). Show your work.

Answers

The circumcenter has equal distance to each of the three vertices. Suppose the coordinates of the circumcenter O are (a,b). Then OD=\sqrt((a-1)^2+(b-3)^2), OE=\sqrt(a-8)^2+(b-3)^2), OF=\sqrt((a-1)^2+(b+5)^2). Let OD=OE=OF, solve the equation. x=9/2, y=-1. O(9/2, -1).

Help! Please. I don't get this.

Answers

a) ∠SQR and ∠2
b) Q
c) QR and QT

MATH HELP PLEASE UGRGENT WILL GIVE BRAINIEST!!
In the figure, YX−→− and YZ−→− are tangents to circle A at points X and Z, respectively.

mXZ=140∘
mXSZ=220∘

What is the measure of ∠XYZ ?

Answers

The measure of an angle formed by two tangent lines intersecting at a point outside the circle is equal to one-half their intercepted arcs.
XYZ = 1/2(XSZ - XZ)
XYZ = 1/2 (220 - 140)
XYZ = 1/2 (80)
XYZ = 40

The measure of angle XYZ is 40 degrees.

Hope this helps =)

Answer:

Step-by-step explanation:

The distance from the origin to the point (-24, 32) is

Answers

The Pythagorean theorem tells you that distance is
.. √((-24)^2 +32^2)) = √(576 +1024) = √1600 = 40

If the height of Mount Everest is about 8.8×103 meters, and the height of the Empire State Building is about 3.8×102 meters, which of these statements is true?

Answers

Mount Everest is about 23 times as tall as the Empire State Building. Hope that helps!

Answer:

option C is correct, i.e. Mount Everest is about 23 times as tall as the Empire State Building .

Step-by-step explanation:

Given options are:-

A. There is no way to compare these heights .

B. Mount Everest is about 40 times as tall as the Empire State Building .

C. Mount Everest is about 23 times as tall as the Empire State Building .

D. The Empire State Building is about 23 times as tall as Mount Everest.

Given the height of Mount Everest is about 8.8×10^3 meters, and the height of the Empire State Building is about 3.8×10^2 meters.

Finding ratios of given heights:-

[tex]\frac{Mount\;\;Everest}{Empire\;\;State\;\;Building} =\frac{8.8*10^3m}{3.8*10^2m} \\\\\frac{Mount\;\;Everest}{Empire\;\;State\;\;Building} =23.15789474 \approx 23 \\\\Mount\;\;Everest=23*(Empire\;\;State\;\;Building)[/tex]

Hence, option C is correct, i.e. Mount Everest is about 23 times as tall as the Empire State Building .

So I've got a math problem I don't understand: simplify (3^ - 2 + 5^ - 2) ^ -1 I got 34 but apparently the answer's 225/34, shouldn't i just multiply -2 and -5 by 1 making it 3^2 + 5^2 which is 34 Pliz help, cramming for a test tmw

Answers

The exponent tells you the number of times that factor is in the product. When the exponent is negative, the product is in the denominator.
.. (3⁻² +5⁻²)⁻¹ = 1/(1/9 +1/25) = 1/(34/225) = 225/34

◆ Exponential Reductions ◆

Hey !!

Check the attachment.
Hope it helps you :)

P.s. In your question the negative no. is in exponentials or in power ,

a^m = a*a*a*a...(m times)

But if m is negative then solve like -
a^-m = 1/a^m

Anyone have a proper answer for this?

Answers

by the same "tangent-chord angle theorem" as you saw before, you have a tangent, and an arc, the arc is 120°, so the enclosed angle by both, namely ∡y, is half that of that arc.

find the slope of the line that passes through the points (2,1) and (-1,-1).

Answers

Answer:

all work is shown and pictured

What is the answer to this question please explain...

Answers

Do what it says.

F = (9*30)/5 +32 . . . . . replace the variable C with the value 30
F = 270/5 +32 . . . . . . . order of operations says do multiplication and division in the order in which they appear. We have multiplied 9*30
F = 54 +32 . . . . . . . . . . division appears next. We have divided 270 by 5
F = 86 . . . . . . . . . . . . . . after multiplications and divisions are done, we add in the order of appearance. There is only one addition to perform.

F = 86 . . . . . . . . we suppose only the numerical value 86 should be entered

Из листа картона длиной 35 см и шириной 20 см Маша вырезала четыре квадрата площадью 1 дм2 каждый.Найди площадь остатка картона.Ответ вырази в дм 2

Answers

the question in Englih is
From a cardboard sheet 35 cm long and 20 cm wide, Masha cut out four squares of 1 dm2 each. Find the area of the cardboard residue. Answer the question in dm2

Step 1
convert cm to dm
we know that
1 cm is---------------> 0.10 dm
then
35 cm--------------> 3.5 dm
20 cm--------------> 2 dm

Step 2
find the area of the cardboard
Area=3.5*2=7 dm²

Step 3
find the area of the cardboard residue
Area=7-4*1=3 dm²

the answer is 3 dm²

the answer in Russian

Шаг 1
преобразовать cm в дм
мы знаем это
1 cm ---------------> 0.10 дм
тогда
35 cm--------------> 3.5 дм
20 cm--------------> 2 дм

Шаг 2
найти область картона
Площадь=3.5*2=7 дм²

Шаг 3
найти область остатка картона
Площадь=7-4*1=3 дм²
ответ 3 дм²

ответ 3 дм²

35*20=700 см2 (площадь картонки)
1 дм2=100 см2
Если она вырезала 4 квадрата по 100 см2, то осталось 700-(100*4)=700-400=300 см2
300 см2=3 дм2
Думаю,что так.

HELP PLS with this geometry problem

Answers

Angle A = arctan(12/5) = 67.4 degrees

Angle A = arccos(5/13) = 67.4 degrees

yes the answer was the same

1. Your total restaurant bill is _____. (1 point)
Captionless Image
*

the items purchased minus sales tax, and plus tip.
the items purchased plus sales tax and tip.
the items purchased minus sales tax, and plus tip.

2. A check is _____. (1 point)
Captionless Image
*

required to be paid by your bank when presented
a promissory note (I.O.U.)
not able to be forged

3. There are several different ways to pay for items. In most modern economies, which is not a way to pay? (1 point)
Captionless Image
*

credit cards
bartering
cash

Answers

First question:

Your total restaurant bill is the items you have purchased plus the sales tax and plus the tip (if there’s any). Sales tax is added to your purchase because this is tax imposed to the consumer and not to the buyer. The buyer is only required to collect this tax from the buyer.

Second question:

A check is a financial instrument wherein the bank is required to pay when presented or encashed to them. You just have to make sure that you have account balance to that certain bank.

Third question:

The way of payment not any more common in the most modern economies is the bartering. Both credit cards and cash are the most common way of paying for your purchases.

Answer:

1. the items purchased plus sales tax and tip.

2. a promissory note (I.O.U.)

3. bartering

The opening of the tunnel can be modeled by the graph of the equation y=-0.18x^2+4.4x-12 where x and y are measured in feet. Find the maximum height of the tunnel.

Answers

1. To find the vertex of a parabolla whose equation is written in the standard form, you must apply the following proccedure:

2. You have:

y=-0.18x²+4.4x-12

a=-0.18
b=4.4

3. You must apply the following formula:

x=-b/2a
x=-4.4/2(-0.18)
x=-4.4/-0.36
x=12.22

4. When you susbtitute x=12.22 into the equation y=-0.18x²+4.4x-12, you obtain:

y=-0.18x²+4.4x-12
y=-0.18(12.22)²+4.4(12.22)-12
y=14.88 feet

5. The answer is: The maximum height of the tunnel is 14.88 feet

Lanas avarage step length is about 0.5 meters. How many steps will she need to finish the race? (5 KILMEMETER RACE)

Answers

The length of the race is 5 kilometers.
5 kilometers equals 5000 meters.

Since Lana's avarege step length is about 0.5 meters, we need to divide 5000 by 0.5

[tex]Steps = \frac{5000}{0.5} = 10000[/tex]

Hence, Lana needs to take about 10000 steps.

The function f(t)=-5t^2+15t+50 models the approximate height in feet of an object t seconds after it is launched. how many seconds does it take for the object to hit the ground?

Answers

f(t) can be factored to find the zeros.
.. f(t) = -5(t -5)(t +2) . . . . f(t) = 0 for t=-2, t=5

The object hits the ground after 5 seconds.

Anyone have the proper answer to this?

Answers

The translation rule used here is (x+2 , y+4).

So the image of (-7,3) will be:

(-7+2 , 3+4)
(-5 , 7)

So the answer is (-5,7).

Hope this helps :)

What does (r−c)(5) mean about George's new store?

Answers

store will have a profit of 5400 after it's fifth month in business
Answer is C

Is 40% bigger than 2/5

Answers

To find the percentage of 2/5 you'll divide them and then multiply the answer by 100.

2/5 = 0.4 = 40%

So 40% and 2/5 are equal.

Hope this helps :)

40% can be rewritten as 0.4
2/5 can be rewritten as 0.4.

As you can see, they are equal, so NO, 40% is not bigger than 2/5.

The net of a square pyramid is shown:
What is the surface area of the figure?

A.0.5625 square inch

B.0.7625 square inch

C.1.5625 square inches

D.1.7625 square inches

Answers

First the square .75^2=0.5625 inch² + A≈0.3 *4=1.2 inch²+ 0.5625 inch²= 1.7625 inches²
Thus d: is your Answer

I think its d because if do the step in the correct way thus may give you d

Triangle ABC has vertices A(5, 3) , B(3, 7) , and C(1, 4) . Triangle ABC is dilated, and the vertices of the image are A′(1.25, 0.75) , B′(0.75, 1.75) , and C′(0.25, 1) . The center of dilation is the origin. What is the scale factor of the dilation? 0.25 0.5 2 4

Answers

fFirst, we have the following points:
A (5, 3)
B (3, 7)
C (1, 4)
We multiply these vertices by a factor k to obtain the new vertices:
A '(k * 5, k * 3) = (1.25, 0.75)
B '(k * 3, k * 7) = (0.75, 1.75)
C '(k * 1, k * 4) = (0.25, 1)
We note that the value of k is: k = 1/4
Answer:
the scale factor of the dilation is:
0.25

This is the answer the other is right

PLEASE HELP ASAP!
You have been hired by a museum to make a scale drawing poster of a painting to sell at the gift shop. The painting is 65in high by 105in wide. You are asked to use a 1in = 5in scale. What will the dimensions of your poster be? (2 points)

Answers

we know that
[scale]=[poster]/[painting]
[poster]=[painting]*[scale]
scale=1/5

then

for high = 65 in the painting
[poster]=[painting]*[scale]-----------> [65]*[1/5]-----> 65/5-------> 13 in

for wide = 105 in the painting
[poster]=[painting]*[scale]-----------> [105]*[1/5]-----> 105/5-------> 21 in

the answer is
The dimensions of the poster will be 15 in x 21 in

The sum of 19.3 and a number is 30.4. which eqation can be used to sole the problem?

Answers

the equation is

19.3 + n = 30.4

Answer:

19.3+n+30.4 (B on edg)

Step-by-step explanation:

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