Find the function p defined by a polynomial of degree 3 with real coefficients that satisfy the given condition. two of the zeros are 4 and 1+i

Answers

Answer 1

The third zero is 1 - i These two complex numbers always come in pairs. If you have one, you always have the other.

y = (x - 4)(x - i)(x + i)
y = (x - 4)(x^2 + 1)
y = x^3 - 4x^2 + x - 4

Related Questions

helppppppppppppppppppppppppppppppp

Answers

Answer:
-3/2

Explanation:
The given is:
(1/36)^n = 216

Take log base 6 both sides:
log base 6 of (1/36)^n = log base 6 of (216)
log base 6 of (1/6)^2n = log base 6 of (1/6)^-3
2n * log base of (1/6) = -3 * log base 6 of (1/6)
This means that:
2n = -3
n = -3/2

Hope this helps :)

Rewriting we have:
(1/36) ^ n = 216
We use log function:
log ((1/36) ^ n) = log (216)
For log properties we have:
nlog ((1/36)) = log (216)
n = log (216) / log ((1/36))
n = -1.5
Rewriting we have that the value of n is:
n = -3 / 2
Answer:
n = -3 / 2
option 2

Express the given integral as the limit of a riemann sum but do not evaluate: the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.

Answers

We will use the right Riemann sum. We can break this integral in two parts.
[tex]\int_{0}^{3} (x^3-6x) dx=\int_{0}^{3} x^3 dx-6\int_{0}^{3} x dx[/tex]
We take the interval and we divide it n times:
[tex]\Delta x=\frac{b-a}{n}=\frac{3}{n}[/tex]
The area of the i-th rectangle in the right Riemann sum is:
[tex]A_i=\Delta xf(a+i\Delta x)=\Delta x f(i\Delta x)[/tex]
For the first part of our integral we have:
[tex]A_i=\Delta x(i\Delta x)^3=(\Delta x)^4 i^3[/tex]
For the second part we have:
[tex]A_i=-6\Delta x(i\Delta x)=-6(\Delta x)^2i[/tex]
We can now put it all together:
[tex]\sum_{i=1}^{i=n} [(\Delta x)^4 i^3-6(\Delta x)^2i]\\\sum_{i=1}^{i=n}[ (\frac{3}{n})^4 i^3-6(\frac{3}{n})^2i]\\ \sum_{i=1}^{i=n}(\frac{3}{n})^2i[(\frac{3}{n})^2 i^2-6][/tex]
We can also write n-th partial sum:
[tex]S_n=(\frac{3}{n})^4\cdot \frac{(n^2+n)^2}{4}
-6(\frac{3}{n})^2\cdot \frac{n^2+n}{2}[/tex]

Final answer:

To express the integral from 0 to 3 of the function as the limit of a Riemann sum, divide the interval into [tex]f(x) = x^3 - 6x[/tex] subintervals of equal width, find a Riemann sum, and then take the limit as n approaches infinity.

Explanation:

To express the given integral as the limit of a Riemann sum without evaluating, we represent the integral of the function [tex]f(x) = x^3 - 6x[/tex]split the interval [0,3] into n equal subintervals, each of width Δx = 3/n. Then we choose sample points x_i in each subinterval [x_{i-1}, x_i]. The Riemann sum is thus [tex]R = Σ(x_i^3 - 6x_i)Δx[/tex]en from i=1 to n and x_i is any point in the ith subinterval.

As n approaches infinity, which is equivalent to Δx approaching zero, the Riemann sums converge to the integral. The limit of the Riemann sum is then represented as lim_{n to ∞} R, which gives the exact area under the curve f(x) between 0 and 3, but we are not evaluating this limit.

You have a bag of bubble gum containing six grape, nine sour apple and five regular flavored pieces. You randomly pick one piece , give it to your friend, and then randomly pick another piece for yourself. What is the probability that both pieces are grape?

Answers

Final answer:

The probability that both pieces of bubble gum picked are grape flavored is 3/38, calculated by multiplying the probability of picking a grape piece first (6/20) and then another after the first is given away (5/19).

Explanation:

The question asks us to calculate the probability that both pieces of bubble gum picked from the bag are grape flavored. The bag contains six grape, nine sour apple, and five regular flavored pieces. To find the probability that both pieces are grape, we calculate the probability of picking one grape piece and then another grape piece after the first has been given away.

The total number of pieces initially is 6 (grape) + 9 (sour apple) + 5 (regular) = 20 pieces. The probability of picking a grape piece first is 6/20. After giving it away, there are 5 grape pieces left and the total number of pieces in the bag is now 19. The probability of then picking another grape piece is 5/19. To find the overall probability of both events occurring, we multiply the individual probabilities: (6/20) * (5/19) = 30/380 = 3/38.

Therefore, the probability that both pieces are grape is 3/38.

PLEASE HELP

BRAINLIEST AVAILABLE THX

PLEASE ASSIST ME N TRY TO HELP ME

Answers

D is the answer

hope i helped

what is the value of x to the nearest tenth?

Answers

x = 6 / tan(67)

x = 2.546

rounded to nearest tenth x = 2.5

A bakery supplier receives an order for 2 Tons of sudar from a bakery chain. The sugar is shipped in crates. Each crate holds eight 10-pound bags of sugar. How many crates does the supplier need to ship to fulfill the order?

Answers

we know that 1 ton=2000 lbs
we have 2 tons=4,000 lbs
each crate holds 10 lbs of sugar
4,000/10=400 crates

The length of a rectangle is 7mm longer than its width. It’s perimeter is more than 62mm. Let W equal the width of the rectangle, write an inequality and solve it

Answers

this is the answer to the question.

First of all, what is the equation for the perimeter of a rectangle?
2(l + w) = p
Since we know the perimeter (p) is greater than 62 we can say:
2(l + w) > 62
It is also given that the length is 7 mm longer than the width, so we know the value of the length in terms of w (the width).
w = w
l = w + 7
Substitute l with (w + 7) into the equation:
2[(w + 7) + w] > 62
Now combine like terms in the parentheses
2(2w + 7) >62
Distribute the 2 into the terms in the parentheses
4w + 14 > 62
Subtract both sides by 14
4w > 62 - 14
Combine like terms
4w > 48
Divide both sides by 4
w > 48

Final answer: w > 48
Hope this helps!

2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.

Answer:
m < C =
m < B =
m < A =
m < D =

Answers

Ans:
1. m ∠C = 88°
2. m ∠B = 100°
3. m ∠A = 92°
4. m ∠D = 80°

Explanation:
∠A and ∠C are supplementary angles; therefore:
∠A + ∠C = 180° --- (A)

Since,
∠A = (x+2)°
and
∠C = (x-2)°

Plug-in the values in equation (A):
(A) => (x+2)° + (x-2)° = 180°
=> x° + 2° + x° - 2° = 180°
=> 2x° = 180°
=> x = 90°

Since x = 90°, therefore,
∠A = (x+2)° = 92°,
and
∠C = (x-2)° = 88°

Since ∠B and ∠D are supplementary angles; therefore,
∠B + ∠D = 180°
∠B + (x-10)° = 180°

Since,
x = 90°; therefore,

∠B + 80° = 180°
∠B = 100°

And since,
∠B + ∠D = 180°
and
∠B = 100°

Therefore,

∠D = 180° - 100°
∠D= 80°

-i

which scale factor would produce a contraction?

A.) 5/2
B.) 1.2
C.) 2.3
D.) 3/4

Answers

we know that
the scale factor produce a contraction when its value must be less than zero

Let
SF---------------> scale factor
SF< 0------------> produce a contraction
A.) 5/2 --------> 2.5 SF>0 not produce a contraction
B.) 1.2 --------> 1.2 SF>0 not produce a contraction
C.) 2.3 --------> 2.3 SF>0 not produce a contraction
D.) 3/4--------> 0.75 SF< 0 produce a contraction

the answer is 3/4

Find an ordered pair (x,y) that is a solution to the equation.

3x-y=3

Answers

There are a number of ordered pairs that will work for this.

One example is (1, 0).

We can see this will work by first selecting any value for x. We'll use the 1 that I gave.

3x - y = 3.

Now sub the value in.

3(1) - y = 3.

Multiply.

3 - y = 3.

Solve for y.

y = 0.

This gives you the ordered pair (1, 0).

Answer: The required ordered pair is (1, 0).

Step-by-step explanation: We are given to find an ordered pair (x, y) that is a solution to the following equation:

[tex]3x-y=3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

To find an ordered pair, we should either take a value of x and find the corresponding value of y,

or,

we should take a value of y and find the corresponding value of x.

Let us consider that

x = 1.

Then, from equation (i), we get

[tex]3\times 1-y=3\\\\\Rightarrow 3-y=3\\\\\Rightarrow y=3-3\\\\\Rightarrow y=0.[/tex]

Thus, the required ordered pair is (1, 0).

ASAP What is the lateral area of this regular octagonal pyramid?? Explain your answer if you can plz thanks

Answers

The lateral area would be 298.7 cm².

The lateral area is the area of all of the lateral faces of the pyramid. There are 8 triangles making up the lateral faces. Each has a base of 6.6. The formula for the area of a triangle is

A=1/2bh,

so we still need the height of the triangle.

The height of each lateral triangle is the slant height of the pyramid. The slant height of the pyramid forms a right triangle with the height of the pyramid and the "radius" as it were of the pyramid. Thus we use the Pythagorean theorem:

8²+8²=h²
64+64=h²
128=h²
√128=√(h²)
8√2 = h

Substituting this into our area formula we have:
A=1/2(6.6)(8√2)

We will go ahead and multiply this by 8, since there are 8 lateral faces:
LA=8(1/2)(6.6)(8√2)
LA = 298.7

Answer:

Hello! The correct answer is 298.7 [tex]cm^{2}[/tex]

Step-by-step explanation:

I am just confirming!

When solving the equation 10x + 2 = 22, what is the first thing you're going to do?

Answers

I would minus 2 from both sides of the equation so that it becomes:

[tex]10x \: = \: 20[/tex]

Subtract 2 from both sides

What is the value of x? The figure shows 2 right triangles, triangle K L J with right angle J and triangle L J M with right angle M. The measure of angle L K J is 30 degrees. The measure of angle L J M is 45 degrees. The length of side K L is 8 square root 2. The length of side L M is x. Enter your answer in the box. x =

Answers

See the attached figure which represents the explanation of the problem

∵ Δ KJL is a right triangle at ∠J
∴ KL is the hypotenuse = 8√2
∵ ∠ JKL = 30°
∴ The side which faces the angle 30° will be the half of the hypotenuse because sin 30° = JL/KL = 0.5
∴ JL = 0.5 KL = 0.5 * 8√2 = 4√2

Δ JML is a right triangle at ∠M
∴ JL is the hypotenuse = 4√2 ⇒⇒⇒ (proved)
∵ ∠LJM = 45° , ML = x
∴ sin 45° = x/JL
∴ x = JL sin 45° = 4√2 * (1/√2) = 4

The correct answer
The length of side L M is x = 4

A box contains 24 light bulbs of which 4 are defective

Answers

The awnser should be either 6 or 20

A regression line was calculated as ŷ = 1.7x + 2.1. What is the slope of the regression line. is _____. Type a numerical answer in the space provided.

Answers

The answer is 1.7

The slope is the number to the left of the x variable. Each time x increases by 1, the value of yhat increases by 1.7

Jonathan bought a new computer for $1,716, using the electronics store's finance plan. He will pay $143 a month for 12 months. Which equation can Jonathan use to find out how much money he still owes after each month of the plan?

Answers

Answer:

y = 1716 -143x

Step-by-step explanation:

You want an equation for the amount owed after x months on a purchase of $1716 paid at the rate of $143 per month.

Paid

After x months, the amount paid will be 143·x. The amount owed is the difference between the original purchase price and the amount paid:

owed = $1716 - paid

y = 1716 -143x . . . . . . . . . the amount Jonathan still owes after x months

Need to find the formula for:
Car problem: Julie wants to borrow her parent's car to drive to a tournament. Her parents tell her she has to pay for the gas she uses. The car gets 26 mpg. Julie wonders how much gas she will need to purchase to get to the tournament and back.

Answers

THE ANSWER IS 5061 -1 =1 AND THE DIVIDE BY 8

Factor. 25m^100−121n^16
(5m10−11n4)(5m10+11n4)(5m50−11n8)2(5m50−11n8)(5m50+11n8)(5m10−11n4)2

Answers

25m¹⁰⁰-121n¹⁶
this question is a difference of squares. the basic equations is when you get 2 square numbers and you have to find their difference ;
x²-y² = (x+ y)(x-y)
you have to then find the product of these factors.
the question given can be rewritten to write the numbers in their square forms
25m¹⁰⁰ - 5²m⁵⁰ˣ² - square root - 5m⁵⁰
121n¹⁶ - 11²n⁸ˣ² - square root - 11n⁸
we have to then factorise them
the answer for 25m¹⁰⁰-121n¹⁶ = (5m⁵⁰ - 11n⁸) (5m⁵⁰ + 11n⁸)

please help asap!!!!!! lots of points

Answers

The answer for this question is c

Point slope form is y-y=m(x-x)
The correct answer is B.

When triangle ABC is rotated about side AB, what figure is formed?

cylinder
prism
pyramid
cone

Answers

if it is rotated along AB it would be a cone

Answer:

Cone

Step-by-step explanation:

We are given that a triangle ABC .

We have to find that what shape is formed when a triangle ABC is rotated about side AB.

A given triangle ABC is a right triangle.

When we rotate the figure about side AB then the figure will be cone .The side AB will be height of cone and side AC will be radius of cone.

Hence, when a triangle ABC is rotated about side AB, the cone is formed.

Answer: Cone

What’s the value of x in 46+(7x+9)

Answers

This is not a full equation. However, if it were set equal to 0, the answer would be roughly -7.86.

Colin was thinking of a number. Colin adds 18 to it, then doubles it and gets an answer of 65.5. What was the original number?

Answers

Do those steps in reverse to figure out the number.

65.5 ÷ 2 = 32.75.
32.75 - 18 = 14.75.

Answer:

14.75

Step-by-step explanation:

65.5/2 = 32.75.

32.75 - 18 = 14.75

thats your answer. hope it helps

Modern Appliances offers a one-year monthly installment plan for a refrigerator. The payment for the first month is $75, and then it increases by 6% each month for the rest of the year. Which expression can be used to find the total paid in the first 12 months?

Answers

75(1-1.06^12/1-1.06) !!

Expression used represents the given paid installment for [tex]12[/tex] months is equal to [tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex].

What is expression?

" Expression is defined as the equation representing the relation between the numbers or the variables using mathematical operation."

Formula used

Geometric progression,

[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]

[tex]a=[/tex] first term

[tex]r=[/tex] common ratio

[tex]n=[/tex] number of terms

According to the question,

Given,

Amount to be paid first month [tex]'a' = \$75[/tex]

Increases by [tex]6\%[/tex] each month

Therefore,

Common ratio [tex]'r' = 1 + \frac{6}{100}[/tex]

[tex]= 1.06[/tex]

Number of months [tex]'n'= 12[/tex]

Substitute the value in the formula to get the expression for the given condition,

Required expression,

[tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex]

Hence, expression used represents the given paid installment for [tex]12[/tex] months is equal to [tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex].

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A car salesman earns 2% commission on all of his sales. If he needs to make $3,000 a month for his living expenses, what total dollar amount must he sell to make that in commission each month?

Answers

He must sell 150,000 dollars worth of something to make 3,000 in commission each month.
I hope this helps!

The total dollar amount he must sell to make that in commission each month is $150000.

What is percentage?

In mathematics →

a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".

Given is that a car salesman earns 2% commission on all of his sales. He needs to make $3,000 a month for his living expenses,

Assume that the total dollar amount he must sell to make that in commission each month is ${x}. Then, we can write -

3000 = 2% of {x}

3000 = (2/100) × {x}

{x} = (3000 x 100)/2

{x] = 300000/2

{x} = 150000

Therefore, the total dollar amount he must sell to make that in commission each month is $150000.

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HOW would I go about figuring this out? I need explanation not just answer

Answers

Set up the proportion:

3/4 = x/24

Cross multiply:

4x = 72

Divide by 4:

x = 18

There were 18 clarinets in the music room.

Hope this helps :)

You made 1/2 quart of lemonade. How many 1/4 quart-sized glasses will you be able to fill with lemonade?

Answers

2 glasses. 2/4 glasses equals 1/2 glasses, so you would be able to fill up two glasses.

The solution is 2 glasses

The number of 1/4 quart-sized glasses to fill the lemonade is given by the equation A = 2 glasses

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of 1/4 quart-sized glasses to fill the lemonade be A

Now , the equation will be

The amount of lemonades = 1/2 quart of lemonade

The size of the glasses = 1/4 quart-sized glasses

So , the equation will be

A x 1/4 quart-sized glasses = 1/2 quart of lemonade

On simplifying the equation , we get

A / 4 = 1/2

Multiply by 4 on both sides of the equation , we get

A = ( 1/2 ) x 4

A = 2 glasses

Therefore , the value of A is 2 glasses

Hence , the number of glasses is 2

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Simplify.

2x5 - 6x2 + 4x4y
-------------------------
2x

Answers

We have the rational expression [tex] \frac{2x^{5}-6x^{2}+4x4y}{2x} [/tex]; to simplify it, we are going to try to find a common factor in the numerator, and, if we are luckily, that common factor will get rid of the denominator [tex]2x[/tex].
Notice that in the denominator all the numbers are divisible by two, so 2 is part of our common factor; also, all the terms have the variable [tex]x[/tex], and the least exponent of that variable is 1, so [tex]x[/tex] will be the other part of our common factor. Lets put the two parts of our common factor together to get [tex]2x[/tex].
Now that we have our common factor, we can rewrite our numerator as follows:
[tex] \frac{2x(x^{5}-6x+2(2y)}{2x} [/tex]
We are luckily, we have [tex]2x[/tex] in both numerator and denominator, so we can cancel those out:
[tex]x^{5}-6x+2(2y)[/tex]
[tex]x^5-6x+4y[/tex]

We can conclude that the simplified version of our rational function is [tex]x^{5}-6x+4y[/tex].

What is the definition of a circle? A circle is a plane figure with no straight sides. A circle is a point and all the points in a plane that are the same distance from it. A circle is the set of all points in a plane that are a given distance from a given line segment. A circle is the set of all points in a plane that are the same distance from a fixed point called the center.

Answers

Lets rule some out off the bat, shall we?
The first one you mentioned, a circle is a plane figure with no straight sides... I can name another shape with no straight sides... an oval.
The second one you mentioned, is a true statement
The third one you mentioned, a circle is from a point, not a line segment.
The last one mentioned is also a true statement.

Answer:

I believe the answer is "A circle is a set of all points in a plane that are the same distance from a fixed point called the center." I am 95% sure but please correct me if I am wrong. Hope this possibly helps someone!

Step-by-step explanation:

1.01 an rational number

Answers

no its not an rational number.The answer is no

Your answer is (8.1) hope it helps and have a great day!

Kevin is 2 times as old as Gabriela. 12 years, Kevin was 6 times as old as Gabriela.How old is Gabriela now

Answers

The answer is that kevin is 30 years old today and gabriela is 15 years old today.

Final answer:

Gabriela's current age is found by setting up algebraic equations based on the information that Kevin is twice as old as Gabriela now, and was six times as old 12 years ago. Solving the equations, we find that Gabriela is 15 years old.

Explanation:

Finding Gabriela's Current Age:

The problem statement tells us that Kevin is currently 2 times as old as Gabriela and that 12 years ago, Kevin was 6 times as old as Gabriela. To solve for Gabriela's current age, let us use algebra. Let's denote Gabriela's current age as G and Kevin's current age as K. The given information can be translated into the following two equations:

K = 2G (Kevin is 2 times as old as Gabriela now)K - 12 = 6(G - 12) (12 years ago, Kevin was 6 times as old as Gabriela)

Substituting the first equation into the second, we get:

2G - 12 = 6(G - 12)

Expanding both sides:

2G - 12 = 6G - 72

Moving all terms involving G to one side and constant terms to the other side, we get:

2G - 6G = -72 + 12

-4G = -60

Dividing both sides by -4 to solve for G:

G = 15

So, Gabriela is currently 15 years old.

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