Let f (x) be a polynomial function with a zero of multiplicity of 1 at 2 and a zero of multiplicity of 2 at 1. Let g(x) be the radical function g of x equals the cube root of x minus 2 Part A: Using the Factor Theorem, determine the polynomial function f (x) in expanded form. Show all necessary calculations. (5 points) Part B: Let h (x) be the piecewise defined function of h of x is the piecewise function of f of x if x is less than 0 and g of x if x is greater than or equal to 0 Are there any breaks in the domain of h (x)? Explain why or why not. (5 points)

Answers

Answer 1

The polynomial functions in their expanded form is given as follows. It is right to state that there are no breaks in the domain of h(x).



What is a polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

For instance, the polynomial 3x+4 has an exponent of 1.

Part A: F(x) has zero at 2 and multiplicity of 1; and

1 at the multiplicity of 2

f(x) = x-2) (x-1)²

= (x-2) (x² - 2x + 1)

= x³ - 4x² + 5x -2

Part B: h (x) = [tex]\left \{ {{x^3 -4x^2 + 5x -2; X < 0} \atop {\sqrt[3]{x-2} ; X\geq 0 }} \right.[/tex]

The domain of X is X ∈ R

Hence it is correct to state that there are no breaks in the domain of h(x).

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Related Questions

Determine what type of model best fits the given situation: principal p is invested at an annual interest of rate r, compounded k times a year for t years.

Answers

The most appropriate model for a given situation is exponential.

What is compound interest?The interest you earn on interest is known as compound interest.Compound interest is a use of exponential functions. A specific sum is added to the account balance each time money is invested (or lent out). Interest is the amount of money that is added to the balance. The sum will continue to accrue interest after that interest has been added during the subsequent compounding period.In the settings of investments and savings, compound interest is used. A = P(1 + RT) is the formula for simple interest. The next section contains a definition of the variables. This indicates that the account value is the sum of the initial investment amount multiplied by one and the rate multiplied by the time.

The most appropriate model for a given situation is exponential.

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.

y = x2 + 3
y = x + 5

Answers

I assume you mean x squared in the first equation

Because both are equal to y, they are equal to each other so x + 5 = x^2 +3
If we then move everything over to one side, we get x^2 - x - 2 = 0

Then factorise it to (x-2)(x+1) = 0
And solve both parts separately

x + 1 = 0
x = -1

x-2 = 0
x = 2

Sub both values into the simplest equation in this case y=x+5
to get y = 4 and y = 7

math related pls help

Answers

Answer:

  (a)  (f +g)(x) = √(x-2) +√(x)

Step-by-step explanation:

The sum of two functions is the sum of their definitions.

Application

  (f +g)(x) = f(x) +g(x)

  (f +g)(x) = √(x -2) +√(x)

Note: the radicals can only be combined if they can be reduced to a form that has the same expression under the radical. Here, that is not the case, so there is no way to simplify the sum.

Find the rectangular coordinates of the point with spherical coordinates (rho,θ,ϕ) : (4,π6,2π3)

Answers

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

I’m going to assume that your values are in the form of:

(r,θ,z)=(4,6π,2π/3)

where

(r,θ)are the polar coordinates of the point’s projection in the xy-plane

z is the usual z-coordinate in the Cartesian coordinate system

Now solving for Cartesian coordinates:

x=rcosθ=4cos(6π)=4(0.86)=3.44

y=rsinθ=4sin(6π)=2

Now for spherical transformation, note that:

(ρ,θ,ϕ)

ρ is the distance between P and the origin

θ is the same angle used to describe the location in cylindrical coordinates

ϕ is the angle formed by the positive z-axis and line segment from the origin and point in space, note that0≤ϕ≤π

OK, now that we have that out of the way, let’s compute:

ρ=r2+z2 = 5

θ=θ=6π

ϕ=arccos(zr2+z2−−−−−−√)=arccos(35)≈0.927rad

The spherical coordinate (4,6π,2π/3) is (5,2π3,0.927) in spherical coordinates.

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Elliott is standing at the top of a store escalator that leads to the ground floor below. the angle of depression from the top of the escalator to the floor is 42.51°, and the escalator is 16 feet long. how far is the top of the escalator from the ground floor? round your answer to the nearest foot.

Answers

By using what we know about right triangles, we conclude that the height is 11ft.

How far is the top of the escalator from the ground floor?

We can think of this as a right triangle.

Where the length of the escalator is the hypotenuse

We know that the angle of depression is 42.51°, then the top angle of our right triangle is:

90° - 42.51° = 47.49°

Now, the height of the top of the escalator would be the adjacent cathetus to said angle, then we can use the relation:

cos(a) = (adjacent cathetus)/(hypotenuse)

Replacing what we know:

cos(47.49°)  = height/16ft

cos(47.49°) *16ft = height = 10.8ft

Rounding to the nearest foot, we get:

height = 11ft

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Use the laplace transform to solve the given initial-value problem. y'' − 4y' + 4y = t3e2t, y(0) = 0, y'(0) = 0

Answers

The Laplace of the given equation is [tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex].

According to the statement

we have given that the equation and we have to solve this problem with the help of the Laplace transform.

So, According to the statement

the given equation is

y'' − 4y' + 4y = t^3e^2t, y(0) = 0, y'(0) = 0

And the Laplace transform is an integral transform method which is particularly useful in solving linear ordinary differential equations.

Firstly fill the value of the Laplace of the second order derivative and put x = 0 in the equation

And same it with the first order of the derivative.

And then the Laplace of the equation become

[tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex]

So, The Laplace of the given equation is [tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex]

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1/4a-3=1/4a(a-?) I need to finish this quick can someone repy fast!

Answers

Answer:

12

Step-by-step explanation:

Factoring out a 1/4 from 1/4a - 3, you get 1/4 (a - 12) as 12 * 1/4 = 3. Thus, ? = 12.

What is the answer to the question: 9 to the second power times 13

Answers

Answer:

1053

Step-by-step explanation:

Find the area of the blue shape below. Use 3.14 for π

If anyone knows the answer please help!

Answers

Answer:

1413.86 ft^2.

Step-by-step explanation:

The diameter of the circle = 50 - 2(18)

= 50-36

=  14 ft.

So its radius is 7 ft.

The total area of the blue shape

= 2(35 * 18) + 3.14*7^2

= 1413.86 ft^2.

4.
Find the perimeter of the triangle.

A. 294 m
B. 119 m
C. 84 m
D. 168 m

Answers

Answer:

84m

Step-by-step explanation:

The perimeter of a triangle is the sum of the length of the external sides.

Therefore, the perimeter of the triangle = 21m + 28m + 35m = 84m.

Hey there!

What is the formula for finding the perimeter of a triangle?
a + b + c = perimeter


What does the labels mean?
a = side 1

b = base

c = side 2

What should the equation look like?
21m + 28m + 35m = perimeter

How do should it be solve?
21m + 28m + 35m = perimeter

49m + 35m = perimeter

84m = perimeter


What is the answer to the question?

84m


Good luck on your assignment and enjoy your day!


~Amphitrite1040

. Factorise the following expression fully

(a+1)²-4b²​

Answers

The factoring the equation (a + 1)² - 4b² we get (a+1+2b)(a+1-2b).

What is the factoring function of (a + 1)² - 4 b²?

Given:  (a + 1)² - 4b²

Apply Perfect Square Formula, and we get

(a + b)² = a² + 2 a b + b²

(a + 1)² = a² + 2a1+1²

= a² + 2a1 + 1² - 4 b²

simplifying the equation, we get

a² + 2a1 + 1² = a² + 2a + 1

= a² + 2a + 1 - 4b²

Factor, a² + 2a + 1 = (a + 1)²

= (a + 1)² - 4 b²

Simplify 4 b² = (2 b)²

= (a + 1)² - (2b)²

Apply the Difference of Two Squares Formula, and we get

x² - y² = (x + y)(x - y)

(a + 1)² - (2b)² = ((a + 1) + 2b)((a + 1) - 2 b)

simplifying the equation, we get

= ((a + 1) + 2b)(a + 1) - 2 b)

= (a + 1 + 2b)(a + 1 - 2b)

Therefore, the correct answer is (a+1+2b)(a+1-2b).

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what is the missing number?

Answers

Answer:

17

Step-by-step explanation:

the pattern

x is the blank

1+5 = 6

5+6 = 11

6+11 = x

11 + x = 28

so x = 17

PLS HELP!!!!
The half-life of Carbon-14 is 5730 years. Suppose a fossil is found with 27% of Carbon-14 as compared to a living sample. How old is the fossil?

Answers

Answer: 1547.10

Step-by-step explanation: Since you are not in a physics class, in which case requires the usage of the radioactive decay formula, definite integrals, and natural logarithms) but an Algebra class which deploys the usage of percentages, this should be rather simple.

I believe they want you to find 27% of the half life of Carbon-14 since it is below 50%. To find the percent of a number (in this case 27%), you multiply the number by 0.27.

5730 * 0.27 = 1547.10

Hope this helped! And if I'm wrong, please don't hesitate to correct me.

I'm not sure how to do both of them

Answers

The total surface area of the shape is 10053 cm²

Calculating Surface area

From the question, we are to determine the surface area of the shape

The surface area of the shape = Surface area of hemispherical part + Surface are of the cylindrical part

∴ Surface area of the shape = 2πr² + 2πrh + πr²

Where r is the radius

and h is the height of the cylindrical part

From the given information.

r = 20

h = 50

Putting the parameters into the equation, we get

Surface area of the shape = 2π(20)² + 2π(20)(50) + π(20)²

Surface area of the shape = 2π×400+ 2π×1000 + π×400

Surface area of the shape = 800π+ 2000π + 400π

Surface area of the shape = 3200π cm²

Surface area of the shape = 10053.096 cm²

Surface area of the shape ≈ 10053 cm²

Hence, the total surface area of the shape is 10053 cm²

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Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive? (–[infinity], –3) (–[infinity], 3) (–3, [infinity]) (3, [infinity])

Answers

the interval in which g(x) is positive is [3, ∞].

On what interval is the function positive?

Here we have the function:

g(x) = ∛(x - 3)

The interval in which the function is positive is defined by:

g(x) > 0.

Then we have:

∛(x - 3) > 0.

We need to solve that inequality for x.

∛(x - 3) > 0

The cube root respects the sign of the argument, then:

x - 3 > 0

x > 3

Then the interval in which g(x) is positive is [3, ∞].

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urgent please help!!

Answers

Answer:

14cm.

Step-by-step explanation:

X is the hypotenus, 7√3 is the opposite and the other side is the adjacent. Choose sin from (soh, cah, toa) because you have to find 'H' (hyp) and opposite is given. Hence, sin 60= 7√3 over x. Cross multiply and you'll get x * sin 60= 7√3. Make x the subject of formula and 14 will be the answer.

What is the measure of 28?
O 90⁰
O 60°
O 180°
O 120°

Answers

Answer: 120

Step-by-step explanation:

Answer:

B. 60°

Step-by-step explanation:

Angle 4 and angle 8 are equal. Find the measure of angle 4 to know the measure of angle 8.

∠4=∠8

180-120=60

∠4=60°

Since angle 4 equals 60 degrees, angle 8 also equals 60 degrees.

Hope this helps!

Y=2x^2+2x-4 what is the x intercepts for the parabola

Answers

Answer:

Step-by-step explanation:

To find the x intercepts, substitute in 0 for y and solve for x

So,

2x^2+2x-4 = 0

2(x^2+x-4) = 0

2/2(x^2+x-4) = 0/2

x^2+x-4 = 0

(x-1) (x+2) = 0

now,

x-1 = 0

x = 1

or

x+2 = 0

x = -2

The x intercepts for the parabola (1,0), (-2,0)

A company reduced the prices of its goals by 13% during a promotional sale. A product was sold for 435.00 during the promotional sales. What was the price before the promotional sales?




Answers

The price of the product before promotional sales was 500,000.

How to find out what the previous price was?

To find what the previous price of the product was, we must take into account that we know that 87% of the value is equal to 435,000. So to find out how much the 13% (discount) that the product had is equivalent to, we do the following operation:

435,000 × 100 ÷ 87 = 500,000

So we know that the 13% discount was 65,000

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what is a real world example of a rational function, and how could you graph it and put it in a table?

Answers

An example of the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.

What is a rational function?

This is the term that is used to refer to the fraction that is represented by the use of a rational fraction. That is there is denominator and a numerator.

The denominator must have a variable and this variable has to be of degree 1. Hence the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.

How to graph a real world situation

First you have to know if it is an inequality or not. Then you have to assign x and y variables to numbers. From here you form an equation. This equation is plotted on a graph.

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A candlemaker uses 240 cubic centimeters of wax to create a scented candle using a cylindrical mold. he decides to offer a larger-sized candle, which uses twice as much wax as the smaller-sized candle. which mold can he use to make the larger-sized candle?

Answers

The mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.

Cylinder

A cylinder is a surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.

smaller-sized candle = 240 cubic centimeters

larger-sized candle = 2(smaller-sized candle)

= 2(240 cubic centimeters)

= 480 cubic centimeters

Therefore, the mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.

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Answer:

A cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold.

Hope this helps!

Step-by-step explanation:

Which statements accurately describe how to determine the y-intercept and the slope from the graph below? On a coordinate plane, a line goes through points (0, negative 6) and (3, 0). To find the y-intercept, begin at the origin and move horizontally to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. To find the y-intercept, begin at the origin and move horizontally to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction. To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction. To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction x 2 minus x 1 Over y 2 minus y 1 EndFraction.

Answers

Answer:

To find the y-intercept, begin at the origin and move vertically to the graphed line. To find the slope, use two ordered pairs on the line and substitute into the equation m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction.

PLEASE HELP

debra has $5. She bought 3 cakes of the same price and has 0.80$ left. what is the pride of 1 cake.​

Answers

Answer:

$1.40

Step-by-step explanation:

5.00-0.80=4.20

4.20 ÷ 3= 1.40

I need help with this one

Answers

A) Sqrt(4^(2/3x)) * 2^x = 1
4^(1/3x) * 2^x = 1
2^(2/3x) * 2^x = 1
2^(5/3x) = 1
Log(2)1 = 5/3x
0 = 5/3x
x = 0

Pls help me,this is Canadian MO 1998 question,i'm very confuse with this​

Answers

The solution to the equation is x = 1.62

How to solve the equation?

The equation is given as:

[tex]x =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]

Next, we split the equations as follows:

y = x

[tex]y =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]

Next, we graph the equations (see attachment)

From the attached graph, the equations intersect at

(x, y)= (1.62, 1.62)

Remove the y value

x = 1.62

Hence, the solution to the equation is x = 1.62

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Rationalize the right side first. Expand and simplify.

[tex]x = \sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}\right) \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right)[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x}\right)^2 - \left(\sqrt{1 - \dfrac1x}\right)^2[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(x - \dfrac1x\right) - \left(1 - \dfrac1x\right)[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = x - 1[/tex]

Rearrange terms as

[tex]\dfrac{x - 1}x = \sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}[/tex]

[tex]\dfrac{x - 1}x + \sqrt{\dfrac{x - 1}x} = \sqrt{x - \dfrac1x}[/tex]

Substitute

[tex]y = \sqrt{\dfrac{x-1}x} = \sqrt{1 - \dfrac1x} \\\\ \implies y^2 = 1 - \dfrac1x \implies x = \dfrac1{1-y^2}[/tex]

(noting that [tex]y>0[/tex]) so that

[tex]x - \dfrac1x = \dfrac1{1-y^2} - (1-y^2) = \dfrac{2y^2 - y^4}{1-y^2}[/tex]

and the equation transforms to

[tex]y^2 + y = \sqrt{\dfrac{2y^2 - y^4}{1-y^2}}[/tex]

[tex]y + 1 = \sqrt{\dfrac{2 - y^2}{1-y^2}}[/tex]

Solve for [tex]y[/tex].

[tex](y+1)^2 = \left(\sqrt{\dfrac{2-y^2}{1-y^2}}\right)^2[/tex]

[tex]y^2 + 2y + 1 = \dfrac{2 - y^2}{1 - y^2}[/tex]

[tex]-y^4 - 2y^3 + 2y + 1 = 2 - y^2[/tex]

[tex]y^4 + 2y^3 - y^2 - 2y + 1 = 0[/tex]

[tex]\left(y^4 + 2y^3 + y^2\right) - 2y^2 - 2y + 1 = 0[/tex]

[tex](y^2 + y)^2 - 2(y^2 + y) + 1 = 0[/tex]

[tex]\left(y^2 + y - 1\right)^2 = 0[/tex]

[tex]y^2 + y - 1 = 0[/tex]

[tex]y = \dfrac{-1 \pm \sqrt5}2[/tex]

Since [tex]y>0[/tex], we take the positive root. Then

[tex]y = \sqrt{\dfrac{x-1}x} = \dfrac{-1 + \sqrt5}2[/tex]

Solve for [tex]x[/tex].

[tex]\left(\sqrt{\dfrac{x-1}x}\right)^2 = \left(\dfrac{-1 + \sqrt5}2\right)^2[/tex]

[tex]\dfrac{x-1}x = \dfrac{6 - 2\sqrt5}4 = \dfrac{3 - \sqrt5}2[/tex]

[tex]x - 1 = \dfrac{3-\sqrt5}2x[/tex]

[tex]\dfrac{-1+\sqrt5}2 x = 1[/tex]

[tex]x = \dfrac2{-1+\sqrt5}[/tex]

Rationalize to clean up the answer.

[tex]x = \dfrac2{-1+\sqrt5}\cdot\dfrac{-1-\sqrt5}{-1-\sqrt5} = \boxed{\dfrac{1+\sqrt5}2} \approx 1.6108[/tex]

i.e. the golden ratio constant.

What is the las digit of the product of all the numbers between 11 and 29?

Answers

The last digit of the product of all the numbers between 11 and 29 is 0.

A product is something that has undergone one or more multiplications.

Here, we're looking for the final digit of the product of all whole numbers greater than 11 and less than 29.

Next, we have the product as: 12*13*14*15*16*17*18*19*20*21*22*23*24*25*26*27*28

Now take note of the 20 that is present.

Any number multiplied by 20 will result in a zero, so:

Product = 20*(12*13*14*15*16*17*18*19*21*22*23*24*25*26*27*28)

Using only that, we can infer that 0 represents the final digit in the product of all the numbers between 11 and 29.

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ms bloom had 4 /7/12 boxes of pencils but 2/1/12 boxes of pencils were broken after she threw out the broken pencils how many boxes of pencils were left

Answers

Concluding, there are (2 + 12) boxes of pencils left.

How many boxes of pencils were left?

We know that Ms. Bloom had (4 + 7/12) boxes of pencils, and we also know that (2 + 1/12) of the boxes were broken.

The number of boxes of pencils left is given by the difference between the two above numbers, then we get:

N = (4 + 7/12) - (2 + 1/12) = (4 - 2) + (7/12 - 1/12) = 2 + 6/12

Now we can simplify the fraction:

N = 2 + 1/2

Concluding, there are (2 + 12) boxes of pencils left.

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What is the correct sequence of organs for the formation and elimination of urine?.

Answers

The analysis of the kidney exists named urology.  The kidney exists as a bean-shaped organ. The Kidney exists metanephric in nature and is located retroperitoneal in position.

What is a kidney?

The organ current in the body which regulates the fluid concentration of the body exists named the kidney.

The nephron exists as the structural and operational unit of the kidney.

The sequence of the appearance of the kidney exists as pursues:-

Minor calyxMajor calyxCollecting ductNephronUreterUrethra

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What number is the height changing by each minute?

Answers

The height is changing by 0.5 units per minute as evident in the given table.

By what number is the height changing?

It follows from the task content that the table given indicates that at, 0min, the height was 150.

While at 1 min, the height is 150.5. On this note, it follows that the height increases by 0.5 units for after every minute.

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Select the reason that best supports statement 5 in the given proof.

Answers

Answer:

B

Step-by-step explanation:

if an angle is congruent, it is the same measurement

Other Questions
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