What is the product in simplest form? State any restrictions on the variable. z^2/z+1 * z^2+3Z+2/z^2+3z

Answers

Answer 1

(z^2/(z +1)) * (z^2 +3z +2)/(z^2 +3z)
= z^2*(z +2)(z +1)/((z +1)(z)(z +3))
= z(z +2)/(z +3)
= (z^2 +2z)/(z +3) . . . . . z not in {-3, -1, 0}

Answer 2

The correct answer is option c. The product in simplest form is [tex]& \frac{z(z+2)}{z+3}[/tex] with restriction of [tex]z \neq-1,0,-3[/tex].

To find the product in simplest form and state any restrictions on the variable, we'll follow these steps:

1. Simplify each fraction where possible.

2. Multiply the fractions together.

3. State the restrictions on the variable.

Given expression:

[tex]\[\frac{z^2}{z+1} \times \frac{z^2 + 3z + 2}{z^2 + 3z}\][/tex]

Step 1: Factor each polynomial where possible

- [tex]$ z^2 $[/tex] cannot be factored further.

- [tex]$ z + 1 $[/tex] cannot be factored further.

- [tex]$ z^2 + 3z + 2 $[/tex] can be factored into [tex]$(z + 1)(z + 2)$[/tex].

- [tex]$ z^2 + 3z $[/tex] can be factored into [tex]$z(z + 3)$[/tex].

So the given expression becomes:

[tex]\[\frac{z^2}{z + 1} \times \frac{(z + 1)(z + 2)}{z(z + 3)}\][/tex]

Step 2: Simplify the expression by canceling common factors

First, rewrite the expression to see the common factors more clearly:

[tex]\[\frac{z^2}{z + 1} \times \frac{(z + 1)(z + 2)}{z(z + 3)} = \frac{z^2 \cdot (z + 1)(z + 2)}{(z + 1) \cdot z \cdot (z + 3)}\][/tex]

Now, cancel the common factors:

- [tex]$ z^2 $[/tex] and [tex]$ z $[/tex] in the numerator and denominator:

[tex]\[\frac{z \cdot (z + 1)(z + 2)}{(z + 1) \cdot (z + 3)}\][/tex]

- [tex]$ z + 1 $[/tex] in the numerator and denominator:

[tex]\[\frac{z \cdot (z + 2)}{z + 3}\][/tex]

Step 3: Simplified expression and restrictions

The simplified expression is:

[tex]\[\frac{z(z + 2)}{z + 3}\][/tex]

Restrictions on the variable

- The denominators in the original expression cannot be zero.

- [tex]$ z + 1 \neq 0 \implies z \neq -1 $[/tex]

- [tex]$ z(z + 3) \neq 0 \implies z \neq 0 \text{ and } z \neq 3 $[/tex]

Thus, the variable restrictions are:

[tex]\[z \neq -1, \quad z \neq 0, \quad z \neq 3\][/tex]

The complete question is

What is the product in simplest form? State any restrictions on the variable.

[tex]& \frac{z^2}{z+1} * \frac{z^2+3 z+2}{z^2+3 z} \\ } \\[/tex]

[tex]a. & \frac{z^2+2 z}{z+3} ; z \neq-1,-3 \\b. & \frac{z+2}{z+3} ; z \neq-1,0,-3 \\c. & \frac{z+2}{z+3} ; z \neq-1,-3 \\d. & \frac{z(z+2)}{z+3}; z \neq-1,0,-3[/tex]

Related Questions

Question 2(Multiple Choice Worth 2 points)
(10.06 MC)

Compare the functions shown below:

f(x) = 4 sin (2x − π) − 1

g(x)
x y
−1 6
0 1
1 −2
2 −3
3 −2
4 1
5 6

h(x) = (x − 2)2 + 4

Which function has the smallest minimum y-value?
f(x)
g(x)
h(x)
Both f(x) and g(x) have the same minimum y-value.

Answers

Answer:

1. f(x)=4 sin (2 x-π)-1

=4 sin [-(π-2 x)] -1

= -4 sin 2 x -1

-1 ≤ sin 2 x ≤1

f(x) is minimum, when, sin 2 x=1

= -4 × 1 -1

= -5→Minimum value of f(x).

2. Minimum y value of g(x) by looking at the table is ,

g(x)=-3→Minimum

3. h(x)=(x-2)²+4

As, (x-2)², will yield always a positive value.

So, minimum of h(x), will be at , x=2

h(2)=(2-2)²+4=4→Minimum

Among the three function given, f(x) has minimum y -value,equal to -5.

Option A: f(x)

Find the length of the hypotenuse of a right triangle with legs of lengths 9 and 12 If necessary round your answer to two decimal places

Answers

you can get help from Pythagoras theorem :
[tex] {x}^{2} = {9}^{2} + {12}^{2} \\ {x}^{2} = 81 + 144 = 225 \\ x = \sqrt{225} = 15[/tex]
hope this helps

A plane begins to descend from a height of 202 meters. The plane decreases in altitude at an average rate of 1.8 meters per second. Which function can be used to find the altitude of the plane in meters x seconds since it started. Show work please!

Multiple choice :
F. t(x) = 202- 1.8x
G. t(x) -1.8 (x + 202)
H. t(x) = 202 + 1.8x
I. t(x) = 1.8 ( x + 202)u

Answers

The plane starts at 202 m.
All altitudes are in meters.
After 1 second, it is at 202 - 1.8
After 2 seconds, it is at 202 - 1.8 * 2
After 3 seconds, it is at 202 - 1.8 * 3
etc.
After x seconds, it is at 202 - 1.8 * x

202 - 1.8 * x is the same as 202 - 1.8x

Answer: F. t(x) = 202 - 1.8x

Polynomials are closed under the operation of subtraction.

Which statement best explains the meaning of closure of polynomials under the operation of subtraction?

A. When any two polynomials are subtracted, the coefficients of like terms are always subtracted.

B. When any two polynomials are subtracted, the result is always a polynomial with negative coefficients.

C. When any two polynomials are subtracted, the result is always a polynomial.

D. When any two polynomials are subtracted, the result is always a monomial or a binomial.

Answers

Answer: Option C. When any two polynomials are subtracted, the result is always a polynomial.

A polynomial is an expression consisting of variables and coefficients, that involves the operations of addition, subtraction, multiplication .

polynomials are closed under the operations of addition, subtraction, and multiplication.

Polynomials will be closed under an operation if the operation produces another polynomial.

The statement that best explains the meaning of closure of polynomials under the operation of subtraction is

option C. When any two polynomials are subtracted, the result is always a polynomial.

Someone help with math?

Answers

The answer is the second one (the one on the top right)

The diagram shows a line with intercepts 3 and 9 and one of many rectangles which can be inscribed under this line and within the first quadrant.
a. Write an equation for the line.
b. Determine if the rectangle can have x = 4 and y = 2 as its dimensions.
c. Find x and y if the rectangle is a square.
d. Write an expression for A, the area of the rectangle, using x as the only variable.
e. Find x if the area of the rectangle is 6.
f. Which x gives the rectangle its largest area?

Answers

a) The easiest way to write an equation for this line is to use intercept form:
.. x/x-intercept +y/y-intercept = 1
.. x/9 +y/3 = 1

b) The point (x, y) = (4, 2) does not satisfy the equation. (see the graph) These cannot be the dimensions of an inscribed rectangle.

c) The intersection with the line y=x is (x, y) = (2.25, 2.25). These are the dimensions of an inscribed square.

d) The equation can be rewritten as
.. x +3y = 9
.. y = 3 -(x/3)
Then the area can be written as
.. A = xy = x(3 -x/3)

e) For x=6, the area is
.. A = 6(3 -6/3) = 6*1 = 6 . . . . square units

f) The parabola described by A has zeros at x=0 and x=9. The vertex of that parabola is on the line of symmetry, at x = 4.5. That value of x gives the maximum area.

How do I solve this?

Answers

In the first step, you match the pattern of
.. (-3/2)x^2 +0x +3
to the pattern of
.. ax^2 +bx +c

and you can see that
.. a = -3/2 . . . b = 0 . . . c = 3
____
Because a is negative, the parabola opens down. Because it opens down, the vertex is the high point, the maximum.

____
The y-intercept is always c. Here c=3, so the y-intercept is (0, 3).

____
The axis of symmetry is given by
.. x = -b/(2a)
.. x = -0/(2*(-3/2)) = 0

____
Because the y-intercept is on the axis of symmetry, it is the vertex.
.. vertex = (0, 3)

____
Put x=±2 in the equation and evaluate.
.. y = (-3/2)*(±2)^2 +3
.. = (-3/2)*4 +3
.. = -6 +3 = -3
The two points are (-2, -3) and (2, -3).

Each chef at "sushi emperor" prepares 151515 regular rolls and 202020 vegetarian rolls daily. on tuesday, each customer ate 222 regular rolls and 333 vegetarian rolls. by the end of the day, 444 regular rolls and 111 vegetarian roll remained uneaten. how many chefs and how many customers were in "sushi emperor" on tuesday?

Answers

Solving the Diophantine equations for chefs (c) and customers (q) ...
.. 15c -2q = 4
.. 20c -3q = 1
we find that c=2 and q=13 are common solutions.

There were 2 chefs and 13 customers on Tuesday.

_____
It looks like this is better solved using proportions, since the ratio of roll production is different than the ratio of roll consumption. There can only be one solution.
.. (15c-4)/(20c-1) = 2/3 . . . . the ratio of rolls produced is the same as the ratio of rolls consumed
.. 3(15c -4) = 2(20c -1)
.. 45c -12 = 40c -2
.. 5c =10
.. c = 2 . . . . there were 2 chefs
They produced 30 rolls, of which 4 were left and the remaining devoured 2 at a time. Hence there were
.. (30 -4)/2 = 13 customers.

Answer:

There were 2 chefs and 13 customers.

Step-by-step explanation:

Elliot and Katy both bought the same lunchbox for $6. Elliot lives in Oklahoma and pays 4.5% in sales tax, while Katy lives in South Carolina and pays 6% in sales tax. How much more did Katy pay in sales tax than Elliot? A.$0.09 B.$0.27 C.$0.63 D.$0.36

Answers

The answer is A.$0.09!

the answer is A.
Elliot pays a total of $0.27 in tax
Katy pays a total of $0.36 in tax
[tex]0.36 - 0.27 = 0.09[/tex]

Dan measures an object to the nearest fourth inch. He records the length as 4 1/4 inches. Geri measures the same object the nearest half inch. Could Dan and Geri get the same measurement? Explain.

Answers

no because u cant get the same answer by measuring with a half inch

Geri's measurements will never have 1/4 inch as part of the measurement, as it will be rounded to the nearest 1/2 inch.

Dan and Geri cannot get the same measurement for whatever object it is that Dan has measured. (They may get the same measurement on other objects.)

The table shows the height of an object, h(t), in meters after t seconds. Use your calculator to find the quadratic function. Find the approximate time, to the nearest hundredth of a second, after which the object will reach its maximum height.

Answers

My calculator models the function as
.. h(t) = -4.9t^2 +23.4t +120

The maximum height is reached at t=-23.4/(2(-4.9)) ≈ 2.39 seconds.

A spinner with
9
equally sized slices is shown below. The dial is spun and stops on a slice at random. What are the odds in favor of landing on a white slice?
note their are 7 white and 2 black

Answers

If a spinner has 9 equally-sized slices, then there is an equal chance of the spinner landing on any one of those slides. If, as in this case, there are 7 white slices and 2 black slices, then the chance of the spinner landing on a black slice is 2/9. And, to answer the question, the odds of landing on a white slice are therefore 7/9, or about 78%.

what is the factored form of the expression? w^2 + 12w + 36

Answers

THE ANSWER IS(w+6)2(w+6)2

Answer:

[tex](w+6)^2[/tex] is the factored form of the given expression.

Step-by-step explanation:

The given expression is:

[tex]w^2+12w+36[/tex]

Simplifying the above given expression, we get

[tex]w^2+6w+6w+36[/tex]

[tex]w(w+6)+6(w+6)[/tex]

[tex](w+6)(w+6)[/tex]

[tex](w+6)^2[/tex]

Which is the required factored form of the given expression.

This is when one word has more than one definition and its 15 letters

Answers

Notwithstanding has 2 definitions and has 15 letters

Given f(x)=x2+14x+40 .
Enter the quadratic function in vertex form in the box.
f(x)=

Answers

we know that
the quadratic function in vertex form is--------------> y=a*(x-h)²+k

we have
f(x)=x²+14x+40
y=x²+14x+40

We can convert to vertex form by completing the square on the right hand side
y-40=x²+14x
y-40-49=x²+14x-49------> subtract 49 on BOTH sides to preserve the equality
y-40=(x²+14x+49)-49
y=(x²+14x+49)-49+40---------> y=(x+7)²-9

the answer is
the quadratic function in vertex form-----------> y=(x+7)²-9
the vertex is the point (-7,-9)

Answer: f(x) = (x+7)^2 -9

Step-by-step explanation:

I know that this is late but hopefully it will help someone else.

Please help !!! Need fast

Answers

4x+30=90
4x = 60
x = 15

answer is B. 15

Since b and d are perpendicular the angles they form are 90 degree angles. Also given that a and b are parallel the angles between a and d are the same as those with b and d.

SO we can say that 4x + 30 = 90
4x = 60
x = 15

Bailey writes 5 + 8 on the left-hand side of a paper and then writes 4 + 9 to the right of it. Which symbol should Bailey write between the two sets of numbers to show they have the same sum
a. +
b. –
c. ≠
d. =

Answers

5 + 8 = 4 + 9
13 = 13

ANSWER: D) =

The equals sign should be in between because the numbers on each side add up to the same number.

Hope this helps! :)

A rectangular box contains 336 cubic inches. If it is 12 inches long and 7 inches wide, how deep is it?

Answers

Hello

Your answer is 4 inches deep :))

Hope this helps

4.36in deep rounded to the nearest hundredth

quick computing company produces calculators they have found that the cost c(x),of making calculators is a quadratic function in terms of x the company also discovers that it costs $45 to produce 2 calculators, $143 to produce 4 calculators, and 869 to produce 10 calculators FIND THE TOTAL COST OF PRODUCING 1 CALCULATOR

Answers

it cost $23 to make one calculator hope this helps

Answer:

$23

Step-by-step explanation:

We will use a quadratic regression to solve this.

Using a graphing calculator, put the number of calculators into the first list (x) and the cost to produce into the second list (y).

Next we run the quadratic (x^2) regression. Doing this gives us an equation in the form

y = ax²+bx+c. The values we are given for a, b and c are

a = 8.9999999999; b = -4.999999999999; c = 18.999999999

These can be rounded to a = 9, b = -5 and c = 19. This gives us the equation

y = 9x²-5x+19

Substituting 1 in place of x, we have

y = 9(1²)-5(1)+19 = 9(1)-5+19 = 9-5+19 = 4+19 = 23

True or False. (0,0) is a solution to problem #1. This means that (0,0) is in the solution region.

Answers

True.

A point that is a solution is in the solution region.

The angle of depression from D to F measures 10°. If DE = 300 m, find DF. Round your answer to the nearest tenth.

304.6 m

1,910.2 m

1,727.6 m

1,701.4 m

Answers

Answer:

Option C) 1727.6 m

Step-by-step explanation:

Given that the angle of depression from D to F measures 10°.

Also given that DE =300 m.

Since 10 is angle of depression, we can visualize a right triangle with hypotenuse DF=300 m and EF, DE two legs.

In the right triangle DEF, the angle opposite 10 is the side DE[tex]\frac{DF}{DE} =\frac{hypotenuse}{opposite side}= cosec 10\\\\DF =300 cosec 10 = 1727.6 m[/tex]

by Using trignometric ratios

Which description best describes the graph?

A graph is shown. A straight line begins at the upper left side of the coordinate plane and moves down towards the right side. The line crosses the y-axis at y equals 3 and the x-axis at x equals 1.5

Linear increasing
Linear decreasing
Nonlinear increasing
Nonlinear decreasing

Answers

This is a linear decreasing graph.

As the x-values increase, the y-values decrease; this means it is a decreasing graph.

The graph shows a straight line with a constant rate of change, so it is linear.

Answer:

B. Linear decreasing

Step-by-step explanation:

We are given that,

The graph of the function is passing through the points (0,3) and (1.5,0).

Then, the rate of change is [tex]m=\frac{0-3}{1.5-0}=\frac{-3}{1.5}=-2[/tex]

So, the function is represented by a straight line with constant rate of change -2.

Thus, the function is a linear function.

Moreover, as the value of x is increasing, we see that the value of y is decreasing.

So, the function is a decreasing function.

Hence, option B is correct.

If someone can answer this, you are BEYOND SMARTT!!! But tell me how to do it too!!!!

Answers

look at all the choices

we know that at t = 0, the height of the rock is 16

choices H and I do not have a value of 16 at t = 0.

H: h(0) = -5.2(0)² + 24(0) - 12 = -12
I: h(0) = -4.2(0)² + 26(0) - 20 = -20

so we are left with F and G

if we take choice F and plug in t = 1
h(1) = -4.7(1)² - 25(1) + 16 = -13.7
if we take choice G and plug in t = 1
h(1) = -4.7(1)² + 25(1) + 16 = 36.3

only choice G works for us since it has 36.3 at t = 1

you could have also put these points in a graphing calculator and then use the quadratic regression feature to get an equation that will model this data

3x - 5y = 17 y = -7 Solve by substitution.

Answers

Substitute the value of y given by the second equation into the first.
.. 3x -5(-7) = 17
.. 3x +35 = 17
.. 3x = -18
.. x = -6

The solution is (x, y) = (-6, -7).

How many feet are in 100 meters if 1 meter is 1.09 yards? Will mark brainliest if you include clear steps. Thank you!

Answers

well, there are 3 feet in 1 yard, and 1.09 yards in 1 meter, so then

[tex]\bf 100~\underline{m}\cdot \cfrac{1.09~\underline{yd}}{\underline{m}}\cdot \cfrac{3~ft}{\underline{yd}}\implies \cfrac{100\cdot 1.09\cdot 3~ft}{1}\implies 327~ft[/tex]

notice, we use the ratio, and whichever unit you want cancelled, you simply flip the ratio to have it cancelled, if the "m" is atop and you need that cancel, use the ratio with the "m" at the bottom, m/m = 1, and so they cancel out, and so on.

The relationship between the monthly fee that the cable company charges for internet service and the fee for downloading over 32KB of information is modeled by the linear function f (x) = 1.25x + 45, where x is the number of KB over 32. If the total bill for a month is $170, how many KB was in excess of 32 KB that month?

Answers

100 Kilobytes.
Because if the total is 170, then
1.25x = 170-45
1.25x = 125
x = 100

1.25x = 170-45
1.25x = 125
x = 100

How many 12 inch sections can you get out of 9 foot calculator?

Answers

To solve this problem, the first thing you should keep in mind is the following conversion:
1 foot = 12 inches.
Therefore doing the conversion:
(12 inch) * (1 foot / 12 inch) = 1 foot.
The number of sections is:
N = (9 feet) / (1 foot) = 9
Answer:
you can get out 9, 12 inch sections of 9 foot calculator

Twice the sum of two consecutive integers equals 42

Answers

Hello,

Let's assume n the first integer
n+1 the greater
n+(n+1)=2n+1 is odd but 42 (universel answer in Robots IE) is even!!!!
Not answer!

The histogram shows the number of hours volunteers worked one week.

What percent of the volunteers worked 8 to 11 hours or 16 to 19 hours?

Enter your answer in the box.

%

Answers

the answer was 45 i just took it

Answer: 45%

Step-by-step explanation:

From the given histogram, The number of volunteers worked 8 to 11 hours = 5

The number of volunteers worked 16 to 19 hours = 4

The number of volunteers worked 8 to 11 hours or 16 to 19 hours =5+4=9

Total number of volunteers = 4+2+5+4+4+1=20

The percent of volunteers worked 8 to 11 hours or 16 to 19 hours is given by :-

[tex]\frac{9}{20}\times100=45\%[/tex]

Hence, the percent of the volunteers worked 8 to 11 hours or 16 to 19 hours =45%

Determine if x + 3 is a factor of -3x^3+6x^2+6x+9, and how do you know?

Answers

Begin by taking out -3 as a common factor.
-3(x^3 - 2x^2 - 2x - 3)
If x + 3 is a factor, what is inside the brackets should be 0 when x = - 3 It is not. There is only one real root and that is when (x - 3) is equated to 0. Just to show the root is +3, the graph is included.

Other Questions

Two sides of a triangle have lengths 5 in. and 16 in. Describe the possible lengths of the third side.5 < x < 215 < x < 1616 < x < 2111 < x < 21Can you construct a triangle that has side lengths 11 cm, 12 cm, and 15 cm?noyes What is the measure of angle S? According to differential association theory, individualsa. become criminal when they are blocked from achieving their goals legitimately.b. internalize the criminal label when others believe they are criminal.c. who have internalized society's moral standards are unlikely to be criminal.d. learn the techniques and motivations for criminal behavior from others. jude earns $54 interest each year on an investment. his principal was $1800. what is jude's interest rate? which best describes the conclusion of U.S involvement in vietnamthe vietnam war drags on and anti-war protests increase; president nixon begins pulling out american troops; south vietnam falls to the communist northpresident nixon escalates american ground troops in vietnam; with the help of the south vietnamese troops, U.S defeats the communist northnorth vietnam quickly defeats the U.S, forcing american troops out of vietnamthe U.S stays in vietnam until the south vietnamese can push back the viet cong into north vietnam. North and south vietnam stay divided after a cease-fire is signed Which is a secondary sex characteristic, growing pains for males ovulation for females breast development for females sperm production for males A student throws a ball straight down off a very high building with a velocity magnitude of 3.0 m/s the ball accelerated in free fall for 2.0s what is the velocity at 2.0s How do u do #10? Plz show on paper What are Draft Riots, Bread Riots, and Copperheads all connected to? A.Native American unrest during the Civil War B.Anger over the Union blockade C.African American unrest D.Opposition to the war QUESTION WORTH 100 POINTS AND BRAINLIST Select all the words that should begin with a capital letter."come here," my brother said, "and don't be slow." Sonya has four straws of different lengths: 2cm,8cm,14cm,and 16cm. How many triangles can she make using the straws? Which of the following statements is true?A.Animals add water vapor to the air through respiration.B.Plants add water vapor to the air through photosynthesis.C.Both plants and animals can make protein using nitrogen compounds.D.Automobiles are the leading cause of acid rain. What number completes the list of prime factors for 36?3.3.2.? In what way were the origins of world war ii in asia and europe similar to each other? In photosynthesis what form of energy is sunlight converted two major reactions that take place Kerry cut an 8 foot long board into 6 pieces that are equal in length. Represent this problem as a fraction What is the conjugate acid of hpo22 ? express your answer as a chemical formula? ________ refers to the assignment of value, or the amount the consumer must exchange to receive the offering or product. Read this passage from "The American Dream." Now may I suggest some of the things we must do if we are to make the American dream a reality. First I think all of us must develop a world perspective if we are to survive. The phrase must develop a world perspective is an example of a reason. a claim. evidence. rhetoric. A diagnostic test has been developed for a rare disease, which affects 1 in 1000 people. suppose that the test gives a positive result 95% of the time when an individual has the disease, and gives a positive result 1% of the time when the individual does not have the disease. suppose an individual is tested and the result is positive. what is the probability that he/she has the disease?