Hence, the product is:
[tex]\dfrac{z(z+2)}{z+3}[/tex] such that: z≠ -1,0 and -3.
Step-by-step explanation:We are asked to represent the product in the simplest form along with the restrictions applied to z.
We have to evaluate the expression:
[tex]\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z^2+3z}\\\\=\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z(z+3)}[/tex]
Hence,
z≠ -1,0 and -3.
Since, otherwise the denominator will be equal to zero and hence the product will not be defined.
Now, we know that:
[tex]z^2+3z+2=z^2+2z+z+2\\\\z^2+3z+2=z(z+2)+1(z+2)\\\\z^2+3z+2=(z+1)(z+2)[/tex]
Hence,
[tex]\dfrac{z^2}{z+1}\times \dfrac{z^2+3z+2}{z^2+3z}=\dfrac{z^2}{z+1}\times \dfrac{(z+1)(z+2)}{z(z+3)}\\\\=\dfrac{z(z+2)}{z+3}[/tex]
( since z and (z+1) term is cancelled as it was same in numerator and denominator)
Hence, the product is:
[tex]\dfrac{z(z+2)}{z+3}[/tex] such that: z≠ -1,0 and -3.
Find the next two terms in the sequence. 0, 1, 4, 9, ...
A. 13, 17
B. 13, 18
C. 16, 25
D 16, 23
Answer:
16, 25
Step-by-step explanation:
the next two terms in the sequence. 0, 1, 4, 9, ...
Lets find the difference between the two terms
1-0 = 1
4-1=3
9-4= 5
the terms are increasing by odd numbers
0, 1, 4, 9, ...
\/ \/ \/
+1 +3 +5
The next term will increase by +7
9+7= 16
Next term is 16
Next term will increase by 9
16 + 9 = 25
so , next two terms are 16 and 25
After t years, the amount of money in a savings account that earns simple interest is p + prt, where p is the starting amount and r is the yearly interest rate. factor this expression.
Final answer:
The equation of simple interest p + prt can be factored by taking out the common factor p, resulting in a factored expression of p(1 + rt).
Explanation:
The equation p + prt represents the total amount of money in a savings account after t years when interest is earned at a simple interest rate of r on the principal amount p. To factor this expression, we look for the greatest common factor present in each term. Here, the common factor is the principal amount p.
Therefore, the factored form of the expression is p(1 + rt). This shows that the total amount is composed of the initial principal plus the product of the principal, the rate, and the time.
This differs from compound interest, where the interest earned is added to the principal at each compounding period, leading to interest on interest. Simple interest calculations are straightforward and don't involve this compounding effect, making it simpler to calculate future values manually or using online calculators.
If cats prowl, mice will scatter. Mice are scattering
What is the degree of the polynomial function shown in the graph?
1
2
3
4
The correct answer is
4
:)
for the equation 7x+3y-5=0, find the missing coordinate or the ordered pair so that it is a solution (?,4)
A line segment is different from a line in that a segment has
Each morning Papa notes the birds feeding on his bird feeder. So far this month, he has seen 59 blue jays, 68 black crows, 12 red robins, and 1 cardinal. If 300 birds visit Papa'S bird feeder, how many blue jays can he expect to see?
Will the solution to the following equation be positive or negative? b ÷ -2 = 5
positive
negative
Part A: Sam rented a boat at $225 for 2 days. If he rents the same boat for 5 days, he has to pay a total rent of $480.
Write an equation in the standard form to represent the total rent (y) that Sam has to pay for renting the boat for x days. (4 points)
Part B: Write the equation obtained in Part A using function notation.(2 points)
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)
The position of a particle on the x-axis at time t, t > 0, is s(t) = e^t with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for 0 ≤ t ≤ In3?
3
2/ln3
3/ln3
3/2
Also please just tell me which on it is
The midpoint of UV is (5, -10). The coordinates of one endpoint are U(3,6). Find the coordinates of endpoint V.
How do I use the midpoint formula for this?
( variable son both sides of an equation)
SHOW ALL WORK AND MAKE SURE IT MAKES SENSE
I WILL GIVE BRAINLIEST WITH BEST ANSWER THAT INCLUDES ALL OF THE ABOVE
Solve: 7b-20=3b+12
What does x equal and what does why equal?
1.
x^2 + 6.4^2 = 8^2
x^2 = 40.96 = 64
x^2 = 64 -40.96
x^2 = 23.04
x = sqrt(23.04) = 4.8
2. y=
y^2 + 3^2 = 5^2
y^2 +9 = 25
y^2 = 25-9
y^2 = 16
y = sqrt(16) = 4
Answer:
x^2 + 6.4^2 = 8^2
x^2 = 40.96 = 64
x^2 = 64 -40.96
x^2 = 23.04
x = sqrt(23.04) = 4.8
y=
y^2 + 3^2 = 5^2
y^2 +9 = 25
y^2 = 25-9
y^2 = 16
y = sqrt(16) = 4
what is the limit as x is approaching 0 of the absolute value of x
The restriction of the outright worth of x as x methodologies 0 will be 0. Outright worth guarantees that the result is non-negative, and as x methodologies zero from one or the other side, the outcome stays at 0.
Explanation:The inquiry you're posing relates to the furthest reaches of the outright worth capability as the variable x methodologies are the worth of nothing. In science, explicitly in math, we assess cutoff points to comprehend the way of behaving of capabilities as they approach a specific point.
To track down the breaking point as x methodologies 0 of the outright worth of x, signified as lim x→0 |x|, we want to think about the meaning of outright worth. The outright worth of a number is the non-negative worth of that number regardless of its sign. In this manner, as x methodologies 0 from either the positive or negative side, the outright worth of x will likewise move toward 0.
Consequently, the cutoff is 0, since as x gets increasingly close to nothing, so does the outright worth of x.
a segment has endpoints (a,b) and (c,d). The segment is translated so that its image is 6 units up and 3 units left of the preimage. Are the two segments parallel, perpendicular, or neither?
The translation of the image can be describe as
x – 3
y + 6
Since the transformation that is made is purely translation, therefore this means that the original image and the new image will never intersect and hence:
Parallel
If the two are extended we can actually see that they will never meet.
Dylan's hiking club is planning to stay overnight at a camping Lodge. Each large room can hold 15 hikers. There are 154 hikers. How many rooms will they have?
Jada typically earns 1545 each month of which 47.20 is spent on eletricity. What percent of jadas earnings are spent on eletricity each month
Can someone tell me what these angles are
Identify the 7th term of the geometric sequence in which a2 = 324 and a4 = 36
Answer:
4/3
Step-by-step explanation:
a2 = 324 and a4 = 36
second term is 324 and fourth term is 36
[tex]a_n= a_1(r)^{n-1}[/tex]
To get second term, replace n with 2
[tex]a_2= a_1(r)^{2-1}[/tex]
[tex]a_2= a_1(r)[/tex]
replace a2 with 324
[tex]324= a_1(r)[/tex] -----------> equation 1
To get fourth term , replace n with 4
[tex]a_4= a_1(r)^{4-1}[/tex]
[tex]a_4= a_1(r)^3[/tex]
Replace the value
[tex]36= a_1(r)[/tex] -----------> equation 2
divide second equation by first equation
[tex]36= a_1(r)^3[/tex] divide by [tex]324= a_1(r)[/tex]
1/9 = r^2
take square root on both sides
1/3= r
now we find a1
[tex]324= a_1(r)[/tex]
[tex]324= a_1(\frac{1}{3})[/tex]
multiply by 3 on both sides
972= a_1
So a1= 972, r= 1/3
now find out 7 term by replacing 'n' with 7
[tex]a_7= 972(\frac{1}{3})^{7-1}[/tex]
So 7th term is 4/3
How do you multiply mixed negative number fractions?
What is the value of x?
Enter your answer in the box.
X=
Write an equation of the line, in point-slope form, that passes through points (3,-10) and (-5,-2)
Equation of the line, in point-slope form, that passes through points (3,-10) and (-5,-2) is y + 10 = -(x - 3).
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given it has points (3,-10) and (-5,-2) and we know slope(m)
= (y₂ - y₁)/(x₂ - x₁).
= (-2 + 10)/(-5 - 3).
= 8/-8.
= -1.
Equation of a line in point-slope form is (y - y₁) = m(x - x₁).
y - (-10) = -1(x - 3).
y + 10 = -(x - 3).
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Sean, a freelance editor, charges the rates shown in the table below to edit manuscripts. The cost per page increases as the quality of editing improves. Sean also gives a 5% discount if the entire amount is paid up front.
A 2 column table with Type of Editing and Cost per page as the column headings. Express Proofreading costs 2 dollars, Basic Pro
Michelle has an 85-page manuscript. The equation below shows the relationship between the total cost of editing 85 pages, T, and the cost per page, c, if she gets the 5% discount:
85c − 0.05(85c) = T
Using the equation, what is the best quality of editing that Michelle can get done for a maximum of $161.50?
a.Express proofreading
b.Basic proofreading
c.Extended proofreading
d. Deep editing
Answer:
option (a) Express proof reading
Step-by-step explanation:
Michelle has an 85-page manuscript. To calculate the total cost of printing equation will be
85c - 0.05( 85c ) = T
where c = cost per page and T = total cost on editing 85 pages.
If total cost of editing is $161.50, then we have to find the best quality of editing Michelle can get.
85(c) - (0.05)(85c) = 161.50
85c - 4.25c = 161.50
80.75c = 161.50
⇒ c = $ 2 per page
As it has been given in the question that express proof reading costs $2.00 per page, so the best quality of editing Michelle can get is option (a) Express proof reading
solve for y 3x - 5y = 8
Final answer:
To solve for y in the equation 3x - 5y = 8, we subtract 3x from both sides and then divide by -5, resulting in y = (3/5)x - 8/5.
Explanation:
Solving for y in the equation 3x - 5y = 8
To solve for y in the equation 3x - 5y = 8, we need to isolate y on one side of the equation. Here are the steps:
Start with the original equation: 3x - 5y = 8.
Subtract 3x from both sides of the equation to get -5y = -3x + 8.
Divide each term by -5 to solve for y: y = (3/5)x - 8/5.
So the solution for y in terms of x is y = (3/5)x - 8/5.
Adam draws three parallelograms. He measures the sides of each figure, as shown.
What is a reasonable conjecture for Adam to make by recognizing a pattern and using inductive reasoning?
In a parallelogram, all sides are congruent.
In a parallelogram, opposite sides bisect each other.
In a parallelogram, opposite sides are congruent.
In a parallelogram, all sides bisect each other.
Answer:
In a parallelogram, opposite sides are congruent.
Step-by-step explanation:
Writing the lengths of the sides of the parallelograms shows him a pattern for the side lengths of opposite sides. Doing this will show him that opposite sides are congruent.
Find the constant of variation and the slope of the direct variation model
y=2x
how many lead cubes of side 3cm could be made from a lead of side 27cm
Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros 2+i, 2
Final answer:
To find a polynomial with given zeros 2+i and 2, include the conjugate 2-i to ensure rational coefficients, resulting in the polynomial x^2 - 4x + 3.
Explanation:
Finding a Polynomial with Given Zeros
To find a polynomial function of the lowest degree with rational coefficients that has 2+i and 2 as some of its zeros, you should remember that complex zeros in polynomials with real coefficients come in conjugate pairs. This means that if 2+i is a zero, so is its conjugate 2-i. You now have three zeros: 2, 2+i, and 2-i.
The polynomial with these zeros can be written as (x-2)(x-(2+i))(x-(2-i)). To find the polynomial, we simply multiply these factors:
(x-2)(x-2+i)(x-2)(x-2) - i(x-2)Now add the resulting quadratics:
(x-2)2 - i2This results in:
x2 - 4x + 4 - 1Which simplifies to x2 - 4x + 3. Thus, the required polynomial function of the lowest degree is x2 - 4x + 3.
The perimeter of a rectangle is 102 cm. if the length is 28 cm, how wide is the rectangle?
Aaron bought 132 inches or wire he cut the wire into 9 pieces that were the same lenght what is the length of each piece or wire
The length of each piece of wire is about 14.7 inches.
What is division?Division is the process of dividing a number by a given number.
Given that, the length of the wire is 132 inches.
Now, the wire is cut into 9 equal pieces, therefore, the length of each piece is:
132/9
= 14.7 inches
Hence, the length of each piece of wire is about 14.7 inches.
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