Find the value of A, B and C, given that 2z^2 + z + C = A (z+1)^2 + B (z+1) + 4 for all values of z. Please show the step by step process. :)

Answers

Answer 1

2z² + z + C = A (z + 1)² + B (z + 1) + 4

Expand the right side completely and collect terms with the same power of z :

2z² + z + C = A (z² + 2z + 1) + B (z + 1) + 4

2z² + z + C = Az² + 2Az + A + Bz + B + 4

2z² + z + C = Az² + (2A + B)z + A + B + 4

Now match up terms on either side that have the same power of z. This gives

2 = A ................. (2nd power)

1 = 2A + B ......... (1st power)

C = A + B + 4 .... (0th power)

Solve for A, B, and C. The first equation gives A = 2 right away, so in the second equation we get

1 = 2*2 + B

B = -3

and in the third equation we get

C = 2 + (-3) + 4

C = 3


Related Questions

The variables y and x have a proportional relationship, and y = 25 when x = 60.


What is the value of x when y = 30?

A. x = 25
B. x = 36
C. x = 50
D. X= 72

Answers

Answer:

A

Step-by-step explanation:

A. x = 25

it’s A. x = 25. :) i hope this helped !!

What is the relationship between the constant propprtionality of 50 and 0.02

Answers

Answer:

Inverse Proportionality

Step-by-step explanation:

Given

Constants 50 and 0.02

Required

Determine the relationship

Let y = 0.02

Convert 0.02 to fraction

y = 2/100

Simplify to lowest form

y = 1/50

Recall that y = 0.02

0.02 = 1/50

From the above expression, we can conclude that the relationship between both is inverse.

In other words, 50 and 0.02 are inversely proportional


What value of x is in the solution set of 8x-6 > 12 + 2x?
3
5

Answers

yes u are correct i believe

Mrs. Simon is teaching a 5th grade class. She is standing 6 meters in front of Britney. Lisa is sitting to Britney's right. If Lisa and Mrs. Simon are 10 meters apart, how far apart are Britney and Lisa?​

Answers

Answer:

they are 4 meters apart from each other i think im not so sure

They’re 4 meters apart. You would subtract 10 from 6 to get 4.

Can a decimal that has repeating digits after the decimal point be converted into a fraction?

Answers

Answer:

yes, because you need to convert the repeating number into a decimal. In this case, you can assume that x is the fraction form of 0.7 repeating.

Answer:

yes I think so ...................

Simplify the expression given below x^2 + x-2

Answers

X^2+x-2
Pls mark brainliest

Please help what is -0.5 divided by -1/5

Answers

-0.5 divided by -1/5 is 0.1

-5x + 9 = -3x + 1 solve the equation

Answers

Answer:

x=4

Step-by-step explanation:

Step 1: Add 3x to both sides.

−5x+9+3x=−3x+1+3x

−2x+9=1

Step 2: Subtract 9 from both sides.

−2x+9−9=1−9

−2x=−8

Step 3: Divide both sides by -2.

−2x/−2=−8/−2

Which of the following statement is false? 8 < 8 2>8 2<8 2<8 2<8

Answers

Answer:

8<8

2>8

Step-by-step explanation:

yw:))

Solve.
x^2 + 4 = 0.

Answers

Answer:

No real solutions

Step-by-step explanation:

You use the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a where y = ax^2 + bx + c

b is 0, a is 1, and c is 4.

-0 ± √(0^2 − 4 x 1 x 4)/ 2(1)

±√(-16)/2

Split √(-16) into √(16) and √(-1).

Now, i = √-1

So you get ±√(-16) = ±4i.

The original equation was ±√(-16)/2.

±4i / 2 = ±2i

The answer is x = ±2i

(Note: ± means positive or negative)

Find the slope of the line that is perpendicular to the graph of the equation y-4x=1

Answers

Answer:

y=-1/4x+1

Step-by-step explanation:

Ava read an article claiming that 10% of people in her county were senior citizens, and she wondered if this held true for residents in her city. She took a random sample of 225 people from her city to test H0 : p = 0.10, where p is the proportion of people in her city that are senior citizens. Ava found that approximately 14% of those sampled were senior citizens. She conducted an appropriate significance test, and the resulting test statistic was z ≈ 1.89z. Assume that the conditions for inference were met.

Answers

Complete Question

Ava read an article claiming that 10% of people in her county were senior citizens, and she wondered if this held true for residents in her city. She took a random sample of 225 people from her city to test H0 : p = 0.10, where p is the proportion of people in her city that are senior citizens. Ava found that approximately 14% of those sampled were senior citizens. She conducted an appropriate significance test, and the resulting test statistic was z ≈ 1.89 z. Assume that the conditions for inference were met.calculate the p-value for Ellie's significance test

Answer:

The p-value is  [tex]p-value  = 0.0588[/tex]

Step-by-step explanation:

From the question we are told that

   The percentage of senior citizens is  p =  0.10  

   The sample size is  [tex]n  =  225[/tex]

   The  sample proportion is  [tex]\^{p} =  0.14[/tex]

   The test statistics is  [tex] z \approx =   1.89[/tex]

The null hypothesis  is  [tex]H_o  :  p = 0.10[/tex]

The alternative hypothesis is   [tex]H_a  :  p \ne 0.10[/tex]

   Generally the p-value is mathematically represented as

       [tex]p-value  =  2 *  P(Z > 1.89 )[/tex]

From the z-table  

       [tex]P(Z > 1.89 )  =   0.029379[/tex]

=>     [tex]p-value  =  2 *   0.029379[/tex]

=>     [tex]p-value  = 0.0588[/tex]

Answer:

No because 0.06>0.05

Step-by-step explanation:

kahn

20 points
A parallelogram has one pair of parallel sides.

True or false

If a quadrilateral is a rectangle then it is also a square. *
True or False

A parallelogram always has four congruent sides.
True or False

If a quadrilateral is a square then it is also a rectangle. *
True or False

If a quadrilateral is a trapezoid then it is also a parallelogram.

True or False

Answers

Answer: true

Step-by-step explanation:

Step-by-step explanation:

"A parallelogram has one pair of parallel sides."

False.  A parallelogram has two pairs of parallel sides.

"If a quadrilateral is a rectangle then it is also a square."

False.  A rectangle isn't necessarily a square.  Rectangles are only squares when all four sides are equal.

"A parallelogram always has four congruent sides."

False.  Parallelograms have two pairs of congruent sides.  All four sides aren't necessarily congruent.

"If a quadrilateral is a square then it is also a rectangle."

True.  All squares are rectangles.

"If a quadrilateral is a trapezoid then it is also a parallelogram."

False.  Trapezoids have only 1 pair of parallel sides, and parallelograms have 2 pairs of parallel sides.

Use partial quotients to divide. Show your work.
)
​___ group(s) of
​___ group(s) of
​___ group(s) of
0
Add the partial quotients.

Answers

I need more information on what I'm meant to be doing so I can help you because I don't understand the question after I re-read it over and over again.

whats 8 more than the product of X and 8

Answers

Answer:

8X +8

Step-by-step explanation:

I believe the answer is 8x+8

Pls help i dont understand :( will give Brainliest + 25 Points

Answers

Answer:

D

Step-by-step explanation:

Find the slope using the formula [ y2-y1/x2-x1 ]

2-2/-5-3

0/-8

0

Find the y-intercept using slope-intercept form [ y = mx + b ] and (3, 2)

y = 0x + b

2 = 0(3) + b

2 = b

Put everything we know into the final form.

y = 0x + 2

y = 2

Best of Luck!

change in y/change in x

y2-y1/x2-x1

2-2/-5-3

0/-8 = 0

The slope is 0 - the answer is d

because when 0x = 0, then you are left with y and only y

when the equation is x=, then the equation is undefined

but, when an equation is y=, that the slope is 0

17. Create an equation that requires distribution on both sides to solve and has a solution of -2.

Answers

Answer:

googl really helps sorry

Find the product, using suitable properties:
437 * (-45) + (- 437) × 55​

Answers

The answer is -4300
That’s the answer

what is 6 1/4 divided by 6 1/2?

Answers

So uh this came up , I hope this helps

multiple and divide signed numbers​

Answers

Answer:

Step-by-step explanation:

Multiply answer = - 106

Divide answer = 1.25

1) Two pieces of a pole arle cut into 5 inches each from an original pole that was 20 inches
long. What is the length of the remaining part of the 20 inch pole?
HELP Please

Answers

Answer:

it is 10 because 5x2= 10and20-10=10

what is 7 - 4 = 5x - 13

Answers

Answer:

x=16/5

Step-by-step explanation:

7-4=5x-13

3=5x-13

+13.  +13

16=5x

16/5 = x

what is the area of a rectangles with the side lengths 5 inches and 4/3 inches?​

Answers

Answer: 20/3 square inches

Step-by-step explanation:

Area = length*width

length = 5 in.

width = 4/3 in.

A = 5 * (4/3) = 20/3 in^2

Line a is parallel to line t solve for x

Answers

Answer:

Sorry dude, I need more context. Can you write out the full equation if there's more? Sorry.

Step-by-step explanation:

If you double 4 and if you double 1/2 then add 1, add 8 +1

Answers

Answer:

19?

Step-by-step explanation:

double of 4 is 8, double of 1/2 is 1 and adding them all together is 19

You never scale down to write a complex rate as a unit rate. True or false?

Answers

Answer:

True

Step-by-step explanation:

We should use simple units while doing any type of calculation, using simple units make it easy for other people to kn ow the calculation, on the contrary if we use complex units then it will make the calculation more complicated thereby increasing the chances of mistake.

Jane rented a movie. She started the movie at 11:42 PM, and it was 2 hours 47 minutes long. When did the movie end?

Answers

I think it would be 2:29
The answer would be 2:29am.

how many inconsiderate people take up space in this world?

Answers

Answer:

Too many :(

Step-by-step explanation:

Its life u know

can i pls have brainliest

Answer:

that number is probably too high to count, don't ya think

3(2h + 7) = 4(9 – h)

Answers

Answer:

h=−2

Step-by-step explanation:

Brenda has to remote controlled race cars painted red and blue. The red car travel 38 feet in two seconds. The blue car traveled 54 feet in four seconds. Which car was faster and by how much

Answers

The red car was faster by 11 feet
To make them even so we compare, divide 54 by 2
So,
: 27 feet in 2 seconds
: 38 feet in 2 seconds
Next, subtract
38 - 27 = 11
So, the red car was faster by 11 feet
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