PLease answer !!! Find constants $A$ and $B$ such that \[\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\] for all $x$ such that $x\neq -1$ and $x\neq 2$. Give your answer as the ordered pair $(A,B)$. and Find all values of $t$ such that $\lfloor t\rfloor = 2t + 3$. If you find more than one value, then list the values you find in increasing order, separated by commas.

Answers

Answer 1

Answer:

1. [tex](A,B) = (3,-2)[/tex]

2. The values of t are: -3, -1

Step-by-step explanation:

Given

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}[/tex]

[tex]|t| = 2t + 3[/tex]

Required

Solve for the unknown

Solving [tex]\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}[/tex]

Take LCM

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{(x - 2)(x-1)}[/tex]

Expand the denominator

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - 2x + x -2}[/tex]

[tex]\frac{x + 7}{x^2 - x - 2} = \frac{A(x+1) + B(x-2)}{x^2 - x -2}[/tex]

Both denominators are equal; So, they can cancel out

[tex]x + 7 = A(x+1) + B(x-2)[/tex]

Expand the expression on the right hand side

[tex]x + 7 = Ax + A + Bx - 2B[/tex]

Collect and Group Like Terms

[tex]x + 7 = (Ax + Bx) + (A - 2B)[/tex]

[tex]x + 7 = (A + B)x + (A - 2B)[/tex]

By Direct comparison of the left hand side with the right hand side

[tex](A + B)x = x[/tex]

[tex]A - 2B = 7[/tex]

Divide both sides by x in [tex](A + B)x = x[/tex]

[tex]A + B = 1[/tex]

Make A the subject of formula

[tex]A = 1 - B[/tex]

Substitute 1 - B for A in [tex]A - 2B = 7[/tex]

[tex]1 - B - 2B = 7[/tex]

[tex]1 - 3B = 7[/tex]

Subtract 1 from both sides

[tex]1 - 1 - 3B = 7 - 1[/tex]

[tex]-3B = 6[/tex]

Divide both sides by -3

[tex]B = -2[/tex]

Substitute -2 for B in [tex]A = 1 - B[/tex]

[tex]A = 1 - (-2)[/tex]

[tex]A = 1 + 2[/tex]

[tex]A = 3[/tex]

Hence;

[tex](A,B) = (3,-2)[/tex]

Solving [tex]|t| = 2t + 3[/tex]

Because we're dealing with an absolute function; the possible expressions that can be derived from the above expression are;

[tex]t = 2t + 3[/tex]    and   [tex]-t = 2t + 3[/tex]

Solving [tex]t = 2t + 3[/tex]

Make t the subject of formula

[tex]t - 2t = 3[/tex]

[tex]-t = 3[/tex]

Multiply both sides by -1

[tex]t = -3[/tex]

Solving [tex]-t = 2t + 3[/tex]

Make t the subject of formula

[tex]-t - 2t = 3[/tex]

[tex]-3t = 3[/tex]

Divide both sides by -3

[tex]t = -1[/tex]

Hence, the values of t are: -3, -1

Answer 2
MIKE WAHOUSEKEYYYYYYYY
PLease Answer !!! Find Constants $A$ And $B$ Such That \[\frac{x + 7}{x^2 - X - 2} = \frac{A}{x - 2}

Related Questions

5•1000000 is how many times as large as 5•10000

Answers

Answer:

100 times

Step-by-step explanation:

5•1000000 has 2 more zeros than 5•10000 so that means the first number is 100 times larger than the second number! hope this helps and please mark as brainiest

100 times. Hope this helps you! Good luck

Plsssssss answer this fast guys plssssss

Answers

Answer:You cant get someone to do all of this try doing a few or getting help from someone older that's what I did

I asked help for one problem and the explanation and now I understand how they did it so the other problems I can do now

It's better to make an effort and try doing some of them instead of asking someone to do all of it

Because when the test comes it won't be that easy so next time just try putting a few so that way you can try understanding it and you can apply it to similar problems

Answer:

Don't ask someone to do this if your question is a test

Step-by-step explanation:

Consider that ALMN is similar to APQR and the measure of ZP is 80°. What is the measure of 2L?
A) 20
B) 70
C) 80
D) 90

Answers

Answer:

80°

Step-by-step explanation:

as ALMN is similar to APQR thus L and P are similar too.measure of ZP =80° i.e. 80 ÷2 = 40° for each Z and P.now P =40° (so L =40° ) , then 2L = 2 × 40° = 80°
the answer is c good luck

Use the formula
A = nr2 and find the area of a circle with
radius 5 cm. Use i = 3.14.​

Answers

Answer:

A = 78.5 cm²

Step-by-step explanation:

A = πr²

A = (3.14)(5)²

A = (3.14)(25)

A = 78.5 cm²

The area of the circle with a radius of 5 cm will be 78.5 cm².

Hope that helps.

what they said is very correct

Evaluate 9x*2 y*−2 for x = –3 and y = 2. Answers:

Answers

Answer:

20 and 1/4.

Step-by-step explanation:

9x^2 * y^(-2), for x = -3 and y = 2.

9(-3)^2 * 2^(-2)

= 9 * 9 * (1/4)

= 81 * 1/4

= 81 / 4

= 20.25

= 20 and 1/4.

Hope this helps!

Answer:

Step-by-step explanation:

Let's fill the values in.

9(-3)*2(2)*-2

Using PEMDAS, we would first multiply the two numbers where x and y used to be.

-27 * 4 * -2

Now we would finish multiplying this.

216.

Hope this helps!! <3

The radius of a circle is 6. Using T, which equation expresses the ratio of the circumference of the circle to the circle's diameter?

Answers

Answer:

Option (B)

Step-by-step explanation:

The given question is incomplete; here is the complete question.

The radius of a circle is 6. Using π, which equation expresses the ratio of the circumference of the circle to the circle's diameter?

A) C/6 = π

B) C/12= π

C) C = 6πr

D) C = 12πr

Formula to get the circumference of the circle is,

C = 2πr = π × D

Where C = circumference of the circle

D = Diameter of the circle

By dividing with D on both the sides of the formula,

[tex]\frac{\text{C}}{\text{D}}=\pi[/tex]

Since, diameter 'D' = 2r,

[tex]\frac{\text{C}}{\text{2r}}=\pi[/tex]

[tex]\frac{\text{C}}{2\times 6}=\pi[/tex]

[tex]\frac{\text{C}}{12}=\pi[/tex]

Therefore, equation given in Option (B) will be the correct expression.

122278272662222211111111

Brian and Zach went to Village Grille for lunch. Brian‟s lunch cost $4 less than 3 times Zach‟s. The total cost for lunch was $25. How much did each boy spend on lunch? (Why did Brian eat so much?)

Answers

Answer:

no

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

help can somewon help me plzz

Answers

Answer:

I would say b

Step-by-step explanation:

3 x 10^-4

The answer is most definitely a

C) look at the scale factor for parts a and b. do they represent a reduction or enlargement of the empire state building? How do you know?

Answers

Answer:

Enlargement

Step-by-step explanation

It is enlargement, because it went up by three. Instead of reducing.

We cannot tell the result because the actual size of blocks used for modelling the Empire State Building is not known.

How are scale construction formed?

For a particular scaled construct, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

[tex]\rm 1\: ft : \dfrac{s}{k}\: in.[/tex]

All feet measurements will then be multiplied by s/k to get the corresponding lengths in the constructed scaled structure.

For case a) or b), we used the scale factors as:

1 block : x feet, where x was either 2 or 5 feet.

But we are not specified what size is of the block which is used to model the building.

It may be that block is greater than x feet, or may be smaller. This will decide whether there is enlargement or reduction of the actual building, respectively.

Thus, we cannot tell the result because the actual size of blocks used for modelling the Empire State Building is not known.

Learn more about scale factors here :

https://brainly.com/question/8765466

Jill has two dimes she is going to use to perform a probability experiment. What will the sample space look like if she flips the two dimes simultaneously?

Answers

The Answer is that they will end up on the same side

Jo kept track of how much TV she watched each day for two weeks. How many hours in all did she spend watching TV?

Answers

Answer:

12 1/2 hours

Step-by-step explanation:

This is because (0*1) + (1/4*1) + (1/2*1) + (3/4*3) + (1*3) + (1 1/4*4) + (1 1/2*1) = 12 1/12.

Tonya wants to estimate what proportion of the students in her dormitory like the dorm food. She interviews an SRS of 50 of the
175 students living in the dormitory. She finds that 14 think the dorm food is good.
What is the numerical value of the sample proportion p from Tonya's sample? Round to two decimal places if necessary.
p = ?

Answers

Answer: [tex]\hat{p}=0.28[/tex]

Step-by-step explanation:

Given : Tonya interviews an SRS of 50 of the 175 students living in the dormitory.

i.e. Sample size : n= 50

Number of students think the dorm food is good: x = 14

Now , the numerical value of the sample proportion p from Tonya's sample:

[tex]\hat{p}=\dfrac{x}{n}[/tex]

[tex]=\dfrac{14}{50}=0.28[/tex]

Hence, the numerical value of the sample proportion p from Tonya's sample is 0.28.

i had problems with this too but i believe it’s 0.280

factorise pls answer will mark u the brainliest

Answers

Answer:

3m(1-2m)(1+2m+4m^2)

Step-by-step explanation:

Answer:

3m(1-2m)(4m²+2m+1)

Step-by-step explanation:

3m - 24m⁴   (factorize 3m)

=3m(1) - 3m(8m³)

= 3m (1-8m³)

=3m (1³ - 2³·m³)

=3m [ 1³ - (2m)³ ]

recall the cubic formula:

a³ + b³ = (a+b)(a² - ab + b²)

if we apply this to [ 1³ - (2m)³ ], we will eventually get

= 3m(1-2m)(4m²+2m+1)

edit: last step got cut off. fixed

edit 2: by request, i added more detail to the last 2 steps

The segments shown below could form a triangle.
A. True
B. False

Answers

Answer:

A True

Step-by-step explanation:

B vertices would be the top of an isosceles

As any equal sides can form an isosceles, the measure of the base could be any size and isnt relevant to the triangle unless we are looking for a calculation for its height, which does not determine shape only equation.

Therefore with sides of triangles if they are equal we cna make the shape consist of any length base as long as it measures less than double than either side length.

Therefore a 1cm base does apply and can form a triangle of two equal sides 7cm and 7cm as the diagram asks.

Answer:

true

Step-by-step explanation:

THE reason it true is because on on the lines doesn't equal to the 2 other lines

PLS HELP ME WITH THIS QUESTION I NEED IT QUICK! anything helps..

Answers

Answer:

Graph A

Step-by-step explanation:

if you look at the numbers on the top row they correspond with the left side of the graph and the bottom row of numbers correspond with the bottom of the Graph.

Answer:

Graph A)

Step-by-step explanation:

The first points 20,70 and 30,70 are both plotted correctly on this graph, same with the other points. :)

Matt measures 3 pieces of string. The first piece is 544 cm. The second piece is 144 cm, and the third piece is 112 cm. How many METERS of the string does he have altogether?

Answers

544 cm + 144 cm + 112 cm = 800 cm = 8m

Answer:

8.10

Step-by-step explanation:

1metre =100 centmetres

1st piece is 5.44m

2nd piece is 1.44m

3rd piece is 1.12m

Total length= 8.10m

Solve the following system. y = (1/2)x^2 + 2x - 1 and 3x - y = 1 The solutions are (____)and (______ ) (remember to include the commas)

Answers

Answer:

x=0, 2. y=-1, 5.

Step-by-step explanation:

y=(1/2)x^2+2x-1

3x-y=1

---------------------

3x-y=1

y=3x-1

-----------

(1/2)x^2+2x-1=3x-1

(1/2)x^2+2x-3x-1-(-1)=0

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

(1/2)x^2-x=0

factor out the x

x[(1/2)x-1]=0

zero property,

x=0, (1/2)x-1=0

-------------------

(1/2)x-1=0

1/2x=0+1

1/2x=1

x=1/(1/2)=(1/1)(2/1)=2/1=2

-----------------------------------

x=0, x=2

-------------

y=(1/2)(0)^2+2(0)-1=0+0-1=-1

-------------

y=3(0)-1=0-1=-1

-----------------------

y=(1/2)(2)^2+2(2)-1=(1/2)(4)+4-1=4/2+4-1=2+4-1=6-1=5

----------------------

y=3(2)-1=6-1=5

Answer:

The solutions are (0, -1) and (2, 5)

Step-by-step explanation:

y = (1/2)x^2 + 2x - 1 ------ eqn(I)

3x - y = 1

y = 3x - 1 ------------- eqn(II)

Equate eqn(I) & (II)

(1/2)x^2 + 2x - 1 = 3x - 1

Multiply each term by 2

x^2 + 4x - 2 = 6x - 2

x^2 + 4x - 6x = -2 + 2

x^2 - 2x = 0

x(x - 2) = 0

x = 0, 2

Substitute the values of x in eqn(II)

y = 3x - 1

When x = 0

y = 3(0) - 1 = 0 - 1 = -1

y = 3x - 1

When x = 2

y = 3(2) - 1 = 6 - 1 = 5

The solutions are (0, -1) and (2, 5)

|x−1|, if x>1 Please Help, as soon as possible

Answers

Answer:

 

x = 2  ,  y = 3  ,   z = 1

Step-by-step explanation:

I believe is the answer correct me if wrong

Answer:

x-1

Step-by-step explanation:

|x-1| if x>1. the expression must be positive, therefore you can remove the absolute values without trouble so you get x-1

How did the temperature change if: At first it increased by 25% and then decreased by 40%

Answers

Answer:

24.6 % decrease

Step-by-step explanation:

Let x be the original temperature

Increase by 25%

x + .25x

1.25x

Decrease by 40%

The amount decreased is

(1.25x) *.40

.496x

Subtract that from 1.25x

1.25x - .496x

.754x

We need to find the percent decrease

1 - .754 = .246

24.6 % decrease

Answer:

Temperature decreased by 25%

Step-by-step explanation:

Let initial temperature be t

Step 1

Increase by 25%:

t + 25% = t + 0.25 t = 1.25 t

Step 2

Decrease by 40%:

1.25 t  - 40% = 1.25 t - 0.4 * 1.25 t= 1.25 t - 0.5 t = 0.75 t

Temperature changed from t to 0.75 t

The difference in %:

0.75 t - t = -0.25 t = 25% decrease

Temperature decreased by 25%

22 is 40% of what number? A) 44 B) 55 C) 64 D) 88

Answers

Hey there! I'm happy to help!

When working with percents, the word "is" means "equals". We can use this to make an equation. The decimal form of 40% is 0.4. Our number will be represented by the variable n.

22=0.4n

Flip equation around so n is on the left (you don't have to do this, but I like having the variable on the left)

0.4n=22

We divide both sides by 0.4

n=55

Therefore, your answer is B) 55.

Have a wonderful day! :D

Answer:

55 =x

Step-by-step explanation:

Is means equals and of means multiply

22 = 40% * x

Change to decimal form

22 = .40x

Divide each side by .40

22/.40 = .40x/.40

55 =x

The following dot plot shows the number of books each student checked out from the library last month. Each dot represents a different student. Which of the following is a typical number of books one student checked out?

Answers

Answer:

The answer isn't 1 because most of the students checked out more than 1 bookThe answer isn't 4 because most of the students checked out more than 4 booksThe answer isn't 12 because most of the students checked out fewer than 12 booksThe answer is 7 because most of the students checked out more books than 1, 4, and 12

In 7, seven kids checked out 7. [tex]7*7=49[/tex] (Correct answer because 49 is the biggest number here)

In 1, only two kids checked out 1. [tex]1 *2=2[/tex] (Wrong answer because 2 is lower than 49)

In 4, only eight kids checked out 4. [tex]4*8=32[/tex] (Wrong answer because 32 is lower than 49)

In 12, only two kids checked out 12. [tex]12*2=24[/tex] (Wrong answer because 24 is lower than 49)

So 7 is the correct answer because [tex]7*7=49[/tex] is the greatest equation here.

The 0 and 11 number book is the typical book one student checked out.

Given, the dot plot shows the no. of book  each student checked out from the library last month.

Since each dot represent a different student, so clearly from the dot plot the 8 number book is checked out by the most of the students because it has most of the dots.

Since the number 0 and 11 has only one dot it represent that only 1 student checked out these books last month.

Hence the 0 and 11 number book is the typical book one student checked out.

For more details on dot plot follow the link:

https://brainly.com/question/4398979

Someone pls help . Thank you sm !!

Answers

Answer:

28 = -3k + 7

28 - 7 = -3k

21 = -3k

21/-3 = k

k = -7

1/5  x - 17 = 3

x/5 = 3 + 17

x/5 = 20

x = 5*20

x = 100

82 = 7/10 G + 12

82 - 12 = 7G/10

70 = 7G/10

70*10 = 7G

700 = 7G

700/7 = G

G = 100

The last 2 are 100 I’m not sure about the first one

help me i need help i want help

Answers

It is the second answer.

Answer:

two feet cubed

Step-by-step explanation:

How would you describe the difference between the graphs of f(x) = 2x2 and
g(x) = -2x2 ?

A. g(x) is a reflection of f(x) over the line y=-1.

B. g(x) is a reflection of f(x) over the line y = x.

C. g(x) is a reflection of f(x) over the yaxis.

D. g(x) is a reflection of f(x) over the x-axis.

Answers

Answer:

D. g(x) is a reflection of f(x) over the x-axis.

Step-by-step explanation:

Given

f(x) = 2x²

g(x) = -2x²

Required

Determine the difference between f(x) and g(x)

Start by expanding g(x)

g(x) = -2x²

g(x) = -1 * 2x²

Substitute 2x² for f(x)

g(x) = -1 * f(x)

g(x) = -f(x)

Using the format (x,y):

Take for instance x = 2

f(x) = 2x² = 2 * 2² = 2 * 4 = 8

This means (x,y) = (2,8)

g(x) = -f(x)= -8

This means that (2,-8)

Notice that only the y value changed in both cases from 8 to -8

From the above expression, g(x) = -f(x) and illustration of when x = 2

This implies that g(x) is a reflection of f(x) along the x axis..

From the list of given options, the correct answer is D.

The correct answer is going to be d

PLEASE HELP ME WITH THIS QUESTION FOR HOMEWORK!!!!!!!!!!

Answers

Answer:

Angle MON is equal to 130 degrees.

Step-by-step explanation:

We are told LON is 180 degrees.

Angles LOM and MON are supplementary meaning they add to 180 degrees.

Using this information we know 12x+120=180.

We can use the subtractive property of equality to subtract 120 from both sides.

Do thins we get 12x=60.

Using the division property of equality we can divide both sides by 12 to get x=5.

We can then use the substitution property of equality to get MNO=8(5)+90.

We can then simplify to get MNO=130.

Angle min is 130 degrees

A 20% discount on pants, and its price became 48 after the sale, what was its price before​

Answers

Answer:

$60

Step-by-step explanation:

Represent the original price by p.  Then:  

1.00 p = original price

0.20 p = discount

0.80p = price after discount = $48

Solving for p, we divide both sides by 0.80:

        $48

p = ---------- = $60

        0.80

Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 40 ft to 72 ft Thankyou!! please hurry tho lol

Answers

Answer:

5/9 is the simplest fraction for this ratio

the easiest fraction would be 5/9 because both the numerator and denominator can be divided by 8

Please help me on this question

Answers

Answer:

DE = 13.4 cm  (to 1 decimal place)

Step-by-step explanation:

Given: ABCD is a square

BC = AC = 12 cm    (opposite sides of a square are congruent)

E is midpoint of BC   (given)

BE = EC  = 12/2 = 6 cm

CD = AB = 12 cm   (opposite sides of a square are congruent)

angle ECD is a right angle (interior angles of a square are 90 deg.)

Consider right triangle ECD

DE = sqrt(EC^2+CD^2)    ............. pythagorean theorem

= sqrt(6^2+12^2)

= sqrt ( 36+144 )

= sqrt (180)

= 2 sqrt(45)

= 13.416 (to three dec. places)

How does 4D Shape look like? and, do (4 < n)D are possible?

Answers

It is entirely possible, and it has length, width, height and depth

5D follows it

ANSWER:

4d shape LOOKS LIKE THIS

If -1< y< 0, which of the following has the greatest value?

Answers

Answer:

[tex]\boxed{\sf B}[/tex]

Step-by-step explanation:

-1 < y < 0

The value of y is negative.

Let’s take the number -0.5.

(-0.5)² = 0.25

1 - (-0.5) = 1.5

1 + (-0.5) = 0.5

2(-0.5) = -1

The greatest value is 1.5.

The answer is 1 - y.

B because the greatest one is 1.5 so the answer is 1-y
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