17. Write a rational function in expanded form that satisfies the
following criteria:
• V.A. x=2
• SI.A y =5x-1
• Zero of function (-1,0)

pls help thank you<3

Answers

Answer 1

Answer:

[tex]f(x) = \frac{5x^2 + 4x - 1}{x - 2}[/tex]

Step-by-step explanation:

Given

VA; [tex]x = 2[/tex]

SLA: [tex]y = 5x - 1[/tex]

Zero of function: [tex](-1,0)[/tex]

Required

Determine the rational function in expanded form

Analyzing the vertical asymptote

The vertical asymptote is given as:

[tex]x = 2[/tex]

Subtract 2 from both sides

[tex]x - 2 = 2 - 2[/tex]

[tex]x - 2 = 0[/tex]

This means that the denominator must be [tex]x - 2[/tex]

Analyzing the zero of the function

The zero of the function is given as: [tex](-1,0)[/tex]

This means that [tex]x = -1[/tex], when [tex]y = 0[/tex]

Equate [tex]x = -1[/tex] to 0 by add 1 to both sides

[tex]x + 1 =- 1 + 1[/tex]

[tex]x + 1 =0[/tex]

This means that one of the numerators must be [tex]x + 1[/tex]

Analyzing the slant asymptote:

[tex]y = 5x - 1[/tex]

This means that one of the numerators must be [tex]5x - 1[/tex]

Hence, the function is:

[tex]f(x) = \frac{(5x - 1)(x+1)}{x - 2}[/tex]

Expand the numerator

[tex]f(x) = \frac{5x^2 + 5x - x - 1}{x - 2}[/tex]

[tex]f(x) = \frac{5x^2 + 4x - 1}{x - 2}[/tex]


Related Questions

She needs a little less than 4 pounds to make 12 turkey burgers because 1/3 times 12 is about 3.99 pounds. But she only has 3 3/8 pounds which is about 3.375 pounds.

Answers

Answer:

10 burgers

Step-by-step explanation:

[tex]{3.375pounds}(\frac{12 burgers}{3.99pounds})=(\frac{xburgers}{3.375pounds}){3.375pounds}\\xburgers=10.15\\[/tex]

so you get 10 burgers

or you could approach it

[tex]\frac{3.375}{(1/3)} =[/tex]3.375×3=10.125

On Tuesday, Ashley walked the first dog for 27 minutes, the second dog for 35 minutes, and the third dog for 15 minutes. If she started walking the first dog at 8:00 am, what time did she finish walking all the dogs?

Answers

Answer:

9:17

Step-by-step explanation:

Answer: 9:17 am

Step-by-step explanation: I added all the minutes together and got 77 minutes. Then I simplified the 77 minutes into an hour and 17 minutes. Then I added the 1hour and 17minutes to 8:00 am.

equation with variables on both sides: decimals & fractions 4x + 8 = 7.2 + 5x

Answers

Answer:

4x + 8 = 7.2 + 5x

1. 4x - 4x + 8 = 7.2 + 5x - 4x

2. 8 = 7.2 + x

3. 8 - 7.2 = 7.2 - 7.2 + x

4. 0.8 = x

Step-by-step explanation:

Final Answer: [tex]x = 0.8[/tex]

Steps/Reasons/Explanation:

Question: Equation with variables on both sides: decimals & fractions [tex]4x + 8 = 7.2 + 5x[/tex].

Step 1: Subtract [tex]4x[/tex] from both sides.

[tex]8 = 7.2 + 5x - 4x[/tex]

Step 2: Simplify [tex]7.2 + 5x - 4x[/tex] to [tex]7.2 + x[/tex].

[tex]8 = 7.2 + x[/tex]

Step 3: Subtract [tex]7.2[/tex] from both sides.

[tex]8 - 7.2 = x[/tex]

Step 4: Simplify [tex]8 - 7.2[/tex] to [tex]0.8[/tex].

[tex]0.8 = x[/tex]

Step 5: Switch sides.

[tex]x = 0.8[/tex]

~I hope I helped you :)~

{Stop scrolling} this is not a question but I just wanted you to know that you are doing absolutely amazing and I am extremely proud of you:) Ik school can be stressful but just know that you got this loves <3

I love u ♥️

Answers

Thanks. I’m not struggling or anything but thanks for the kind words.

Answer:

Ty :D

Step-by-step explanation:

School is hard

A cylindrical water tank having radius rcm and height 2rcm has a hemispherical top. if the cylindrical portion can hold 600l water, then how much liters of water can the tank hold.​

Answers

sorry for bad picture

Step-by-step explanation:

hope it helps you have a great day keep smiling be happy stay safe

The following cards are used in a game.If each of the cards is turned over and shuffled

Answers

Answer:

than that means the cards are not turned over

im sorry i didnt really get you question

Step-by-step explanation:

There is 1/2 of a greater chance in drawing a spade over drawing a 7

How to determine the probability?

From the complete question added as an attachment, we have the following parameters:

n(Spade) = 4n(7) = 1Total = 6

The probability of getting a spade is:

P(Spade) = 4/6

The probability of getting a 7 is:

P(7) = 1/6

The difference between both probabilities is:

Difference = 4/6 - 1/6

Evaluate

Difference = 3/6

Simplify

Difference = 1/2

Hence, there is 1/2 of a greater chance in drawing a spade over drawing a 7

Note that the question is incomplete, and the missing part of the question can be found online

Read more about probability at:

https://brainly.com/question/251701

#SPJ2

A towel set consisting of a towel and 6 napkins cost rupees 200 if the cost of each napkin is rupees 95 less than the cost of the towel what is the cost of the towel

Answers

Answer:

The towel costs 110 rupees

Step-by-step explanation:

Let n be napkins, and t be towels. Then:

6n+t=200

and

n=t-95

So:

6(t-95)+t=200

7t-570=200

7t=770

t=110....................

Among the set of towels and napkins, the cost of the towel will be equal to 110 rupees.

What is an expression?

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.

As per the data given in the question,

Assume that n is for napkins, and t is for towels then,

6n + t = 200  (i)

Also,

The cost of the napkin is rupees 95 less than the towel,

n = t - 95 (ii)

Use equations (i) and (ii)

6(t-95)+t=200

7t-570=200

7t=770

t=110

To know more about Expressions:

https://brainly.com/question/14083225

#SPJ5

Can you help me with this i have other questions to if u can't solve this one

Answers

Answer:

I think its -12 and increasing, but i may be wrong. Sry

Step-by-step explanation:

Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!

Answers

Answer :

[tex]\pink{\sf Third \: side \: of \: the \: triangle = 45}[/tex]

Solution :

As, the given triangle is a right angled triangle,

Hence, We can use the Pythagoras' Theorem,

[tex]\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}[/tex]

Here,

H = Hypotenuse of triangleB = Base of triangle P = Perpendicular of triangle

In given triangle,

Base = 24Hypotenuse = 51Perpendicular = ?

Now, by Pythagoras' theorem,

[tex]\star\:{\boxed{\sf{\pink {H^{2} = B^{2} + P^{2}}}}}[/tex]

[tex] \sf : \implies (51)^{2} = (24)^{2} + P^{2}[/tex]

[tex] \sf : \implies 51 \times 51 = 24 \times 24 + P^{2} [/tex]

[tex] \sf : \implies 2601 = 576 + P^{2}[/tex]

[tex] \sf : \implies P^{2} = 2601 - 576[/tex]

[tex] \sf : \implies P^{2} = 2025[/tex]

By squaring both sides :

[tex] \sf \sqrt{P^{2}} = \sqrt{2025}[/tex]

[tex] \sf : \implies P^{2} = \sqrt{2025}[/tex]

[tex] \sf : \implies P^{2} = \sqrt{(45)^{2}}[/tex]

[tex] \sf : \implies P^{2} = 45 [/tex]

[tex]\pink{\sf \therefore \: Third \: side \: of \: the \: triangle \: is \: 45}[/tex]

━━━━━━━━━━━━━━━━━━━━━

calculate the quotient 9/4 divided by 3/8

Answers

Answer:

6

....................................

6 ordhejfhrjdjdjrjdiehe

18. The length of the minor arc AB of a circle,
centre 0, is 27 cm and the length of the major
arc is 221 cm. Find (a) the radius of the circle,
(b) the acute angle AOB.​

Answers

Hope this might help u

Tritan played in a football game he caught the ball at the goal line and ran forward 30 yards before he was tackled how could tristansrun be represented as a fraction and decimal of the whole football field

Answers

Answer:

As a fraction = [tex]\dfrac{30}{100}[/tex]

As a decimal = 0.3

Step-by-step explanation:

Recall that: The total yard of a football field = 100 yards

Tritan played in a football game he caught the ball at the goal line and ran forward 30 yards before he was tackled,

As a fraction;

Tristan run can be represented as = number of run from goal-line/ total length of the field

= [tex]\dfrac{30}{100}[/tex]

As a decimal= 0.3

Choose the best graph that represents the linear equation:
6x = y + 8
Graph A
On a coordinate plane, a line goes through (negative 2, 4) and (0, negative 8).
Graph B
On a coordinate plane, a line goes through (0, negative 8) and (2, 4).
Graph C
On a coordinate plane, a line goes through (negative 2, negative 4) and (0, 8).
Graph D
On a coordinate plane, a line goes through (0, 8) and (2, negative 4).
a.
Graph A
c.
Graph C
b.
Graph B
d.
Graph D

Answers

Graph B



Graph B the person above me got before I did

Given 3m+6n-6 when m=4 and n=3. I need help with this

Answers

Answer: 24

Step-by-step explanation:

Since we are given the value for m and n, we can plug them in and solve the expression.

3(4)+6(3)-6          [multiply]

12+18-6                [add]

30-6                     [subtract]

24

Now, we know the value of the expression is 24.

how do we find the place value of 3a + b given that a=4, b=3, and c=-2

Answers

Answer:

3a+b

3(4)+3

12+3

15

Step-by-step explanation:

You substitute the variables with the given numbers. I think this is correct.

which of the following types of figures may not be a parallelogram?
(1) a rhombus. (3) a square

(2) a trapezoid. (4) a rectangle​

Answers

Answer:

2) a trapezoid

Trapezoids have only one pair of parallel sides; parallelograms have two pairs of parallel sides. A trapezoid can never be a parallelogram.

B
E
A
C
If the length of AC equals 50, what is the length of the midsegment DE?

Answers

If the length of AC equals 50, the length of the midsegment DE is 25.

help me ill mark u brainliest xd

Answers

20 x 42= 840
So the area would be 840 mm^2.
the area would be 840 because you multiply 42 and 20 .

Bill is making accessories for the soccer team. He uses 777.35 inches of fabric on headbands for 32 players and 3 coaches. He also uses 301.76 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?

Answers

Answer:

Fabric used on a headband for each player = 22.21 inches

Fabric used on a wristband for each player = 9.43 inches

Step-by-step explanation:

Let fabric used on each headband = [tex]h[/tex] inches

Let fabric used on each wristband = [tex]w[/tex] inches

Number of players for which headband is made = 32

Fabric used on 32 players = 32[tex]h[/tex] inches

Number of coaches for which headband is made = 3

Fabric used on 3 coaches = 3[tex]h[/tex] inches

As per question statement:

Total fabric used on headbands = 777.35 inches

[tex]32h + 3h = 777.35\\\Rightarrow 35h = 777.35 inches \\\Rightarrow h = 22.21\ inches[/tex]

Number of players for which wristband is made = 32

As per question statement:

Fabric used on wristbands = 301.76 inches

[tex]32w = 301.76\\\Rightarrow w = 9.43\ inches[/tex]

Therefore, the answer is:

Fabric used on a headband for each player = 22.21 inches

Fabric used on a wristband for each player = 9.43 inches

Solve for
x
x/
12
+
1
=
6

Answers

Answer:

x

=

2

1

2

Step-by-step explanation:

Answer:

x = 60

Step-by-step explanation:

x/12 is the same as 1/12x

so now the equation is 1/12x+1=6

then to simplify it even more we do -1 from both sides so

1/12x+1=6

         -1  -1

again the equation is 1/12x=5

then we multiply both sides by 12 and get x = 60

Circumference of the circle

Answers

Answer:

The formula of circumference in a circle is 3.14 times diameter.

Step-by-step explanation:

3.14×20=62.8

The circumference is 62.8

Congruent Triangles and Proofs

Given: JK bisects

Answers

Answer:

Step-by-step explanation:

1S. JM bisects ∠ KJL and  ∠JMK ≅ ∠JML

1R. Given

2S. ∠KJM ≅ ∠LJM

2R. Angle bisectors form ≅ ∠s

3S. JM≅JM

3R. Reflexive Propriety ( segment is ≅ with itself)

4S. ΔJMK ≅ΔJML

4R. ASA theorem of congruency

5S. JK≅JL

5R. Coresponding parts of congruent Δs are congruent (CPCTC)

please help i dont know how to do this

Answers

Answer:

B.

Step-by-step explanation:

jason is filling up a 3/4 gallon pitcher. the one he has to fill it up with is 1/3 of a gallon.

1/3 * x = 3/4

x/3 = 3/4

3 (x/3) = 3 (3/4)

3x/3 = 9/4

x = 9/4

9/4 is 2.25 so the answer is B

Factor completely.
25x2-121

Answers

Assuming you meant x to the 2nd power:

Factor: 25x2−121

25x2−121

=(5x+11)(5x−11)

Answer:

(5x+11)(5x−11)

PLSSSS SOMEONE HELP MEEE IM STUCK the question is below

Answers

Answer:

x=8, y=73/3

Step-by-step explanation:

they ask to solve by substitution so from second equation find y

4x-3y= -41 isolate y

4x+41 = 3y divide both sides by 3

(4x+41)/3= y substitute this y in the first equation

5x+2y = -34

5x+2(4x+41)/3 = -34 distribute and find the common denominator

3*5x+(8x+82)/3 = -34

15x+8x+82=-34*3 cross multiply

23x = -102-82

x=-184/23=8

y=(4*8+41)/3=73/3 is about 24.333..

Find the slope of the line through each pair of points (5, 18), (15, -17)

Answers

Answer:

-3.5

Step-by-step explanation:

Slope of the line

[tex] = \frac{ - 17 - 18}{15 - 5} = \frac{ - 35}{10} = - 3.5 \\ [/tex]

15PTS PLEASE HELP ASAP!
(dont write random answers pls)
look at the pic attached:

Answers

Answer:

a

Step-by-step explanation:

how wide is a poster that has a length of 9/2 feet and area of 45/4​

Answers

Answer:

5/2 is your answer

Step-by-step explanation:

A certain manufacturing plant produces electric fuses of which 20% are defective. Find the probability that in a sample of 8 fuses selected at random there will be atleast one defective and not more than one defective.

Answers

Answer:

0.419

Step-by-step explanation:

To calculate this, we shall make use of Bernoulli approximation of Binomial distribution

if 20% are defective, then 80% are not defective

Probability of selecting a defective fuse is 20/100 = 0.2

Probability of selecting a non defective one is 0.8

Probability of at least 1 being defective is = 1 - Probability of none being defective

Mathematically that will be;

0.8^8 = 0.168

The above is probability of none defective

So the probability of at least one will be

1 - 0.168 = 0.832

Probability of not more than 1 means;

Probability of none + probability of 1 being defective

We already have probability of none above

Probability of 1 being defective means 8 will be non defective

The probability in this case is;

8 C 1 0.2^1 0.8^7

= 8 * 0.2 * 0.8^7 = 0.336

Add this to the probability of none = 0.336 + 0.168 = 0.504

So the probability that we want to calculate from the question will be;

Probability of at least one defective * probability of not more than one defective

= 0.832 * 0.504 = 0.419

One litre of paint covers 1.5 square meters. How many litres must I buy so that I have enough to paint a wall 6 m long and 3 m high ?

Answers

Answer:

12 litres

Step-by-step explanation:

The area to be covered is

A = 6 × 3 = 18 m²

Divide the area by 1.5 for required amount of paint, that is

18 ÷ 1.5 = 12 litres

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