givin the standard form for a trinomial ax^2+bx+c, and factored form (px+r)(qx+s) match the following:
a=
b=
c=
to
(p*s)+(q*r)
r*s
p*q

Answers

Answer 1

Answer:

[tex]a = p*q\\b = (p*s)+(q*r)\\c = r*s[/tex]

Step-by-step explanation:

We are given the standard form of trinomial

[tex]ax^2+bx+c[/tex]

After factorization, the form is:

[tex](px+r)(qx+s)[/tex]

We have to compare the factored form and the standard form to find the values of a,b and c in terms of p,q,r and s. For this purpose, the factored form will be converted into standard form.

Multiplying the both factors

[tex](px+r)(qx+s)\\=px(qx+s)+r(qx+s)\\= pqx^2+psx+qrx+rs\\= pqx^2+(ps+qr)x+rs[/tex]

Comparing both forms with each other

After comparing

[tex]a = pq = p*q\\b = ps+qr = (p*s)+(q*r)\\c = rs = r*s[/tex]

Hence,

[tex]a = p*q\\b = (p*s)+(q*r)\\c = r*s[/tex]


Related Questions

Aaron is bicycling on a bike trail at an average of 10 miles per hour. Jada starts cycling on the same trail 30 minutes later. If Jada averages 16 miles per hour, how long would it take her to pass Aaron?

Answers

Answer:

36 miles per hour

Step-by-step explanation:

36 miles per hour

Solve each proportion.

5/2=6/x

Wat is x

Answers

Answer:

12/5

Step-by-step explanation:

5/2 = 6/x

in order to solve for x, you can do cross multiplication hence,

5x = 6(2)

x = 12/5

Answer:

12/5

Step-by-step explanation:

5/2=6/x

5x=12

X=12/5.

So the answer is 12/5

The Empire State Building in New York City is 1,454 feet tall. The observatory on the 86th floor is 404 feet from the top of the building. How high is the observatory above ground?

Answers

Answer:

1,050 feet

Step-by-step explanation:

All you have to do is take the total height 1,454 and subtract the distance from the top to the 86th floor. 1,454-404 which gives you 1,050.

PLLLLSSS HELLPP
Use the substitution method to solve the system of equations.
8x + 5y = 9
y = x + 7

Answers

Answer:

point form: (-2,5)

Step-by-step explanation:

8x + 5y = 9

y = x + 7

sub. y into the first one

8x + 5(x + 7) = 9

8x + 5x + 35 = 9

13x + 35 = 9

solve for x

13x = -26

x = -2

solve for y

y = x + 7

y = -2 + 7

y = 5

Answer: I believe the answer would be (-2, 5) Hope this helped!

Joe has 80 video games and ally has 3 times as many.
How many video games do they have in all?

Answers

Answer: First we multiply 80 by 3 which gives us 240, then we add the initial 80 that Joe has, which gives us a total of 320 video games. So, they have 320 video games in all.

Answer:

320

Step-by-step explanation:

joe has 80 three times eighty is 240 so they have 240+80=320 so they have 320 games in total

Jayvie has a VIP membership to a movie theater, so she pays $27 a year and $6.00 for each movie she sees. Claire doesn't have a membership, so she pays $8.25 each movie she sees. Which equation shows when they will pay the same amount of money?

Answers

Answer:

27 + 6x = 8.25x

Number of movies (x) = 12

Step-by-step explanation:

Given that:

VIP membership :

Membership fee = $27 per year

Amount per movie = $6

Hence ;

Membership fee + (amount per movie * number of movies)

27 + 6x - - - (1)

Non member :

Amount paid per movie = $8.25

amount per movie * number of movies)

8.25x - - (2)

Let Numbe of movies = x

In other to pay the same amount of money :

Equate (1) and (2)

Equation :

27 + 6x = 8.25x

8.25x - 6x = 27

2.25x = 27

X = 12 movies

PLEASE help me I’m failing !! Leonard wants to buy some snacks at the FFA snack machine. He has $5.00 on
him and he wants to buy 2 beef sticks (.50 apiece), 2 crackers and cheese (.75
apiece) and 2 chocolate milks ($1.00 apiece). How much change will he get back?

Answers

Answer:

He will have 0.50 chage back

Step-by-step explanation:

Answer:

.50 cents

Step-by-step explanation:

2 beef sticks price will add to $1. 2 crackers of cheese add to $1.50. And 2 chocolate milks add to $2. Now add them all and you will get .50 cents

I NEED HELP . I'm having trouble trying to figure out how to answer this can anyone help please?

Answers

Answer:

what is it?

Step-by-step explanation:

You spin the spinner twice.
What is the probability of landing on a 4 and then landing on a number less than 4?
Write your answer as a fraction or whole number.
Submit

Answers

Answer:

landing on a 4 would be 1/3 chance

and

landing on a number less than 4 would be 2/3 chance

Step-by-step explanation:

The probability of landing on a 4 is 1/3 and then landing on a number less than 4 is 2/3.

What is probability?

Probability is the chance of happening an event or incident.

The probability of landing on a 4 is 1/3.

Then, the probability on landing on a number less than 4 = 2/3.

Learn more about probability here: https://brainly.com/question/11234923

#Tag #SPJ2

There were 5 boys for every 8 girls at Foster High School last year. If there were 390 students at the school, how many were girls and how many were boys?​

Answers

Answer:

it would be 150 boys and 240 girls

Step-by-step explanation:

a que vista del solido corresponde la figura 2

Answers

Donde esta la foto para poder ayudarte ??

¿Dónde está la pregunta que estás haciendo? No veo opciones, amigo.

Simon wants to build a cube-shaped storage container that holds 125 cubic feet of water for some frogs he recently purchased.Using the formula, V=s3, where represents the volume of the container and represents its side length, find the length of one side of the container.

Answers

Answer:

Length of one side of the container = 5 feet

Step-by-step explanation:

Given:

V = s³

Where,

V = volume of the container

s = side length of the container

V = 125 cubic feet

Find s?

V = s³

125 = s³

Find the cube root of both sides

3√125 = 3√s³

5 = s

s = 5 feet

Length of one side of the container = 5 feet

What is the quotient? -3/8 divided by -1/4

Answers

-3/8= -0.375
-0.375/-.25 = 1.5
Answer: 1.5
Answer is 1.5 because it is b

Last one , will mark brainliest !!!!

Answers

Answer:

Step-by-step explanation:

Part 1:y=426x+4298

        y=223x+6129

Part 2: x=9.020 (x is the number of months and y is the miles)

Part 3: y=8140.394, or 8,140 since it's rounding to the nearest mile

Answer:

See answers in explanation below

Step-by-step explanation:

1.   4298 + 426t = 6129 + 223t

2. Basically get into the graphing page and find "function" section then select "f(x) = mx + b", then graph f(x) = 426x + 4298 and f(x) = 223x + 6129

and find the answer at where these two lines intersect with each other, x=9.0197 (months)

3. sub x=9.0197 into any of the two equation and f(x) = 8140 (miles)

what does x= but it has to equal 10​

Answers

Answer:

No solutions.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Step-by-step explanation:

Step 1: Define equation

-2(4 - 3x) - 6x = 10

Step 2: Solve for x

Distribute -2:                    -8 + 6x - 6x = 10Combine like terms:        -8 ≠ 10

Here we see that -8 does not equal 10.

∴ This equation has no solutions.

Last one plsssssssssss help

Answers

Add 5 to both sides and then multiply by 21 to eliminate fraction

I need help!
Comepare each pair of fractions using Greater than sign , less than sign and equal to.

Answers

Answer:

<< >> >=>= =>=< >><< ><<< >>==

Step-by-step explanation:

Answer:

>,>,>,>

>,>,>,<

<,>,<,>

>,<,<,<

=,=,=,<

Can someone please help me it’s due in a few minutes.

Answers

Answer:

150

Step-by-step explanation:

go submit it

Brantley tosses a ball out of a window that is 75 feet in the air. Its initial velocity is 12 feet per second. The path of the ball is represented by h=-16t^2+12t+75. How long does it take for the ball to hit the ground to the nearest hundredth?

Answers

Answer:

[tex]t = 2.57[/tex]

Step-by-step explanation:

Given

[tex]h=-16t^2+12t+75[/tex]

Required

Determine the time to hit the ground

The ground is at point 0.

So, to solve this; we simply set [tex]h =0[/tex], then calculate the value of t

[tex]0=-16t^2+12t+75[/tex]

Multiply through by -1

[tex]0=16t^2-12t-75[/tex]

Reorder

[tex]16t^2-12t-75 = 0[/tex]

Solve using quadratic formula:

[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]

Where

[tex]a = 16; b = -12; c = -75[/tex]

[tex]t = \frac{-(-12)\±\sqrt{(-12)^2 - 4*16*(-75)}}{2*16}[/tex]

[tex]t = \frac{12\±\sqrt{144 +4800}}{32}[/tex]

[tex]t = \frac{12\±\sqrt{4944}}{32}[/tex]

[tex]t = \frac{12\±70.31}{32}[/tex]

Split:

[tex]t = \frac{12+70.31}{32}[/tex] or [tex]t = \frac{12-70.31}{32}[/tex]

[tex]t = \frac{82.31}{32}[/tex] or [tex]t = \frac{-58.31}{32}[/tex]

But time (t) can't be negative;

So, we make use of only

[tex]t = \frac{82.31}{32}[/tex]

[tex]t = 2.57[/tex]

Hence, the time to hit the ground is 2.57 seconds

what is 2² of 36
you can use google or a calculator

Answers

Answer is 144 my dude

it's tooo easy

answer -1296

Jae is constructing an open box from a piece of cardboard that is 9 in. Wide and 12 in. Long. Jae cuts squares of equal size from each corner of the cardboard, and then folds up the sides of the box. Write and simplify a polynomial function V for the volume of the box in terms of x.

Answers

Answer:

The volume of the open box is [tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}\,\,\,[in^{3}][/tex].

Step-by-step explanation:

Geometrically speaking, the volume of the open box ([tex]V[/tex]), measured in cubic inches, is described by the volume of a right parellelepiped. That is:

[tex]V = w\cdot l \cdot h[/tex] (1)

Where [tex]w[/tex], [tex]l[/tex] and [tex]h[/tex] are the width, length and height of the open box, respectively, measured in inches. Please notice that width of the open box is the width of the piece of cardboard ([tex]w'[/tex]), measured in inches, minus two times the side of the cut squares ([tex]x[/tex]), measured in inches, length of the open box is the length of the piece of cardboard ([tex]l'[/tex]), measured in inches, minus two times the side of the cut squares and the height of the open box is the side of the cut squares. That is:

[tex]w = w' -2\cdot x[/tex] (2)

[tex]l = l' - 2\cdot x[/tex] (3)

[tex]h = x[/tex] (4)

By applying (2), (3), (4) in (1), we expand and simplify the volume function:

[tex]V = (w'-2\cdot x)\cdot (l'-2\cdot x)\cdot x[/tex] (5)

If we know that [tex]w' = 9\,in[/tex] and [tex]l' = 12\,in[/tex], then the equation above is:

[tex]V = (9-2\cdot x)\cdot (12-2\cdot x)\cdot x\,\,\,[in^{3}][/tex]

[tex]V = (108-24\cdot x-18\cdot x+4\cdot x^{2})\cdot x\,\,\,[in^{3}][/tex]

[tex]V = (108-42\cdot x +4\cdot x^{2})\cdot x \,\,\,[in^{3}][/tex]

[tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}\,\,\,[in^{3}][/tex]

The volume of the open box is [tex]V = 108\cdot x -42\cdot x^{2}+4\cdot x^{3}\,\,\,[in^{3}][/tex].

Tom has a fair spinner with six sides. They are labelled red, red, blue, green, red, blue. Choose the word that best describes the likelihood that the spinner will land on a colour not green.

Answers

Answer:

It is MOST LIKELY NOT going to land on green.

Step-by-step explanation:

Since the spinner has 6 sides, the total possible outcome is 6. There are 3 reds, 2 blues and 1 green.

The probability that the spinner will land on a green is [tex]\frac{1}{6}[/tex]. But since we are looking for the probability that it won't land on green, we have [tex]1 $-$ \frac{1}{6} = \frac{5}{6}[/tex]

From here we can best describe the likelihood that the spinner will land on a colour not green as: it is MOST LIKELY NOT going to land on green

can someone help me with thiis?

Answers

I believe the expression would be 7(g)+7

Madison is a high school basketball player. How many points would Madison score in a game if she made 8 free throws (worth one point each) and 6 three point shots?

How many points would Madison score in a game if she made x free throws and y
three point shots?

Answers

Answer:

26  and 1x+3y   on Delta math

Step-by-step explanation:

Explanation:

Each free throw scores 1 point, so 8 free throws would score 1\times 81×8 or 8 points. Each three point shot scores 3 points, so 6 three point shots would score 3\times 63×6 or 18 points. Therefore, the total number of points Madison would score is 26.

Answer:

3?

Step-by-step explanation:

Please help its7to10 it’s easy but I’m lazy

Answers

Answer:

sure

Step-by-step explanation:

Hi, this isn't a math question or anything. But I have a question about high schools. So I have all A's for my first marking period and one C for an enirchnment. But do you think I could get into a good high school like Central? Also, I'm not taking the PSSA or big tests. Also, I'm in 7th grade if your wondering.

Answers

Answer:

Depends on your GPA

Step-by-step explanation:

De acuerdo con una encuesta se determino que en una region hay igual numero de personas lic en administracion comercio servicio de salud y servicio municipal ademas se encontro que 35% de los administrativos 25% de los comerciantes 20% de los servidores de salud y 15% de servicio municipal son mujeres cual es la probabilidad de que una mujer escogida al azar del grupo sea administradora

Answers

Answer:

La probabilidad de que una mujer sea administradora es de 0,35

Step-by-step explanation:

Sean A B, C y D los eventos de las mujeres administrativas, comerciantes, trabajadoras de salud y proveedoras de servicios municipales.

Sus probabilidades están dadas por

P (a) = 35% = 0,35

P (b) = 25% = 0,25

P (c) = 20% = 0,2

P (d) = 15% = 0,15

Como los eventos son independientes, la probabilidad conjunta sería

P (B∩C∩D) = P (D) * P (B) * P (C) = 0.25 * 0.2 * 0.15 = 0.0075

P (A / B∩C∩D) = P (A∩B∩C∩D) / P (B∩C∩D)

                        = 0,35 * 0,0075 / 0,0075 = 0,35

Por lo tanto, la probabilidad condicional de obtener la mujer administradora es la misma que la probabilidad individual de obtener la administradora, ya que los eventos son independientes.

La probabilidad de que una mujer sea administradora es de 0,35

English

Let A B, C and D be the events of the women administrative, merchants, health workers and municipal services providers.

Their probabilities are given by

P (a) = 35% = 0.35

P (b)= 25% = 0.25

P (c) =20% = 0.2

P (d) = 15 % = 0.15

As the events are independent then the joint probability would be

P (B∩C∩D)= P(D) * P(B)* P (C) = 0.25* 0.2*0.15= 0.0075

P(A/B∩C∩D) = P(A∩B∩C∩D)/P(B∩C∩D)

                        = 0.35*0.0075/ 0.0075= 0.35

Therefore the conditional probability of getting the administrator woman is the same as the individual probability of getting the woman administrator  as the events are independent.

Probability of woman administrator is 0.35

What are the factors of 7x2 + 25x – 12?

Answers

Answer:

Simplify the expression.

25

x

+

2

Step-by-step explanation:

Answer:

(7x-3)(x+4)

Step-by-step explanation:

hope this helps:)

What are three inequalities equal to 15x+20y=150?

Answers

Answer:

1. 3x+4y=30

2. 30x+40y=300

3. x+4/3y=10

Step-by-step explanation:

Identify the polynomial divisor, dividend, and quotient represented by the synthetic division.

Divisor:
A. –3
B. 3
C. x – 3
D. x + 3

Dividend:
A. 2x3 + 11x2 + 18x + 9
B. -6x3 - 15x - 9
C. 2x2 + 5x + 3

Quotient:
A. 2x4 + 11x3 + 18x + 9
B. 2x3 + 5x2 + 3x
C. 2x2 + 5x + 3

Answers

Answer:

Divisor:D

Divedend: A

Quotient:C

Step-by-step explanation:

The divisor = (x+3), the dividend = (2x³+11x²+18x+9) and the quotient = (2x²+5x+3)

What is synthetic division?

Synthetic division is a method for manually performing Euclidean division of polynomials.

Given that polynomial divisor, dividend and quotient ;

The correct divisor, dividend and quotient are (x+3), (2x³+11x²+18x+9) and (2x²+5x+3) respectively

Hence, The divisor = (x+3), the dividend = (2x³+11x²+18x+9) and the quotient = (2x²+5x+3)

For more references on Synthetic division, click;

https://brainly.com/question/28824872

#SPJ2

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