Expand the following using the Binomial Theorem and Pascal’s triangle (2x − 3y)^4

Answers

Answer 1

Answer:

Step-by-step explanation:

Binomial Expansion:

[tex](2x-3y)^4 \\\\= 4C_0(2x)^4 (-3y)^0 + 4C_1(2x)^3 (-3y)^1 + 4C_2(2x)^2(-3y)^2 \\\\+ 4C_3(2x)^1 (-3y)^3 + 4C_4(2x)^0 (-3y)^4\\\\=16x^4 + 4(8x^3)(-3y) + 6(4x^2)(9y^2) + 4(2x)(-27y^3) + 81y^4\\\\=16x^4 - 96x^3y + 216x^2y^2-216xy^3 +81y^4[/tex]

Pascal's Triangle:

  Zero row                        1

 First row                  1                 1

 Second row          1           2             1

 Third  row         1         3              3          1

 Fourth row    1       4            6           4          1


Related Questions

On the last math test in Kenzie’s class, 17 out of 25 students scored an 80 or higher. Which percent is closest to the experimental probability that a student selected at random will score an 80 or higher on the next test?

Answers

Answer

There is a 68 percent that a student selected a random will score an 80 or higher on the next test.

Explanation

You just need to find the percentage of 17 out of 25, or 17/25.

You can do this by dividing 17 by 25.

17/25 equals 0.68, or 68 percent.

if f(r)= 3.14 r^2 what is f(3)

Answers

Answer:

f(3) = 28.26

Step-by-step explanation:

Substitute r = 3 into f(r) , that is

f(3) = 3.14 × 3² = 3.14 × 9 = 28.26

The first and last term of an A. P are 1 and 121 respectively. Find the number of terms in the A.P and the common difference between them if the sum of the term is 1281​

Answers

Answer:

No.of terms=21

Common difference=6

Someone pls help me ill give out brainliest pls don’t answer if you don’t know

Answers

Answer:

Step-by-step explanation:

The area of a sector has the formula

[tex]A_s=\frac{\theta}{360}*\pi r^2[/tex] Hopefully, this looks somewhat familiar to you. Theta is the central angle given as 75, r is the radius given as 4. Filling in:

[tex]A_s=\frac{75}{360}*(3.14)(4)^2[/tex] and simplifying that a bit to look less threatening, but not by much:

[tex]A_s=\frac{5}{24}(3.14)(16)[/tex] and

[tex]A_s=\frac{251.2}{24}=\frac{157}{15}=10.466666666...[/tex] Not sure how you're supposed to express your answer so I gave both the fraction and its decimal equivalency.

use the diagram to compute the perimeter and area of the triangle.​

Answers

Answer:

The area is 22.5 units

The perimeter is 24.3 units

Step-by-step explanation:

The formula for the area of a triangle is A=bh(1/2)

So, base*height (5*9) is 45. Divide that by 2, and you get 22.5.

To find the perimeter, it looks like the triangle is a right triangle. To solve for that, use the Pythagorean theorem formula: a2 + b2 = c2.

5^2+9^2=c^2

25+81=106=c^2

Find the square root of 106

10.2956301

If your teacher usually asks to round, round.

I'll just round to the tenths place. 10.3

Add all the sides: 5+9+10.3

You get 24.3

Answer:

perimeter= 24.29

area=22.5

Step-by-step explanation:

a^2+b^2=c^2

5^2+9^2=106

106^(1/2)=10.29

perimeter= sum of all sides

""= 5+9+10.29

""=22.29

area= base × height ÷ 2

""= (5×9)÷2

""=22.5

If copies of all your computer data are stored on four independent hard disk​ drives, what is the probability that during a​ year, you can avoid catastrophe with at least one working​ drive? With four hard disk​ drives, the probability that catastrophe can be avoided is

Answers

Answer:

[tex]P(Atleast\ 1) = 0.9999992[/tex]

Step-by-step explanation:

Given

[tex]p = 3\%[/tex] --- rate of hard disk drives failure

[tex]n = 4[/tex] --- number of hard disk drives

See comment for complete question

Required

[tex]P(Atleast\ 1)[/tex]

First, calculate the probability that the none of the 4 selected is working;

[tex]P(none) = p^4[/tex]

[tex]P(none) = (3\%)^4[/tex]

[tex]P(none) = (0.03)^4[/tex]

Using the complement rule, the probability that at least 1 is working is:

[tex]P(Atleast\ 1) = 1 - P(none)[/tex]

This gives:

[tex]P(Atleast\ 1) = 1 - 0.03^4[/tex]

[tex]P(Atleast\ 1) = 0.9999992[/tex]

Please answer this to the best of your ability

Answers

Answer:

For this exercise we need to solve the next equation:

3 +6x = 2x + 27

We can start substracting 3 at both sides:

3 + 6x - 2 = 2x + 27 - 3

6x = 2x + 25

And then, we can substract 2x::

6x - 2x = 2x + 24 - 2x

4x = 25

Then, we divide by 4:

4x/4 = 24/4

x = 24/4 = 6

Now, we can see if we have done it correctly:

3 + 6*6 = 39

2 * 6 + 27 = 39

And we have seen our result is correct

Multiply the polynomial by distribution. Show your work and explain the steps you used to solve.
(a – 3)(a2 + 2a – 6)



help please

Answers

Hello,

Why "Multiply the polynomial by distribution"  ?

It's s t u p i d, you compliquate the equation.

In order to find the roots of P(a)=(a-3)(a²+2a-6)=0

a²+2a-6

=(a²+2a+1)-7

=(a+1)²-7

=(a-√7)(a+√7)

P(a)=(a-3)(a-√7)(a+√7)

Roots are 3,√7 and -√7

(If i have well understood the question , sorry if not)

hallar "x"
...................................

Answers

X = 22o

30 + 20 + 3x + 20 + 2x = 180
=> x = 110/5 = 22

Un par de zapatos más dos pantalones valen $ 70.000 en una tienda. Se ofrece una oferta, al comprar dos o más pares de zapatos del mismo precio se descuenta un 10% en cada par y por tres o más pantalones del mismo precio un 15% en cada pantalón. Juan paga por tres pantalones $ 38.250 y luego, compra dos pares de zapatos. ¿Cuánto pagó Juan por los dos pares de zapatos?

Answers

Answer:

49.5 $

Step-by-step explanation:

Comencemos por lo siguiente:

Si llamamos  x al precio del  par de zapatos  y  "y"  al precio de cada pantalón, entonces la tienda ofrece:

un par de zapatos   x    más dos pantalones   2*y  en  70.000 $  (deben ser 70 $ pero esa cifra no importa a los fines de resolver el problema, habrá solo que hacer el ajuste correspondiente, en lo que aqui respecta hablaremos de 70 $)

Entonces  de acuerdo a lo expuesto

x  +  2y  =  70         or    y  =  ( 70 - x) /2      (1)

Esa es la condición inicial.

Ahora bién  Juan paga por tres pantalones  38.25 $

Eso quiere decir ( como los pantalones son iguales) que pago 38.25/3 por cada pantalón

38.25/3  =  12.75 $

Ahora bién ese precio tubo una rebaja del precio original del 15 % ( quiere decir que el precio original de cada pantalón es de

12.75/0.85  =  15 $            x =  15 $

Entonces si nos vamos a la ecuación (1) (alli los precios son originales) tenemos que

y  =  ( 70  - x ) / 2       y  =  ( 70 - 15 ) / 2    y  = 55/2     y  =  27.5 $

Ahora Juan paga por dos pares de zapatos donde según las ofertas de la tienda el debera tener un descuento del 10 % en cada par

Por lo que si  un par cuesta  27.5 $  le darán un descuento del 10% es decir pagará  27.5 *0.9 =   24.75  por cada par, como son dos pares

pagará 2 * 24.75  =   49.5 $

Arrange the numbers as they appear from left to right on a horizontal number line.
2.85
-1.58
-2.5
-1.85
-2.57
-2.76
2.5

Answers

2.5 -2.76 -2.57 -1.85 -2.5 -1.58 2.85

Answer:

-2.76, -2.57, -2.5, -1.85, -1.58, 2.5, 2.85

Which of these steps will eliminate a variable in this system
3x-3y=6
6x+9y=3

Answers

Answer:

A

Step-by-step explanation:

This is because when you do a the answer states, multipliying the top by 2, makes the top equation 6x-6y=12. When you subtract the second from the first you get:

 6x - 6y = 12

- 6x + (-)9y = (-)3

Which results in -15y = 9.

This results in an eliminated variable from the start of the system of equation.

The steps that will eliminate a variable in this system are:

Multiply the first equation by 2.

Then subtract the second equation from the first.

What is method of elimination?

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with multiplication or division of coefficients of the variables.

[tex]3x - 3y = 6\\6x +9y = 3\\\\6x - 6y = 12\\6x +9y = 3\\\\15y = -9\\y = -3/5\\x= 2-3/5 = 7/5[/tex]

Learn more about method of elimination here

https://brainly.com/question/14619835

#SPJ2

what is a square plus b square?????????????????

Answers

Answer:

c squared

Step-by-step explanation:

Answer:

C Squared

Step-by-step explanation:

Find the inverse of the function y = x2 – 12

Answers

Answer: [tex]y=\sqrt{x+12}[/tex]

Step-by-step explanation:

I hope you mean y = x² - 12 and not y = 2x - 12.

You switch the y and x variables:

x = y² - 12

And solve for y:

x + 12 = y²

[tex]y=\sqrt{x+12}[/tex]

Solve the equation and enter the value of d below. 6d + 7 d= 39​

Answers

Answer:

d=3

Step-by-step explanation:

13d=39

d=39/13

d=3

Hello!

6d + 7d = 39 <=>

<=> 13d = 39 <=>

<=> d = 39 : 13 <=>

<=> d = 3 => 6 × 3 + 7 × 3 = 39

Good luck! :)

y=-3x+5
5x-4y=-3
pls help

Answers

Hello!

[tex]\large\boxed{x = 1, y = 2}[/tex]

We can solve this system using substitution.

Since y = -3x + 5, we can substitute this into the following equation:

5x - 4(-3x + 5) = -3

Simplify:

5x - 4(-3x) - 4(5) = -3

5x + 12x - 20 = -3

Combine like terms:

17x - 20 = -3

Add 20 to both sides:

17x = 17

x = 1

Substitute to find y:

y = -3(1) + 5

y = -3 + 5

y = 2

Solution: (1, 2)

Answer:

(1,2) x=1; y=2

Step-by-step explanation:

We can plug the value of Y into the second equation like so:

[tex]5x-4(-3x+5)=-3\\5x+12x-20=-3\\17x=-3+20\\17x=17\\x=1[/tex]

Then we can plug the value of x into the first equation.

[tex]y=-3+5\\y=2[/tex]

(1,2)

Hope this helped! Please mark brainliest :)

Joshua is 1.45 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 31.65 meters. He stands 26.2 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter .

Answers

Answer:

height of the tree ≈ 8.42 m

Step-by-step explanation:

The diagram given represents that of two similar triangles. Therefore, the corresponding lengths of the similar triangles are proportional to each other.

height of tree = h

Therefore:

1.45/h = (31.65 - 26.2)/31.65

1.45/h = 5.45/31.65

Cross multiply

h*5.45 = 1.45*31.65

h*5.45 = 45.8925

h = 45.8925/5.45

h ≈ 8.42 m (nearest hundredth)

Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 3 with A(6, -10) and B(9, -1).

Answers

Answer:

Step-by-step explanation:

Use the formulas that allow us to find the point that divides the segment into a ratio which is

[tex]x=\frac{bx_1+ax_2}{a+b}[/tex]  and  [tex]y=\frac{by_1+ay_2}{a+b}[/tex] where a is 1 (comes from the ratio) and b is 3 (comes from the ratio as well). Filling in:

[tex]x=\frac{3(9)+1(6)}{1+3}=\frac{27+6}{4}=\frac{33}{4}[/tex] and then y:

[tex]y=\frac{3(-1)+1(-10)}{1+3}=\frac{-3-10}{4}=-\frac{13}{4}[/tex] so the coordinates in question are

[tex](\frac{33}{4},-\frac{13}{4})[/tex]

Answer:

Step-by-step explanation:

the answer would be (7,-7)

OMG HELP NOW PLZZ <3

Answers

Answer:

I think it would be Maxine's, since they did more tests.

help please please i beg​

Answers

Answer:

Ste㏒㏒㏑p-by-step explanation:

Answer:

[tex]x=-1[/tex]

Step-by-step explanation:

[tex]3^{x}+3^{x+2}=\frac{10}{3} \\=> 3^{x} + 3^{x}*3^{2}= \frac{10}{3} \\\\=> 3^{x} (1+9)=\frac{10}{3} \\=> 3^{x}=\frac{10}{3}:10\\=> 3^{x}=\frac{1}{3} \\ \\=> x=-1[/tex]

In a triangle ABC, if a=16m c=14m b=19m. Find the angles​

Answers

Step-by-step explanation:

went to a calculator

it said

Angle ∠A = 55.543°

Angle ∠B = 78.28°

Angle ∠C = 46.177

Find the value of y.
A.74 B.20 C.66 D.62

Answers

Answer:

It's letter D.

Step-by-step explanation:

3.14÷60×50= 2.61 but you have to opposite remember if the number is a little number you have to opposite and that is the answer 6.2 but do not joy like this . so the real answer is 62

What is the volume of the sphere in terms of pi?
V=

6 in.

Answers

Answer:

= 288π in2

Step-by-step explanation:

Volume of a sphere is given by;

V =(4/3)πr3

V = volume

r is radius

Therefore V = {(4/3) × π × (6^3)} in3

= 288π in2

Find the measure of ∠AED for m∠BEC = 118

Answers

Answer: 118°

Step-by-step explanation:

It would be great if someone helped me with this

Answers

Answer:

Step-by-step explanation:

They appear to be linear so that's easy enough to find out. What we are being asked is to find the equation represented by each table. Knowing that they are linear, we need the slope of each one and then the y-intercept of each one (each "one" being each table). Let's begin with the y-intercept. The y-intercepts exist where x = 0. In the first table, where x = 0, y = -4; in the second table, where x = 0, y = 3.

The equation we will finally fill in is y = mx + b, where m is the slope and b is the y-intercept.

Solving for slope in the first table:

[tex]m=\frac{-4-(-7)}{0-(-1)}=\frac{3}{1}=3[/tex] and the equation for this table is

y = 3x - 4

Solving for the slope in the second table:

[tex]m=\frac{3-4}{0-(-1)}=\frac{-1}{1}=-1[/tex] and the equation for this table is

y = -1x + 3 or just y = -x + 3

That's the system, which happens to be choice D

a ratio equivalent to 10:15

Answers

Answer:

3/2, 6/4, 9/6, 12/8, 15/10, 18/12, 21/14, 24/16, 27/18, 30/20, 33/22, 36/24, 39/26, 42/28, 45/30, 48/32, 51/34, 54/36, 57/38, 60/40

Step-by-step explanation:

Answer:

20 : 30

Step-by-step explanation:

Given Ratio :-

10 : 15

Equivalent Ratio :-

10 : 15 10 / 15 10 * 2 / 15 *2 20 / 30 20 : 30

Find the constant of proportionality if y is
proportional to x.

A. 25
B. 21
C. 26
D. 28

HELPPP!!!!!!

Answers

B. 21 because 21+21=42 42+21=63 etc

Find the measurement of ∠D and ∠C

Answers

Answer:

∠D = 125° and ∠C = 55°

Step-by-step explanation:

We should first solve for variable x, which should give us angle C, and then solve for angle D.

[tex]3x+15=180[/tex][tex]3x=165[/tex][tex]x=55[/tex]°

Thus ∠C = 55°

Knowing that supplementary angles add to 180°, we set up the equation:

[tex]55+D=180[/tex][tex]D=125[/tex]°

Thus ∠D = 125°

Use the substitution method to solve the system of equations.

A. (5,-7)

B. (-1,-5)

C. (-1,5)

D. (2,-1)

Answers

Answer:

correct ans is d

Step-by-step explanation:

click the photo to see process

the right answer is d

Simplify: 4y2 + 5y + 2 + 8y2 + 4y + 5.

Answers

Answer:

12y² + 9y + 7

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify

4y² + 5y + 2 + 8y² + 4y + 5

Step 2: Simplify

Combine like terms (y²):                                                                                   12y² + 5y + 2 + 4y + 5Combine like terms (y):                                                                                    12y² + 9y + 2 + 5Combine like terms:                                                                                         12y² + 9y + 7

Answer:

12y² + 9y + 7

Step-by-step explanation:

4y² + 5y + 2 + 8y² + 4y + 5

Simplify :-

4y² + 5y + 2 + 8y² + 4y + 5

arranging like terms

4y² + 8y² + 5y + 4y + 2 + 5

Combine like terms

12y² + 9y + 7

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