What is the coefficient of x3 in the expansion of (2x−3)5?

Group of answer choices

a) -360

b) 720

c) 10

d) -5

e) -120

Answers

Answer 1

Answer:

B 720

Step-by-step explanation:

same process as the previous image I sent ya

Answer 2

Answer:

B) 720.

Step-by-step explanation:

We can use the Binomial Expansion Theorem:

[tex]\displaystyle (a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^kb^{n-k}[/tex]

We have the expression:

[tex]\displaystyle (2x-3)^5[/tex]

Therefore, a = 2x, b = -3, and n = 5.

We want to find the coefficient of . To get x³, we can cube a. Therefore, we can find our coefficient by letting k = 3. Hence:

[tex]\displaystyle \binom{5}{3}(2x)^3(-3)^{5-3}[/tex]

Evaluate:

[tex]\displaystyle =10(8x^3)(9)=720x^3[/tex]

Our answer is B.


Related Questions

Please help due incredibly soon!!!!

Answers

Answer:

The surface area is 116.

Step-by-step explanation:

does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?​

Answers

Given equation of the Circle is ,

[tex]\sf\implies x^2 + y^2 = 25 [/tex]

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]

Here we can see that the distance of point from centre is less than the radius.

Hence the point lies within the circle .

inside the circle

Step-by-step explanation:

we want to verify whether (-4,2) lies inside or outside or on the circle to do so recall that,

if [tex]\displaystyle (x-h)^2+(y-k)^2>r^2[/tex] then the given point lies outside the circleif [tex]\displaystyle (x-h)^2+(y-k)^2<r^2[/tex] then the given point lies inside the circleif [tex]\displaystyle (x-h)^2+(y-k)^2=r^2[/tex] then the given point lies on the circle

step-1: define h,k and r

the equation of circle given by

[tex] \displaystyle {(x - h)}^{2} + (y - k) ^2= {r}^{2} [/tex]

therefore from the question we obtain:

[tex] \displaystyle h= 0[/tex][tex] \displaystyle k= 0[/tex][tex] {r}^{2} = 25[/tex]

step-2: verify

In this case we can consider the second formula

the given points (-4,2) means that x is -4 and y is 2 and we have already figured out h,k and r² therefore just substitute the value of x,y,h,k and r² to the second formula

[tex] \displaystyle {( - 4 - 0)}^{2} + (2 - 0 {)}^{2} \stackrel {?}{ < } 25[/tex]

simplify parentheses:

[tex] \displaystyle {( - 4 )}^{2} + (2 {)}^{2} \stackrel {?}{ < } 25[/tex]

simplify square:

[tex] \displaystyle 16 + 4\stackrel {?}{ < } 25[/tex]

simplify addition:

[tex] \displaystyle 20\stackrel { \checkmark}{ < } 25[/tex]

hence,

the point (-4, 2) lies inside the circle

Graph the line with slope -5 and y-intercept 1.

Answers

Answer:y=-5+1

Step-by-step explanation:

Linda had dinner at a restaurant for $56 and leaves behind a tip of 18%. What is the tip amount?

Answers

Answer:

[tex] = \frac{18}{100} \times 56 \\ = 10.08 \: dollars[/tex]

Answer:

$10.08

Step-by-step explanation:

To solve for the tip amount, we multiply 56 by 0.18.

56 · 0.18 = 10.08.

Linda tipped $10.08.

Given: ABCD is a parallelogram.

Prove: ∠A and ∠D are supplementary.

Parallelogram A B C D is shown.

By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are
angles. Because AB and DC are
, the same-side interior angles must be
by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.

Answers

Answer:

AB = DC So ∠A and ∠D are bigger then 90%

Answer:

E2020

Step-by-step explanation:

if <ABC measures 100 and is inscribed in a circle O. find <BAO and <BCO​

Answers

Answer:

<BCO​ = <BAO​ = 20degrees

Step-by-step explanation:

If <ABC measures 100 and is inscribed in a circle O. find <BAO and <BCO​

To get <BAO and <BCO​, we need to get <AOC first.

From the figure, it can be seen that triangle ABC is an isosceles trinagle. Hence;

<BAC + <BCA + 100 = 180

Since <BAC = <BCA

<BAC + <BAC = 180 - 100

2<BAC = 80

<BAC = 80/2

<BAC = 40

Also;

<BAO = <BCO​ and <BAO = <BAC/2

<BAO = 40/2 = <BCO​

Hence <BCO​ = <BAO​ = 20degrees

Hi guys can please help me


using a calculator or otherwise evaluate each of the following giving Your answer to two decimal place .

(i) 73.18-5.23×90







Answers

Answer: 26.11

Step-by-step explanation:

73.18 - 5.23 × 90 = 73.18 - 47.07 = 26.11

What is the equation of the line graphed below?

Answers

Answer:

y=2/5x

Step-by-step explanation:

Rise over run: you rise by 2, run by 5. Or you can use the slope formula: m=y2-y1/x2-x1

2-0/5-0=2/5=m

en el diagrama de venn donde van ubicados estos numeros?
0,88888....
1 sobre 7 pi
-6 sobre 3
4E
55 sobre 0
56 sobre 9
-0,65999999

Answers

Answer:

Step-by-step explanation:

Aslam's age is half of his father's age but 15 years ago his age was just
the father's age. Find his present age now.

Answers

Answer:

not possible or not determined is answer

Step-by-step explanation:

because let his father be 33

ad his son be 17

15 years ago

son will be 2

and father will be 18

not possible father's age ≠son's age in any respect unless and until father's age is decreased

PLEASE HELP! asap:)
i would really appreciate it

Answers

Answer:

[tex]{ \tt{ = 2\pi \: rh}} \\ = 2 \times 3.14 \times 12 \times 1 \\ = 75.4 \: {cm}^{2} [/tex]

Whose solution strategy would work?

Answers

Answer:

1452628383763637£838

Answer:

B

Step-by-step explanation:

A - H, please! thank you.

Answers

Answer:

First exercise

a) 1/8=0.125

b) 5$

c) y = 0.125 * x - 5

Second exercise

a) 0.11 $/KWh

b) no flat fee

c) y = 0.11 * x

Step-by-step explanation:

(See the pictures)

An 80-mile trip is represented on a gridded map by a directed line segment from point M(3, 2) to point N(9,
13). What point represents 60 miles into the trip? Show your work and explain your reasoning.

Answers

Answer:

Step-by-step explanation:

If the distance from M to N is 80 miles and we want to find the coordinates of the point 60 miles into the trip, we are looking for the point 3/4 of the way from M to N, since 60 is 3/4 of 80. This is the process:

First we need to consider that MN is a directed vector. We first find the components of the directed vector, which is found in the change in x and the change in y. First step, then, looks like this:

<Δx, Δy> = <9-3, 13-2> = <6, 11> We will call those the x and y components of the vector (which comes from vector study in both physics and math, so if you don't understand that, it's ok! Just follow the process here and you'll be fine). Knowing that 60 is 3/4 of the way from M to N, we find 3/4 of both the x and y components, like this:

[tex]<\frac{3}{4}(6), \frac{3}{4}(11)>[/tex] which will give us 3/4 of the change in x and 3/4 of the change in y:

[tex]<\frac{18}{4},\frac{33}{4}>=<4.5,8.25>[/tex]

Since we are going 3/4 of the way from M to N, we add that component to the x and y coordinates of M, giving us 3/4 of the way from M to N, which translates to 60 miles of the 80 mile trip:

(3 + 4.5, 2 + 8.25) = (7.5, 10.25)

Those are the coordinates of the point that represents 60 miles into the 80 mile trip.

En una radio, 1/8 del dia esta destinado a emitir publicidad. Del total de publucidad, 3/5 corresponden a comerciales de univercidades. En esta radio,¿que fraccion del tiempo diario corrsponde a publicidad de univercidades.

Answers

Respuesta:

3/40

Explicación paso a paso:

Dado :

Fracción de tiempo diario dedicado a publicidad = 1/8

Del tiempo diario dedicado a publicidad, 3/5 corresponde a comerciales de universidad

Fracción del tiempo diario dedicado a la publicidad de las universidades:

3/5 de 1/8

3/5 * 1/8 = (3 * 1) / (5 * 8) = 3/40

24 more than Holly's age is 67

Answers

Answer:

This question isn't really complete, but if you're asking what Holly's age is, then that's just 67 - 24, which is 43.

So Holly is 43, if that's the question.

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]h + 24 =67[/tex]

[tex]h = 43[/tex]

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

We are given that 24 more than Holly's age is 67.

⸻⸻⸻⸻

[tex]\boxed{\text{Setting up an equation:}}\\\\\text{'24 more than Holly's age'} \rightarrow h + 24\\\\\text{'is 67'} \rightarrow = 67\\\\\boxed{h + 24 = 67}[/tex]

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'h'...}}\\\\h + 24 = 67\\-------------\\\rightarrow h + 24 - 24 = 67 - 24\\\\\rightarrow \boxed{h=43}\\\\\\\text{Holly should be 43 years old.}[/tex]

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

pls help i need this answer

Answers

Decimal form 0.0625
Fraction form 1/16

I think,sorry if it’s wrong
In fraction form it’s 1/16

on a coordinate gride what is the distance between (1,3) and (6,15)

Answers

Answer:

13

Step-by-step explanation:

Distance between points (1, 3) and (6, 15) is 13

13 is the right answer for sure

Can sb help me it’s due soon

Answers

Answer:

I think 84 but you may need to check just to be sure :)

Let ABCD and EFGH be two quadrilaterals such that ABCD ~ EFGH. If AB = 15 cm, EF = 18 cm and the perimeter of ABCD is 40 cm, find the perimeter of EFGH.​

Answers

Step-by-step explanation:

this photo is correct answer of this question.

Solve the following

(23-45)+(93÷6)×23 ​

Answers

334.5 ,699/2 , 334 , 1/2

help me pls i dont get this

Answers

Answer: B. 80

Step-by-step explanation:

Solve the equation they've given you:

[tex]\frac{3}{4} S=60\\\frac{3S}{4} =60\\3S=60*4\\3S=240\\S=80[/tex]

Answer:

B.  80

Step-by-step explanation:

(3/4)S = 60

You want to isolate S. S is being multiplied by 3/4.

You need to multiply 3/4 by its reciprocal to get rid of the 3/4 on the left side.

The reciprocal of 3/4 is 4/3.

The rule with equations is that you are allowed to multiplied both sides of an equation by the same number. Multiply both sides of the equation by 4/3.

4/3 * (3/4) * S = 4/3 * 60

12/12 * S = 4/3 * 60/1

1 * S = 240/3

S = 80

Answer: B.  80

A certain medical test is known to detect 59% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that:

Answers

Answer:

[tex]P(x = 3) = 0.048[/tex]

Step-by-step explanation:

Given

[tex]n = 10[/tex]

[tex]p=59\% = 0.59[/tex]

Required

[tex]P(x = 3)[/tex] --- probability that 3 are afflicted

This question illustrates binomial probability and it is calcuated using:

[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]

So, we have:

[tex]P(x = 3) = ^{10}C_3 * 0.59^3 * (1 - 0.59)^{10-3}[/tex]

[tex]P(x = 3) = ^{10}C_3 * 0.59^3 * 0.41^7[/tex]

[tex]P(x = 3) = 120 * 0.59^3 * 0.41^7[/tex]

[tex]P(x = 3) = 0.048[/tex]

if p-1/p = 4 Find (p+1/p)²​

Answers

Answer:

4

Step-by-step explanation:

[tex] \frac{p - 1}{p} = 4[/tex]

Solve for p.

The numerator. difference has to be 4 times the answer of the denomiator.

So we can say

[tex]p - 1 = 4p[/tex]

Solve for p

[tex] - 1 = 3p[/tex]

[tex]p = - \frac{1}{3} [/tex]

Now plug this in for the other formula.

[tex]( \frac{ - \frac{1}{3} +1}{ \frac{1}{3} } ) {}^{2} = 2 {}^{2} = 4[/tex]

So

According to class 8 please solve

Answers

Answer:

i) 2 + 2x

ii) 154 = 2(2 + 2x + x)

iii) Length = 52m

Breadth = 25m

Step-by-step explanation:

Perimeter of swimming pool = 154m

Breadth = x

Length = 2 + 2x

Formula for finding perimeter = P = 2(l + b)

Therefore,

154 = 2 ( 2 + 2x + x)

154 = 4 + 4x + 2x

154 = 4 + 6x

154 - 4 = 6x

150 = 6x

150/6 = x

25 = x

With the value of x,

we can fInd the length and the breadth

Breadth = x

= 25

Length = 2 + 2x

= 2 + 2(25)

= 2 + 50

= 52

Kylie has only quarters and
nickels in a jar. The total value in
the jar is $2.00. If there are a total
of 20 coins, how many of each
type of coin are in the jar?

? Quarters. ? Nickels

Answers

15 nickels and 5 quarters

What value of g makes the equation true?

Answers

Answer:

[tex](x + 7)(x - 4) \\ = { \tt{ {x}^{2} + 7x - 4x - 28 }} \\ = { \tt{ {x}^{2} + 3x - 28 }} \\ { \boxed{ \bf{g \: is \: 3}}}[/tex]

Answer:

g=3

Step-by-step explanation:

Hi there!

To find the value of g, we can expand the two binomials using the distributive property:

[tex](x+7)(x-4)\\= x(x-4)+7(x-4)\\= x^2-4x+7x-28\\= x^2+3x-28[/tex]

Therefore, the value of g that makes the equation true is 3.

I hope this helps!

Which expression can be used to convert 22 Australian dollars to US dollars?
Assume 1.2 Australian dollars equals 1 US dollar.
O $22 AUD X
1.2 USD
1 AUD
O $22 AUD X
1 USD
1.2 AUD
O $1.20 AUD X
1 USD
1.2 AUD
O $1.20 AUD X
1.2 USD
1 AUD

Answers

Answer:

The answer is B

Step-by-step explanation:

B

The 22 Australian dollar in USD is 18.33.

What is currency?

Currency is a medium of exchange for goods or services within an economy, usually issued by a government or central bank and generally accepted at its face value.

Given that, we need to determine that there are how many USD in 22 AUD,

So, 1.2 Australian dollars equals 1 US dollar.

Therefore,

22 AUD = 22 x 1 / 1.2 = 18.33

Hence, the 22 Australian dollar in USD is 18.33.

Learn more about currency, click;

https://brainly.com/question/14372075

#SPJ7

Create an exponential function, and then create a second exponential function that shifts your original function down 7 units

Answers

Answer:

A general exponential function is written as:

f(x) = A*e^(k*x)

Where A and k are real numbers.

Because we want to "create" a exponential function, we must assign numbers to A and k, let's assign:

A = 1

k = 1

then our function is just:

f(x) = e^(x)

Now we want to shift down 7 units.

So let's describe a general vertical shift.

For a general function f(x), a vertical shift is written as:

g(x) = f(x) + N

if N is positive, the shift is upwards

if N is negative, the shift is downwards.

Here we want to have a shift down of 7 units, then we would write:

g(x) = f(x) - 7

Replacing by the actual function f(x) we get:

g(x) = e^x - 7

Below you can see the graphs of both functions:

Where the orange one is f(x) and the purple one is g(x).

What is the value of x?
1/2(x+6)=18

Answers

Answer:

30

Step-by-step explanation:

Multiply by 2 to 18, x+6=36

subtract 6 x=30

x=30

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