Mathematics High School

What is the second term in the binomial expansion of (2r – 3s)12? –73,728r11s 73,728r11s 608,256r10s2 –608,256r10s2?

Answers

Answer 1

It is A, my friend. I have taken the test and got it right ;)

Answer 2

Solution:

A is the correct option.

Explanation:

We have been given that [tex](2r - 3s)^{12}[/tex]

The [tex]r^{th}[/tex] term of a binomial expansion [tex](a+b)^n[/tex] is given by

[tex]t_r=^{n}C_{r-1}a^{n-r+1}b^{r-1}[/tex]

For the given binomial expansion, we have

[tex]a=2r,b=-3s,r=2,n=12[/tex]

On plugging this value in the above formula, we have

[tex]t_2=^{12}C_{2-1}(2r)^{12-2+1}(-3s)^{2-1}\\\\t_2=^{12}C_1 (2r)^{11}(-3s)^{1}\\\\t_2=\frac{12!}{1!11!}(2)^{11}r^{11}(-3)s\\\\t_2=12\cdot (2)^{11}(-3)r^{11}s\\\\t_2=-73728r^{11}s[/tex]

Therefore, the second term is -73728r^11 s

A is the correct option.

Related Questions

The diameter of a bowling ball is 12.57 centimeters. What is this value rounded to the nearest tenth of a centimeter?

Answers

For this case we have the following numerical value:
12.57 centimeters
We note that the number is rounded to the nearest hundredth.
If we want to round the number to the nearest decimal we must rewrite the number.
Rewriting we have:
12.6 centimeters
Answer:
this value rounded to the nearest tenth of a centimeter is:
12.6 centimeters

12.6 cm is the correct answer.

Can someone please help me with this??

(PLEASE USE THE PICTURES ABOVE)

And please do what it says.

Thanks soo much

thanks

Answers

Asked and answered elsewhere.
https://brainly.com/question/9951374

-2x+3 > x +24

Show steps how you got your solution

Answers

- 2x + 3 > x + 24

First we must get all variables on the same side and constants on the opposite side. To do so we subtract x from the right and the left. Then subtract 3 from both sides as well.

- 2x - x > 24 - 3

Now we combine like terms:

- 3x > 21

We must isolate the variable x. In order to do so, we divide both sides by - 3. When you divide by a negative number, you must also flip the inequality so the greater than becomes a less than.

x < 21 / - 3

x < - 7 is your answer.

Hello!

You can solve this algebraically

-2x + 3 > x + 24

Subtract x from both sides

-3x + 3 > 24

Subtract 3 from both sides

-3x > 21

Divide both sides by -3

Since you divided by a negative you flip the sign

x < -7

The answer is x < -7 or any number that is greater than -7

Hope this helps!

Kenny is making creamy rice pudding his recipe requires 4 cups of milk he has a quart of milk in his fridge dose he have enough milk explain

Answers

yes, because 4 cups = 1 quart

When he was 40 Keefer began investing $150 per month in various securities for his retirement savings. His investments averaged a 4.5% annual rate of return until he retired at age 70. What was the value of Keefer's retirement savings when he retired? Assume monthly compounding of interest.

Answers

At retirement, Keefer will have saved for 30 (that is, 70-40) years.
Monthly saving, P = $150, Annual rate of return, R = 4.5% = 0.045.

Therefore, future value (FV) at the time of retirement will be;

FV = P*[1+(R/12)^12*30]/(R/12)
Substituting all the parameters;
FV = 150*[1+(1+0.045/12)^360]/(0.045/12) = $113.907.92

on Sunday Mary pay $6 each on two tickets to a movie theater movies for $9.58 each Mary paid with 3 $20 bills how much changed

Answers

$50.42

hjdjdjdjdbdhshssjdjdjdjdj

A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using the following parametric equations. rewrite the parametric equations by eliminating the parameter.
x(t)=2t-1
y(t)= square root of t; t> or equal to 0

Answers

Answer:

The equation is [tex]y ^ 2 = \frac{x + 1}{2}[/tex]

Step-by-step explanation:

The parameter that we have is t. We want to eliminate this parameter in both equations, therefore in the first equation we solve for t and in the second equation we solve for the variable t.

We have:

[tex]x = 2t-1\\\\x + 1 = 2t\\\\t = \frac{x + 1}{2}[/tex]

Now we solve the other equation for t.

[tex]y= \sqrt{t}[/tex]

[tex]y ^ 2 = t[/tex] because [tex]t> 0[/tex]

As [tex]t = y ^ 2[/tex] and also [tex]t = \frac{x + 1}{2}[/tex]

Then:

[tex]y ^ 2 = \frac{x + 1}{2}[/tex]

The correct answer is:

D. [tex]x=2y^{2} -1, y\geq 0[/tex]

Help me solve this please!

Answers

The problem statement suggests you use a calculator. A graphing calculator can give the answers you seek.

a) The calculator shows 5 solutions:
{5π/23, 5π/17, 25π/23, 25π/17, 45π/23}
These have approximate decimal values of
{0.6830, 0.9240, 3.4148, 4.6200, 6.1466}

b) The calculator shows 2 solutions with approximate decimal values of
{1.2925, 4.4341}

c) The calculator shows 2 solutions with approximate decimal values of
{1.3694, 4.9137}

_____
This (desmos) calculator displays intercepts to 3 decimal places. Since you want 4 decimal places, some additional refinement of the answer was necessary. That was accomplished using Newton's method iteration. The details are not shown. A suitable graphing calculator (for example, a TI-84) will supply the intercept coordinates to full calculator accuracy.

HELP!!!!!!NEED TO PASS!!!!WILL GIVE THE BRAIN!!!!!!!!!!!

Answers

Shifting left means adding a number to x.

So, x³ shifted 5 units to left will be (x + 5)³

Shifting 4 units upwards means adding 4 to the function value,

So, previous function shifted 4 units up will be (x + 5)³ + 4

Thus, g(x) = (x + 5)³ + 4

So, option b gives the correct answer

So, option b gives the correct answer

"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1% of examinees, what is the cutoff score on the test for admission?"

Answers

The cutoff will be evaluated as follows:
let the cutoff be x

but
P(x>0.01)=1-P(x<0.01)=1-0.01=0.99
the z value corresponding to 0.99% is z=2.33
thus
2.33=(x-600)/60
solving for x we get:
139.8=x-600
x=739.8

What is the linear function that best fits the data set?

Answers

Answer: Fourth option y=-3x+15
Please, see the attached file.
Thanks.

How do you use properties of exponents and logarithms to rewrite functions in equivalent forms and solve equations?

Answers

Some of the logarithmic properties most used to solve equations are the following.
1) log (a) ^ b = b * log (a)
2) log (a * b) = log (a) + log (b)
3) log (a / b) = log (a) - log (b)
These logarithmic properties can be used to solve equations.
For example:
2 ^ x = 56
If we apply to this equation the logarithm function on both sides that we have left
log (2) ^ x = log (56)
This function is equivalent to the first.
If we now apply the property 1) of the previous logarithms, we can reveal x of the equation.
x * log (2) = log (56)
x = log (56) / log (2)
x = 5,807
Thus, thanks to the properties of the logarithms, this exponential function could be solved

Final answer:

To use properties of exponents and logarithms effectively, one must apply specific rules such as the logarithm of a product being the sum of the logarithms and the logarithm of a number raised to an exponent being the product of the exponent and the logarithm. Log transformations help linearize and solve equations involving exponents.

Explanation:

To rewrite functions in equivalent forms and solve equations using the properties of exponents and logarithms, one must understand several key rules and relationships. For example, the common logarithm (log) indicates the power to which 10 must be raised to equal a given number.

Two essential properties we use are:

The logarithm of a product of two numbers is the sum of the logarithms of the two numbers (log xy = log x + log y).The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (log x^n = n log x).

Exponential and logarithmic functions are inverses. This relationship allows us to simplify complex expressions and solve exponential equations by taking the logarithm of both sides. For instance, the natural logarithm (ln or loge) and the base e exponential are inverse functions, so ln (e^x) = x and e^(ln x) = x.

A log transformation can linearize functions that involve an exponent by taking the log of both sides of the equation. This technique is valuable in solving equations where the variable is an exponent.

What is the value of x? Round the answer to the nearest tenth. The diagram is not drawn to scale.

Answers

x = 50

Reason: Chord AB and Chord CD are equal.

We have been given that the chords AB and CD are equal.

Now, we know that two equal chords subtends equal angle at the center of the circle.

The chord CD subtends and angle CPD at the center and the chord AB subtends an angle APB at the center.

Hence, from above mentioned theorem, we can say that

[tex]\angle CPD = \angle APB[/tex]

Now, we have been given that

[tex]\angle CPD =50 ^{\circ} [/tex]

[tex]\angle APB =x ^{\circ} [/tex]

Hence, we have

[tex]x=50^{\circ}[/tex]

Find the value of the combination 9 c 4

Answers

9C4= 126.

Hope this helps

PLEASE HELP 50 point will give brainlyest
Evaluate 81000−−−−√3 .

1/125

6/500

8/500

2/10

Answers

when I did it I got 140296.11541307

THE ANSWER IS B: 6/500 :) JUST LIKE IT AND VOTE ON IT PLZ THANK U AND HAVE A OOF DAY XD have a good day lel

the diagonals of a rhombus are 12 centimeters and 16 centimeters. what is the length of one side of the rhombus?

Answers

in a rhombus, the diagonals meet at right-angles, and they bisect each other, namely they cut each other in half, check the picture below.

thus we can use the pythagorean theorem to get one side, keeping in mind that, slanted as it may be, all sides in a rhombus are equal in length.

The Venn diagram represents the results of a survey that asked participants whether they would want a bird or a fish as a pet.

Enter your answers in the boxes to complete the two-way table based on the given data.

Answers

Answer with Step-by-step explanation:

As we can see the venn diagram:

number of bird+fish=6

number of bird+not fish=8

number of fish+not bird=19

and number of not fish and not bird=22

Hence, we get the following table

Fish Not Fish Total

Bird 6 8 14

Not Bird 19 22 41

Total 25 30 55

Fish Not Fish Total

Bird 6 18 14

Not Bird 19 22 41

Total 25 30 55

Solve the quadratic equation. 8x2 + 16x + 8 = 0 A) 1 B) -1 C) 1 and 8 D) 1 and -1

Answers

[tex]8x^2+16x+8=0\\\\8(x^2+2x+1)=0\ \ \ |:8\\\\x^2+2x+1=0\\\\x^2+x+x+1=0\\\\x(x+1)+1(x+1)=0\\\\(x+1)(x+1)=0\\\\(x+1)^2=0\iff x+1=0\\\\\boxed{x=-1}[/tex]
Answer: B. -1

Alan is giving a basic math test in his class. One of the questions in the test is about finding two factors of the number 221. Which are the two factors of the given number? The two factors of the number 221 are ___ and ____.

Answers

1,13,17 are three of them

The two factors of the number 221 are 13 and 17.
A factor refers to a whole number, which fits evenly into another whole number. Thus, factors are the numbers, which we multiply together to get another number. The two numbers that can be multiply together to get 221 are 13 and 17.

3.2km/50min X 60min/1hr X 1mi/1.6km

A) 2.4mi/hr
B) 2.4km/hr
C) 12mi/hr
D) 12km/hr

Answers

3.2km 60min 1mi km min
-------- x -------- x ----------- (cancel out: ---- and ------ )
50min 1hr 1.6km km min

2.4 mi
= ---------
hr

answer
A) 2.4mi/hr

Final answer:

The student's conversion calculation of speed units from kilometers per minute to miles per hour yields a speed of 2.4 miles/hour, so the answer is choice A.

Explanation:

The question is a conversion exercise in speed units from kilometers per minute to miles per hour. We have the following information: 3.2 km in 50 min, and we know that 1 mile is equivalent to 1.6 km and 60 min is equivalent to 1 hour. Thus, the conversion is as follows:

3.2 km ÷ 50 min. = 0.064 km/min.

Converting km/min to mi/hr involves multiplying by 60 (minutes in an hour) and dividing by 1.6 (km in a mile), and we get:

(0.064 km/min x 60 min/hr) ÷ 1.6 km/mi. = 2.4 mi/hr.

Hence, the correct answer is (A) 2.4 miles/hour.

Learn more about Conversion Exercise here:

https://brainly.com/question/32748122

#SPJ2

Help Geometry!!
AC is tangent to circle O at A. If , m<BY= 24 , what is m<YAC?

a) 48

b) 156

c) 78

d) 132

Answers

we know that
The inscribed angle measures half of the arc it comprises.
so
∡BAY=BY/2------> 24/2------> 12°

angles YAC and BAY are complementary angles
∡YAC+∡BAY=90°
∡YAC=90-∡BAY-------> ∡YAC=90-12-----> 78°

the answer is
78°

Need help on this question

Answers

Total Area: T.A.=2*Ab+Al

Area of the base: Ab=p*K

Semi-perimeter of the base: p
p=P/2
Perimeter of the base: P=20
p=P/2=20/2→p=10
Ab=p*k=10*K→Ab=10K

Lateral Area of the prism: Al
Al=P*h
Height of the prism: h=6
Al=P*h=20*6→
Al=120

T.A.=2*Ab+Al
T.A.=2*(10K)+120
T.A.=20K+120
T.A.=120+20K

Answer: (120+20K)

how do I solve (x-5)(x-1)=0

Answers

With this equation, you'd distribute one set of parenthesis into the other. Doing so you'd get "X^2 - 1x - 5x + 5 = 0". Simplified, you'd have "X^2 - 6x + 5 = 0"

Next, you'd find the factors of 5, that when multiplied equal 5, and when added, equal -6. Being that 5 is a prime number (a number that is only divisible by 1 and itself) those numbers are 1 and 5. Both numbers have to be negative, in order to get -6.

-1*-5 = 5
-1 + -5 = -6

Finally you split up the X^2 to a single x with each of the factors and make it equal to zero (X - 1 = 0) and (X - 5 = 0). Then you solve each.

(X - 1 = 0) Add 1 to each side. X = 1
(X - 5 = 0) Add 5 to each side. X = 5

I hope this helps!

someone help me please

Answers

For this case we have the following functions:
f (x) = 3x + 1
g (x) = x ^ 2 - 6
Subtracting both functions we have:
(f-g) (x) = f (x) - g (x)
(f-g) (x) = (3x + 1) - (x ^ 2 - 6)
(f-g) (x) = 3x + 1 - x ^ 2 + 6
(f-g) (x) = - x ^ 2 + 3x + 7
Answer:
(f-g) (x) = - x ^ 2 + 3x + 7
option B

Which triangles are similar?

a
b
c
d

Answers

i think A. and D.

hope that's right!!!

Hey there!

The two triangles that are similar are triangles A and D.

I hope this helped! :-)

Haley read three less than twice as many books as her brother did last summer. haley read five books.which equation could you use to find how many books her brother read (b)?

Answers

Your answer would be 2b-3=5
The 2 stands for the "twice as many"
The b stands for her brother.
The 3 stands for the "3 less books"
And the 5 stands for Haley's total.

I hope this helps!

Answer:

2b - 3 = 5

Step-by-step explanation:

If her brother read b number of books last summer, twice the number of books her brother read

= 2b

three less than twice as many books as her brother read

= 2b - 3

If haley read five books and it is same as three less than twice as many books as her brother last summer, then

2b - 3 = 5

I need help on this show steps pleaseeee!!!

Answers

Step #1 - convert 1 ⅓ into a mixed number,

[tex] \frac{1}{2}r - \frac{1}{3} - \frac{4}{3} = - \frac{7}{3} [/tex]

Step #2 - calculate the sum or difference of - ⅓ by -4/3,

[tex] \frac{1}{2}r - \frac{5}{3} = - \frac{7}{3} [/tex]

Step #3 - Multiply both sides by 6,

[tex] \frac{1}{2} (6)r - \frac{5}{3} (6) = - \frac{7}{3} (6)[/tex]

[tex]3r - 10 = - 14[/tex]

Step #4 - Move constant ( - 10 ) to the right and change its sign,

[tex]3r = - 14 + 10[/tex]

Step #5 - Calculate the sum

[tex]3r = - 4[/tex]

Step #6 - Divide both sides by 3 so we can isolate the variable r,

[tex]r = - \frac{4}{3} [/tex]

~~

I hope that helps you out!!

Any more questions, please feel free to ask me and I will gladly help you out!!

~Zoey

suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. how high will the ball rebound after its third bounce? round to the nearest tenth

Answers

The answer would be 10.84

please help- Your supposed to find x, y, and z and round to the nearest tenth

Answers

Didn't you mean "you are" or "you're?"

You didn't indicate which problem you wanted your helper to focus on. So I will arbitrarily choose #2.

This large triangle is made up of two smaller triangles: the smaller triangle has sides of 2 and x and hypotenuse of y. The larger triangle has sides x and 5 and hypotenuse z. Look carefully: The largest triangle has hypotenuse (2+5) and sides y and z. Now you have three equations in three unknowns and thus have enough info to find the values of x, y and z.

Think about this. What should you do first? Type back your ideas. Then I'll help you solve this problem.

Plato explains that we know geometry by _________.

Answers

Plato explains that we know geometry by our gain knowledge through recollection. Our soul is what recollects this place hence we came where there exist unchanging truths. Delivered the theory of Forms, according to which the world people know by means of the senses is just an imitation of the eternal, pure, eternal, and fixed world of the Forms.

Other Questions

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