1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Advocard [28]
3 years ago
10

For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4

Mathematics
1 answer:
Elina [12.6K]3 years ago
3 0

Answer:

<em>C.</em> (5-\frac{1}{2})^6

Step-by-step explanation:

Given

15(5)^2(-\frac{1}{2})^4

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

Sum = 2 + 4

Sum = 6

Each term of a binomial expansion are always of the form:

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

Where n = the sum above

n = 6

Compare 15(5)^2(-\frac{1}{2})^4 to the above general form of binomial expansion

(a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......

Substitute 6 for n

(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......

[Next is to solve for a and b]

<em>From the above expression, the power of (5) is 2</em>

<em>Express 2 as 6 - 4</em>

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

By direct comparison of

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

and

(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......

We have;

^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4

Further comparison gives

^nC_r = 15

a^{n-r} =(5)^{6-4}

b^r= (-\frac{1}{2})^4

[Solving for a]

By direct comparison of a^{n-r} =(5)^{6-4}

a = 5

n = 6

r = 4

[Solving for b]

By direct comparison of b^r= (-\frac{1}{2})^4

r = 4

b = \frac{-1}{2}

Substitute values for a, b, n and r in

(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......

(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......

Solve for ^6C_4

(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......

(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......

<em>Check the list of options for the expression on the left hand side</em>

<em>The correct answer is </em>(5-\frac{1}{2})^6<em />

You might be interested in
Felipe has 28 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them.
Debora [2.8K]
Ok let’s say he folds N=14 so F would be the other q4
8 0
3 years ago
A container holds a combination of nickels and quarters. There are 156 coins in all, and their total value is $21.60. The system
Tatiana [17]
X+y=156
<span>0.05x+0.25y=21.6

-1/4*/ x+y=156
1/20x+1/4y=216/10

-1/4x-1/4y=156*-1/4=-39

</span>1/20x+1/4y=216/10
<span>+--------------------------
-4/20x=-17,4

x=87

</span>x+y=156
<span>
87+y=156    y=69

this question answer is </span><span>87 nickels and 69 quarters</span><span>

</span>
3 0
3 years ago
20,000 has been placed in a bank account that earns 5.7% interest. How much money will be in the account if it is compounded sem
tamaranim1 [39]

Answer:

$25 821.69

Step-by-step explanation:

The formula for the future value (FV) of an investment is

FV =PV(1 + r/n)^nt

FV = 20 000(1 + 0.087/2)^(2×3)

FV = 20 000(1 + 0.0435)⁶

FV = 20 000(1.0435)⁶

FV = 20 000 × 1.291 0847

FV = $25 821.69

5 0
3 years ago
How do you find y? ∣3y−1∣+∣2y+3∣&gt;5
Alexandra [31]
Let's solve your inequality step-by-step.

<span><span><span><span><span>3y</span>−1</span>+<span>2y</span></span>+3</span>>5

</span>Step 1: Simplify both sides of the inequality.<span><span><span>5y</span>+2</span>>5

</span>Step 2: Subtract 2 from both sides.<span><span><span><span>
5y</span>+2</span>−2</span>><span>5−2</span></span><span><span>
5y</span>>3</span>
Step 3: Divide both sides by 5.<span><span><span>
5y/</span>5</span>><span>3/5</span></span><span>
y><span>3/<span>5

hopefully this helps and here's a link that i used to use a lot in middle school 
https://www.symbolab.com/solver/solve-for-equation-calculator
</span></span></span>
5 0
3 years ago
What is true regarding genes and DNA?
notsponge [240]
Genes vary in size from a few DNA bases
8 0
3 years ago
Other questions:
  • 6x equals 7-4y solve for y
    14·2 answers
  • Does someone know the answer
    7·1 answer
  • Six times the difference of 2a and B increased by 4B
    10·2 answers
  • adult tickets to a football game were $3.25 and student tickets were $1.75 if 1,350 fans paid a total of$2,700 to attempt the ga
    6·1 answer
  • PLEASE HELP I WILL GIVE A LOT OF POINTS
    15·2 answers
  • A movie at Walmart costs $14.97. Tax is 6%. What will the total be, including tax?
    13·1 answer
  • To make the chocolate shake, Dona added 40 mL of chocolate syrup, 200 mL of milk, and 400 mL of water. How much milk, in liters,
    7·1 answer
  • Which box-and-whisker plot represents this data: 6,9, 13, 13, 18, 20, 24, 25, 26, 28, 30, 30?
    10·1 answer
  • Section 5.2 Problem 19:
    14·1 answer
  • Pls pls help me answer ii put this attachment
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!