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dimulka [17.4K]
3 years ago
15

Which expression is equivalent to

Mathematics
2 answers:
Bezzdna [24]3 years ago
7 0

Answer:

The correct answer is option 2.

The equivalent of given expression is,  

3/5x⁶y⁶

Step-by-step explanation:

Identities:

xᵃ/xᵇ = x⁽ᵃ⁻ᵇ⁾

1/x-ᵃ=xᵃ

It is given that,

(-9x⁻¹y⁻⁹)/(-15x⁵y⁻³)

<u>To find the equivalent expression </u>

The expression is,

(-9x⁻¹y⁻⁴)/(-15x⁵y⁹)

By using the above identities we can write,

-9x⁻¹y⁻⁹/-15x⁵y⁻³ = 3/(5x⁽⁵⁺¹⁾y⁽⁹⁻³⁾)

since xᵃ/xᵇ = x⁽ᵃ⁻ᵇ⁾

1/x-ᵃ=xᵃ

-9x⁻¹y⁻⁹/-15x⁵y⁻³  = 3/5x⁶y⁶

Therefore the correct answer is second option.

3/5x⁶y⁶ is the equivalent fraction of given expression.

nirvana33 [79]3 years ago
3 0

For this case, we must find an expression equivalent to:

\frac {-9x ^ {- 1} y ^ {- 9}} {- 15x ^ 5y ^ {- 3}}

By definition of power properties we have:

a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}

Rewriting the previous expression we have:

The "-" are canceled and we take into account that:

\frac {9} {15} = \frac {3} {5}

So:

\frac {3} {5x^5 * x ^ 1 *y ^ 9* y ^ {- 3}} =

According to one of the properties of powers of the same base, we must put the same base and add the exponents:

\frac {3} {5x ^ {5 + 1} * y ^ {9-3}} =\\\frac {3} {5x ^ 6 * y ^ 6}

Answer:

\frac {3} {5x ^ 6 * y ^ 6}

Option B

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Answer:

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Step-by-step explanation:

<u>Binomial Series</u>

(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n

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2 years ago
A store is having a sale on walnuts and chocolate chips. For 7 pounds of walnuts and 9 pounds of chocolate chips, the total cost
Jlenok [28]

Answer:

  • Walnuts  cost $1.75, chocolate chips cost $2.75

Step-by-step explanation:

<h3>Let the costs be:</h3>

  • Walnuts - x
  • Chocolate chips - y

<h3>Set equations as per question</h3>

For 7 pounds of walnuts and 9 pounds of chocolate chips, the total cost is $37:

  • 7x + 9y = 37

For 5 pounds of walnuts and 3 pounds of chocolate chips, the total cost is $17:

  • 5x + 3y = 17

<h3>Solve the system by elimination</h3>

Multiply the second equation by 3 and subtract the first equation, solve for x:

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  • 15x + 9y - 7x - 9y = 51 - 37
  • 8x = 14
  • x = 14/8
  • x = 1.75

Find the value of y:

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  • 12.25 + 9y = 37
  • 9y = 37 - 12.25
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