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SVETLANKA909090 [29]

3 years ago

7

Two numbers total 61 and have a difference of 33. Find the two numbers

1 answer:

umka21 [38]3 years ago

7 0

$x,\ y-the\ numbers\\\\\underline{+\left\{\begin{array}{ccc}x+y=61\\x-y=33\end{array}\right}\qquad\text{add both sides of equations}\\\\.\qquad2x=94\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=47}\\\\\text{Put the value of x to the first equation}\\\\47+y=61\qquad\text{subtract 47 from both sides}\\\\\boxed{y=14}\\\\Answer:\ \boxed{\boxed{47\ and\ 14}}$

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Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressio

Sidana [21]

9514 1404 393

Answer:

x = 16/3

Step-by-step explanation:

a) The rewritten equation is ...

$\dfrac{x-2}{x+8}=\dfrac{x-1}{x+12}$

__

b) The solution can be found as ...

$\dfrac{x-2}{x+8}-\dfrac{x-1}{x+12}=0\\\\(x-2)(x+12)-(x+8)(x-1)=0 \qquad\text{numerator of the difference}\\\\(x^2+10x-24)-(x^2+7x-8)=0\\\\3x-16=0\qquad\text{simplified}\\\\x=\dfrac{16}{3}\qquad\text{one solution}$

The solution set is {16/3}.

_____

The applicable rule of logarithms is ...

log(a) -log(b) = log(a/b)

8 0

3 years ago

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butalik [34]

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2 years ago

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Which expression is equivalent to sqrt128x^5y^6/2x^7y^5 ? Assume x 0 and y > 0.

kolbaska11 [484]

<u>Answer:</u>

$\frac{8\sqrt{y} }{x}$

<u>Step-by-step explanation:</u>

We are given the following expression and we are to simplify it:

$\sqrt {\frac {128x^5y^6} {2x^7y^5} }$

To make it easier to solve, we can also write this expression as:

$\sqrt {\frac{128}{2} * \frac {x^5} {x^7} * \frac {y^6} {y^5}}$

Now we will cancel out the like terms to get:

$\sqrt {64*\frac{1} {x^2}*y }$

Taking the square root of the terms to get:

$8*\frac {1}{x} .\sqrt{y}$

$\frac{8\sqrt{y} }{x}$

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3 years ago

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zheka24 [161]

Answer:

Step-by-step explanation:

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6 0

2 years ago

6m-6=9m+15 (Show work)

9966 [12]

Answer:

$m=-7$

Step-by-step explanation:

$6m-6=9m+15$

Add 6 to both sides:

$6m-6+6=9m+15+6$

$6m=9m+21$

Subtract 9m from both sides:

$6m-9m=9m+21-9m$

$-3m=21$

Divide both sides by -3:

$\frac{-3m}{-3}=\frac{21}{-3}$

$m=-7$

6 0

3 years ago

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