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3 years ago

11

a person's rectangular dog pen for his dog must have an area of 300 square feet also the length must be 40 feet longer than the

width find the dimensions of the pen

1 answer:

Tema [17]3 years ago

4 0

The with should be 7.5 feet

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Find the value of the variable y, where the sum of the fractions 6/(y+1) and y/(y-2) is equal to their product.

Blizzard [7]

Answer:

The answer is

$y = 3$

$y = - 4$

Step-by-step explanation:

We must find a solution where

$\frac{6}{y + 1} + \frac{y}{y - 2} = \frac{6}{y + 1} \times \frac{y}{y - 2}$

Consider the Left Side:

First, to add fraction multiply each fraction on the left by it corresponding denomiator and we should get

$\frac{6}{y + 1} \times \frac{y - 2}{y - 2} + \frac{y}{y - 2} \times \frac{y + 1}{y + 1}$

Which equals

$\frac{6y - 12}{(y -2) (y + 1)} + \frac{ {y}^{2} + y }{(y - 2)(y + 1)}$

Add the fractions

$\frac{y {}^{2} + 7y - 12 }{(y - 2)(y + 1)} = \frac{6}{y + 1} \times \frac{y}{y - 2}$

Simplify the right side by multiplying the fraction

$\frac{6y}{(y + 1)(y + 2)}$

Set both fractions equal to each other

$\frac{6y}{(y + 1)(y - 2)} = \frac{ {y}^{2} + 7y - 12}{(y + 1)(y - 2)}$

Since the denomiator are equal, we must set the numerator equal to each other

$6y = {y}^{2} + 7y - 12$

$= {y}^{2} + y - 12$

$(y + 4)(y - 3)$

$y = - 4$

$y = 3$

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What is the slope of the line passing through (-2, 4) and (3,-4)

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Solve the following equation. log Subscript 2 Baseline (3 x plus 7 )equals 5 The solution set is StartSet nothing EndSet . (Sim

tigry1 [53]

Answer: $x=\dfrac{25}{3}$

Step-by-step explanation:

The given equation : $\log_2(3x+7)=5$

Using logarithmic property : $\log_a N=M\to N=a^M$

The given equation will be equivalent to $(3x+7)=2^5$

$\Rightarrow\ 3x+7=32$

Subtract 7 from both sides , we get

$3x=25$

Divide both sides by 3 , we get

$x=\dfrac{25}{3}$

Hence, the solution is $x=\dfrac{25}{3}$

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