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kicyunya [14]
3 years ago
8

A rectangular box has a perimeter of 36 inches. Which of the following equations represents the area of the rectangular box in t

erms of its width, w?
a.) A = 36w - w^2
b.) A = 18w - w^2
c.) A = 36 - w^2
d.) A = 18 - w^2
Mathematics
1 answer:
mote1985 [20]3 years ago
5 0
Perimeter=2(l+w)
36=2(l+w)
(l+w)=18
l=18-w

area of a rectangle=w*l

put value of l here
Area=w*(18-w)
Area=18w-w^2

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What are the potential solutions of log4x+log4(x+6)=2?
lions [1.4K]

The potential solutions of log_4x+log_4(x+6)=2 are 2 and -8.

<h3>Properties of Logarithms</h3>

From the properties of logarithms, you can rewrite logarithmic expressions.

The main properties are:

  • Product Rule for Logarithms - log_{b}(a*c)=log_{b}a+log_{b}c
  • Quotient Rule for Logarithms - log_{b}(\frac{a}{c} )=log_{b}a-log_{b}c
  • Power Rule for Logarithms - log_{b}(a^c)=c*log_{b}a

The exercise asks the potential solutions for  log_4x+log_4(x+6)=2. In this expression you can apply the Product Rule for Logarithms.

                                  log_4x+log_4(x+6)=2\\ \\ x*(x+6)=4^2\\ \\ x^2+6x=16\\ \\ x^2+6x-16=0

Now you should solve the quadratic equation.

 

 Δ=b^2-4ac=36-4*1*(-16)=36+64=100. Thus, x will be x_{1,\:2}=\frac{-6\pm \:\sqrt{100} }{2\cdot \:1}=\frac{-6\pm \:10}{2}. Then:

x_1=\frac{-6+10}{2}=\frac{4}{2} =2\\ \\ \:x_2=\frac{-6-10}{2}=\frac{-16}{2} =-8

The potential solutions  are 2 and -8.

Read more about the properties of logarithms here:

brainly.com/question/14868849

4 0
2 years ago
You have $83 in your bank account each week you plan to deposit eight dollars from your allowance and $15 from your paycheck the
docker41 [41]
We know that you have 83$ in your bank account.

Okay so what is 15+8=23 So that means you get 23$ per week.

Now what is 83+23=106
106+23=129
129+23=152
152+23=175
Now that was four 23's


That means it would take 4 weeks for you to have 175 dollars in your bank account.
Hope this helped.
7 0
3 years ago
6 &amp; 7 please help me show work please and thank you!
lara31 [8.8K]

Answer:

6. \frac{29}{15} or 1\frac{14}{15}

7. \frac{133}{96} or 1\frac{37}{96}

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3 years ago
Write in terms of i.<br> Simplify your answer as much as possible.<br> -8
Goryan [66]

Answer:

In order to begin figuring that out, we need to know about the equation.

3 0
2 years ago
Estimate: 43 divide by 6
Nadya [2.5K]

Answer:

7

Step-by-step explanation:

42/ 6 = 7

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