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3 years ago

6

The area of a rectangle is 20 square inches. If the length is 4 inches less than 6 times the width, then find the dimensions of

the rectangle.

1 answer:

Tpy6a [65]3 years ago

8 0

Step-by-step explanation:

Let the width=x

Length =6x-4

As we know that in a rectangle

${\boxed{\sf Area=LB}}$

Substitute the values

$\hookrightarrow\sf x (6x-4)=20$

$\hookrightarrow\sf 6x^2-4x=20$

$\hookrightarrow\sf 6x^2-4x-20=0$

Here a=6, b=-4, c=-20.
use quadratic formula

$\hookrightarrow\sf x=\dfrac {1}{3}+\dfrac {1}{3}\sqrt {31} \quad or \quad \dfrac {1}{3}+\dfrac {-1}{3}\sqrt {31}$

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3 years ago

PLEASE HELP ASAP! I don’t recall how to do this!

MakcuM [25]

Answer:

Step-by-step explanation:

For a. we start by dividing both sides by 200:

$(1.05)^x=1.885$

In order to solve for x, we have to get it out from its position of an exponent. Do that by taking the natural log of both sides:

$ln(1.05)^x=ln(1.885)$

Applying the power rule for logs lets us now bring down the x in front of the ln:

x * ln(1.05) = ln(1.885)

Now we can divide both sides by ln(1.05) to solve for x:

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Do this on your calculator to find that

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For b. we will first apply the rule for "undoing" the addition of logs by multipllying:

$ln(x*x^2)=5$

Simplifying gives you

$ln(x^3)=5$

Applying the power rule allows us to bring down the 3 in front of the ln:

3 * ln(x) = 5

Now we can divide both sides by 3 to get

$ln(x)=\frac{5}{3}$

Take the inverse ln by raising each side to e:

$e^{ln(x)}=e^{\frac{5}{3}}$

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x = 5.29449005

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$\frac{1}{2}=e^{.1x}$

"Undo" that e by taking the ln of both sides:

$ln(.5)=ln(e^{.1x})$

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-.6931471806 = .1x

x = -6.931471806

Question d. is a bit more complicated than the others. Begin by turning the base of 4 into a base of 2 so they are "like" in a sense:

$(2^2)^x-6(2)^x=-8$

Now we will bring over the -8 by adding:

$(2^2)^x-6(2)^x+8=0$

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But don't forget the substitution that we made earlier to make this easy to factor. Now we have to put it back in:

$2^x=4,2^x=2$

For the first solution, we will change the base of 4 into a 2 again like we did in the beginning:

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Now that the bases are the same, we can say that

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Now that the bases are the same, we can say that

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3 years ago

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olga_2 [115]

Answer:The formula is P=2 L=2 W or V= L x W X H

Step-by-step explanation:

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