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3 years ago

Simplify the expression: ( X + 5)( X-7)

Mathematics

2 answers:

Hitman42 [59]3 years ago

7 0

(x + 5)(x - 7)
x(x - 7) + 5(x - 7)
x(x) - x(7) + 5(x) - 5(7)
x² - 7x + 5x - 35
x² - 2x - 35

Igoryamba3 years ago

3 0

Answer is in the photo UwU

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marishachu [46]

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Step by step explanation This is how I got the answer to your question and I gave you the solution I hope this helps you out

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2 years ago

A 39-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate

LenaWriter [7]

Answer:

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

Step-by-step explanation:

A 39-foot ladder is leaning against a vertical wall. We are given that the bottom of the ladder is being pulled away at a rate of two feet per second, and we want to find the rate at which the area of the triangle being formed is is changing when the bottom of the ladder is 15 feet from the wall.

Please refer to the diagram below. x is the distance from the bottom of the ladder to the wall and y is the height of the ladder on the wall.

According to the Pythagorean Theorem:

$\displaystyle x^2+y^2=1521$

Let's take the derivative of both sides with respect to time t. Hence:

$\displaystyle \frac{d}{dt}\left[x^2+y^2\right] = \frac{d}{dt}\left[ 1521\right]$

Implicitly differentiate:

$\displaystyle 2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$

Simplify:

$\displaystyle x\frac{dx}{dt} + y \frac{dy}{dt} = 0$

The area of the triangle formed will be given by:

$\displaystyle A = \frac{1}{2} xy$

Again, let's take the derivative of both sides with respect to time t:

$\displaystyle \frac{dA}{dt} = \frac{d}{dt}\left[\frac{1}{2}xy\right]$

From the Product Rule:

$\displaystyle \frac{dA}{dt} = \frac{1}{2}\left(y\frac{dx}{dt} + x\frac{dy}{dt}\right)$

At that instant, the ladder is 15 feet from the base of the wall. So, x = 15. Using this information, find y.

$\displaystyle y = \sqrt{1521-(15)^2}=36$

The bottom of the ladder is being pulled away from the wall at a rate of two feet per second. So, dx/dt = 2. Using this information and the first equation, find dy/dt:

$\displaystyle \frac{dy}{dt} =-\frac{x\dfrac{dx}{dt}}{y}$

Evaluate for dy/dt:

$\displaystyle \frac{dy}{dt} = -\frac{(15)(2)}{(36)}=-\frac{5}{6}$

Finally, using dA/dt, substitute in appropriate values:

$\displaystyle \frac{dA}{dt} = \frac{1}{2}\left((36)(2)+(15)\left(-\frac{5}{6}\right)\right)$

Evaluate. Hence:

$\displaystyle \frac{dA}{dt} = \frac{119\text{ ft}^2}{4\text{ s}} = 29.75\text{ ft$^2$/s}$

The area of the triangle formed is increasing at a rate of 29.75 square feet per second.

8 0

3 years ago

What is an opposite number?

EleoNora [17]

Answer:

In mathematics, opposite number or additive inverse of any number is a number n which, if added to n, results in 0 (the identity element of addition). The opposite number for n is written as −n. For example, −7 is the opposite number of 7

Step-by-step explanation:

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3 years ago

A shoreline is eroding at a rate of 1/3 3 foot per 3 months. How many feet are eroding per year?

salantis [7]

7ft if 3+1/3 hopefully this helps i did hwat i can

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4 years ago

Read 2 more answers

At a restaurant, 8 plates are accidently

inessss [21]

Y=-8x+7
explanation-
-8 is the growth rate and 7 is the amount of days the -8 is happening.
Hope this helps!

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3 years ago