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3 years ago

PLEASE HELP!!!!!! what is the simplified expression to represent the area of the shaded region???

Mathematics

1 answer:

Furkat [3]3 years ago

4 0

Answer: 29x+23

Step-by-step explanation:

In order to find the area of the shaded region, we need to subtract the unshaded region in middle from the large rectangle

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Step 1. Find the area of the large rectangle

A=lw (length × width)

A=(2x+4)(3x+6)

A=6x²+12x+12x+24 ⇔ Use FOIL (First Outer Inner Later)

A=6x²+24x+24

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Step 2. Find the area of the unshaded region

A=lw

A=(2x-1)(3x-1)

A=6x²-2x-3x+1 ⇔ Use FOIL

A=6x²-5x+1

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Step 3. Subtract unshaded from the large rectangle to get the area of shaded region

A (shade region)=large rectangle-unshaded region

A (shade region)=(6x²+24x+24)-(6x²-5x+1)

A (shade region)=6x²+24x+24-6x²+5x-1 ⇔ get off parenthesis

A (shade region)=6x²-6x²+24x+5x+24-1 ⇔ move the like term together

A (shade region)=29x+23 ⇔ combine like term

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Answer:

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Step-by-step explanation:

The equation of a line in slope- intercept form is

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Rearrange 3x - y = 9 into this form by subtracting 3x from both sides

- y = - 3x + 9 ( divide all terms by - 1 )

y = 3x - 9 ← in slope- intercept form

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Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{3}$ , thus

y = - $\frac{1}{3}$ x + c ← is the partial equation

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a guy wire for a tree is 20 ft long, making a 21 angle with the ground. How far is the base of the tree from a stake anchoring t

evablogger [386]

Answer:

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Step-by-step explanation:

Based on the information given we can conclude that our set up will be a Right triangle (i.e. one angle is 90°), where the hypotenuse will be denoted by the guy wire of $20ft$ and angle of 21° is the angle formed between then hypotenuse and the base (i.e. ground).

Thus we want to find the base length (lets call it $x$ ) of this triangle, so we can use trigonometry as we have one angle and the hypotenuse, as follow:

$cos(21)=\frac{adjacent side}{hypotenuse}=\frac{baselength}{guywire}\\\\ cos(21)=\frac{x}{20} \\x=20cos(21)\\x=18.671\\x=18.7ft$

So the base is approximately 18.7 feet far from the tree of the anchored wire.

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3 years ago