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2 years ago

What is the slope of a line perpendicular to the line whose equation is 3x-3y=54. Fully simplify your answer.

1 answer:

7 0

Perpendicular = opposite sign and reciprocal slope
Make equation into y = mx + b
Add 3y to both sides
3y + 54 = 3x
Subtract 54
3y = 3x - 54
Divide by 3
y = x - 18
The slope is 1
Make it negative and reciprocal
= -1/1 = -1

Solution: the slope will be -1

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3 years ago

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2 years ago

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Tpy6a [65]

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Step-by-step explanation:

A F is 13 using pythagorean theorem on triangle CED and applying the hypotenuse length to A F.

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3 years ago

Find 2 common angles that sum to (17pi/12) 2. Evaluate tan(17pi/12) using the sum identity for tangent.

Dmitry [639]

Note that
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Note that
$x= \frac{ \pi }{4}:\,\, sin(x) =cos(x)= \frac{1}{ \sqrt{2} },\,tan(x)=1\\x= \frac{7 \pi }{6} :\,\,sin(x)=- \frac{1}{2} ,\,\,cos(x)=- \frac{ \sqrt{3} }{2} ,\,\,tan(x)= \frac{1}{ \sqrt{3} }$

Use the identity
$tan(x+y)= \frac{tan(x)+tan(y)}{1-tan(x)tan(y)}$

Therefore
$tan( \frac{17 \pi }{12} )= \frac{1+ \frac{1}{ \sqrt{3} } }{1- \frac{1}{ \sqrt{3} } } = \frac{ \sqrt{3}+1 }{ \sqrt{3}-1} = \frac{( \sqrt{3}+1 )^{2}}{( \sqrt{3}-1 )( \sqrt{3}+1 )} = \frac{3+1+2 \sqrt{3}}{3-1} =2+ \sqrt{3}$

Answer: 2 + √3

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3 years ago

On a bicycle, Miranda rides for 4 hours and is 50 miles from her house. After riding for 6 hours, she is 74 miles away. What is

Vera_Pavlovna [14]

<h2> Miranda's rate is 12 hours per mies.</h2>

Step-by-step explanation:

Given by question,

Miranda began her ride from home merely that she was 50 miles away from home after 4 hours of riding.

To find, Miranda's rate = ?

2 hours later she was 974 miles from home.

∴ 2 hours she rode = 74 miles - 50 miles

Miranda rides 24 miles in 2 hours.

∴ Miranda rides in 1 hour = $\dfrac{24}{2}$ $\dfrac{miles}{hour}$

= $12$ $\dfrac{miles}{hour}$

Thus, Miranda's rate is 12 hours per mies.

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3 years ago

What is the slope of a line perpendicular to the line whose equation is 3x-3y=54. Fully simplify your answer.​

What is the slope of a line perpendicular to the line whose equation is 3x-3y=54. Fully simplify your answer.