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Mathematics

1 answer:

Alex Ar [27]2 years ago

4 0

Answer:

CD = 6.3

Step-by-step explanation:

The triangles CED and CGF are similar since two sides are on same line and one side is parallel.

<u>Corresponding sides have equal ratios:</u>

CG/CE = CF/CD
CG/CE = (CD - 1.8)/CD
6/(6 + 2.4) = (CD - 1.8)/CD
6/8.4 = (CD - 1.8)/CD
1/1.4 = (CD - 1.8)/CD
1*CD = 1.4CD - 1.4*1.8
0.4CD = 2.52
CD = 2.52/0.4
CD = 6.3

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2x + 3 + 4x + 6 + 12x + 18 = 477<br><br> Please answer with solving steps. Thanks guys :)

dybincka [34]

Answer:

x= 25

Step-by-step explanation:

2x + 3 + 4x + 6 + 12x + 18 = 477

FIRST combine like terms

take all "x"

2+4+12= 18x

take all whole numbers

3+6+18= 27

18x+27= 477

now solve for x

-27 on both sides

18x= 450

÷18 on both sides

x= 25

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3 years ago

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Akimi4 [234]

Hope this answer helps you! If it did, please mark it as the brainiest! I would really appreciate it! :)

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3 years ago

Consider the circle of radius 5 centered at (0,0), how do you find an equation of the line tangent to the circle at the point (3

Flauer [41]

$\text{We know that the tangent at any point on a circle is perpendicular}\\
\text{to the radius at that point.}\\
\\
\text{so first we find the equation of the line joining (0,0) and (3,4)}\\
\text{and then using the slope, we find the line perperndicular to it at (3,4)}\\
\\
\text{the equation of the line passing through (0,0) and (3,4) is}\\
\\
y-0=\frac{4-0}{3-0}(x-0)$

$\Rightarrow y=\frac{4}{3}x\\
\\
\text{so the slope of radius is }m=\frac{4}{3}.\\
\\
\text{we know that the product of the perpendicular lines is }-1. \\
\\
\text{so the slope of the perpendicular line would be}=-\frac{1}{4/3}=-\frac{3}{4}\\
\\
\text{So the equation of the tangent line has slope }-\frac{3}{4} \text{ and}\\
\text{passing through (3,4). so equation of tangent line is}$

$y-4=-\frac{3}{4}(x-3)\\
\\
\Rightarrow y-4=-\frac{3}{4}x+\frac{9}{4}\\
\\
\Rightarrow y=-\frac{3}{4}x+\frac{9}{4}+4\\
\\
\Rightarrow y=-\frac{3}{4}x+\frac{9+16}{4}\\
\\
\text{so the equation of tangent line is:} y=-\frac{3}{4}x+\frac{25}{4}$