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3 years ago

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On Saturday, Mark sold 2 7/8 gallons of lemonade. On the same day, Regan sold 2/3 as much lemonade as Mark. How much lemonade, i

n gallons did Regan sell?

1 answer:

MAXImum [283]3 years ago

6 0

2 7/8= 2/3L
Divide both sides by 2/3 and get 4.31 or 4 5/16
Hope this helps!!

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Which equation results from adding the equations in this system?

Diano4ka-milaya [45]

Answer:

D. - 5x = - 10

Step-by-step explanation:

<u>Given equations:</u>

-8x+8y = 8
3x-8y=-18

<u>Add together:</u>

-8x + 8y + 3x - 8y = 8 - 18
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Correct option is D

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3 years ago

What is the length of the longest side of a triangle that has vertices at (4, -2), (-4,-2),

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Find f.<br><br> A) 7.4<br><br> B) 8.2<br><br> C) 10.5<br><br> D) 11.1

tatyana61 [14]

F=72

g=6

------------

$\cos { \left( F \right) } =\frac { { e }^{ 2 }+{ g }^{ 2 }-{ f }^{ 2 } }{ 2eg }$

Therefore:

$\cos { \left( 72 \right) } =\frac { { e }^{ 2 }+{ 6 }^{ 2 }-{ f }^{ 2 } }{ 2\cdot e\cdot 6 } \\ \\ \cos { \left( 72 \right) } =\frac { { e }^{ 2 }+36-{ f }^{ 2 } }{ 12e }$

$\\ \\ 12e\cdot \cos { \left( 72 \right) } ={ e }^{ 2 }+36-{ f }^{ 2 }\\ \\ \therefore \quad { f }^{ 2 }={ e }^{ 2 }-12e\cdot \cos { \left( 72 \right) } +36\\ \\ \therefore \quad f=\sqrt { { e }^{ 2 }-12e\cdot \cos { \left( 72 \right) +36 } } \\ \\ \therefore \quad f=\sqrt { e\left( e-12\cos { \left( 72 \right) } \right) +36 }$

But what is e?

E=76

G=32

g=6

And:

$\frac { e }{ \sin { \left( E \right) } } =\frac { g }{ \sin { \left( G \right) } }$

Which means that:

$\frac { e }{ \sin { \left( 76 \right) } } =\frac { 6 }{ \sin { \left( 32 \right) } } \\ \\ \therefore \quad e=\frac { 6\cdot \sin { \left( 76 \right) } }{ \sin { \left( 32 \right) } }$

If you take this value into account, you will discover that f is...

$f=\sqrt { \frac { 6\cdot \sin { \left( 76 \right) } }{ \sin { \left( 32 \right) } } \left( \frac { 6\cdot \sin { \left( 76 \right) } }{ \sin { \left( 32 \right) } } -12\cos { \left( 72 \right) } \right) +36 } \\ \\ \therefore \quad f=10.8\quad \left( 1\quad d.p \right)$

So I would have to say that the answer is approximately (c).

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amid [387]

Special Triangles Theorem
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