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schepotkina [342]
2 years ago
4

Evelyn bought 8.4 gallons of gas for $23.94. Which equation can be used to determine the price of each gallon of gas?

Mathematics
2 answers:
Reil [10]2 years ago
7 0
The equation would be
8.4x = 23.94
Paladinen [302]2 years ago
3 0

Answer:

8.4x=23.94

First option is correct.

Step-by-step explanation:

Let the price of each gallon of gas is $x.

And we have been given that 8.4 gallons of gas for $23.94.

So, we can make the below proportion

\frac{8.4}{23.94}=\frac{1}{x}

Cross multiplying, we get

8.4x=23.94

Hence, the equation that can be used to determine the price of each gallon of gas is

8.4x=23.94

First option is correct.

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If cos(t) = 2/7 and t is in the 4th quadrant, find sin(t).
Yuliya22 [10]
We can use the Pythagorean Trigonometric Identity which says:
sin^2(t)+cos^2(t)=1

Since we need to find sin(t), we have to solve for it:
sin(t)= \sqrt{1-cos^2(t)}

Let's plug in the given cos(t) value:
sin(t) = \sqrt{1-cos^2( \frac{2}{7})}

And solve sin(t):
sin(t) = \sqrt{1- \frac{4}{49} } = \frac{x}{y} \sqrt{ \frac{49}{49}- \frac{4}{49} }

Simplify further:
sin(t) = \sqrt{ \frac{45}{49} } = \frac{ \sqrt{45} }{7} = \frac{ \sqrt{9*5} }{7}

And it all simplifies down to:
sin(t) = \frac{3 \sqrt{5} }{7}

Since it's in the 4th quadrant, the sin(t) value is going to be negative. So, your final answer is: 
sin(t) = - \frac{ 3\sqrt{5} }{7}

Hope this helps!
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2 years ago
Ernest is purchasing a $175,000 home and is making a 20% down payment toward the cost. He is also buying 2 points in order to lo
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Answer:

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