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2 years ago

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Alina spent no more than $45 on gas for a road trip. The first gas station she used charged $3.50 per gallon and the second gas

station charged $4.00 per gallon. Which inequality relates the number of gallons of gas she bought at the first station, x, the number of gallons of gas she bought at the second station, y, and the total amount she paid? What are the possible values of y?

2 answers:

Paraphin [41]2 years ago

8 0

Answer: 3.50x + 4.00y ≤ 45

0 < y < 11.25

<u>Step-by-step explanation:</u>

$3.50x + 4.00y \leq 45\\\\\\\text{Subtract 3.50x from both sides:}\\4.00y\leq -3.50x+45\\\\\\\text{Divide everything by 4.00 (to isolate y):}\\\dfrac{4.00y}{4.00}\leq \dfrac{-3.50x}{4.00}+\dfrac{45}{4.00}\\\\\\y\leq-0.875x+11.25\\\\\\\text{Both x and y must be greater than zero, so:}\\0$

Naddik [55]2 years ago

8 0

Answer:

c

Step-by-step explanation:

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If cos() = − 2 3 and is in Quadrant III, find tan() cot() + csc(). Incorrect: Your answer is incorrect.

nydimaria [60]

Answer:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

Step-by-step explanation:

Given

$\cos(\theta) = -\frac{2}{3}$

$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

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Take LCM and solve

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So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

$\csc(\theta) = \frac{-3}{\sqrt 5}$

Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

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So, we have:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

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Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

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Take LCM

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

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