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Answer:
The inequality is $200 + x*$8≤ $350
Step-by-step explanation:
An inequality is an inequality between letters (unknowns) and numbers related by arithmetic operations. Its solution set is the set of real numbers that satisfy it. In other words, an algebraic inequality in which its members are linked by the signs <(less than), ≤ (less than or equal to),> (greater than) or ≥ (greater than or equal to) is called an inequality.
Solving an inequality is to find the values of the unknown for which the inequality holds. The solution of an inequality is an interval or a union of intervals of real numbers.
In this case, you know that Carmen wants to buy 2 pairs of sneakers that cost $ 100 each.So the 2 pairs of sneakers will cost Carmen:
2 * $ 100 = $ 200
On the other hand, Carmen wants to find the possible amount of socks that she can buy, knowing that a pair costs $ 8. Being x the amount of socks that she can buy, then Carmen spends on socks:
x*$8
Knowing that Carmen has a $ 350 gift card to spend at Modell's, then what she spent on sneakers and socks cannot be more than $ 350. That is to say, the sum of what was spent on sneakers and socks must be less than or equal to $ 350, because Carmen cannot spend more than she has. This is expressed by the following inequality:
<u><em>$200 + x*$8≤ $350</em></u>
Solving for x:
x*$8 ≤ $350 - $200
x*$8≤ $150
x≤
x≤ 18.75
<u><em>Carmen can buy 2 sneakers and 18 or fewer socks with the $ 350 gift card.</em></u>
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We can draw a unit circle as:
The sine is the vertical leg (or vertical projection) of the triangle formed by the angle.
The cosine will be the horizontal leg (or horizontal projection) of this same triangle.
The hypotenuse of this triangle will be the radius if the unit circle (r = 1).
a) The sine will be increasing from θ = 0° until it reaches its maximum at 90°.
Then it will be decreasing for angles between 90° and 270°.
Between 270° and 0° it will be increasing again.
b) The cosine has a maximum value for an angle of 0°.
It will decrease until 180°.
Then it will be increasing from angles between 180° and 360°.
c) We can see in the unit circle that the sine is 0 when the angle is one the horizontal axis, like when θ = 0° or θ = 180°.
The cosine will be equal to 0 when the angle is vertical: θ = 90° and θ = 270°.
Answer:
a) Increasing: (0°, 90°) and (270°, 360°)
Decreasing: (90°, 270°)
b) Increasing: (180°, 360°)
Decreasing: (0°,180°).
c) Sin(θ) = 0 for θ = 0° and θ = 180°
Cos(θ) = 0 for θ = 90° and θ = 270°
