If 2x+9 < 32, then x could be

A box contains 100 colored chips; some are pink and some are blue. Milton chooses a chip at random, records the color, and place

Lena [83]

The approximate number of pink chips is 40. Here's why: what you need to do is set up the problem as shown below. 12 goes above 30 because you have to know what the total number of chips chosen is in order to relate it to 100 chips. From there, all you have to do is cross-multiply and divide (or my middle school teacher used to call it fish.... I'll explain why). First you are going to draw a line from the 100 to the 12 and multiply them. then you are going to curve the line that you will draw from the 12 to the 30 and divide the product of 12 and 100 by 30. Then you will draw a line from the 30 to the X meaning that the quotient that you find from the product of 120 and 100 divided by 30 equals X. Hope that helps.

12 x

30 100

4 0

2 years ago

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Find cos q if q is an angle in standard position and the point with coordinates (3, –4) lies on the terminal side of the angle.

gayaneshka [121]

Answer:

cos q = 3/5

Step-by-step explanation:

Standard position means the vertex (point or corner of the angle) is at (0,0) and one side of the angle is glued to the positive x-axis (facts, but not technical math terms) See image. Special triangles have all three sides nice and clean with whole number lengths, we call these Pythagorean triples. 3-4-5 is your most basic Pythagorean triple. So we don't even have to calculate the hypotenuse, see image. Now the triangle shown is easy to work with, using entry-level trig...cos = ADJ/HYP. So we get 3/5=.6 BUUuuuut, the angle q in the original problem is actually the giant angle, marked in yellow (see image) and we're in the fourth quadrant which means there's negative numbers all over the place. So just to be sure the answer is .6 and not -.6 Check your signs. One trick to remember is the ASTC markings in the quadrants. I use All Students Take Calculus, but what it means is in the first quadrant All the trig functions are positive. Only Sine (and fam) are positive in the 2nd quadrant. Tan (and fam) in the 3rd and Cos and fam in the 4th quadrant. It's a good quick check.

cos q = 3/5 OR cos q = .6