3. Find the number which is 32,586 more than 87,65,432.
1 answer:
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Answer:
17. See below
18. 750
Step-by-step explanation:
17. Since the lollipops are being sold at the same price, 50 cents, for each one sold, they make a constant amount of money. For each increase in lollipops sold, there is a constant increase in money made, and thus the situation is a linear function.
18. To solve this equation, let's say y is the money made at the convention in dollars and x is the number of lollipops sold. If the principal gave them 125 dollars before they sold any lollipops (0 lollipops sold), then 125 is the y-intercept of the function, and in the equation y=mx+b, b=125. If each lollipop costs 50 cents (half of a dollar), then for each lollipop, x, sold, .5 dollars are made and are added to the profit, y. Thus, .5 dollars is the slope. The equation then becomes:
Now, if they need 500 dollars, y is thus equal to 500 dollars. Solving the equation:
Thus, 750 lollipops must be sold.
105° can be expressed as 60°+45°. What we have then is sin(60°+45°). The sum pattern for sin is sin(a)cos(b)+cos(a)sin(b). We will fill in as follows: sin(60)c0s(45)+cos(60)sin(45). Now draw those special right triangles in the first quadrant to get the exact values for each. The sin of 60 is 
, the cos of 45 is 
, the cos of 60 is 1/2, and the sin of 45 is . When we put all that together we get 
. Simplifying all of that we have 
. We can put that over the common denominator that is already there and get 
. Not sure if that's simplified enough; you may be at the point in class where you are rationalizing your denominator, but I'm not sure, and if you're not, I don't want to confuse you.