Well, given that a quarter equals 5 nickels, we can reason that, in order to get 12 coins, we would have to get 10 nickels (equals 50 cents) and 2 quarters (the other 50 cents, to make a dollar).
You didn't say whether you needed this expressed in a mathematical formula, but knowing the answer already, it shouldn't be hard to come up with one if necessary.
Hope this helps.
Answer:
the picture can't clean. so I can't solve the problem
Answer:
14.40646471 =x
Step-by-step explanation:
tan (42) = x/16
Multiply each side by 16
16 tan 42 = x/16 *16
16 tan 42 = x
16 * .900404044 = x
14.40646471 =x
Step-by-step explanation:
you would do 3 ÷ .99 and then when you get the answer from that you would multiply it by 5.
By "which is an identity" they just mean "which trigonometric equation is true?"
What you have to do is take one of these and sort it out to an identity you know is true, or...
*FYI: You can always test identites like this:
Use the short angle of a 3-4-5 triangle, which would have these trig ratios:
sinx = 3/5 cscx = 5/3
cosx = 4/5 secx = 5/4
tanx = 4/3 cotx = 3/4
Then just plug them in and see if it works. If it doesn't, it can't be an identity!
Let's start with c, just because it seems obvious.
The Pythagorean identity states that sin²x + cos²x = 1, so this same statement with a minus is obviously not true.
Next would be d. csc²x + cot²x = 1 is not true because of a similar Pythagorean identity 1 + cot²x = csc²x. (if you need help remembering these identites, do yourslef a favor and search up the Magic Hexagon.)
Next is b. Here we have (cscx + cotx)² = 1. Let's take the square root of each side...cscx + cotx = 1. Now you should be able to see why this can't work as a Pythagorean Identity. There's always that test we can do for verification...5/3 + 3/4 ≠ 1, nor is (5/3 + 3/4)².
By process of elimination, a must be true. You can test w/ our example ratios:
sin²xsec²x+1 = tan²xcsc²x
(3/5)²(5/4)²+1 = (4/5)²(5/3)²
(9/25)(25/16)+1 = (16/25)(25/9)
(225/400)+1 = (400/225)
(9/16)+1 = (16/9)
(81/144)+1 = (256/144)
(81/144)+(144/144) = (256/144)
(256/144) = (256/144)
