Answer:
the inverse for each relation:
1. {(1,-2), (2, 3),(3, -3),(4, 2)} is
<u>{</u><u>(</u><u>-</u><u>2</u><u>,</u><u>1</u><u>)</u><u>,</u><u>(</u><u>3</u><u>,</u><u>2</u><u>)</u><u>,</u><u>(</u><u>-</u><u>3</u><u>,</u><u>3</u><u>)</u><u>,</u><u>(</u><u>2</u><u>,</u><u>4</u><u>)</u><u>}</u><u>.</u>
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)
Answer: Simple interest rate = 3%.
Step-by-step explanation: We are given invested amount = $5000.
Number of years of investment = 4 years.
Interest earned = $600.
Simple interest formula.
I = P R T.
Where I is the earned interest, P is the invested amount , R is the rate of interest and T is the time in years.
Plugging values in formula, we get
600 = 5000 × R × 4
600 = 20000R.
Dividing both sides by 20000, we get
0.03 = R.
Multiplying by 100 to convert it in percentage, we get
0.03 × 100 = R
R = 3 %.
Answer:
3 ounces
Step-by-step explanation:
1 pound = 16 ounces
2(16) + 2(16) = 16 = 80 ounces of train mix - 5 from sister = 75 remaining
75 ounces of trail mix / 25 snack bags = 3 ounces of mix in each bag
Answer:
Y-intercept=5 Slope=-1/4
Step-by-step explanation:
Plot a point on (0,5)
From that point, you can either go down 1 point and right 4 points, or you can go up 1 point and go left 4 points.
Whichever one you choose, plot a point after each 2 movements
if this is too confusing, another point would be (4, 4) then make a line through both points.
