5. The blue one is y >= 5x - 7
and green is y >= -0.65x + 3
6. y <= (4/5)x
y >= -(5/4)x
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:
2.2
Step-by-step explanation:
This is because you can use long divison on paper, 25 goes in 50 2 times so it would be remaining with 5 and since you need no remainers bring down a zero which gives you an extra 50 and 25 goes in 50 2 times so 2.2
Answer:
38.28 cm = D. 38
Step-by-step explanation:
Area of the Rectangle: l x w
Length: 6 cm
With: 4 cm
Area = 4 x 6
Area of Rectangle: 24 cm
Area of the Triangle: lw(1/2)
Length: 4 cm
Width: 4 cm
Area: 4 x 4 = 16 x 1/2 = 8
Area of Triangle: 8 cm
Area of the Circle: pi x r^2 x 1/2
Radius: 2 cm
Pi: 3.14
Area: 3.14 x 2^2
Area: 3.14 x 4 = 12.56
Area of Circle: 12.56 x 1/2
Lastly, you add them all together:
24 + 8 + 6.28 = 38.28 cm
