Answer:
A
Step-by-step explanation:
y = (-2/5)x + 1
By inspection of the equation, the slope of the line is -2/5 and the y-intercept is 1.
Therefore, we can immediately discount option B and D, as their y-intercepts are NOT 1.
Find the point where the line crosses the x-axis by setting the equation to 0 and solving for x:
0 = (-2/5)x + 1
⇒ -1 = (-2/5)x
⇒ -5 = -2x
⇒ x = 5/2
Therefore, the line of the function intersects the x-axis at x = 5/2 = 2.5
From inspection of the graphs, the line in option A intersects the x-axis at 2.5. Therefore, this is the correct graph.
2 1/3
You would do 6 3/4- 1 3/4=5
5-1 1/3= 2 2/3
Answer:
x=7/3
Step-by-step explanation:
8 ^ (x - 1 ) = 16
We need to rewrite 8 as 2^3 and 16 as 2^4
2^3 ^ (x - 1 ) = 2^4
We know that a^b^c = a^(b*c)
2^(3(x-1)) = 2^4
The bases are the same so the exponents are the same
3(x-1) = 4
Distribute
3x-3 = 4
Add 3 to each side
3x-3+3 = 4+3
3x = 7
Divide by 3
3x/3 = 7/3
x=7/3
Remember:
sec t=1/cos t
sin²t+cos²t=1 ⇒sin²t=1-cos² t
Therefore:
cos t(sec t- cost)=(cos t* sec t)- cos² t=(cos t * 1/cos t)-cos² t=1-cos²t=sin² t
Answer: cos t(sec t-cos t)=sin² t
