Answer:
Option B. Cosec θ = –5/3
Option C. Cot θ = 4/3
Option D. Cos θ = –4/5
Step-by-step explanation:
From the question given above, the following data were obtained:
Tan θ = 3/4
θ is in 3rd quadrant
Recall
Tan θ = Opposite / Adjacent
Tan θ = 3/4 = Opposite / Adjacent
Thus,
Opposite = 3
Adjacent = 4
Next, we shall determine the Hypothenus. This can be obtained as follow:
Opposite = 3
Adjacent = 4
Hypothenus =?
Hypo² = Opp² + Adj²
Hypo² = 3² + 4²
Hypo² = 9 + 16
Hypo² = 25
Take the square root of both side
Hypo = √25
Hypothenus = 5
Recall:
In the 3rd quadant, only Tan is positive.
Therefore,
Hypothenus = –5
Finally, we shall determine Sine θ, Cos θ, Cot θ and Cosec θ to determine which option is correct. This can be obtained as follow:
Opposite = 3
Adjacent = 4
Hypothenus = –5
Sine θ = Opposite / Hypothenus
Sine θ = 3/–5
Sine θ = –3/5
Cos θ = Adjacent / Hypothenus
Cos θ = 4/–5
Cos θ = –4/5
Cot θ = 1/ Tan θ
Tan θ = 3/4
Cot θ = 1 ÷ 3/4
Invert
Cot θ = 1 × 4/3
Cot θ = 4/3
Cosec θ = 1/ Sine θ
Sine θ = –3/5
Cosec θ = 1 ÷ –3/5
Invert
Cosec θ = 1 × –5/3
Cosec θ = –5/3
SUMMARY
Sine θ = –3/5
Cos θ = –4/5
Tan θ = 3/4
Cot θ = 4/3
Cosec θ = –5/3
Therefore, option B, C and D gives the correct answer to the question.
Answer:
Option C is correct
Step-by-step explanation:
We need to factorize the expression:
For factorization we need to break the middle term such that the product is equal to 24x^2 and the sum is equal to 10x
We know that 6*4 = 24 and 6+4 =10
So, solving
Taking common
So, the factors of
are
Hence Option C is correct
Answer:
x=12
Step-by-step explanation:
f(x)=16x-30 and g(x)=14x-6
(f-g)(x)=0
f(x)=16x-30 -(14x-6)
Distribute
= 16x -30 -14x +6
Combine like terms
= 16x-14x -30+6
2x-24
Set this equal to zero
2x-24 =0
Add 24 to each side
2x-24 +24=0+24
2x=24
Divide by 2
2x/2 =24/2
x = 12
A= 4 points
B= 3 points
C= 2 points
D= 1 point
F= 0 points
So you add 2+2+4+4+3+3+3+1
Which equals 22
Now divide 22 by 8
You get 2.75
So yes with a 2.75 gpa you should pass 8th grade as most schools require nothing less than a 2.0
