12 + 5k + 15 -24
------------------- = -----------------------
k + 3 k - 4
5k + 27 -24
------------ = ---------------
k + 3 k - 4
(k - 4)(5k + 27) = -24 (k + 3)
5k^2 - 20k + 27k -108 = - 24k - 72
5k^2 + 31k - 36 = 0
(5k + 36)(k - 1) = 0
5k + 36 = 0; k = -36/5 = -7.2
k - 1 = 0; k = 1
solutions
k = 1 and k = -7.2
500,000 is that number rounded.
Answer:
sin θ = (√21) / 5
tan θ = (√21) / 2
Step-by-step explanation:
Remember the formulas for the <u>trigonometry ratios</u> with SohCahToa:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
If cos θ = 2/5, then:
adjacent = 2
hypotenuse = 5
Remember all right triangles follow the <u>Pythagorean Theorem</u>. So if you are missing one side, you can solve.
Let's find the opposite side.
a² + b² = c²
2² + b² = 5²
4 + b² = 25
b² = 21
b = √21
opposite = √21
Now we know all three sides. <u>Use the trigonometry ratios</u> to find sine and tangent.
sin θ = opposite / hypotenuse
sin θ = (√21) / 5
tan θ = opposite / adjacent
tan θ = (√21) / 2
It will take 20 days to make 20 craft pieces.
If she can make 5 in 5 days, then it will take her 20 days to make 20 craft peices
