Answer: $2,000,000
Explanation: Let X be the amount of Avery's investment. Since she will receive $40,000 every year for the next six years, the most she will earn is
$40,000 × 6 = $240,000.
Since she wants to earn 12% on her investment, her earnings is equal to 12% of X = 0.12X. Since the most she will earn is $240,000,
0.12X ≤ 240,000
X ≤ 240,000 ÷ 0.12 = 2,000,000 (Divide both sides by 0.12)
Hence X ≤ 2,000,000. Therefore, the most amount she should invest is $2,000,000.
We have proven that the trigonometric identity [(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] equals 1 + (secθ * cosec θ)
<h3>How to solve Trigonometric Identities?</h3>
We want to prove the trigonometric identity;
[(tan θ)/(1 - cot θ)] + [(cot θ)/(1 - tan θ)] = 1 + sec θ
The left hand side can be expressed as;
[(tan θ)/(1 - (1/tan θ)] + [(1/tan θ)/(1 - tan θ)]
⇒ [tan²θ/(tanθ - 1)] - [1/(tan θ(tanθ - 1)]
Taking the LCM and multiplying gives;
(tan³θ - 1)/(tanθ(tanθ - 1))
This can also be expressed as;
(tan³θ - 1³)/(tanθ(tanθ - 1))
By expansion of algebra this gives;
[(tanθ - 1)(tan²θ + tanθ.1 + 1²)]/[tanθ(tanθ(tanθ - 1))]
Solving Further gives;
(sec²θ + tanθ)/tanθ
⇒ sec²θ * cotθ + 1
⇒ (1/cos²θ * cos θ/sin θ) + 1
⇒ (1/cos θ * 1/sin θ) + 1
⇒ 1 + (secθ * cosec θ)
Read more about Trigonometric Identities at; brainly.com/question/7331447
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<span>−6a + 6a + 5 = 8
5 = 8 False
So, </span><span>No solution.</span>
Answer: He would have traveled 248 miles
Explanation: This is a ratio
To find how many miles he would have traveled after 4 hours, we need to apply the information givin into a ration table
(We can put miles on the top and hours on the bottom)
217 ?
------- ------
3.5 4
Now, we can do two things:
1. cross multiply
we would take 217 times 4 (868) and divide that by 3.5 (248)
2. Divide the top and bottom by 3.5 (numerator= 62 denominator= 1)
multiply 62 by 4 to get 248
Hope this helps!
The x intercepts occur when you set the factors equal to 0. x+1=0 & x-6=0 gives you the x-intercepts. x+1=0 -> x=-1. x-6=0 -> x=6. Therefore, -1 & 6 are your x intercepts
