Total funds available with Betsy = $50,000
Interest rate in B-rated bonds = 13% per year
Let amount invested in B-rated bonds be x
Interest rate in certificate of deposit (CD) = 5% per year
Amount invested in CD = 50,000-x
Now, we have to determine x such that Betsy can get exactly $6,000 in interest per year. Hence:
x * 13% + (50,000 - x) * 5% = 6,000
⇒ 0.13x - 0.05x + 2,500 = 6,000
⇒ 0.08x = 3,500
⇒ x = 43,750
Hence, Betsy should invest $43,750 in B-rates bonds
And 50,000 - x = 50,000 - 43,750 = 6,250
And she should invest 6,250 in CD
Let <em>a</em> and <em>b</em> be the zeroes of <em>x</em>² + <em>kx</em> + 12 such that |<em>a</em> - <em>b</em>| = 1.
By the factor theorem, we can write the quadratic in terms of its zeroes as
<em>x</em>² + <em>kx</em> + 12 = (<em>x</em> - <em>a</em>) (<em>x</em> - <em>b</em>)
Expand the right side and equate the coefficients:
<em>x</em>² + <em>kx</em> + 12 = <em>x</em>² - (<em>a</em> + <em>b</em>) <em>x</em> + <em>ab</em>
Then
<em>a</em> + <em>b</em> = -<em>k</em>
<em>ab</em> = 12
The condition that |<em>a</em> - <em>b</em>| = 1 has two cases, so without loss of generality assume <em>a</em> > <em>b</em>, so that |<em>a</em> - <em>b</em>| = <em>a</em> - <em>b</em>.
Then if <em>a</em> - <em>b</em> = 1, we get <em>b</em> = <em>a</em> - 1. Substitute this into the equations above and solve for <em>k</em> :
<em>a</em> + (<em>a</em> - 1) = -<em>k</em> → 2<em>a</em> = 1 - <em>k</em> → <em>a</em> = (1 - <em>k</em>)/2
<em>a</em> (<em>a</em> - 1) = 12 → (1 - <em>k</em>)/2 • ((1 - <em>k</em>)/2 - 1) = 12
→ (1 - <em>k</em>)²/4 - (1 - <em>k</em>)/2 = 12
→ (1 - <em>k</em>)² - 2 (1 - <em>k</em>) = 48
→ (1 - 2<em>k</em> + <em>k</em>²) - 2 (1 - <em>k</em>) = 48
→ <em>k</em>² - 1 = 48
→ <em>k</em>² = 49
→ <em>k</em> = ± √(49) = ±7
Using the distributive law:-
this = sqrt 14 sqrt 12 + sqrt 14 sqrt 7 - sqrt 3 sqrt 12 - sqrt 3 sqrt 7
= sqrt1 68 + sqrt 91 - sqrt 36 - sqrt 21
= sqrt 168 + sqrt 91 - sqrt21 - 6
Answer:
4/3
Step-by-step explanation:
TanC = opposite/adjacent
TanC = 40/30 ➡ 4/3
Answer:
Hi, There! my Name is jay and I'm here to help!
<h2>Question</h2>
Which graph best represents the number of hours Casey worked each week
<h2>Answer</h2>
(Option A . . .)
Step-by-step explanation:
According to the Question it says "Casey worked no more than 40 hours each week"
So we are looking for a graph that goes no more than 40 hours and the best choice would be option A
Hope this helps!
Take Care!
![-Jay-](https://tex.z-dn.net/?f=-Jay-)