Answer:
Step-by-step explanation:
13.
<h3>Given</h3>
<u>Quadratic equation</u>
- 4x² - 3x - 4 = 0
- With the roots of α and β
<h3>To Find </h3>
- The quadratic equation with roots of 1/(3α) and 1/(3β)
<h3>Solution</h3>
<u>The sum and the product of the roots of the given equation:</u>
- α + β = -b/a ⇒ α + β = -(-3)/4 = 3/4
- αβ = c/a ⇒ αβ = -4/4 = - 1
<u>New equation is:</u>
- (x - 1/(3α))(x - 1/(3β)) = 0
- x² - (1/(3α) + 1/(3αβ))x + 1/(3α3β) = 0
- x² - ((3α + 3 β)/(3α3β))x + 1/(3α3β) = 0
- x² - ((α + β)/(3αβ))x + 1/(9αβ) = 0
- x² - (3/4)/(3(-1))x + 1/(9(-1)) = 0
- x² + 1/4x - 1/9 = 0
- 36x² + 9x - 4 = 0
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14.
<h3>Given</h3>
<u>Quadratic equation</u>
- 3x² +2x + 7 = 0
- With the roots of α and β
<h3>To Find </h3>
- The quadratic equation with roots of α + 1/β and β + 1/α
<h3>Solution</h3>
<u>The sum and the product of the roots of the given equation:</u>
- α + β = -b/a ⇒ α + β = -2/3
- αβ = c/a ⇒ αβ = 7/3
<u>New equation is:</u>
- (x - (α + 1/β))(x - (β + 1/α)) = 0
- x² - (α + 1/β + β + 1/α)x + (α + 1/β) (β + 1/α) = 0
- x² - (α + β + (α + β)/αβ )x + αβ + 1/αβ + 2 = 0
- x² - (-2/3 - (2/3)/(7/3))x + 7/3 + 1/(7/3) + 2 = 0
- x² - (-2/3 - 2/7)x + 7/3 + 3/7 + 2 = 0
- x² + (14 + 6)/21x + (49 + 9 + 42/21) = 0
- x² + 20/21x + 100/21 = 0
- 21x² + 20x + 100 = 0
Answer:
Slope intercept form y= mx+b
y= 3/2x-5
slope= 3/2
y-int= -5
Step-by-step explanation:
Since r = h/6 ; r' = h'/6; = 5/6
<span><span>V′</span>=<span><span>10(2)(5)(5) / </span><span>3(3)(6)</span></span>pi+ <span><span>5⋅<span>5^2 / </span></span><span>3⋅<span>3^2</span></span></span> pi</span>
<span><span>V′</span>=<span>250 / 27</span>pi+<span>125 / 27</span>pi</span>
<span><span>V′</span>=<span>375 / 27</span>pi;<span> at the given moment specified
</span></span>
Answer:
C. Town A has the greater average number of dogs per neighborhood.
Step-by-step explanation:
First, find Town A's average number of dogs per neighborhood. Since the graph is a straight line, you can find the number of dogs per neighborhood by dividing a given y-value by its x-value counterpart:
(4,60)
60 dogs / 4 neighborhoods
<u>15 dogs / neighborhood.</u>
Now, we must find the average number of dogs per neighborhood in Town B. Since the equation is y = 10x, where x is the number of neighborhoods, in 1 neighborhood, there are 10 dogs:
<u>10 dogs / neighborhood.</u>
Finally, compare the two values:
15 > 10
<u>C. Town A has the greater average number of dogs per neighborhood.</u>
