Need help with 25 & 27 PLEASE!!!
1 answer:
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Answer:
15 miles
Step-by-step explanation:
Let be the miles in the circular park path,
the time Louisa takes to finish and
the time Calvin takes to finish both in hours.
Then , the longitude is equal to the velocity times the time used to finish. So
And the difference between Louisa's time and Calvin' time is 30 minutes, half an hour. So:
Three equations, three unknowns, the system can be solved.
Equalizing the equation with x :
In this last equation replace with the other equation and solve:
With Louisa's time find x:
Answer:
Valentina and Laura finished the same total number of shirts in hours.
Total number of shirts finished by Valentina
Total number of shirts finished by Laura
Step-by-step explanation:
Suppose that Valentina and Laura finished the same total number of shirts in hours.
Valentina can embroider 2 shirts per hour and Valentina has already completed 15 shirts.
Total number of shirts finished by Valentina
Laura can get through 3 shirts per hour and Laura has completed 11 shirts.
Total number of shirts finished by Laura
Therefore,
So,
Valentina and Laura finished the same total number of shirts in hours.
Total number of shirts finished by Valentina
Total number of shirts finished by Laura
Answer:
k = - , k = 2
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
The condition for equal roots is b² - 4ac = 0
Given
kx² + 2x + k = - kx ( add kx to both sides )
kx² + 2x + kx + k = 0 , that is
kx² + (2 + k)x + k = 0 ← in standard form
with a = k, b = 2 + k and c = k , thus
(2 + k)² - 4k² = 0 ← expand and simplify left side
4 + 4k + k² - 4k² = 0
- 3k² + 4k + 4 = 0 ( multiply through by - 1 )
3k² - 4k - 4 = 0 ← in standard form
(3k + 2)(k - 2) = 0 ← in factored form
Equate each factor to zero and solve for k
3k + 2 = 0 ⇒ 3k = - 2 ⇒ k = -
k - 2 = 0 ⇒ k = 2