Answer:
Review the explanation
Step-by-step explanation:
The triangles ΔABC and ΔBAD are congruent, establishing:
- AB ≅ BA;
- AC ≅ BD;
- BC ≅ AD;
- ∠ABC ≅ ∠BAD;
- ∠BCA ≅ ∠ADB;
- ∠CAB ≅ ∠DBA.
Now, consider triangles AEC and BED. In these triangles, we have:
- AC ≅ BD;
- ∠EAC ≅ ∠EBD (due to ∠CBA ≅ ∠BAD);
- ∠AEC ≅ ∠BED (being vertical angles).
Therefore, ΔAEC ≅ ΔBED, which leads to the conclusion that:
AE ≅ EB.
This indicates that line segment CD bisects segment AD.
In this scenario, the first step is to assign variables.
We define:
x: time measured in minutes
y: distance covered.
The equations formulated are as follows:
For Kathleen:

For Arnob:

At the moment Arnob meets Kathleen, we have:

Next, we isolate x.
We now have:


Answer:
Arnob takes a total of 75 minutes to catch up to Kathleen:
d. 75
Answer:
$12.18
Step-by-step explanation:
Provided:
The price of a 0.8 liter bottle of Mexican wine amounts to 101 pesos.
Consequently,
The price for 1 liter of Mexican wine can be determined as
pesos.
Additionally,
Converting, 1 Mexican peso equates to 0.051 dollars.
As a result, the equivalent cost of 1 liter of Mexican wine is
dollars.
Moreover,
Knowing that 1 gallon equals 3.78541 liters;
Thus, half a gallon equals
= 1.892705 liters.
Therefore, the cost for a half-gallon jug would be
dollars.
In conclusion, the price for a half-gallon of this wine is $12.18.
Answer:
StartFraction negative 1 Over k cubed EndFraction
Detailed breakdown:
3k / (k + 1) × (k² - 1) / 3k³
= 3k(k² - 1) / (k + 1)(3k³)
= 3k³ - 3k / 3k⁴ + 3k³
= -3k / 3k⁴
= -1/k³
StartFraction k + 1 Over k squared EndFraction
(k + 1) / k²
StartFraction k minus 1 Over k squared EndFraction
(k - 1)/k²
StartFraction negative 1 Over k cubed EndFraction
= -1/k³
StartFraction 1 Over k EndFraction
= 1/k
Response:
470.12??? not certain!!!!
Step-by-step explanation: