Answer:
The farthest distance would be 32.5 miles
Step-by-step explanation:
Given,
Speed = 65 miles per hour,
If t represents the time ( in hours ) taken in travelling,
Since, time has to commute down less than 30 minutes,
Also, 1 hour = 60 minutes,
Thus,
i.e. the highest time taken = 1/2 hours,
We know that,
Distance = speed × time,
∵ Distance ∝ time,
⇒ Distance will farthest for largest time taken,
Hence, the farthest distance = 
= 32.5 km.
Answer:
Yes, it will reach or exceed 141 degree F
Step-by-step explanation:
Given equation that shows the temperature T in degrees Fahrenheit x minutes after the machine is put into operation is,
Suppose T = 141°F,
Since, a quadratic equation 
has,
Real roots,
If Discriminant, 
Imaginary roots,
If D < 0,
Since, 
Thus, roots of -0.005x² + 0.45x + 125 are real.
Hence, the temperature can reach or exceed 141 degree F.
Answer:
(x, y) = (3, 1)
Step-by-step explanation:
given the 2 equations
2x + 3y = 9 → (1)
x + 5y = 8 → (2)
multiplying (2) by - 2 then adding to (1) will eliminate the term in x
multiply (2) by - 2
- 2x - 10y = - 16 → (3)
add 1(1) and (3) term by term
(2x - 2x) + (3y - 10y) = (9 - 16)
- 7y = - 7 ( divide both sides by - 7 )
y = 1
Substitute y = 1 in either (1) or (2) and solve for x
(1) : 2x + 3 = 9 ( subtract 3 from both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Solution is (3, 1 )
9514 1404 393
Answer:
2. (only)
Step-by-step explanation:
The Pythagorean theorem tells you the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. To determine if these are right triangles, determine if that condition is met.
1. 3^2 +5^2 = 9 + 25 = 34 ≠ (√35)^2 . . . . not a right triangle
2. 5^2 +4^2 = 25 +16 = 41 = (√41)^2 . . . a right triangle
3. 6^2 +8^2 = 36 +64 = 100 ≠ (√10)^2 . . . . not a right triangle
4. 3^2 +3^2 = 9 +9 = 18 ≠ (3√3)^2 = 27 . . . . not a right triangle
