Answer:
A. 5
Step-by-step explanation:
The triangle will be a right triangle when the side lengths satisfy the Pythagorean theorem: the sum of the squares of the legs is equal to the square of the hypotenuse.
(x +1)^2 +x^2 = (√61)^2
x^2 +2x +1 +x^2 = 61 . . . eliminate parentheses
2x^2 +2x = 60 . . . . . . .subtract 1, collect terms
x^2 +x -30 = 0 . . . . . divide by 2, subtract 30
(x +6)(x -5) = 0 . . . . factor the quadratic
x = -6 or +5
The solution is x = 5.
_____
Side lengths cannot be negative. Solution values are values of x that make the factors zero. x+6=0 when x=-6, for example.
Answer:
I believe x is greater than or equal to 1
Assuming your solving for y:
py+7=6y+q
-6y -7 -6y -7
(p-6)y = q-7
divide both sides by p-6
y=(q-7)/(p-6)
Recall your d = rt, distance = rate * time
one car is going at 55kph, at say hmmm "t" time
the second car zooms by at 75kph, an hour later, thus " t + 1 "
notice, overtaking the 1st car, simply means, the second car comes from behind approaches the first car from behind and "gets there", at that very second, both cars have travelled a distance, say "d"
if the first car travelled "d" kilometers
for the second car to "get there" has to had travelled "d" distance as well

solve for "t"
Answer:
A. g(x) = f(x - 6) + 2
Step-by-step explanation:
Vertex moves from:
(-6,-2) to (0,0)
g(x) = f(x - 6) + 2