What type of triangle is created by the three cities?
the distance between city a and city b is 22 miles. the
distance between city b and city c is 54 miles. the distance
between city a and city c is 51 miles.
an acute triangle, because 222 + 542 > 512
an acute triangle, because 222 + 512 > 542
an obtuse triangle, because 222 + 542 > 512
an obtuse triangle, because 222 + 512 > 542

An acute triangle, because

Step-by-step explanation:

Given:

The distance between city A and city B is 22 miles.

The  distance between city B and city C is 54 miles.

The distance  between city A and city C is 51 miles.

thus we have a triangle ABC with side lengths :

AB = 22 miles (shortest side)

BC= 54 miles  (longest side)

AC = 51 miles (shorter side)

For an obtuse triangle :

For acute triangle :

Comparing sum of squares of shorter sides with the square of longest side:

We see that:

Thus, the condition  fulfills proving this triangle to be an acute triangle.

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

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step-by-step explanation: