The product of two consecutive negative integers is 110. find both numbers.

  -11, -10

Step-by-step explanation:

You can look at the number 110 and see that it is the product of 10 and 11. The opposites of these numbers are the ones you're looking for:

  -11 and -10

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For numbers close together, their geometric mean is close to their arithmetic mean. That is, you can find the average of the two numbers of interest by looking at the square root of 110.

  √110 ≈ 10.5

so the magnitudes of the consecutive integers of interest are 10 and 11. We want negative values, so those will be ...

  -11 and -10

Conventionally, you would solve this by assigning a variable to one of the numbers and writing the quadratic equation ...

  x(x+1) = 110

Its solution can be by a variety of means, one of which is factoring:

  x² +x -110 = 0

  (x +11)(x -10) = 0

  x = -11 or +10 . . . . . . x = -11 is the solution we want; then x+1 = -10.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180

sas (side angle side)

aa(angle angle)

sss(side side side)

sas you have to find two sides with an angle in between

aa you find two angles because it will always add up to 180

sss find all sides

step-by-step explanation: