21x + 14 = 7(3x + a) In the equation above, a is a constant. For what value of a does the equation have an infinite number of solutions? If a + b = 6 and a - b = 4, What is the value of 2a + 3b?

Step-by-step explanation:

1. For there to be an infinite number of solutions, both sides of the equation need to have the same values.

  21x +14 = 21x +7a

That is, 7a must be 14. For a = 2, there are infinite solutions.

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2. To find the value of b, we can substitute for a in the second equation using the value of a we find from the first equation:

  a = 6 -b . . . . . . . expression for a

  (6 -b) -b = 4 . . . . substituted into the second equation

  2 -2b = 0 . . . . . . subtract 4

  1 - b = 0 . . . . . . . divide by 2

  b = 1 . . . . . . . . . . add b

We want 2a +3b = 2(a+b) +b = 2(6) +1 = 13. The value of 2a +3b is 13.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq