Which table will have the greatest value of y when x = 7? x y(a) -1 3 0 0 1 3 2 12 3 27 x y (b) -1 -10 0 2 1 14 2 26 3 38 x y (c) -1 0.5 0 1 1 2 2 4 3 8 x y (d) -1 -8 0 2 1 12 2 22 3 32

(a) (x, y) = (7, 147)

Step-by-step explanation:

Table A represents a quadratic function: y = 3x², so for x=7, y = 3·7² = 147.

Table B represents a linear function: y = 12x +2, so for x=7, y = 86.

Table C represents an exponential function: y = 2^x, so for x=7, y = 128.

Table D represents a linear function: y = 10x +2, so for x=7, y = 72.

The greatest value of y for x=7 will be found in Table A.

Table a's values go down and up, with symmetry about x=0. This suggests a quadratic function. A plain y=x² function will have the value 1 at x=1. This one has the value 3, so looks like y = 3x². Checking values for x=2 and x=3 confirms this.

Table b's values go consistently up, with a difference of 12 each time. The value for x=0 is 2, so we know this linear function has equation y=12x+2.

Table c's values double from one value of x to the next, so the function is exponential with a base of 2. The multiplier is 1, the value for x=0, so the equation is y = 1·2^x.

Table d is similar to table b, except the common difference is 10 instead of 12. So, the slope in slope-intercept form is 10 instead of 12: y = 10x + 2.

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.