Determine the points of intersection of the line y = -2x + 7 and the parabola y = 2x2 + 3x - 5.

Step-by-step explanation:

The x-values of those points can be found by equating the expressions for y, then solving for x.

... -2x +7 = 2x² +3x -5

... 2x² +5x -12 = 0 . . . . . . . . subtract the left side to put into standard form

This can be factored by looking fro two factors of 2·(-12) = -24 that add to give 5, the x-coefficient. Those factors are 8, -3.

... 2x² +8x -3x -12 = 0 . . . . rewrite the middle term

... 2x(x +4) -3(x +4) = 0 . . . factor by pairs

... (x +4)(2x -3) = 0 . . . . . . . complete factorization

... x = -4, x = 3/2 . . . . . . . . values of x that make the factors be zero

The corresponding y-values are ...

... for x = -4, y = -2(-4) +7 = 15

... for x = 3/2, y = -2(3/2) +7 = 4

The points of intersection are (-4, 15) and (3/2, 4).

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.

2/3

step-by-step explanation:

the slope of a line is equal to the rise/run. in this case the line rises 2 units for every +3 units it moves