answer:Since -7 is a solution to x^2 + bx - 28 = 0, we know that (-7)^2 + b(-7) - 28 = 0. Simplifying, we get 49 - 7b - 28 = 0, so 21 - 7b = 0. Therefore, b = boxed{3}. The answer is: 3

answer:We want the expression to be equal to (x+k)^2 for some constant k. Expanding, we have x^2 + 2kx + k^2. Comparing coefficients, we get 2k = 100 and k^2 = c. Solving for k, we find k = 50. Substituting this back into the equation k^2 = c, we get c = 50^2 = 2500. Thus, the value of c is boxed{2500}. The answer is: 2500

answer:Kate saved 27 in March, 13 in April, and 28 in May. The total amount she saved is 27 + 13 + 28 = 68. Kate spent x on a keyboard and 5 on a mouse. The total amount she spent is x + 5. To find out how much money Kate has left, we subtract the total amount she spent from the total amount she saved: 68 - (x + 5) = 68 - x - 5 = 63 - x. We are given that Kate has 14 left, so we can write: 63 - x = 14. Solving for x, we get: x = 49. The value of x is 49. 49 The answer is: 49

answer:Let's assume the number of toys in the smaller pile is x. Since the larger pile is twice as big as the smaller pile, the number of toys in the larger pile is 2x. The total number of toys when the piles are combined is x + 2x = 3x. We are given that the total number of toys is 120, so 3x = 120. Dividing both sides of the equation by 3, we find that x = 40. Therefore, the number of toys in the larger pile is 2x = 2(40) = 80. 80 The answer is: 80