An electrical heating element produces heat depending on the resistance of the element and the current passed through it. the heat produced can be given by the formula h = i2r where h is the heat generated, i is the current, and r is the resistance. if the element has a fixed current of 2 amps passing through it and a variable current of x amps, it is able to produce a heat of 10x3 + 80, depending on the variable resistance for different additional values of current x. determine the formula for the variable resistance.

Beatrice decides she wants to babysit a few children at the same time to earn the money faster. she tells parents that if they allow her to babysit their children at her house, she will eliminate her automatic $5 tip and will give them an additional $5 discount. (a) write an equation showing the total cost for each client. identify all variables. (b) four parents bring their children to beatrice’s house at the same time for babysitting. beatrice wants to find out how many hours she must babysit the 4 children to earn exactly the $100 she needs in order to buy the present for her mother. write and solve an equation to find the number of hours. justify each step in the solution. (c) one parent decides not to drop off her child. the remaining 3 parents drop their children off at 9 a. m. two of the parents say they will be back at 1 p. m. the third parent says she will pick up her child at 2 p. m. at noon, beatrice realizes she needs feeding the 3 ch

If the value of x increases by 5, how does the value of m(x + 3) change? a) it increases by 5m. b) it increases by 8m. c) it decreases by 5m. d) it decreases by 8m.

1) in triangle the, what is the measure of angle t (in degrees)? 2) in triangle bat, the measure of angle b is 66∘, and the measure of angle t is 77∘.what is the measure of the exterior angle at a (in degrees)?