Grayson and his children went into a movie theater where they sell bags of popcorn for $7.50 each and candies for $5 each. Grayson has $70 to spend and must buy a
minimum of 10 bags of popcorn and candies altogether. If x represents the number
of bags of popcorn purchased and y represents the number of candies purchased,
write and solve a system of inequalities graphically and determine one possible
solution.

Find the domain and range of the following function f(x) = 51x - 21+ 4

Examine the paragraph proof. which theorem does it offer proof for? prove jnm – nmi according to the given information in the image. jk | hi while jnm and lnk are vertical angles. jnm and lnk are congruent by the vertical angles theorem. because lnk and nmi are corresponding angles, they are congruent according to the corresponding angles theorem. finally, jnm is congruent to nmi by the transitive property of equality alternate interior angles theorem gorresponding angle theorem vertical angle theorem o same side interior angles theorem

Astudent is determining the influence of different types of food on the growth rate of spiders. she feeds one group of spiders two caterpillars twice a week. the other group received similarly-sized beetles twice a week. she records the amount of time required for individuals to reach sexual maturity. her hypothesis is that the spiders feeding on caterpillars will have a faster growth rate because caterpillars have a higher protein content compared to beetles. in this experiment, what is the dependent variable? spiders assigned to different feeding groups. time required to reach sexual maturity number of prey items fed twice a week. growth rates of each group.