Multiply the following using the vertical multiplication method:

3x^2+5x+1
* x^2-2x+4


a. 3x^4-x^3+3x^2+x+4

b. 3x^4+5x^3+10x^2+18x+4

c. 3x^4-x^3+3x^2+18x+4

d. 3x^4+x^3+x^2+x+4

Acompany that manufactures and sells guitars made changes in their product range. from the start they had 20 models. then they reduced the number of models to 15. as a result, the company enjoyed a 10% increase in turnover. - how much did the stock level change? in (%)

Abdul is making a map of his neighborhood he knows the following information: his home, the middle school, and high school are all on the same street. his home, the elementry school, and his friends house are on the same street. the angle between the elementary school, middle school, and his home is congruent to the angle between his friends house, the high school, and his home. what theorem can abdul use to determine the two triangles are similar? a- side side side similarity theoremb- angle angle similarity theoremc- corresponding parts of similar triangles are congruentd- pieces of right triangles similarity theorem

Match the vocabulary to the proper definition. in probability, two events in which 1. conditional probability the outcome of one event is independent of the outcome of a second event. 2. dependent events in probability, two events in which the outcome of one event is dependent on the outcome of a second event. the probability of an event in which the outcome of the event is conditional on the outcome of one or more different events. 3. independent events