Answer the following questions 21:440.0KB/s al411605197375691_...This is Algebra teaching skill test, which means that all problems must bemethodically solved and each step should be explained. Otherwise, the taskwill not be considered completed. Sketch and graph problems if needed. If youuse a theorem (or property) to solve a problem, state which theorem (orproperty) you use and why. You do not need to prove it, unless it is required inthe task. Make sure you answer every question. Good luck!1. Find the 30th term of an arithmetic sequence whose ninth term equals199 and fifteenth term equals 343. Explain each step.2.Find the inverse of the matrix A =if it exists. Explain each step.3. Identify the function given with the graph. Explain your answer. Iden-tify the maximum value, minimum value, amplitude, and period of thefunction.-6-4. Jenny's Bakery makes two types of birthday cakes: yellow cake, whichsells for $25, and strawberry cake, which sells for $35. Both cakes are thesame size, but the decorating and assembly time required for the yellowcake is 2 hours, while the time is 3 hours for the strawberry cake. Thereare 450 hours of labor available for production. How many of each typeof cake should be made to maximize revenue? Use linear programming.Explain each step.5. The Earth revolves around the Sun along an ellipse. The Sun lies in thefocus of the ellipse. The largest distance from the Sun to the Earth is 152.1million kilometers, and the shortest is 147.1 million kilometers. Find thelength of the semi-minor axis of the ellipse and the eccentricity of the el-lipse. What is the distance between the two foci of the ellipse? ID: ala6685aName:This is Algebra teaching skill test, which means that all problems must bemethodically solved and each step should be explained. Otherwise, the taskwill not be considered completed. Sketch and graph problems if needed. If youuse a theorem (or property) to solve a problem, state which theorem (orproperty) you use and why. You do not need to prove it, unless it is required inthe task. Make sure you answer every question. Good luck!1. Find the 30th term of an arithmetic sequence whose ninth term equals199 and fifteenth term equals 343. Explain each step.2.Find the inverse of the matrix A =if it exists. Explain each step.3. Identify the function given with the graph. Explain your answer. Iden-tify the maximum value, minimum value, amplitude, and period of thefunction.4. Jenny's Bakery makes two types of birthday cakes: yellow cake, whichsells for $25, and strawberry cake, which sells for $35. Both cakes are thesame size, but the decorating and assembly time required for the yellowcake is 2 hours, while the time is 3 hours for the strawberry cake. Thereare 450 hours of labor available for production. How many of each typeof cake should be made to maximize revenue? Use linear programming.Explain each step.The Earth revolves around the Sun along an ellipse. The Sun lies in thefocus of the ellipse. The largest distance from the Sun to the Earth is 152.1million kilometers, and the shortest is 147.1 million kilometers. Find thelength of the semi-minor axis of the ellipse and the eccentricity of the el-lipse. What is the distance between the two foci of the ellipse?

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Description: Answer the following questions 21:440.0KB/s al411605197375691_...This is Algebra teaching skill test, which means that all problems must bemethodically solved and each step should be explained. Otherwise, the taskwill not be considered completed. Ske

Question

Accepted Answer

Given: T9=199, T15=343
we know that nthTn term of an arithmetic progression is given by
Tn=a+n-1d…

1. Find the 30th term of an arithmetic sequence whose ninth term equals 199 and fifteenth term equals 343. Explain each step.