What is the sum or difference? 1. 2x^4 - 8x^4(A). -6x^8(B). -6x^4(C). -16x^4(D). -16x^8 What is the sum or difference?2. 6y^5 - 9y^5(A). -3y^10(B). 15y^5(C). -54y^5(D). -3y^53. Write the Polynomial in standard form. Then name the Polynomial based on its degree and number of terms. 6 - 12x + 13x^2 - 4x^2(A). 9x^2 - 12x; quadratic binomial (B). 9x^2 - 12x + 6; quadratic trinomial (C). -3x^2 + 6; quadratic binomial (D). 9x^2 - 12x - 6; cubic trinomial 4. A biologist studied the populations of common guppies and Endler's guppies over a 6-year period. The biologist modeled the populations, in ten of thousands, with the following polynomials where x is time, in years. Common guppies: 3.1x^2 + 6x + 0.3Endler's guppies: 4.2x^2 - 5.2x + 1 What polynomial models the total number of common and Endler's guppies? (A). 7.3x^2 + 0.8x + 0.7(B). 7.3x^2 - 0.8x + 1.3(C). 7.3x^2 + 0.8x + 1.3(D). 7.3x^2 + 0.8x - 1.35. A family is building a circular fountain in the backyard. The yard is rectangular and measures 14x by 19x and the fountain is going to be circular with a radius of 6x. Once the fountain is built, what will be the area of the remaining yard?(A). 230πx^2(B). 230x^2(C). 266x^2 - 6πx^2(D). 2x^2(133 - 18π)6. A sports team is building a new stadium on a rectangular lot of land. If the lot measures 6x by 10x and the sports field will be 1x by 4x, how much of the lot will be left over to build bleachers on?(A). 56x^2(B). 64x^2(C). 30x^2(D). 60x^2Can someone please help!! This is lesson 9, Unit 3, Polynomials and Factoring!!
Accepted Solution
A:
1. Ans: Option (B) [tex]-6x^4[/tex]
Explanation: Given: [tex]2x^4 - 8x^4[/tex] Take the common out: => [tex]x^4(2 - 8)[/tex]
Hence: => [tex][tex]-6x^4[/tex][/tex] (Option B)
2. Ans: Option (D) [tex]-3y^5[/tex]
Explanation: Given: [tex]6y^5 - 9y^5[/tex] Take the common term(s) out: => [tex]y^5(6-9)[/tex]
Explanation: In order to find the total number of Common and Endler's guppies, you need to add both Common and Endler's guppies' polynomials, as follows:
Common guppies: [tex]3.1x^2 +6.0x + 0.3[/tex] Endler's guppies: [tex]4.2x^2 - 5.2x + 1.0 [/tex] (add both) ----------------------------------------------------------------- Total number: [tex]7.3x^2 +0.8x + 1.3[/tex] ----------------------------------------------------------------- Hence the ans is Option(C) [tex]7.3x^2 + 0.8x + 1.3[/tex]
5. Ans: Option (D) [tex]2x^2(133 - 18 \pi )[/tex]
Explanation: First let's find the total area of the yard: Total Area of the Yard = 14x * 19x = [tex]266x^2[/tex]
Now the area of the circular fountain: Area of the Circular Fountain = [tex] \pi r^2[/tex] Since, r=6x Therefore, Area of the Circular Fountain = [tex] \pi (6x)^2 = 36 \pi x^2[/tex]
Now the final Area of the yard would be: Final area of the Yard = Total Area of the Yard - Area of the Circular Fountain Final area of the Yard = [tex]266x^2[/tex] - [tex]36 \pi x^2[/tex] => Final area of the Yard = [tex]2x^2(133 - 18 \pi)[/tex] (Option D)
6. Ans: Option (A) [tex]56x^2[/tex]
Explanation: First let's find the total area of the lot: Total Area of the lot= 6x * 10x = [tex]60x^2[/tex]
Now the area of the stadium: Area of the stadium = 1x * 4x = [tex]4x^2[/tex]
Now the final Area of the lot would be: Final area of the lot= Total Area of the lot - Area of the stadium Final area of the lot= [tex]60x^2[/tex] - [tex]4x^2[/tex] => Final area of the lot = [tex]56x^2[/tex] (Option A)