Question

lesson 17.3 checkpoint□ once you have completed the above problems and checked your solutions, complete the lesson checkpoint below.□ complete the lesson reflection above by circling your current understanding of the learning goal.find each difference.1. $(3x^{3}-2y^{2}+5x^{2})-(3x^{3}-2y^{2}+5x^{2})$2. $(14n^{3}+16n^{2})-(-7n^{3}-5n^{2}-19)$3. $(2x^{2}-5x-7)-(7x^{2}+3)$4. $(32mn^{2}+50m^{2}n)-(10mn^{2}-16m^{2}+64)$find the difference between the two polynomials to solve a real-world problem. the models needed for the situation are provided.5. a companys cost, in dollars, of making $x$ tablet computers can be represented by $25x + 150$. the predicted revenue of selling $x$ tablet computers is $50 + 30x$ dollars.(a) write a polynomial that represents the profit of selling $x$ computers.(b) if the company sells 150 computers, will it make a profit? if so, how much?

Explanation:

Step1: Distribute the negative sign

$3x^3 - 2y^2 + 5x^2 - 3x^3 + 2y^2 - 5x^2$

Step2: Combine like terms

$(3x^3-3x^3)+(-2y^2+2y^2)+(5x^2-5x^2) = 0$

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Step1: Distribute the negative sign

$14n^3 + 16n^2 + 7n^3 + 5n^2 + 19$

Step2: Combine like terms

$(14n^3+7n^3)+(16n^2+5n^2)+19 = 21n^3 + 21n^2 + 19$

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Step1: Distribute the negative sign

$2x^2 - 5x - 7 - 7x^2 - 3$

Step2: Combine like terms

$(2x^2-7x^2)-5x+(-7-3) = -5x^2 - 5x - 10$

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Step1: Distribute the negative sign

$32mn^2 + 50m^2n - 10mn^2 + 16m^2 - 64$

Step2: Combine like terms

$(32mn^2-10mn^2)+50m^2n+16m^2-64 = 22mn^2 + 50m^2n + 16m^2 - 64$

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5(a)

Step1: Recall profit formula

$\text{Profit} = \text{Revenue} - \text{Cost}$

Step2: Substitute given polynomials

$\text{Profit} = (25x + 150) - (50 + 30x)$

Step3: Distribute and combine like terms

$25x + 150 - 50 - 30x = -5x + 100$

5(b)

Step1: Substitute $x=150$ into profit polynomial

$\text{Profit} = -5(150) + 100$

Step2: Calculate the value

$-750 + 100 = -650$

Step3: Interpret the result

A negative value means no profit (a loss).

Answer:

1. $0$
2. $21n^3 + 21n^2 + 19$
3. $-5x^2 - 5x - 10$
4. $22mn^2 + 50m^2n + 16m^2 - 64$

5(a). $-5x + 100$
5(b). No, it will not make a profit; it will have a loss of $\$650$.