Mathematics, 30.06.2019 11:30 khynia11

Jocelyn and lorlesha are comparing the size of their villages in the clash of clans app. the area of jocelyn's village is represented by the polynomial, 2w2+10w+12. the area of lorleshas village is represented by the polynomial, 3w2+4w-5, where e represents the width, in meters of their town hall. part a: find the expression that represents the additional area jocelyns village. part b: find the expression that represents the combined total area of their villages.

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Answer from: afonseca73

A: $-w^{2}+6w+17$

B: $5w^{2}+14w+7$

Step-by-step explanation:

We have been given that the area of Jocelyn's village is represented by the polynomial $2w^{2}+10w+12$ . The area of Lorlesha's village is represented by the polynomial $3w^{2}+4w-5$ , where w represents the width, in meters of their Town hall.

A: To find the expression that will represent the additional area of Jocelyn's village, we will subtract the total area of Lorlesha's village from the total area of Jocelyn's village.

$\text{Additional area of Jocelyn's village}=2w^{2}+10w+12-(3w^{2}+4w-5)$

Let us distribute negative sign to simplify our expression.

$\text{Additional area of Jocelyn's village}=2w^{2}+10w+12-3w^{2}-4w+5$

Upon combining like terms we will get,

$\text{Additional area of Jocelyn's village}=2w^{2}-3w^{2}+10w--4w+12+5$

$\text{Additional area of Jocelyn's village}=(2-3)w^{2}+(10-4)w+12+5$

$\text{Additional area of Jocelyn's village}=-w^{2}+6w+17$

Therefore, the expression that represents the additional area Jocelyn's village is $-w^{2}+6w+17$ .

B: To find the expression that represents the combined total area of their villages we will add areas of Jocelyn's and Larlesha's village.

$\text{Combined total area}=2w^{2}+10w+12+(3w^{2}+4w-5)$

Upon combining like terms we will get,

$\text{Combined total area}=2w^{2}+3w^{2}+10w+4w+12-5$

$\text{Combined total area}=(2+3)w^{2}+(10+4)w+12-5$

$\text{Combined total area}=5w^{2}+14w+7$

Therefore the expression represents the combined total area of their villages is $5w^{2}+14w+7$ .

Answer from: Quest

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

What is the length of the unknown leg in the right triangle ?

Answer from: Quest

40 because it’s just a little longer than 32 feet
Find the length of the missing side. a) 56 ft b) 45 ft c) 42 ft d) 40 ft

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