Show all ! the base of a triangle measures (8x + 2) units and the height measures (4x − 5) units. part a: what is the expression that represents the area of the triangle? show your work to receive full credit. (4 points) hint: area = 0.5bh part b: what are the degree and classification of the expression obtained in part a? (3 points) part c: how does part a demonstrate the closure property for polynomials? (3 points)

Part A:

As given,

Base of the triangle = 8x + 2 units

Height of the triangle = 4x − 5 units

Formula to find area of a triangle =

= 0.5bh

we have been given base and height, so the area becomes,

area =

area = 0.5(8x+2)(4x-5)

= 0.5(32x²-32x-10)

= 16x²-16-5

after factoring it, we get

area = (4x-5)(4x+1) units.

Part B:

It is a degree 2 polynomial as the polynomial has one variable that is x, and the largest exponent of that variable is 2.

Part C:

Part A demonstrates the closure property of polynomials because after multiplying two polynomials we get another polynomial.

the answer is 489

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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