Simplify by combining like terms 5x+3y+3x

Mathematics

1 answer:

Aliun [14]2 years ago

8 0

Answer:

8x+3y

Step-by-step explanation:

1. Find like terms: 5x and 3x share the same constant "x" so you can combine them. There is nothing to combine with the 3y since there is no other term with the constant "y".

2. Rearrange to make it easier to see: 5x+3x+3y

3. Add the 5x and 3x: 8x+3y

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A basketball player shoots a basketball that reaches a height above 15 feet before landing back on the ground exactly after 7 se

Papessa [141]

Answer:

I and IV

Step-by-step explanation:

Since the height of the basketball reaches above 15 feet, hence the maximum of the function should be greater than 15 feet. Also at 7 seconds, the ball is on the ground, hence f(7) = 0 feet

The maximum of a function is at x = -b/2a

i) f(x) = -(x-3)² + 16 = -(x² - 6x + 9) + 16 = -x² + 6x + 7

The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3

f(3) = -(3-3)² + 16 = 16 > 15

Also f(7) = - (7 - 3)² + 16 = 0

Hence this option is correct

ii) f(x) = -x² + 8x - 7

The maximum of a function is at x = -b/2a = -8 / 2(-1) = 4

f(4) = -4² + 8(4) - 7 = 9 < 15 not correct

Also f(7) = - 7² + 8(7) - 7 = 0

Hence this option is not correct since the maximum f(4) = 9 < 15

iii) f(x) = -(x-3)² + 14 = -(x² - 6x + 9) + 14 = -x² + 6x + 5

The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3

f(3) = -(3-3)² + 14 = 14 < 15

Also f(7) = - (7 - 3)² + 14 = -2

Hence this option is not correct since the maximum f(4) = 9 < 15 and f(7) ≠ 0

iv)f(x) = -x² + 6x + 7

The maximum of a function is at x = -b/2a = -6 / 2(-1) = 3

f(3) = -(3)² + 6(3) + 7 = 16 > 15

Also f(7) = - (7)² + 6(7) + 7 = 0

Hence this option is correct

3 0

2 years ago

The height 'h' (in feet) of a ball in a baseball game can be modeled by h = -16t² + 28t + 8 , where 't' is the time (in seconds)

lidiya [134]

Answer:

a) No. t < 0 is not part of the useful domain of the function

b) 2.0 seconds

Step-by-step explanation:

a) A graph of the function is shown below. It shows t-intercepts at t=-0.25 and t=2.0. We presume that t is measured forward from some event such as the ball being thrown or hit. The model's predicted ball location has no meaning prior to that event, when values of t are negative.

b) It is convenient to use a graphing calculator to find the t-intercepts. Or, the equation can be solved for h=0 any of several ways algebraically. One is by factoring.

h = 0 = -16t² +28t +8 . . . . . . . . . . . . the ball hits the ground when h = 0

0 = -4(4t² -7t -2) = -4(4t +1)(t -2)

This has t-intercepts where the factors are zero, at t=-1/4 and t=2.

The ball will hit the ground after 2 seconds.