Answer:
Remainder when p(x) is divided by (x+2) is -29
Step-by-step explanation:
p(x) =
When p(x) is divided by (x-2), remainder is 19.
p(x - 2 = 0) gives the remainder when p(x) is divided by (x-2)
x - 2 = 0
x = 2
p(x-2=0) = p(2) = = 19
8 - 8 + 16 + k = 19
k = 3
p(x) =
p(x + 2 = 0) gives the remainder when p(x) is divided by (x+2)
x + 2 = 0
x = -2
p(x+2=0) = p(-2) =
p(-2) = - 8 - 8 - 16 + 3 = -29
Remainder when p(x) is divided by (x+2) is -29
I added a screenshot of the complete question along with the given choices.
<em><u>Answers:</u></em>
w = 10 ft and l = 50 ft ................> second option
w = 20 ft and l = 60 ft ...............> third option
w = 50 ft and l = 40 ft ...............> fifth option
<em><u>Explanation:</u></em>
<u>We are given that:</u>
length should be at least 20 ...........> length ≥ 20
equation for perimeter is : 2l + 2w ≤ 200
<u>We will check each option as follows:</u>
<u>Option 1:</u>
w = 50 ft and l = 10 ft
This option is incorrect as the proposed length is less than 20.
<u>Option 2:</u>
w = 10 ft and l = 50 ft
Since the length is greater than 20, the first condition is satisfied.
Now, we check the second condition:
2l + 2w = 2(50) + 2(10) = 100 + 20 = 120 ≤ 200
The second condition is also satisfied.
This option is correct
<u>Option 3:</u>
w = 20 ft and l = 60 ft
Since the length is greater than 20, the first condition is satisfied.
Now, we check the second condition:
2l + 2w = 2(60) + 2(20) = 120 + 40 = 160 ≤ 200
The second condition is also satisfied.
This option is correct
<u>Option 4:</u>
w = 90 ft and l = 30 ft
Since the length is greater than 20, the first condition is satisfied.
Now, we check the second condition:
2l + 2w = 2(30) + 2(90) = 60 + 180 = 240 > 200
The second condition is not satisfied.
This option is incorrect
<u>Option 5:</u>
w = 50 ft and l = 40 ft
Since the length is greater than 20, the first condition is satisfied.
Now, we check the second condition:
2l + 2w = 2(50) + 2(40) = 100 + 80 = 180 ≤ 200
The second condition is also satisfied.
This option is correct
Hope this helps :)
