Answer:
(i) (f - g)(x) = x² + 2·x + 1
(ii) (f + g)(x) = x² + 4·x + 3
(iii) (f·g)(x) = x³ + 4·x² + 5·x + 2
Step-by-step explanation:
The given functions are;
f(x) = x² + 3·x + 2
g(x) = x + 1
(i) (f - g)(x) = f(x) - g(x)
∴ (f - g)(x) = x² + 3·x + 2 - (x + 1) = x² + 3·x + 2 - x - 1 = x² + 2·x + 1
(f - g)(x) = x² + 2·x + 1
(ii) (f + g)(x) = f(x) + g(x)
∴ (f + g)(x) = x² + 3·x + 2 + (x + 1) = x² + 3·x + 2 + x + 1 = x² + 4·x + 3
(f + g)(x) = x² + 4·x + 3
(iii) (f·g)(x) = f(x) × g(x)
∴ (f·g)(x) = (x² + 3·x + 2) × (x + 1) = x³ + 3·x² + 2·x + x² + 3·x + 2 = x³ + 4·x² + 5·x + 2
(f·g)(x) = x³ + 4·x² + 5·x + 2
Answer:
B & C
Step-by-step explanation:
Use the Pythagorean Theorem: a^2 + b^2 = c^2
A) 18^2 + 24^2 = 2,088 | 42^2 = 1,764 [NOT A]
B) 33^2 +56^2 = 4,225 | 65^2 = 4,225 [B IS CORRECT]
C) 19^2 + 180^2 = (32,761) = 181^2 = (32,761) [C IS CORRECT]
D) 3^2 + 4^2 = 25 | 7^2 = 49 [NOT D]
I hope this helped you ! In return, please deem this the most brainliest answer.
Answer:
d because its big
Step-by-step explanation:
<u>Answer:</u>
- The cost of 1 dozen doughnut is $6 and the cost of a dozen croissant is $10.
<u>Step-by-step explanation:</u>
<u>We know that:</u>
- D = Cost of a dozen doughnut
- C = Cost of a dozen croissant
- 10D + 7C = 130
- 6D + 4C = 76
<u>Work:</u>
6D + 4C = 76
7(6D + 4C = 76)
42D + 28C = 532
- 40D - 42D = 520 - 532
- => -2D = -12
- => 2D = 12
- => D = 6
<u>Now, let's substitute the value of D into the first equation.</u>
- 10D + 7C = 130
- => 10(6) + 7C = 130
- => 60 + 7C = 130
- => 7C = 70
- => C = 10
Hence,<u> the cost of 1 dozen doughnut is $6 and the cost of a dozen croissant is $10.</u>
Hoped this helped.
We have to find the slope of the line that passes through this points:
p1(-2,15), p2(-8,-5)
the slope of a line through two points is calculated like this:
m = (y2 - y1)/(x2 - x1)
where x1,y1,x2,y2 are the coordinates of the two points, so we have:
m = (-5 - 15)/(-8 - (-2))
m = (-20)/(-8 + 2)
m = -20/-6
m = 10/3
that is the line slope
