Answer:
56 cm
Step-by-step explanation:
The ratio of the lengths of the pieces is 3:4.
The longer piece is 32 cm.
We set up a proportion to find the length of the smaller piece.
Let the length of the smaller piece be x.
3 is to 4 as x is to 32
3/4 = x/32
4x = 3 * 32
4x = 96
x = 24
The smaller piece is 24 cm.
24 cm + 32 cm = 56 cm
Step-by-step explanation:
<u>Given</u>
- f(x) = 4x³ + 3x² - 2x - 1
<u>Divide it by the following:</u>
<u>(a) 2x + 1</u>
- 4x³ + 3x² - 2x - 1 =
- (4x³ + 2x²) + (x² + 1/2x) - (5/2x + 5/4) + 1/4 =
- 2x²(2x+1) + 1/2x(2x + 1) - 5/4(2x + 1) + 1/4 =
- (2x + 1)(2x² + 1/2x - 5/4) + 1/4
Quotient = 2x² + 1/2x - 5/4
Remainder = 1/4
<u>(b) 2x - 3</u>
- 4x³ + 3x² - 2x - 1 =
- (4x³ - 6x²) + (9x² - 13.5x) + (11.5x - 17.25) + 16.25 =
- (2x -3)(2x² + 4.5x + 5.75) + 16.25
Quotient = 2x² + 4.5x + 5.75
Remainder = 16.25
<u>(c) 4x - 1</u>
- 4x³ + 3x² - 2x - 1 =
- (4x³ - x²) + (4x² - x) - (2x - 1/2) - 3/2 =
- (4x - 1)(x² + x - 1/2) - 3/2
Quotient = x² + x - 1/2
Remainder = - 3/2
<u>(d) x + 2</u>
- 4x³ + 3x² - 2x - 1 =
- (4x³ + 8x²) - (5x² + 10x) + (8x + 16) - 17 =
- (x + 2)(4x² - 5x + 8) - 17
Quotient = 4x² - 5x + 8
Remainder = - 17
Answer:
67.5 - 67.5 - 45 °
Step-by-step explanation:
Sum of INTERIOR angles of a polygon
(n-2) * 180 <====<u>ya just have to remember/know this !</u>
n is the number of sides n = 8 in this case
(8-2)*180 = 1080 ° < === this is the SUM of the 8 interior angles
EACH interior angle is then 1080 / 8 = 135 °
you can see from the picture that each of the two outside angles of the green triangle are 1/2 of this = 67.5° each
so the triangle measurements are
67.5 - 67.5 - 45 ( they have to sum to 180 for triangle)
The correct answer is b
a thanks and a brainliest would be appreciated :)
<span>23863.05 is the answer to the problem</span>
