Answer:
The answer to your question is below
Step-by-step explanation:
Side 1: 3x² - 2x - 1
Side 2: 9x + 2x² - 3
Perimeter: 5x³ + 4x² - x - 3
a) Length of side 1 and side 2
Length = (3x² - 2x - 1) + (9x + 2x² - 3)
= 3x² - 2x - 1 + 9x + 2x² - 3
= (3x² + 2x²) + (-2x + 9x) + (-1 - 3)
= 5x² + 7x - 4
b) Length of the third side
Third side = Perimeter - side 1 - side 2
Third side = 5x³ + 4x² - x - 3 - (5x² + 7x - 4)
Third side = 5x³ + 4x² - x - 3 - 5x² - 7x + 4
Third side = 5x³ + (4x² - 5x²) + (-x - 7x) + (-3 + 4)
Third side = 5x³ - x² - 8x + 1
c) Yes, in this problem we did both operations (addition and subtraction) and we can notice that the polynomials are closed. Also they follow the closure property the addition or subtraction of two polynomials gives another polynomial.
The two angles are supplementary angles, which when added together equal 180 degrees.
6x -10 + 6x +10 = 180
Combine like terms:
12x = 180
Divide both sides by 12:
x = 180/12
x = 15
The answer is C) 15
The factor form for this will be (3x+1)(2x+1). Hope it help!
Answer:
Step-by-step explanation:
To find : Acceleration in first 15 min . Distance between two cities Average speed of journey
Solution:
Each horizontal block is 1/8 hr = 7.5 min
Each vertical block is 10 km/hr
Time Velocity km/hr
0 Min ( 0 hr) 0
15 Min (1/4 hr) 50
45 Min (3/4 hr) 50
60 MIn ( 1 hr) 100
90 Min ( 3/2 hr) 100
120 Min ( 2hr) 0
Acceleration in first 15 min (1/4 hr) = (50 - 0)/(1/4 - 0) = 50/(1/4)
= 200 km/h²
Distance between two cities
= (1/2)(0 + 50)(1/4 - 0) + 50 * (3/4 - 1/4) + (1/2)(50 + 100)(1 - 3/4) + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)
= 25/4 + 25 + 75/4 + 50 + 25
= 125
Distance between two cities = 125 km
Average Speed of journey = 125/2 = 62.5 km/hr
Acceleration in first 15 min = 200 km/h²
Distance between two cities = 125 km
Average Speed of journey = 62.5 km/hr
Hope this helps..
We have been given an equation 
. We are asked to fill in the blanks using our given equation.
The axis of symmetry will be the vertical line passing through vertex.
First of all, we will convert our given equation in standard vertex form of parabola as:
Standard vertex form of parabola: 
, where (h,k) is vertex of parabola.
Upon comparing our function with standard vertex form, we can see that vertex of parabola is at 
.
The axis of symmetry will be vertical line passing through point . The vertical line will pass through 
, therefore, the axis of symmetry is .
Since our given parabola is an upward opening parabola, so it has a minimum at . This means that parabola will intersect the x-axis at two points. Therefore, there are two real solutions for the given function.
