Given:
A quadratic function has a line of symmetry positioned at x = –3.5 with one root located at –9.
To find:
The second root.
Solution:
It is understood that the line of symmetry splits the quadratic function's graph into two identical halves. Hence, both roots are equidistant from this line.
This implies that the line of symmetry passes through the midpoint of the two roots.
Let the other root be denoted as x.
Multiply both sides by 2.
Add 9 to both sides.
Consequently, the other zero of the quadratic function is concluded to be 2.
Out of 100 surveyed individuals, 35 work out in the morning, 45 in the afternoon, and 20 at night.
Jim is accurate.....
The ratio of morning exercisers to the whole group is 35/100.
The ratio of afternoon exercisers is 45/100.
The ratio for night exercisers is 20/100.
Response:
The fence's length is expressed as 6.28x - 150 cm.
Detailed Breakdown:
Assuming the circular pool has a radius (r) of x cm.
As the pool is circular, its circumference represents the length of the fence. Additionally, subtracting the 150 cm for the gate gives us the actual length of the fence.
Length of fence = Circumference of pool – gate's width.
Length of fence = 2 π r – 150
Length of fence = 2 × 3.14 × x – 150
Therefore, the fence length is 6.28x – 150 cm.
Utilizing the Law of Sines (sinA/a=sinB/b=sinC/c) and recognizing that the angles in a triangle add up to 180°.
The angle C calculates to 180-53-17=110°
Thus, we have 27/sin53=b/sin17=c/sin110
This leads to b=27sin17/sin53, c=27sin110/sin53
The perimeter is defined as a+b+c, so
p=27+27sin17/sin53+27sin110/sin53 units
p≈68.65 units (rounded to the nearest hundredth of a unit)
Detailed explanation:
Information provided:
Tran possesses a credit card that allows up to $2000 in spending with an APR of 12%.
In the initial month, Tran incurred charges of $450 and settled $150 within that billing period.
The formula to determine the interest that will accrue for Tran in the first month is (0.012)(300)
Here, 0.01 signifies the monthly interest rate.
The 300 reflects the outstanding balance, as Tran charged $450 but only paid back $150.
