Answer:
Step-by-step explanation:
Hypotenuse² =base² + altitude²
(3x + 4)² = (2x + 1)² + (3x)²
{Use (a+b)² = a² + 2ab + b²}
(3x)² + 2*3x+4 + 4² = (2x)² + 2*2x*1 + 1² + 9x²
9x² + 24x + 16 = 4x² + 4x + 1 + 9x²
9x² + 24x + 16 = 13x² + 4x + 1
0 = 13x² + 4x + 1 - 9x² - 24x - 16
13x² - 9x² + 4x - 24x +1 - 16 = 0
4x² - 20x - 15 = 0
a = 4 ; b =-20 ; c = -15
D = b² - 4ac = (-20)² - 4*4*(-15) = 400 + 240 = 640
√D = √640 = 25.30

x = 5 .66 ; x = -0.66
Ignore x = -0.66 as length of a side cannot be negative
Answer : x = 5.66
Find the mean, median, mode, and range of this data: 49, 49, 54, 55, 52, 49, 55. If necessary, round to the nearest tenth.
krok68 [10]
Answer:
Mean = 51.4.
Mode = 49.
Median = 52.
Range = 6.
Step-by-step explanation:
Mean = Sum of all observations / Number of observations.
Mean = (49+49+54+55+52+49+52)/7
Mean = 360/7
Mean = 51.4 (to the nearest tenth).
Mode = The most repeated values = 49 (repeated 3 times).
Range = Largest Value - Smallest Value = 55 - 49 = 6.
Median = The central value of the data.
First, arrange the data in the ascending order: 49, 49, 49, 52, 54, 55, 55.
It can be seen that the middle value is 52. Therefore, median = 52!!!