Answer:
5.7
Step-by-step explanation:
The altitude divides right triangle ABC into similar right triangles ADB and BDC. The ratios of short leg to long leg will be proportional in these similar triangles, so you have ...
AD/BD = BD/CD
Cross multiplying gives ...
AD·CD = BD²
(x+3)(2x+3) = 5²
2x² +9x = 16 . . . . . perform the multiplication, subtract 9
2(x² +4.5x) = 16
2(x² +4.5x +2.25²) = 16 +2(2.25²) . . . . . add 2(2.25²) to complete the square
2(x +2.25)² = 26.125 . . . . . write as a square
x +2.25 = √13.0625 . . . . . .divide by 2, take the positive square root
x = -2.25 +√13.0625 . . . . subtract 2.25 to find x
We want the value of CD, so ...
CD = 2x +3 = 2(-2.25 +√13.0625) +3
CD = -1.5 +2√13.0625 ≈ 5.7284
The length of CD is about 5.7 units.
Answer:
a. We are 99% confident that the average age of all golfers that play on the golf course is greater than 21.29
Step-by-step explanation:
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
In this question:
99% confidence interval for the average age of golfers that play on the area is (35.683, 43.763), which means that we are 99% confident that the mean age of all golfers who play in the area is a value in this interval, and the best conclusion is given by option A, as the lower bound of the interval is greater than 21.
Answer: A
Step-by-step explanation: Hope this help :D
ANSWER
the area of the trim around the glass in the window is option ( D)
i.e (x²+7x+3)
REASON
As given in the question
A window frame has a length of (5x+3) inches an a width of (x+6) inches.
As the shape of the window in the form of rectangle.
Formula
Area of the rectangle = length × breadth
put the value in the above equation
we get
Area of window = (5x+3)× ( x + 6)
= 5x² + 33x + 18 inches²
As given in the question
The area of the glass in the window is (4x²+26x+15) square inches.
Area trim around the glass in the window = area of the window - area of the glass.
put the value
we get
= ( 5x² + 33x + 18 ) - ( 4x²+26x+15)
= 1x²+ 7x + 3 inches²
therefore the correct option is (D)
Hence proved
Answer:
56/16 = 3.5
Step-by-step explanation:
