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.
7x^2 - 3x^2 = 4x^2
-2x+4X=4X
5+ 10 = 15
4x^2 + 4x + 15
Answer:
13, 15, 17
Step-by-step explanation:
Gọi 3 STN lẻ cần tìm là a, a+2, a+4 (a thuộc N*)
Theo đề bài ta có:
(a + 2)(a + 4) - 177 = 6a
=> a^2 + 4a + 2a + 8 = 6a + 177
=> a^2 + 6a + 8 = 6a + 177
=> a^2 + 6a - 6a = 177 - 8 (chuyển vế)
=> a^2 = 169 = 13^2
=> a = 13
=> a+2 = 15, a+4 = 17
Vậy 3 STN lẻ cần tìm là 13, 15, 17
Answer:
Step-by-step explanation:
Derivative indicates rate of change of dependent variable with respect to independent variables. It indicates the slope of a line that is tangent to the curve at the specific point.
Given:
Number of bees is modeled by the function 
The daily high temperature is increasing at a rate of 2 °F per day when the number of bees spotted is 100.
To find:
rate of change of number of bees when 100 bees are spotted
Solution:
Differentiate with respect to t,
Put 
At x = 100,
Answer:
She rode 17.4 miles in 1 hour
Step-by-step explanation:
A cyclist rode for 3.5 hours and completed a distance of 60.9 miles. If she kept the same average speed for each hour, how far did she ride in 1 hour?
Part A Estimate the quotient. Include an equation to show your work. Explain your thinking.?
The quotient is the average speed and this is calculated as:
Speed = Distance(miles)/Time(hours)
Where speed = quotient
Distance = Dividend
Time = Divisor
Speed = 60.9 miles/3.5 hours
= 17.4 miles/hour
Part B Find the exact distance she rode in 1 hour by completing the division. PLEASE HELP!
If :
3.5 hours = 60.9 miles
1 hour = x miles
Cross Multiply =
3.5x = 60.9 miles
x = 60.9/3.5
x = 17.4 miles
Hence, she rode 17.4 miles in 1 hour
