12m
10m
9m
Answer:
The correct answer is: d=9m
Step-by-step explanation:
Ok, the ladders leaned against a building make two right triangles with same the same height, which we will call h. For the 20m ladder, its leg is (7+d) and for the 15m ladder, its leg is d, and the two hypotenuses are 20 and 15 respectively.
Then, using the Pythagorean Theorem we have:
20m ladder:
20^2 = h^2 + (d+7)^2 (Eq. 1)
400 = h^2 + d^2 + 2*7*d + 7^2 (expanding the theorem)
400 = (h^2 + d^2) + 14*d + 49 (Eq. 2)
15m ladder:
15^2 = h^2 + (d)^2 (Eq. 3)
Since h^2 + (d)^2 is equal to 15^2, we can substitute (2) into (3):
400 = (15^2) + 14*d + 49
400 = 225 + 14*d + 49
14*d = 400 - 225 - 49 (clearing the variable d)
14*d = 126
d = 9 m
And since we now know that d is equal to 9m. For the longer ladder is (d+7)=(9+7)=16m.
And, then the shorter ladder is 9m from the building and the longer ladder is 16m from the building
Answer:
The brace is ft ≅ 12.806 ft long
Step-by-step explanation:
The length of the diagonal of a rectangle can be found using this rule
, where
∵ The gate has shaped a rectangle
∵ Its length = 10 ft
∵ Its width = 8 ft
∴ l = 10 and w = 8
∵ The brace is the diagonal
→ By using the rule above
∴
∴ The length of the brace = ≅ 12.806 ft
∴ The brace is ≅12.806 ft long
5.75, 5.16, 6, 5.25, 5.5, 6.25, 5.66, 5.33, 5.33, 6, 5.75. 5.66, 5.16
What is the interquartile range (IQR) of the data set?
A. 0.585
B. 1.09
C. 5.6
D. 5.875
Answer:
Option: A(0.585)
Step-by-step explanation:
After arranging our data in ascending order we get that:
5.16 5.16 5.25 5.33 5.33 5.5 5.66 5.66 5.75 5.75 6 6 6.25
Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively.
The interquartile range is equal to Q3-Q1.
So, the Median()of data is given by: 5.66
also the lower half is:
5.16 5.16 5.25 5.33 5.33 5.5
Hence, the middle value or median of this lower half of this data lie between 5.25 and 5.33 which is 5.29.
Hence, =5.29
Similarly the upper half is:
5.66 5.75 5.75 6 6 6.25
Hence, the middle value or median of this upper half of this data lie between 5.75 and 6 which is 5.875
Hence, =5.875
Hence, the interquartile range=
Hence, option A is correct.
Answer: Option: A(0.585)
Step-by-step explanation:
(3xy) (7xy^2)
= 21(x^2)(y^3) is the simplified expression represents the number of colored tiles
What's the center?
t^2+10t=75