Answer:
A. Hypotenuse-leg (HL) congruence.
HL, when you have 2 right triangles and their hypotenuses are congruent you are able to say HL
Step-by-step explanation:
We know that the hypotenuse-leg theorem states that if the hypotenuse and one leg of a right triangle are congruent to hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.
hypotenuse(AB) of △BDA equals to hypotenuse (CD) of △DBC.
BDA and DBC share a common side DB.
Using Pythagorean theorem we will get,
![CD^{2}=DB^{2}+BC^{2}...(1) \\\\AB^{2}=DB^{2}+AD^{2}...(2)](https://tex.z-dn.net/?f=CD%5E%7B2%7D%3DDB%5E%7B2%7D%2BBC%5E%7B2%7D...%281%29%20%20%5C%5C%5C%5CAB%5E%7B2%7D%3DDB%5E%7B2%7D%2BAD%5E%7B2%7D...%282%29)
We have been given that CD=AB, Upon using this information we will get,
![DB^{2}+BC^{2}=DB^{2}+AD^{2}](https://tex.z-dn.net/?f=DB%5E%7B2%7D%2BBC%5E%7B2%7D%3DDB%5E%7B2%7D%2BAD%5E%7B2%7D)
Upon subtracting
from both sides of our equation we will get,
![BC^{2}=AD^{2}\\\\BC=AD](https://tex.z-dn.net/?f=BC%5E%7B2%7D%3DAD%5E%7B2%7D%5C%5C%5C%5CBC%3DAD)
<h3>Therefore, by HL congruence △BDA ≅ △DBC.</h3>
Yes what’s the question ?
Answer:
1. Answer -48$
72-20 = 52
20 * 5 = 100
52 - 100= -48
2. 248$
-48 + 248 = 200
Step-by-step explanation:
hope this helps lovely
Answer: The wheels turn about 3771 times in 5 miles.
Step-by-step explanation:
Given, Kelly rides on her bicycle such that the number of times wheels turn for every 140 feet = 20
Turns for every feet =
...(i)
To find : Number of times wheels turn in 5 miles.
Since , 1 mile = 5,280 feet
Then, 5 miles = 5 x (5,280 feet) = 26,400 feet
Now , Number of times the wheels turn in 26,400 feet = 26400 x (Turns for every feet)
[From (i)
Hence, the wheels turn about 3771 times in 5 miles.
Question (1):
Assume that the first number is n. Since the two number are consecutive even numbers, this means that the second number is n + 2
We know that the sum of the two numbers is 70. This means that:
n + n + 2 = 70
2n + 2 = 70
2n = 68
n = 68/2
n = 34
This means that the two numbers are: 34 and 34+2 = 36 .......> last option
Question (2):
Assume dog's age is x. We know that cat's age is 5 less than twice dog's age. This means that:
cat's age = 2x - 5
We know that cat's age is 11, therefore:
11 = 2x - 5
11 + 5 = 2x
16 = 2x
x = 16/2 = 8
Dog's age is 8 .......> first option
Question (3):
The three numbers are consecutive. This means that we can assume the numbers to be n, n+1 and n+2. We know that their sum is 46. Therefore:
n + n + 1 + n + 2 = 46
3n + 3 = 46
3n = 43
n = 43/3
The three numbers are 43/3 , 46/3 and 49/3 .......> none of the given options in correct
Question (4):
The three consecutive numbers are all even. This means that we can assume the numbers to be n , n+2 and n+4
We know that their sum is 198. This means that:
n+n+2+n+4 = 198 .........> second option
Question (5):
The four consecutive numbers can be assumed as n, n+1 , n+2 and n+3. We know that their sum is 86. Therefore:
n + n+1 + n+2 + n+3 = 86 .......> third option
Question (6):
Assume the width is w. We know that the length is 15 cm greater than the width. This means that:
length = w + 15
Now, we have:
perimeter = 2(length + width)
150 = 2 (15 + w + w)
75 = 15 + 2w
60 = 2w
w = 60/2
w = 30 cm
This means that:
length = 15 _ 30 = 45 cm
Based on the above, the dimensions of the rectangle are:
length = 45 cm and width = 30 cm .......> first option
Question (7):
Assume original price before taxes is x
Total price = original price + taxes
825 = x + 0.1x = 1.1 x
x = 825/1.1
x = $750 .........> second option
Question (8):
Assume cost of helmet is x and that cost of bicycle is 5x. We know that the total is 240. This means that:
240 = x + 5x = 6x
x = 240/6
x = 40
This means that:
price of helmet = $40
price of bicycle = 5(40) = $200
..........> first option
Hope this helps :)