Louisa put her nickels collection into rolls that hold 40 nickles each. She filled 15 rolls and had 7 nickels left over. Altoget
1 answer:
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Answer:
A. 12 and 43
Step-by-step explanation:
Pythagorean theorem is given as =
Where, a and b are the two legs of the right triangle, while c is the hypotenuse/longest leg of the triangle.
In the figure given, the side of the largest square = the hypotenuse of the triangle = c
While the side of the other squares = a and b respectively, of the triangle.
Area of square = s², where s is the side length of the square.
Since we are given that the area of the largest square = 55, this is also equivalent to c² in the Pythagorean theorem.
The side length of the largest square = √55 ≈ 7.4 = c
Therefore, to determine the area of the other squares, check the options given if they add up to give 55.
Option A: 12 + 43 = 55
Option B: 14 + 40 = 54
Option C : 16 + 37 = 53.
The correct possible areas of the smaller squares would be A. 12 and 43.
Answer:
C. y = 3x - 5
Step-by-step explanation:
Given the general equation of a hyperbola:
The equation for the asymptote line is given by:
In your problem, we have
we have:
h=2,
k=1
a²=4 --> a=2, im just taking the squareroot
b²=36 --> b=6
put it into your equation
y = 1 + 3(x-2)
y = 1 + 3x - 6
y = 3x - 5
Answer:
75
Step-by-step explanation:
<em><u>Refer to attachment</u></em>
As the first step extending the segment BC until intersection with AD.
Since ∠A + ∠B = 90° we get right triangle by extending CB
Naming the segments a, b, c, d as pictured
<u>The are of (ABCD) is equal to sum of areas of two right triangles:</u>
- Area = 1/2c(a+b) + 1/2bd
<u>Substitute d with a-c as a = c+d, then:</u>
- Area = 1/2(ac+bc) + 1/2b(a-c) = 1/2(ac + bc + ab - bc) = 1/2(ab + ac)
- Area = 1/2(ab+ac)
<u>Applying Pythagorean to small triangle:</u>
- 10² = b² + (a-c)²
- 100 = b² + a² - 2ac + c²
<u>Applying Pythagorean to bigger triangle:</u>
- 20² = (a+b)² + c²
- 400 = a² + 2ab + b² + c²
<u>Subtracting equations we got:</u>
- 400 - 100 = a² + 2ab + b² + c² - (b² + a² - 2ac + c²)
- 300 = 2ab + 2ac
<u>This gives us the 4 times of the area which is 1/2(ab + ac), so the area is </u>
- 300/4 = 75
