Hello,
<u>Perimeter of a rectangle :</u> 2 * (length + width)
<u>Area of a rectangle :</u> length * width
We know that the perimeter of the rectangle is equal to 10 feet and its area is equal to 6 square feet.
Let's call x the length of the rectangle and y the width of the rectangle. The pair (x ; y) verifies the following system :
2 (x + y) = 10 ⇔ x + y = 5 ⇔ x = 5 - y
x * y = 6 ⇔ (5 - y) * y = 6 ⇔ 5y - y² - 6 = 0 ⇔ y² - 5y + 6 = 0
⇔ y² - 3y - 2y + 6 = 0 ⇔ y(y - 3) - 2(y - 3) = 0 ⇔ (y - 2)(y - 3) = 0
⇔ y = 2 ou y = 3
x = 5 - y ⇔ x = 5 - 2 or x = 3 - 2 ⇔ x = 3 or y = 2
S = {(3 ; 2) ; (2 ; 3)}
The width of the rectangle is 2 or 3 feet.
:-)
Answer:
D. 2
Step-by-step explanation:
soh cah toa rule
sine equals opposite over hypotenuse,
cosine equals adjacent over hypotenuse, and
tangent equals opposite over adjacent
csc is 1/sin which is hypotenuse over opposite
if csc is -√5/2 then
hypotenuse is -√5
opposite is 2
3rd quadrant on a graph is bottom left
both x and y values are negative
hypotenuse means its a triangle
pythagorean theorem
a^2 + b^2 = c^2
a^2 + 2^2 = (-√5)^2
a^2 + 4 = 5
a = 1 = adjacent
tangent equals opposite over adjacent
tan is 2 / 1 which is 2
third quadrant means it's still positive
because tan is positive in quadrant 3
intmathcom
revisionmathscom
mathworldwolframcom
50 miles since 1 inch equals 10 miles and there's 5 inches that means 5x10=50
Answer:
445.5min=595²ft
Step-by-step explanation:
y=0.9x
y=0.9*495
y=445.5
Earthquake measuring 4.5 is 10 times more powerful than earthquake measuring 3.5 on Richter scale.
Step-by-step explanation:
Earthquake refers to the violent shaking of the Earth crust in response to its extremely dynamic interior. Sometimes the rocks are loaded or stressed beyond its elastic limit, following which it rebounds thus emitting a wave(seismic), which is received by us as seismic waves.
The energy released during an earthquake is measured in Richter scales (named after Charles Richter). While 1 is the lower limit, there is no such upper limit. However, earthquakes above 7 are considered fragile for human existence. It is a logarithmic scale meaning successive numbers of the scale by a factor of 10.
Thus, an earthquake measuring 4.5 would be around 10 times more powerful than an earthquake measuring 3.5 following logarithmic scale.