The square root of -3 is 1.73205081
Answer: D) No; If x is 5, the expression on the left simplifies to 8, making the inequality false.
In other words, if x = 5, then x+3 becomes 5+3 which ultimately becomes 8, but this is not greater than 8 on the right side.
Your steps could look like this
x+3 > 8
5+3 > 8 ... replace x with 5
8 > 8 ... this is a false inequality
Answer:
The length of each rope is 9.93 feet (Approx).
Step-by-step explanation:
As given
Emma, Brandy, and Damian will cut a rope that is 29.8 feet long into 3 jump ropes.
Each of the three jump ropes will be the same length.
Thus
![Length\ of\ each\ rope = \frac{29.8}{3}](https://tex.z-dn.net/?f=Length%5C%20of%5C%20each%5C%20rope%20%3D%20%5Cfrac%7B29.8%7D%7B3%7D)
![Length\ of\ each\ rope = 9.93\ feet(Approx)](https://tex.z-dn.net/?f=Length%5C%20of%5C%20each%5C%20rope%20%3D%209.93%5C%20feet%28Approx%29)
Therefore the length of the each rope is 9.93 feet (Approx).
Answer:
The answer is below
Step-by-step explanation:
Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion.
The distance between two points on the coordinate plane is given as:
![Distance=\sqrt{(x_2-x_1}^2+(y_2-y_1)^2 \\\\Therefore\ in\ triangle\ PQR:\\\\|QR|=\sqrt{(-2-(-2))^2+(4-0)^2}=4\\\\|PQ|=\sqrt{(-2-4)^2+(0-4)^2}=\sqrt{52}=2\sqrt{13} \\\\|PR|=\sqrt{(-2-4)^2+(4-4)^2}=6](https://tex.z-dn.net/?f=Distance%3D%5Csqrt%7B%28x_2-x_1%7D%5E2%2B%28y_2-y_1%29%5E2%20%5C%5C%5C%5CTherefore%5C%20in%5C%20triangle%5C%20PQR%3A%5C%5C%5C%5C%7CQR%7C%3D%5Csqrt%7B%28-2-%28-2%29%29%5E2%2B%284-0%29%5E2%7D%3D4%5C%5C%5C%5C%7CPQ%7C%3D%5Csqrt%7B%28-2-4%29%5E2%2B%280-4%29%5E2%7D%3D%5Csqrt%7B52%7D%3D2%5Csqrt%7B13%7D%20%20%20%20%5C%5C%5C%5C%7CPR%7C%3D%5Csqrt%7B%28-2-4%29%5E2%2B%284-4%29%5E2%7D%3D6)
In triangle STU:
![|ST|=\sqrt{(-1-2)^2+(-2-(-4))^2}=\sqrt{13}\\\\|SU|=\sqrt{(-1-2)^2+(-4-(-4))^2} =3\\\\|TU|=\sqrt{(-1-(-1))^2+(-4-(-2))^2}=2](https://tex.z-dn.net/?f=%7CST%7C%3D%5Csqrt%7B%28-1-2%29%5E2%2B%28-2-%28-4%29%29%5E2%7D%3D%5Csqrt%7B13%7D%5C%5C%5C%5C%7CSU%7C%3D%5Csqrt%7B%28-1-2%29%5E2%2B%28-4-%28-4%29%29%5E2%7D%20%20%3D3%5C%5C%5C%5C%7CTU%7C%3D%5Csqrt%7B%28-1-%28-1%29%29%5E2%2B%28-4-%28-2%29%29%5E2%7D%3D2)
|QR| / |TU| = 4/2 = 2
|PR| / |SU| = 6/3 = 2
|PQ| / |ST| = 2√13 / √13 = 2
Hence:
|QR| / |TU| = |PR| / |SU| = |PQ| / |ST|
Therefore, △PQR and △STU are similar triangles since the ratio of their sides are in the same proportion.
Perimeter:
The perimeter of the triangle is the sum of its sides.
We have then:
P = 8 + 12 + 10
P = 30 units
Semi-perimeter:
In geometry, the semiperimeter of a polygon is half its perimeter.
s = P / 2
s = 30/2
s = 15 units.
Area:
Knowing the semiperimeter and the sides, the area is:
A = root (s * (s-a) * (s-b) * (s-c))
where,
s: semi-meter
a, b, c are sides.
A = root (15 * (15-8) * (15-12) * (15-10))
A = 39.68626967
A = 40 units ^ 2