The set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that:
The side length of the triangle is shown in the option:
As we know,
Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
Using Pythagoras' theorem:
From option(D):
3, 4 and 5
(3)² + (4)² = 5²
9 + 16 = 25 (True)
Thus, the set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.
Learn more about the right-angle triangle here:
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Answer:
The correct option is:
A) L'' (-4 , -4) , M'' (-1 , -4) , N'' ( -1 , 0) , O'' (-4 , 0)
Step-by-step explanation:
The following are the vertices of a rectangle LMNO
L (-4 , 6)
M (-1 , 6)
N (-1 , 2)
O (-4 , 2)
First we have to reflect it across x-axis
When we reflect a shape across x-axis, the x components of the points remain the same while y components change their signs. After reflection:
L' (-4 , -6)
M' (-1 , -6)
N' ( -1 , -2)
O' (-4 , -2)
After we translate it up by two units, we add +2 to y components of each reflected point.
L'' (-4 , -4)
M'' (-1 , -4)
N'' ( -1 , 0)
O'' (-4 , 0)
Hence, the correct option is A
Answer:
The solution to this system is (-2,1)
Step-by-step explanation:
The given system of equations is;
...eqn1
and
....eqn2
We make y the subject of the second equation to get:
...eqn3
We put eqn3 into eqn1 to get;
We expand to get:
Simplify both sides to get:
Put x=-2 into eqn3
The solution to this system is therefore (-2,1)