Answer:
1. A rotation of 90°.
2. A reflection in the y-axis.
4. A translation of 3 units to the left.
The three consecutive integers are: x, (x+1) and (x+2).
We can suggest this equation:
x+(x+1)+(x+2)=126
3x+3=126
3x=126-3
3x=123
x=123/3
x=41
x=41
(x+1)=41+1=42
(x+2)=41+2=43
Answer: the three consecutive integers would be: 41,42 and 43.
We know that
the law of sinus established
a/sin A=b/sin B=c/sin C
so
A=30°
B=45°
b=10 units
a/sin A=b/sin B---------> a/sin 30=10/sin 45------> a=10*sin 30/sin 45
a=7.07 units
C=180-(A+B)-------> C=180-(75°)-----> C=105°
b/sin B=c/sin C--------> c=b*sin C/sin B----> c=10*sin 105/sin 45
c=13.66 units
Area=(1/2)*b*c*sin A-------> Area=(1/2)*10*13.66*sin 30°-----> 34.15 units ²
the area of triangle is 34 units²
Answer:
Yes, parallelogram OABC is a rectangle.
Step-by-step explanation:
The vertices of a parallelogram are O(0,0), A(-4,1), B(-3,5) and C(1,4).
A parallelogram is a rectangle if its any two adjacent sides are perpendicular to each other.
product of slopes of two perpendicular lines is -1.
Formula for slope is
Using the formula we get
It means OA is perpendicular to AB.
Since two adjacent sides are perpendicular, therefore the given parallelogram OABC is a rectangle.
