Answer:
31.7 cm²
Step-by-step explanation:
The area (A) of the triangle is calculated as
A = 
absinC
where a, b are the 2 sides given and C the angle between them
∠ C = 180° - (72 + 59)° = 180° - 131° = 49° , thus
A = 0.5 × 12 × 7 × sin49° ≈ 31.7 cm² ( to 1 dec. place )
Answer: X = 27
Step-by-step explanation: If we observe very closely, we have two similar triangles in the diagram. The first one is ABC and the other triangle is EDC. Also take note that angle ACB in the first triangle is equal in measurement to angle ECD (45 degrees) in the other triangle, (Opposite angles).
Hence in triangle ECD, we have identified two angles so far which are angle 2x + 10 and angle 45. Same applies to triangle ABC, we already have two angles which are, 3x - 10 and 45.
However angle D in the second triangle is equal in measurement to angle B in the first triangle
(Alternate angles).
Hence we have a third angle in triangle ABC which is
Angle B = 2x + 10.
Therefore 3x - 10 + (2x + 10) + 45 = 180
(Sum of angles in a triangle)
3x - 10 + 2x + 10 + 45 = 180
By collecting like terms we now have
3x + 2x = 180 + 10 - 10 - 45
5x = 135
Divide both sides by 5,
x = 27
Answer:
(-3,-2)
Step-by-step explanation:
y = -x - 5
y = 2x + 4
plug in one of the y equations
(2x+4)= -x - 5
2x+4=-x-5
3x=-9
x= -3
plug in x to one of the y equations
y= -(-3) -5
y=3-5
y= -2
x= -3, y= -2
9514 1404 393
Answer:
3 < b-a < 7
Step-by-step explanation:
The maximum difference will occur when the smallest 'a' value is subtracted from the largest 'b' value:
9 -2 = 7
The minimum difference will occur when the largest 'a' value is subtracted from the smallest 'b' value:
7 -4 = 3
So, the possible range of values of b-a is ...
3 < b-a < 7
