Answer:
Hope this helps.
Step-by-step explanation:
So for ASA, the two triangles have to have two angles congruent, and in the middle of those angles, they have to have a line that's congruent.
For SAS, the two triangles have to have two lines congruent, and in the middle of those lines, they have to have an angle that's congruent.
For AAS, the two triangles have to have two angles congruent, but the line that's congruent has to be on the side, not in the middle.
Answer:
x = 2/3 or x = -1
Step-by-step explanation by completing the square:
Solve for x:
3 x^2 + x - 2 = 0
Divide both sides by 3:
x^2 + x/3 - 2/3 = 0
Add 2/3 to both sides:
x^2 + x/3 = 2/3
Add 1/36 to both sides:
x^2 + x/3 + 1/36 = 25/36
Write the left hand side as a square:
(x + 1/6)^2 = 25/36
Take the square root of both sides:
x + 1/6 = 5/6 or x + 1/6 = -5/6
Subtract 1/6 from both sides:
x = 2/3 or x + 1/6 = -5/6
Subtract 1/6 from both sides:
Answer: x = 2/3 or x = -1
SOLUTION:
Let's establish the formula for a cylinder as displayed below:
Let volume of cylinder = V
V = ( Pi )r^2h
Now let's substitute the values from the problem into the formula to find the volume.
V = ?
r = 8
h = 4
V = ( Pi )( 8 )^2( 4 )
V = ( Pi )( 64 )( 4 )
V = ( Pi )( 256 )
V = 256( Pi )
FINAL ANSWER:
Therefore, the answer is:
C. 256( Pi ) units^3
Hope this helps! :)
Have a lovely day! <3
What we know so far:
Side 1 = 55m
Side 2 = 65m
Angle 1 = 40°
Angle 2 = 30°
What we are looking for:
Toby's Angle = ?
The distance x = ?
We need to look for Toby's angle so that we can solve for the distance x by assuming that the whole figure is a SAS (Side Angle Side) triangle.
Solving for Toby's Angle:
We know for a fact that the sum of all the angles of a triangle is 180°; therefore,
180° - (Side 1 + Side 2) = Toby's Angle
Toby's Angle = 180° - (40° + 30°)
Toby's Angle = 110°
Since we already have Toby's angle, we can now solve for the distance x by using the law of cosines r² = p²+ q²<span>− 2pq cos R where r is x, p is Side1, q is Side2, and R is Toby's Angle.
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x² = Side1² + Side2² - 2[(Side1)(Side2)] cos(Toby's Angle)
x² = 55² + 65² - 2[(55)(65)] cos(110°)
x² = 3025 + 4225 -7150[cos(110°)]
x² = 7250 - 2445.44
x = √4804.56
x = 69.31m
∴The distance, x, between two landmarks is 69.31m
