Answer:
Perimeter = 10x + 8 units.
Area = 6x^2 + 13x - 5 units^2.
Step-by-step explanation:
The perimeter is 2*length + 2*breadth
= 2(2x + 5) + 2(3x - 1)
= 4x + 10 + 6x - 2
= 10x + 8 units.
The area = length * breadth
= (2x + 5)(3x - 1)
= 6x^2 - 2x + 15x - 5
= 6x^2 + 13x - 5 units^2.
Answer:
there is a 12.5% increase
BE is congruent to overline CF since they are altitudes of the same trapezoid(S).
AB is congruent to overline CD (Given)
AE is congruent to overline FD by the Hypotenuse Leg Theorem.
triangle ABC is congruent to triangle DCF (SSS Triangle Congruence)
angle A is congruent to angle D since corresponding parts of congruent triangles are congruent.
Answer:
Step-by-step explanation:
The formula for the dot product of vectors is
u·v = |u||v|cosθ
where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.
which is 
which is 
I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.
We also need the angle, which of course has its own formula.
where uv has ITS own formula:
uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.
uv = 96.
To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:
which returns an angle measure of 30.7. Plugging that all into the dot product formula:
gives you a dot product of 96
Answer:
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If you know the measure of the angle of one particular angle, the alternate interior angle that corresponds to said particular angle will have that same measurement.
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