Answer:
36 ft²
Step-by-step explanation:
If BE = 3√2 ft, then the diagonal BD is 6√2 ft. The area of the square (as with any rhombus) is half the product of the diagonals. Since both diagonals are the same length, the area of the square is ...
area = 1/2·(6√2 ft)² = 36 ft²
The area of the square is 36 square feet.
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You may be expected to find the length of one side of the square using the Pythagorean theorem.
AB² = AE² + EB² . . . . . = the area of the square
AB² = (3√2 ft)² +(3√2 ft)² = 18 ft² + 18 ft²
AB² = 36 ft² . . . . . . . . . the area of the square
Answer:
sinθ = 5/13
Step-by-step explanation:
cosθ = adjacent/hypotenuse (or you could think of it as x/r)
cosθ = -12/13
adjacent = -12
hypotenuse = 13
opposite = ?
To get the opposite, we use the Pythagorean theorem
Now sub in the numbers:
opposite = 5
Now sinθ = opposite/hypotenuse
so sinθ = 5/13
The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
The triangles ΔLNO and ΔLMO have the same leg Lo, therefore you need the equality of hypotenuses LM=LN.
Answer:
A
Step-by-step explanation:
Given
2k² - k - 3
Consider the factors of the product of the k² term and the constant term which sum to give the coefficient of the k- term.
product = 2 × - 3 = - 6 and sum = - 1
The factors are + 2 and - 3
Use these factors to split the k- term
2k² + 2k - 3k - 3 ( factor the first/second and third/fourth terms )
= 2k(k + 1) - 3(k + 1) ← factor out (k + 1) from each term
= (2k - 3)(k + 1) → A
