Answer:10
Step-by-step explanation:
12-5+3=10
Answer:
Since the legs of the right triangle measure x + 1 and x + 15, respectively, and since the hypotenuse measures x + 17, the Pythagorean Theorem can be used as follows: (x + 1)2 + (x + 15)2 = (x + 17)2. This equation becomes (x2 + 2x + 1) + (x2 + 30x + 225) = x2 + 34x + 289, which then becomes 2x2 + 32x + 226 = x2 + 34x + 289. When all the terms are moved to one side, the equation becomes x2 – 2x – 63 = 0, and when the left side of the equation is factored, it becomes (x – 9)(x + 7) = 0. At this point, it seems as if x can equal 9 or –7, but if x were –7, one of the legs would have a negative length, and this is impossible. For this reason x equals 9, and the legs of the triangle measure 10 and 24, respectively, while the hypotenuse measures 26. Since cosine is
length of adjacent leg
length of hypotenuse
, the cosine of angle C is
24
26
, or
12
13
.
Answer:
total area of the garden and walkway = 2a² + 21a + 54
Step-by-step explanation:
The walkway surrounds the rectangular garden. The width of the garden is 9 ft and the length is 12 ft. Since the width of the walkway around the garden is the same on every side let us use a to represent the width around the garden.
The garden is rectangular and the width of the walkway around the garden is uniform. The width added on both end of the width of the rectangle will be 2a while the width added to the both length of the rectangle will be 2a also.
Therefore
total area of the garden and walkway = length × width
length of garden and the walkway = 2a + 12
width of garden and the walkway = 2a + 9
total area of the garden and walkway = (2a + 12)(2a + 9)
total area of the garden and walkway = 4a² + 18a + 24a + 108
total area of the garden and walkway = 4a² + 42a + 108
divide through by 2
total area of the garden and walkway = 2a² + 21a + 54
Answer:
both substitutions
Step-by-step explanation:
in 5. based on 3 BC is substituted by its equal counterpart AB.
and in 6. we use 1. to substitute AC by its associated absolute value.