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butalik [34]
2 years ago
5

What value in place of the question mark makes the polynomial below a perfect square trinomial?

Mathematics
1 answer:
UkoKoshka [18]2 years ago
7 0

Answer:

144

Step-by-step explanation:

x^2+24x +144\\\\=x^2 + 2\cdot 12x +12^2\\\\=(x+12)^2

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How much greater is 0.0543 than 0.002?
aleksley [76]

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Step-by-step explanation:

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Jane was baking cookies. She needed 1/3 cup sugar and 1 2/4 cups flour. How much more flour does she need than sugar?
Bas_tet [7]

Answer:

1 and 1/6 cups more

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1/3 cup sugar

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3 years ago
How to solve this trigonometric equation cos3x + sin5x = 0
mrs_skeptik [129]

Answer:

  x = {nπ -π/4, (4nπ -π)/16}

Step-by-step explanation:

It can be helpful to make use of the identities for angle sums and differences to rewrite the sum:

  cos(3x) +sin(5x) = cos(4x -x) +sin(4x +x)

  = cos(4x)cos(x) +sin(4x)sin(x) +sin(4x)cos(x) +cos(4x)sin(x)

  = sin(x)(sin(4x) +cos(4x)) +cos(x)(sin(4x) +cos(4x))

  = (sin(x) +cos(x))·(sin(4x) +cos(4x))

Each of the sums in this product is of the same form, so each can be simplified using the identity ...

  sin(x) +cos(x) = √2·sin(x +π/4)

Then the given equation can be rewritten as ...

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  2·sin(x +π/4)·sin(4x +π/4) = 0

Of course sin(x) = 0 for x = n·π, so these factors are zero when ...

  sin(x +π/4) = 0   ⇒   x = nπ -π/4

  sin(4x +π/4) = 0   ⇒   x = (nπ -π/4)/4 = (4nπ -π)/16

The solutions are ...

  x ∈ {(n-1)π/4, (4n-1)π/16} . . . . . for any integer n

5 0
3 years ago
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