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3 years ago

Simplify the sun if possible 3/6+2/6

Mathematics

2 answers:

natima [27]3 years ago

8 0

3. 2. 5
6. 6. 6

5/6 is already in simplest form

Inga [223]3 years ago

5 0

3+2=5
6+6=6 just carry over the six
it's at its simplest form

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Find the length of BC.

Murrr4er [49]

Answer:

C, 53.68 units

Step-by-step explanation:

tan 54° = $\frac{x}{39}$

39 tan 54° = x

x= 53.6788949 (just plug it in a scientific or graphing calculator)

x≈53.68

4 0

2 years ago

What is the solution of sqrt (x-4)+5=2

worty [1.4K]

Answer:

x = 13

Step-by-step explanation:

sqrt (x-4) + 5 = 2

The equation is √(x+4) + 5 = 2

√(x-4) = 2 - 5

√(x-4) = -3

x-4 = (-3)²

x-4 = 9

x = 9 + 4

x = 13

Therefore, the second option x = 13 is correct.

7 0

2 years ago

Evaluate Dx / ^ 9-8x - x2^

Solnce55 [7]

It depends on what you mean by the delimiting carats "^"...

Since you use parentheses appropriately in the answer choices, I'm going to go out on a limb here and assume something like "^x^" stands for $\sqrt x$ .

In that case, you want to find the antiderivative,

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}$

Complete the square in the denominator:

$9-8x-x^2=25-(16+8x+x^2)=5^2-(x+4)^2$

Now substitute $x+4=5\sin y$ , so that $\mathrm dx=5\cos y\,\mathrm dy$ . Then

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\int\frac{5\cos y}{\sqrt{5^2-(5\sin y)^2}}\,\mathrm dy$

which simplifies to

$\displaystyle\int\frac{5\cos 
y}{5\sqrt{1-\sin^2y}}\,\mathrm dy=\int\frac{\cos y}{\sqrt{\cos^2y}}\,\mathrm dy$

Now, recall that $\sqrt{x^2}=|x|$ . But we want the substitution we made to be reversible, so that

$x+4=5\sin y\iff y=\sin^{-1}\left(\dfrac{x+4}5\right)$

which implies that $-\dfrac\pi2\le y\le\dfrac\pi2$ . (This is the range of the inverse sine function.)

Under these conditions, we have $\cos y\ge0$ , which lets us reduce $\sqrt{\cos^2y}=|\cos y|=\cos y$ . Finally,

$\displaystyle\int\frac{\cos y}{\cos y}\,\mathrm dy=\int\mathrm dy=y+C$

and back-substituting to get this in terms of $x$ yields

$\displaystyle\int\frac{\mathrm dx}{\sqrt{9-8x-x^2}}=\sin^{-1}\left(\frac{x+4}5\right)+C$

4 0

3 years ago

Find the domain of the function. (Enter your answer using interval notation.)

Andreas93 [3]

Answer:

$(-\infty,-9)\cup(-9,\infty)$