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Leni [432]
2 years ago
7

The parallelogram has the angle measures shown. Can you conclude that it is a rhombus, a

Mathematics
1 answer:
nasty-shy [4]2 years ago
5 0

Answer:

Rhombus

Step-by-step explanation:

The angles add up to 144 degrees, so they can't be a rectangle or a square. Also, diagonals of rhombuses bisect the angles.

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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
The mean of 4 numbers is 21. calculate the sum of the 4 numbers
Ugo [173]

Answer:

84

Step-by-step explanation:

The mean is calculated as

mean = \frac{sum}{count} , then

\frac{sum}{4} = 21 ( multiply both sides by 4 )

sum = 84

8 0
2 years ago
P(x) = 4x^2 - 15x - 25
Airida [17]
The answear is P(x)=4x
5 0
2 years ago
Read 2 more answers
Sarah was raising money for a fundraiser. Her fundraising goal was $40. What would 50% of her fundraising goal be??
Delvig [45]

Answer:

$20

Step-by-step explanation:

50% of Fundraising goal= 0.5 x $40

                                        = $20

4 0
2 years ago
0 = -5x + 4y in standard form
Effectus [21]

Answer:

5x - 4y = 0

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given 0 = - 5x + 4y ( multiply through by - 1 )

5x - 4y = 0 ← in standard form


6 0
3 years ago
Read 2 more answers
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