find the missing angle of the triangle.

The slope of the line tangent to the curve y^2 + (xy+1)^3 = 0 at (2, -1) is -3/4.

The slope of the line tangent to the curve y^2 + (xy+1)^3 = 0 at (2, -1) can be found using the concept of implicit differentiation. To find the slope, we need to differentiate the equation with respect to x and then substitute the coordinates (2, -1) into the resulting equation. Let's solve it step by step.

First, we differentiate the equation implicitly with respect to x:

2y * dy/dx + 3(xy + 1)^2 * (y + x * dy/dx) = 0

Next, we substitute the values x = 2 and y = -1 into the equation:

2(-1) * dy/dx + 3(2(-1) + 1)^2 * (-1 + 2 * dy/dx) = 0

Simplifying the equation:

-2dy/dx - 3 * 1 * (-1 + 2dy/dx) = 0

-2dy/dx + 3 + 6dy/dx = 0

Combining like terms:

4dy/dx = -3

Finally, solving for dy/dx, we get:

dy/dx = -3/4

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The slope of the tangent line to the curve at the point \((2, -1)\) is:

[tex]\[\boxed{\frac{3}{4}}\][/tex]

To find the slope of the tangent line to the curve given by the equation [tex]\( y^2 + (xy + 1)^3 = 0 \)[/tex] at the point [tex]\( (2, -1) \)[/tex], we need to use implicit differentiation.

Given the curve:

[tex]\[y^2 + (xy + 1)^3 = 0\][/tex]

We differentiate both sides with respect to x . Using the chain rule and implicit differentiation, we get:

[tex]\[\frac{d}{dx} [y^2] + \frac{d}{dx} [(xy + 1)^3] = 0\][/tex]

First, differentiate [tex]\( y^2 \):[/tex]

[tex]\[\frac{d}{dx} [y^2] = 2y \frac{dy}{dx}\][/tex]

Next, differentiate [tex]\( (xy + 1)^3 \)[/tex] using the chain rule:

[tex]\[\frac{d}{dx} [(xy + 1)^3] = 3(xy + 1)^2 \cdot \frac{d}{dx} [xy + 1]\]\[= 3(xy + 1)^2 \cdot (y + x \frac{dy}{dx})\][/tex]

Putting it all together, we get:

[tex]\[2y \frac{dy}{dx} + 3(xy + 1)^2 (y + x \frac{dy}{dx}) = 0\][/tex]

Now, substitute [tex]\( x = 2 \) and \( y = -1 \)[/tex] into the equation:

[tex]\[2(-1) \frac{dy}{dx} + 3((2)(-1) + 1)^2 \left( -1 + 2 \frac{dy}{dx} \right) = 0\]\[-2 \frac{dy}{dx} + 3(-2 + 1)^2 \left( -1 + 2 \frac{dy}{dx} \right) = 0\][/tex]

[tex]\[-2 \frac{dy}{dx} + 3(-1)^2 \left( -1 + 2 \frac{dy}{dx} \right) = 0\]\[-2 \frac{dy}{dx} + 3(1) \left( -1 + 2 \frac{dy}{dx} \right) = 0\][/tex]

[tex]\[-2 \frac{dy}{dx} + 3(-1 + 2 \frac{dy}{dx}) = 0\]\[-2 \frac{dy}{dx} + 3(-1 + 2 \frac{dy}{dx}) = 0\][/tex]

[tex]\[-2 \frac{dy}{dx} + 3(-1) + 6 \frac{dy}{dx} = 0\][/tex]

[tex]\[-2 \frac{dy}{dx} - 3 + 6 \frac{dy}{dx} = 0\][/tex]

[tex]\[4 \frac{dy}{dx} - 3 = 0\][/tex]

[tex]\[4 \frac{dy}{dx} = 3\][/tex]

[tex]\[\frac{dy}{dx} = \frac{3}{4}\][/tex]

So, the slope of the tangent line to the curve at the point \((2, -1)\) is:

[tex]\[\boxed{\frac{3}{4}}\][/tex]

The solution of the system of equation [tex]5x+2y = 29[/tex] ; [tex]x+4y =13[/tex] will be (3,2) and this can be determined by using the arithmetic operations.

Given :

[tex]5x+2y = 29[/tex]  ----- (1)

[tex]x+4y =13[/tex]  ----- (2)

Now, solve for x in equation (2).

[tex]x = 13-4y[/tex]  --- (3)

Now, put the value of x obtained above in equation (1).

[tex]5(13-4y)+2y=29[/tex]

[tex]65-20y+2y=29[/tex]

[tex]36=18y[/tex]

[tex]y=2[/tex]

Now, put the value of y in equation (3).

[tex]x=13-(4\times 2)[/tex]

[tex]x=5[/tex]

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Answer:

[tex]9\frac{13}{20}\text{ inches}[/tex]

Step-by-step explanation:

Given,

Tucson's average rainfall = [tex]12\frac{1}{4}\text{ inches}=\frac{49}{4}\text{ inches}[/tex]

Also, Yumas's average rainfall = [tex]2\frac{3}{5}\text{ inches}=\frac{13}{5}\text{ inches}[/tex]

Difference between Tucson's average rainfall and Yumas's average rainfall

[tex]=\frac{49}{4}-\frac{13}{5}[/tex]

[tex]=\frac{245-52}{20}[/tex]

[tex]=\frac{193}{20}[/tex]

[tex]=9\frac{13}{20}[/tex]

Hence, Tucson gets [tex]9\frac{13}{20}[/tex]  inches more rainfall.

Answer: [tex]x(7y)[/tex]

Step-by-step explanation:

The given expression: [tex]7(xy)[/tex]

i.e. a product of 7 and xy.

The operation used here: Multiplication.

Commutative property of multiplication  :-

[tex]a\times b=b\times a[/tex] for any numbers a and b.

Associative property of multiplication :-

[tex]a\times(b\times c)=(a\times b\times c)[/tex] for any numbers a , band c.

Now, [tex]7(xy)=(7x)y[/tex] [Associative property of multiplication]

[tex]=(x7)y[/tex]  [Commutative property of multiplication]

[tex]=x(7y)[/tex]    [Associative property of multiplication]

Answer: Second option is correct.

Step-by-step explanation:

The two interior angles that are not adjacent to an exterior angle are called "Remote interior angles"

As remote interior angles are those interior angles that are inside the are inside the triangle but opposite to the exterior angles.

Hence, Second option is correct.

The value of the solution is, 3 is 1 percent of 300.

We have to give that,

To find the amount for 1 percent is 3.

Let us assume that,

3 is 1 percent of x.

Hence, It can be written as,

3 = 1% of x

Solve for x,

3 = 1/100 × x

3 × 100 = x

x = 300

Therefore,  3 is 1 percent of 300.

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The probability of getting 5 hearts from the deck of cards is 0.0962.

We need to find the probability of getting 5 hearts.

A "standard" deck of playing cards consists of 52 Cards in each of the 4 suits of Spades, Hearts, Diamonds, and Clubs. Each suite contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

P(E)=Number of favourable outcomes/Total number of outcomes.

Now, P(E)=5/52=0.0962

Therefore, the probability of getting 5 hearts from the deck of cards is 0.0962.

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Answer:

30.27272727272727 and repeating.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

(Michigan online school.)

Answer:

48√3 sq. in.

Step-by-step explanation:

I know this is correct bc I just had this question and this was the correct answer