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2 years ago

The terminal side of ∅ in standard position contains the point (-4, -2). Find the exact value for cot∅.

Mathematics

1 answer:

iogann1982 [59]2 years ago

4 0

<h3>Answer: C) 2</h3>

====================================================

Work Shown:

cot(theta) = cos(theta)/sin(theta)

cot(theta) = x/y

cot(theta) = -4/(-2)

cot(theta) = 2

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What is the sign of f on the interval -2

TEA [102]

Answer:

$f$ is sometimes positive and sometimes negative.

Step-by-step explanation:

$f(x)=(x-3)(x+2)(x+4)(x+4)(x-1)(2x-9)$

Take $x=-1\in(-2,\frac{9}{2})\ as-2$

$f(-1)=(-1-3)(-1+2)(-1+4)(-1-1)(-2-9)\\\\=(-4)(1)(3)(-2)(-11)\\\\=-264\\\\f(-1)$

Take $x=2\in(-2,\frac{9}{2})\ as\ -2$

$f(2)=(2,-3)(2+2)(2+4)(2-1)(2\times2-9)\\\\=(-1)(4)(6)(1)(-5)\\\\=120\\\\f(2)>0$

Hence $f(x)$ for $x=-1$ and $f(x)>0$ for $x=2$

So $f$ is sometimes positive and sometimes negative in the interval.

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3 years ago

Solve the system of equations by transforming a matrix representing the system of equation into reduced row echelon form.

Gekata [30.6K]

Take the augmented matrix,

$\left[\begin{array}{ccc|c}2&1&-3&-20\\1&2&1&-3\\1&-1&5&19\end{array}\right]$

Swap the row 1 and row 2:

$\left[\begin{array}{ccc|c}1&2&1&-3\\2&1&-3&-20\\1&-1&5&19\end{array}\right]$

Add -2(row 1) to row 2, and -1(row 1) to row 3:

$\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&-3&4&22\end{array}\right]$

Add -1(row 2) to row 3:

$\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&9&36\end{array}\right]$

Multiply through row 3 by 1/9:

$\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&-5&-14\\0&0&1&4\end{array}\right]$

Add 5(row 3) to row 2:

$\left[\begin{array}{ccc|c}1&2&1&-3\\0&-3&0&6\\0&0&1&4\end{array}\right]$

Multiply through row 2 by -1/3:

$\left[\begin{array}{ccc|c}1&2&1&-3\\0&1&0&-2\\0&0&1&4\end{array}\right]$

Add -2(row 2) and -1(row 3) to row 1:

$\left[\begin{array}{ccc|c}1&0&0&-3\\0&1&0&-2\\0&0&1&4\end{array}\right]$

So we have $\boxed{x=-3,y=-2,z=4}$ .

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2 years ago

Alex wants to paint one side of his skateboard ramp with glow-in-the-dark paint, but he needs to know how much area he is painti

Svetach [21]

The answer of the question is 140. hope i help you ;)

8 0

3 years ago

Read 2 more answers

Sebastian saved money in his piggy bank. He kept track on how much money he saved at the end of each week on the line graph belo

Luba_88 [7]

Answer:

$90

Step-by-step explanation:

Look at the number 7 on the bottom right of the graph. That means at the end of 7 weeks. Now look vertically up from there until you see a point directly above 7 weeks. Look to the left of that point, and you see that the point directly above 7 weeks is at the level of $90. That means that at the end of 7 weeks, he had $90.

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3 years ago

Read 2 more answers

What is the area of a rectangle with vertices at (6,-3), (3,-6), (-1,-2), and (2,1). Enter your answer In the box

vladimir2022 [97]

Answer:

24 units

Step-by-step explanation:

Start by plotting on the rectangular coordinate system the four points given: (6,-3), (3,-6), (-1,-2) , and (2, 1)

Please see attached image for guidance with the answer.

These four points are represented with green dots in the image.

Notice that such rectangle can be viewed as inscribed in a larger square that is 7 units by 7 units, and on which these four points (the vertices of the rectangle) touch the square's perimeter.

So to make the calculation simple, we can find the area of the larger square (very simple to calculate since it is 7 times 7 = 49) and subtract from it the area of the four triangles that are depicted in yellow and in light green. Such result will give us the area of the rectangle (white background).

Out of the four triangles whose areas we need to extract, we notice that they are all right angle triangles with simple formulas to calculate their areas: base times height divided by 2.

The triangles in green have base 3 and height 3 so their areas are: (3 * 3) /2 = 4.5. since they are two of these the total area of the green triangles is 4.5*2 = 9

We do something similar with the yellow triangles, noticing that their base and heights are 4 and 4 respectively which gives an area of (4*4)/2 = 8

Again, since there are two of them, we multiply this by 2: 8 * 2 = 16

Now to calculate the area of the white rectangle we do:

Area of big square minus area of green triangles minus area of yellow triangles: 49 - 9 - 16 = 24

3 0

2 years ago