Prove the following identity:
[tex] \frac{1 + \cos( \alpha ) }{ \sin( \alpha ) } + \frac{ \sin( \alpha ) }{1 + \cos( \alpha ) } = 2 \csc( \alpha ) [/tex]
​

Answer:Pythagorean therome

Step-by-step explanation:a^2+b^2=c^2

d)

[tex] \frac{2 {x}^{2} - xy + 2xy - {y}^{2} }{6xy - 3 {y}^{2} } = \frac{x(2x - y) + y(2x - y)}{3y(2x - y)} = \\ [/tex]

[tex] \frac{(x + y)(2x - y)}{3x(2x - y)} = \frac{x + y}{3x} \\ [/tex]

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e)

I think -6 should be +6

or +3x should be -3x

[tex] \frac{ {x}^{2} + 2x + x + 2 }{ {x}^{2} + 2x + 3x + 6 } = \frac{x(x + 2) + (x + 2)}{x(x + 2) + 3(x + 2)} = \\ [/tex]

[tex] \frac{(x + 1)(x + 2)}{(x + 3)(x + 2)} = \frac{x + 1}{x + 3} \\ [/tex]

Or

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

[tex] \frac{x + 1}{x - 3} \\ [/tex]

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f)

[tex] \frac{ {a}^{2} - 5a - 4a + 20 }{ {a}^{2} - 5a + 2a - 10 } = \frac{a(a - 5) - 4(a - 5)}{a(a - 5) + 2(a - 5)} = \\ [/tex]

[tex] \frac{(a - 4)(a - 5)}{(a + 2)(a - 5)} = \frac{a - 4}{a + 2} \\ [/tex]

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️

Answer:

[tex](x^2)^\frac{1}{3}[/tex]

Step-by-step explanation:

1). [tex]\sqrt[n]{x}[/tex] = [tex]x^\frac{1}{n}[/tex]

Step-by-step explanation:

500 hundred students attend McCord Middle School.

Answer:

the answer is C: 500 students

Step-by-step explanation:

Answer:

d. number of students wearing blue shirts

(12, 5)

equations:

To solve with elimination, either the x or y coefficient should be similar.

Then,

[tex]\sf 3x-5y=11[/tex]

[tex]\sf 3x-12y=-24[/tex]

==============       [ subtract equation 2 from equation 1 ]

[tex]\sf 7y = 35[/tex]

[tex]\sf y = 5[/tex]

For x,

[tex]\sf 3x-5(5)=11[/tex]

[tex]\sf 3x-25=11[/tex]

[tex]\sf 3x=11+25[/tex]

[tex]\sf x=\dfrac{36}{3}[/tex]

[tex]\sf x=12[/tex]

In ordered pair: (x,y) → (12, 5)

Answer:

The area of the original garden is x^2 square feet.

The lengths of the sides of the new garden are x + 2 feet and x + 7 feet.

The area of the new garden, in square feet, is

[tex](x + 2)(x + 7)[/tex]

[tex] {x}^{2} + 9x + 14[/tex]

1) the area of his garden is, x² feet²

2) the lengths of the sides of the new garden are,

⇒ (x + 2)

⇒ (x + 7)

And, the area of the new garden is,

Area = x² + 9x + 14

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Farmer Bob has a small square garden that is x feet by x feet.

Now,

We know that;

Area of square = Side²

Here, Side = x feet

Hence, the area of his garden is,

Area = x × x

Area = x² feet²

Now, When He decides to add 2 feet to one side of the garden and 7 feet to the other side.

Then, the lengths of the sides of the new garden are,

⇒ (x + 2)

⇒ (x + 7)

Hence, the area of the new garden is,

Area = (x + 2) (x + 7)

Area = x² + 2x + 7x + 14

Area = x² + 9x + 14

Thus, 1) the area of his garden is, x² feet²

2) the lengths of the sides of the new garden are,

⇒ (x + 2)

⇒ (x + 7)

And, the area of the new garden is,

Area = x² + 9x + 14

Learn more about the multiplication visit:

https://brainly.com/question/10873737

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Answer:

5/9 divided by 10

Step-by-step explanation:

B. Square

There are numerous different types of squares in the world. A parallelogram with four congruent sides and four right angles is called a quadrilateral. There are two sets of parallel sides and four right angles in a square, so it is also a rectangle. Because the sides of a square are parallel, it is also a parallelogram.

D. I and IV

[tex]The\ statement\ is\ always\ true\ is\\ I\ All\ square\ is\ a\ rectanjile\ and\ IV\ Any\ two\ opposite\\ -sides\ of\ a\ perallelogran\ are\ parallel[/tex]

[tex]So\ Chase\ D[/tex]

{[tex]{A\ souare\ is\ a\ special\ rectangle[/tex]

B. 500 cm²

Calculate area of the rectangle:

[tex]\curvearrowleft\\ area=500[/tex]

I hope this helps you

:)

a os is correct.....,,..................

Answer:

45

Step-by-step explanation:

Answer:

x = 6°

Step-by-step explanation:

We know that all the interior angles of a triangle sum up to 180°.

(7x+3)°+(80°)+(55°) = 180°

(7x+3)°+(135°) = 180°

(7x+3)°= 45°

7x = 42°

x = 6°

Answer:

slope: 5/1x (or just 5x)

y-int: -3

Step-by-step explanation:

The y-intercept is (0,-3)

The slope of the line is 4

         [tex]\frac{y2-y1}{x2-x1} =\frac{2--3}{1-0} =\frac{5}{1} =5[/tex]

Hope it helps!

[tex]Answer:[/tex]

The line stops at 100/900.

Hope this helps, have a great day! ♣

Answer:

fourth graph in second pic

Step-by-step explanation:

first lets substitute points to see whether the graph increases or decreases

sooo

y = -2(2^0)

y = -2

(0, -2)

y = -2(2^1)

y = -4

(1, -4)

y = -2(2^2)

y = -2(4)

y = -8

(2, -8)

with these points we can tell that the graph is decreasing, since there is two graphs decreasing, we can use the points to see if the parabola lies on the points (i think its called parabola)

its the last graph. fourth graph on page 2

Answer:

Multiple of 4 = {4,8,12,16,20,24}

Step-by-step explanation:

After the dilation, the lengths are multiplied by the value of the scale factor while the angles remain same.

Given is to find how dilation affect the side lengths and angle measures of a figure

Assume that the initial length of the figure

After the dilation, the coordinates will become -

(x, y) → (Kx, Ky)

Where {K} is the scale factor by which the image is dilated.

The angles after the dilation remain same.

Therefore, after the dilation, the lengths are multiplied by the value of the scale factor while the angles remain same.

To solve more questions on dilation, visit the link below -

brainly.com/question/2859427

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Answer:

744

Step-by-step explanation:

solved on calcultor

Budget of a film = 1200

Money they spend on equipment :-

= 62% of total expense

= 62% of 1200

[tex]= \frac{62}{100} \times 1200[/tex]

[tex] = \frac{62 \times 1200}{100} [/tex]

[tex] = \frac{74400}{100} [/tex]

[tex]\color{purple}= 744[/tex]

Which means , the group of friends spent 744 on equipment .

Then , money they spent on costume :-

= 100 - 62 % of 1200

= 38% of 1200

[tex] = \frac{38}{100} \times 1200[/tex]

[tex] = \frac{38 \times 1200}{100} [/tex]

[tex] = \frac{45600}{100} [/tex]

[tex] \color{orange} = 456[/tex]

Which means the group of friends spent 456 on costumes .

Therefore , the group of friends spent 456 on costumes .

The point on a number line is the location of the point.

The points are given as:

x = 10 and x = 0

This means that we mark a point at the point 10 on the number line, and another point at the point 0 on the same number line

However, the point 0 would come before point 10 because 0 is less than 10

See attachment for the number line

Read more about number lines at:

https://brainly.com/question/10851163

Answer:

Height = 108.35 cm

Step-by-step explanation:

Given :-

Radius = 26 cm

Total Volume = 230,000 cm³

To Find :-

Height

Formula Required :-

Volume (cylinder) = π x (radius)² x height

=> height = volume / π x (radius)²

Solving :-

h = 230,000 / (3.14 x 676)

h = 230,000 / 2122.64

Solution :-

Height = 108.35 cm

Answer:

63 ft^2

Step-by-step explanation:

3x3 + 6x9 = 63 ft^2

Answer:

The negative signs were switched. This is the answer.

Answer:

$1920

Step-by-step explanation:

12800 X 0.15 = 1920

Answer:

should be 4x+5*(-3)^x

Step-by-step explanation:

Multiplying two neg equals a positive

any expression multiplied by 1 stays the same

use commutative property to reorder the terms

Answer:

-60

Step-by-step explanation:

Yeah, of course!.

Step one: Breaking the problem into different problems is probably the best!

Step two: 4× (-1) is simple multiplication, any number multiplied by 1 is always the number. 4 multiplied by 1 is always 4, but there is a negative sign in front of the 1, so that means we have to go into the positive an negative rules, final answer is 4 for that step.

Then were going to ignore the multiplication sign for now.

Step three: (-3) times (-5) is 15 but we have to look at the rules of positives and negatives, a negative plus a negative is a positive. So its 15.

Step four: Multiply the two answers (4 times 15) is 60. Now were going to add our negative sign because a positive plus a positive number is a negative.

Hope this helped! :)

Answer:

there were rivalries between African leaders.

Step-by-step explanation:

Answer:

x = 1 and

x = 3

Step-by-step explanation:

The solution is the x for each row where the f(x) and g(x) are the same. When x is 1, f(x) and g(x) are both 0.

When x is 3, f(x) and g(x) are both 6.

Using an exponential function, it is found that f(5.5) = 19.8.

An exponential function is a function in which the growth rate is a percentage, modeled by:

[tex]y = ab^x[/tex]

In which:

f(3.5) = 25 means that:

[tex]ab^{3.5} = 25[/tex]

[tex]a = \frac{25}{b^{3.5}}[/tex]

f(8.5) = 14 means that:

[tex]ab^{8.5} = 14[/tex]

Hence:

[tex]\frac{25}{b^{3.5}} \times b^{8.5} = 14[/tex]

[tex]25b^5 = 14[/tex]

[tex]b = \sqrt[5]{\frac{14}{25}}[/tex]

[tex]b = 0.89[/tex]

[tex]a = \frac{25}{0.89^{3.5}} = 37.59[/tex]

Hence, the function is given by:

[tex]y = 37.59(0.89)^x[/tex]

Then, when x = 5.5:

[tex]f(5.5) = 37.59(0.89)^{5.5} = 19.8[/tex]

More can be learned about exponential functions at https://brainly.com/question/25537936

Answer:

Step-by-step explanation:

19.83