prove the identity.
(1-sin^2x)tanx=cosxsinx
Note that each Statement must be based on a Rule

When a shape is rotated, it must be rotated through a point

The new position of point B is point A

The angle of rotation is given as:

[tex]Angle = 288^o[/tex]

The shape is a regular pentagon (with 5 sides).

The smallest angle of rotation that maps the pentagon onto itself is calculated using:

[tex]\theta = \frac{360}n[/tex]

So, we have:

[tex]\theta = \frac{360}5[/tex]

[tex]\theta = 72[/tex]

Let the number of rotations be n.

So, we have:

[tex]\theta \times n= Angle[/tex]

This gives

[tex]72 \times n= 288[/tex]

Divide both sides by 72

[tex]n= 4[/tex]

This means that the new position of B is 4 points away from B.

Point A is 4 points away from B, in clockwise direction

Hence, the new position of point B is point A

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Formula:

We know that

nth term of the AP is Tn = a+(n-1)d

Where, a = First term

d = Common difference

n = number of terms

Now,

Given that

pth term of the A.P. = Tp = q

⇛a + (p-1)d = q

⇛(p-1)d = q - a

⇛d = (q-a)/(p-1) →→→→(i)

and

qth term of the A.P. = Tq = p

⇛a + (q-1) d = p

⇛ (q-1)d = p-a

⇛ d = (p-a)/(q-1) →→→→(ii)

From Eqn(i) and Eqn(ii)

⇛(q-a)/(p-1) = (p-a)/(q-1)

On applying cross multiplication then

⇛(q-a)×(q-1) = (p-a)×(p-1)

⇛q²-q-aq+a = p²-p-ap+a

⇛q²-q-aq = p²-p-ap

⇛ap-aq = p²-p+q-q²

⇛a(p-q) = (p²-q²)-(p-q)

⇛a(p-q) = (p+q)(p-q)-(p-q)

⇛ a(p-q) = (p-q){(p+q)-1}

On cancelling (p-q) both sides then

⇛a = (p+q-1) →→→→Eqn(iii)

On Substituting the value of a in Eqn(ii) then

⇛ d = [p-(p+q-1)]/(q-1)

⇛d = (p-p-q+1)/(q-1)

⇛d = (-q+1)/(q-1)

⇛d = -(q-1)/(q-1)

⇛d = -1

We have,

a = p+q-1 and d = -1

Now, rth term of the AP

⇛ Tr = a + (r-1)d

⇛Tr = (p+q-1)+(r-1)(-1)

⇛ Tr = p+q-1+(-r+1)

⇛ Tr = p+q-1-r+1

⇛ Tr = p+q-r

Therefore, Tr = p+q-r

Answer: rth term of the given A.P. is p+q-r

Answer:

rth=q+p+qxp

Step-by-step explanation:

rth= 3 of the T and Tq added together and joined.

4 3/4 = 19/4

133/(19/4) = 133(4/19) = 1197/19 = 63 mph

Answer:

246b  

Step-by-step explanation: i did this

Answer:

Step-by-step explanation:

-3x + 6y = 11

Put into slope-intercept form to find the slope

6y = 3x + 11

 y = 3x/6 + 11/6

 y = ½x + 11/6

so slope is ½

perpendicular lines have negative reciprocal slopes, so our perpendicular line has slope -2

the slope point form of the perpendicular line will be

(y - 3) = -2(x -(-2))

(y - 3) = -2(x +2)

the slope intercept form will be

y = -2x - 4 + 3

y = -2x - 1

Slope is the change in Y over the change in x.

Use 2 points on the graph(x,y) to use to solev6.

(2,3) and (0,-7)

Slope = (-7 -3) / (0-2)

Slope = -10/-2

Slope = 5

Answer: A the slope is 5

Option A

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The set of ordered pairs is {(2, 1), (2, 3), (3, 4)} which represents ƒ -1, which is the correct answer that would be an option (C).

An ordered pair is made up of two components isolated by a comma and put inside parentheses. (x, y) indicates an ordered pair, where 'x' is the first component and 'y' is the second component in the ordered pair.

Given the function ƒ = {(1 , 2), (2 , 3), (3 , 4)}

According to option (A),

The set of ordered pairs is {(1, 2), (3, 2), (4, 3)}

This represents ƒ -3,

According to option (B),

The set of ordered pairs is {(2,1), (3, 2), (4, 3)}

This represents ƒ -2,

According to option (C),

The set of ordered pairs is {(2, 1), (2, 3), (3, 4)}

This represents ƒ -1,

Thus, the set of ordered pairs is {(2, 1), (2, 3), (3, 4)} which represents ƒ -1.

Hence, the correct answer would be option (C).

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The strategy that won't help her to calculate 9 - 7 is (a) Make 10

The given parameters are:

[tex]Yellow = 7[/tex]

[tex]Red = 9[/tex]

To determine 9 - 7,

However, she cannot make 10.

This is so, because 9 and 7 are not up to 10

Hence, the strategy that won't help her to calculate 9 - 7 is (a)

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Answer:

6.4 should be the correct answer

Step-by-step explanation:

if im wrong and you wanted it in a different format im sorry

Answer: 8.5

Step-by-step explanation: (42.50 - 17) ÷ (5 - 2)

= 25.50 ÷ 3

= 8.5

Thank me later

Step-by-step explanation:

although there is no graph visible here, I suspect this is the same question as I just answered twice already.

the slope is -6.

D is the right answer.

Let's simplify step-by-step.

2a(x+y)+b(x+y)

Distribute:

=(2a)(x)+(2a)(y)+(b)(x)+(b)(y)

=2ax+2ay+bx+by

The simplification of the expression is 2ax+2ay+bx+by.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

An algebraic equation is a statement of the equality of two expressions formulated by applying algebraic operations to a set of variables.

Given expression is 2a(x+y)+b(x+y). The expression will be solved as below,

E = 2a(x+y)+b(x+y)

Multiply the values in the whole bracket and simplify,

E = (2a)(x)+(2a)(y)+(b)(x)+(b)(y)

E = 2ax+2ay+bx+by

The simplified expression is given as 2ax+2ay+bx+by.

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Answer:

A: 437.1 cm³

Step-by-step explanation:

You find the area of the prism by the base of the prism & height multiplied together.

Here, the base of the prism is a triangle.

All the triangles sides are given, so lets lave them: A:8, B:8, and C:10.

Using SSS, we can find the area, which is ≈ 31.1.

If we multiply that number by 14.

We get he area of the prism.

Depending on how your rounded, the area of the prism is:

≈437.2, which is close enough to know that the asswer is A: 737.1 cm³

Hope this helped <3

Answer:

x + (4x-20) = 180

by linear pair

therefore x= 70

Applying the definition of linear pair, the value of x is: D. 40.

Therefore:

x + (4x - 20°) = 180°

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 40

Therefore, applying the definition of linear pair, the value of x is: D. 40.

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Step-by-step explanation:

Solution A is 40% acid and solution B is 80% acid. How many

liters of each should be used in order to make 100 L of a solution

is 64% acid

There should be 40 L of solution A and 60 L of solution B should be added in order to make 100 L of a solution that is 64% acidic.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, solution A is 40% acidic and solution B is 80% acidic, they are mixed to get a 100 L solution which is 64% acidic.

Establishing the equations,

A+B = 100

A = 100-B.......(i)

40% of A + 80% of B = 64% of 100

0.4A + 0.8B = 64......(ii)

Solving the equations,

0.4(100-B) + 0.8B = 64

40 - 0.4B + 0.8B = 64

0.4B = 24

B = 24/0.4

B = 60

Putting, B = 60 in Eq(i)

A = 100-60

A = 40

Hence, The amount of solutions needed is A = 40 L and B = 60 L.

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Step-by-step explanation:

again (I just answered the same question), the slope is the ratio "y coordinate change / x coordinate change".

I see e.g the points

(-1, -1) and (0, -7) on the line.

x changes by +1 (from -1 to 0).

y changes by -6 (from -1 to -7).

so, the slope is -6/1 = -6.

so, D is the right answer.

Answer:

applied to the motor it reaches a steady-state speed of rotation of 20 rev/s and draws 40 A. What will be (a) the power input to the motor, (b) the power loss in the armature, (c) the torque generated at that speed

voltage of 120 V is applied to the motor it reaches a steady-state speed of rotation of 20 rev/s and draws 40 A. What will be (a) the power input to the motor, (b) the power

Answer:

d.

Step-by-step explanation:

Answer:

-5x - 6y

Step-by-step explanation:

Firstly,  you remove any uncessary parentheses and collect like terms.

So that becomes -8x - 6y + (3x)

Hence, the brackets can be removed, which means we can continue to collect like terms which gives the final answer of -5x - 6y

Answer:

w=4

Step-by-step explanation:

72/48=6/w

3/2=6/w

12=3w

w=4

[tex]y = x^{\tfrac 1{\ln x}}\\\\\implies \ln y = \ln \left( x^{\tfrac 1{\ln x}} \right)\\\\\implies \ln y = \dfrac{1}{\ln x} \cdot \ln x\\\\\implies \ln y = 1\\\\\implies y =e\\\\\\\text{Now,}\\\\\ \lim \limits_{x \to \infty} x^{\tfrac 1{\ln x}}=\lim \limits_{x \to \infty} y = \lim \limits_{x \to \infty} e = e[/tex]

Answer:

1,3,4,6,8} { 1 , 3 , 4 , 6 , 8 }. Range:{2,4,5,7,9}

Step-by-step explanation:

The domain is the set of all the values of x x . The range is the set of all the values of y y .

Slope = change in y / change in x

Slope = (2-1)/(3 - -1)

Slope = 1/4

Answer:

pic?

Step-by-step explanation:

send me the picture please

Answer:

[tex]{ \rm{V = \frac{lwh}{3} }} \\ \\ { \rm{3V = lwh}} \\ \\ { \boxed{ \rm{ \: w = \frac{3V}{lh } \: }}}[/tex]

Answer:

{x,y,z} = {-22/13,29/13,6/13} 

Write the system as the following augmented matrix:

[tex]\left[ \begin{array}{ccc|c} 3 & -2 & 5 & -7 \\ 1 & -1 & 3 & -5 \\ 4 & 1 & 1 & 6 \end{array} \right][/tex]

Swap rows 1 and 2 :

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 3 & -5 \\ 3 & -2 & 5 & -7 \\ 4 & 1 & 1 & 6 \end{array} \right][/tex]

Eliminate the x coefficient from the last two rows by add -3 (row 1) to row 2, and -4 (row 1) to row 3 :

[tex]\left[ \begin{array}{ccc|c} 1 & -1 & 3 & -5 \\ 0 & 1 & -4 & 8 \\ 0 & 5 & -11 & 26 \end{array} \right][/tex]

Eliminate the y coefficient from the first and last rows by adding row 2 to row 1, and -5 (row 2) to row 3 :

[tex]\left[ \begin{array}{ccc|c} 1 & 0 & -1 & 3 \\ 0 & 1 & -4 & 8 \\ 0 & 0 & 9 & -14 \end{array} \right][/tex]

Eliminate the z coefficient from the second row by adding 4 (row 3) to 9 (row 2) :

[tex]\left[ \begin{array}{ccc|c} 1 & 0 & -1 & 3 \\ 0 & 9 & 0 & 16 \\ 0 & 0 & 9 & -14 \end{array} \right][/tex]

Eliminate the z coefficient from the first row by adding row 3 to 9 (row 1) :

[tex]\left[ \begin{array}{ccc|c} 9 & 0 & 0 & 13 \\ 0 & 9 & 0 & 16 \\ 0 & 0 & 9 & -14 \end{array} \right][/tex]

Then the solution to the system is (x, y, z) such that

9x = 13 and 9y = 16 and 9z = -14

or

x = 13/9 and y = 16/9 and z = -14/9

Answer:

This is false.

Step-by-step explanation:

The easiest thing to do is notice that 8 goes into 16 whilst 9 doesn't so that shows 9/16 would not be the unit rate.

The ratio 5/8 to 10/9 has a unit rate of 9/16 is false.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given are two ratios 5/8 and 10/9.

The unit rate of (5/8) is (5/8)/(8/8) = 5/8 = 0.625 similary the unit rate of the ratio 10/9 is 1.11.

Now, the unit rate of 9/16 is 0.5625 which is not in the range of two ratio's unit rates.

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Answer:

y = 2x + -3

Step-by-step explanation:

Use the equation y=mx+b

m is the slope (2 in this case)

b is the y intercept (-3 in this case)

The equation of the line would be y = 2x + -3