Which of the following recursive formulas represents the same arithmetic sequence as the explicit formula an = 5+ (n-1)2?

Answer:

(k) cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)

From trigonometric identities, we have;

1 + cot²θ = cosec²θ

On the Left Hand Side of the equation, we get;

cos(θ)·√(1 + cot²θ) = cos(θ) × cosec(θ) = cot(θ)

On the Right Hand Side of the equation, we have;

√(cosec²(θ) - 1) = √(1 + cot²(θ) - 1) = √(cot²(θ)) = cot(θ)

∴ √(cosec²θ - 1) = cot(θ)

By transitive property of equality, therefore;

cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)

(l) sin⁶A + cos⁶A = 1 - 3·sin²A·cos²A

sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³

(sin²A)³ + (cos²A)³ = ((sin²A) + (cos²A))³ - 3·((sin²A)·(cos²A))·((sin²A) + (cos²A))

∴ (sin²A)³ + (cos²A)³ = (1)³ - 3·((sin²A)·(cos²A))·(1) = 1 - 3·((sin²A)·(cos²A))

sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³ = 1 - 3·((sin²A)·(cos²A))

sin⁶A + cos⁶A = 1 - 3·((sin²A)·(cos²A))

(m) (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1

(sinA - cosecA)²  = sin²A - 2×sinA×cosecA + cosec²A = sin²A - 2 + cosec²A

(cosA - secA)² = cos²A - 2×cosA×secA + sec²A = cos²A - 2 + sec²A

∴ (sinA - cosecA)² + (cosA - secA)² = sin²A - 2 + cosec²A + cos²A - 2 + sec²A

Where;

sin²A - 2 + cosec²A + cos²A - 2 + sec²A = sin²A + cos²A  - 2  - 2 + cosec²A + sec²A

sin²A + cos²A  - 2  - 2 + cosec²A + sec²A = 1 - 4 + cosec²A + sec²A

1 - 4 + cosec²A + sec²A = cosec²A + sec²A - 3

Where;

cosec²A = cot²A + 1

sec²A = tan²A + 1

∴ cosec²A + sec²A - 3 = cot²A + 1 + tan²A + 1 - 3 = cot²A + tan²A - 1 = The Right Hand Side of the equation

∴ (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1

(n) [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA

Squaring the Right Hand Side of the equation, we get;

(sinA - cosA)² = sin²A -2·sinA·cosA + cos²A = sin²A + cos²A -2·sinA·cosA

sin²A + cos²A -2·sinA·cosA = 1 - 2·sinA·cosA

∴ (sinA - cosA)² =  1 - 2·sinA·cosA

Taking the square root of both sides gives;

√((sinA - cosA)²) = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]

∴ sinA - cosA = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]

By symmetric property of equality, we have;

[tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA

Step-by-step explanation:

Answer:

38.46%

Step-by-step explanation:

total readers=16000

population=26000

no of non-readers=total population-total readers

=26000-16000

=10000

percentage of non-readers=non-readers×100%

population

=10000×100%

26000

percentage of non-readers is 38.46%

Answer:

15a

18x -24

Step-by-step explanation:

5(a+a+a)

Combine terms in the parentheses

5(3a)

Multiply

15a

6(3x-4)

Distribute

18x -24

The expression has y and x variables in denumerator and numerator, these variables will form the results as y^1/2 / x^3/2.

This expression is given in choice A.

The correct expression will place the y in denomerator with change in power sign in the numerator and x value will become in denomerator form the expression under root power 3 over 2.

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Answer:

x+10

Step-by-step explanation:

f(x) = (x+3)^2 and g(x) = sqrt(x)+7

g(f(x)) =

Replace f(x) in for x in the function g(x)

        = sqrt((x+3)^2)+7

        = x+3 +7

         = x+10

Answer:

is this geomtey

Step-by-step explanation:

Make sure to put what kind of maths (geometry algebra ect.) this is so others can meet your needs better. Also might want to put what unit or type of problem this is as well.

Answer: The equation to describe the situation is  p-3= 17

And, the total weight of the basket of apples was 20 pounds.

Step by step: Now, to write an equation to describe the situation. And to find the total weight of the basket of apples.

So, the basket of apples total weighed = p pounds

Liang ate apples weighed = 3 pounds.

And the apples left for the pies weighed = 17 pounds.

Now, to write an equation describing the situation:

p-3=17 .

Thus, the equation is p-3=17

Now, to get the total weight of the basket of apples:

p-3=17

adding both sides by 3 we get : p=20

Hence, the basket of apples total weighed = 20 pounds.

Therefore, the equation to describe the situation is p-3=17

And, the total weight of the basket of apples was 20 pounds.

THIS SHOULD HELP U

HAVE A GOOD DAY !

Answer:

[tex]x = 1 + \sqrt{5} x = 1 - \sqrt{5} [/tex]

Answer:

A(9,3)

B(9,0)

C(5,1)

Step-by-step explanation:

Answer:

217

Step-by-step explanation:

53 + 44 + 46 = 143

360 - 143 = 217

Answer:

since those are angles on a straight line.

we work out as follows

∠DBA and ∠DBC are making linear pair.

Linear pair of angles are formed when two lines intersect each other at a single point.

[tex]\rm \large\longrightarrow \: \: x \: + \: 126 \degree \: = \: 180 \degree[/tex]

[tex]\rm \large\longrightarrow \: \: x \: = \: 180 \degree \: - \: 126 \degree [/tex]

[tex]\rm \large\longrightarrow \: \: x \: = \: 54 \degree[/tex]

Answer:

The diameter would be 11 feet

Step-by-step explanation:

C = pi * d

we don't know D so we rearrange the equation to solve for D by dividing both sides by pi:

C/pi = d

Now we plug in everything

11pi/pi = d

The pi cancel each other out leaving with 11 feet

Therefore D = 11 feet

Answer:

1. (4)

2. (2)

Step-by-step explanation:

Answer:

2 solutions

Step-by-step explanation:

x^4-6x^2-7=0

Replace x^2 by y

(x^2)^2-6x^2-7=0

y^2-6y-7=0

D=b^2-4ac= (-6)^2-4*1*(-7)= 36+28=64

sqrtD=8

y1=(-b-sqrtD)/2a=-2/2=-1

y2= (-b+sqrtD)/2a=14/2=7

x^2=-1(n0 roots)    x^2=7 x=sqrt7 or x=-sqrt7

2 roots

Answer:

The net change is -.30

Step-by-step explanation:

increase means add

decrease means subtract

+3.50

-3.70

+3.30

-3.40

-------------

-.30

The net change is -.30

Answer:

R = [tex]\left[\begin{array}{ccc}-3&-2\\1&-3\\\end{array}\right][/tex]

Step-by-step explanation:

P - Q + R = I ( I is the identity matrix )

[tex]\left[\begin{array}{ccc}2&4\\3&5\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}-2&2\\4&1\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] ( subtract corresponding elements )

[tex]\left[\begin{array}{ccc}2-(-2)&4-2\\3-4&5-1\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}4&2\\-1&4\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}4&2\\-1&4\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-3&-2\\1&-3\\\end{array}\right][/tex]

Answer: No solution

Step-by-step explanation:

-6(x - 2) + 3x = -3(x + 3) + 21

-6x + 12 + 3x = -3x - 9 + 21

Collect like terms

-6x + 3x + 3x = -9 + 21 - 12

-6x + 6x = - 9 + 9

0 = 0

In this scenario, it can be deduced that there is no solution to Kenya's equation.

Answer:

infinitely many solutions

Step-by-step explanation:

i got it right

Answer: final answer is (x+1) (x+8)

We need two numbers that...

Add together to get 9

Multiply together to get 8

Try 1 and 8:

1+8 = 9

1*8 = 8

therefor the answer is  (x+1) (x+8)

are you sure about the ques?

Answer:

x^2, 10-x , 1.5x -5  

Step-by-step explanation:

I can't type it I have to solve on a paper for you

Answer:

Imperfect substitutes

explanation:

The choices above are not perfect substitutes, meaning they can not be perfectly or directly replace the other. Imperfect substitutes are close substitutes but not perfect substitutes. Unlike perfect substitutes, imperfect substitutes satisfies same utility but has different characteristics and therefore not entirely substitutable. For example, while one may want to have the 40 marks too, he'd rather have 60 marks even if the criteria for a 60 mark score was increasingly hard.

Answer:

27 1/2 cm^2

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = 5 * 5 1/2

Change to an improper fraction

A = 5 * (2*5+1)/2

A = 5*11/2

A = 55/2

Change back to a mixed number

A = 27 1/2

Answer:

20 mm^3, 20 cubic millimeters

Step-by-step explanation:

The volume of a prism is length times width times height.

Length, width, and height can have units of mm.

mm * mm * mm = mm^3

The units of a volume must be cubic units.

Answer: 20 mm^3, 20 cubic millimeters

Answer:

365.65

Step-by-step explanation:

you can find the formula online

Answer:

[tex] \bf \: y = 2 {x}^{2} - 6x - 8[/tex]

It is equation of a parabolla.

It is to be noted that the graph of y = 2x * 2-6x-8 which when simplified is  y = -12x² - 12x. is attached accordingly.

The graph of y = -12x² - 12x is a downward-opening parabola.

It has a concave shape and its vertex is the highest point on the graph. The axis of symmetry is a vertical line passing through the vertex.

The graph may intersect or be tangent to the x-axis at two points, one point, or no points, depending on the discriminant.

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9514 1404 393

Answer:

  2/3

Step-by-step explanation:

Let x represent the fraction of Cheryl's income she spent in September. Then 1-x is the fraction she saved.

In October, her spending increased by 0.2x, and her savings decreased by 0.4(1 -x). Since Cheryl spends or saves all of her income, these two change amounts must be equal:

  0.2x = 0.4(1 -x)

  x = 2(1 -x) . . . . . . multiply by 5 to clear fractions

  x = 2 -2x . . . . . . eliminate parentheses

  3x = 2 . . . . . . . . add 2x

  x = 2/3 . . . . . . divide by 3

Cheryl spent 2/3 of her income in September.

Answer:

(7;2)

Step-by-step explanation:

[tex]3x - 2y = 17 \\ - 2y = 17 - 3x \\ 2x + 17 - 3x = 10 \\ 2x - 3x = 10 - 17 \\ - x = - 7 \\ x = 7 \\ - 2y = 17 - 21 \\ - 2y = - 4 \\ y = 2[/tex]

Answer:

C. $1,260

Step-by-step explanation:

80 × 14.5 = 1,160

2,500 × 0.04 = 100

Answer:

C. $1260

Step-by-step explanation: