Please help me with this trigonometry math question ASAP! Thanks so much!

Answer:

The given symbol for the nth triangular number = Tₙ

The given symbol for the nth square number = Qₙ

The given symbol for the nth pentagonal number = Pₙ

The mathematical formula for the nth triangular number, Tₙ = n·(n + 1)/2

The nth square number is given by Qₙ = n²

The nth pentagonal number is given by Pₙ = n·(3·n - 1)/2

(a) T₃.ₙ₋₁ = (3·n - 1)·(3·n - 1 + 1)/2 = (3·n - 1)·(3·n)/2  = 3·(3·n - 1)·(n)/2 = 3·Pₙ

Therefore;

T₍₃.ₙ ₋ ₁₎ = 3·Pₙ

(b) Pₙ - Qₙ = n·(3·n - 1)/2 - n²

Expanding the above equation gives;

n·(3·n - 1)/2 - n² = (3·n² - n - 2·n²)/2 = (n² - n)/2 = n·(n - 1)/2

T₍ₙ ₋ ₁₎ = ((n - 1)· ((n - 1) + 1))/2 =  ((n - 1)· n)/2 = n·(n - 1)/2

∴ Pₙ - Qₙ = n·(3·n - 1)/2 - n² = n·(n - 1)/2 = T₍ₙ ₋ ₁₎

∴ Pₙ - Qₙ = T₍ₙ ₋ ₁₎

Therefore, we get;

P₃.ₙ - Q₃.ₙ = T₍₃.ₙ ₋ ₁₎

Where, T₍₃.ₙ ₋ ₁₎ = 3·Pₙ from (a) above, gives;

P₃.ₙ - Q₃.ₙ = 3·Pₙ

∴ P₃.ₙ - 3·Pₙ = Q₃.ₙ

Plugging in the values, gives;

P₃.ₙ = (3·n)·(3·(3·n) - 1)/2 = (3·n)·((9·n) - 1)/2

3·Pₙ = 3·n·(3·n - 1)/2

P₃.ₙ - 3·Pₙ = (3·n)·((9·n) - 1)/2 - 3·n·(3·n - 1)/2 = (3·n)·(((9·n) - 1) - (3·n - 1))/2

(3·n)·(((9·n) - 1) - (3·n - 1))/2 = (3·n)·(9·n - 1 - 3·n + 1)/2 = (3·n)·(6·n )/2 = 9·n²

Q₃.ₙ = (3·n)² = 9·n²

∴ P₃.ₙ - 3·Pₙ = P₃.ₙ - 3·Pₙ

Step-by-step explanation:

Answer:

-36/35  or -1 1/35

Step-by-step explanation:

-8/5 + 4/7

Get a common denominator of 35

-8/5 * 7/7   + 4/7 *5/5

-56/35  + 20/35

-36/35

-35/35 - 1/35

-1  1/35

Answer:

-36/35

Step-by-step explanation:

First, we need to find the LCM of 5 and 7 (the denominators) which is 35.

-8*7/35 + 4*5/35 = -56/35 + 20/35 =  -36/35

Your answer is -36/35, or if it asks for a mixed number it's -1 1/35.

Hope this helps

Answer:

247/7 = 35 2/7

247/7 = 35 reminder 2

247/7 = 35.2857142857...

Step-by-step explanation:

             35      

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

   7    |   247

             21

          -----------

               37

               35

             ---------

                 2

247/7 = 35 2/7

247/7 = 35 reminder 2

247/7 = 35.2857142857...

9514 1404 393

Answer:

  5/48, 5/46, 5/44, 5/42

Step-by-step explanation:

We can choose unit fractions with denominators between 8 and 10, separated by (10-8)/5 = 0.4 units:

  1/8.4 = 5/42

  1/8.8 = 5/44

  1/9.2 = 5/46

  1/9.6 = 5/48

__

Check

_____

Additional comment

There are an infinite number of such fractions. We are given unit fractions with different denominators, so it works reasonably well to choose denominators between those given. Then the trick is to convert the fraction to a ratio of integers. In this case, multiplying by (5/5) does the trick.

__

Another approach is to write the fractions with a common denominator, then choose numerators between the ones given. For example, 1/10 = 4/40, and 1/8 = 5/40, so you could write some fractions with numerators between 4 and 5. Possibilities are 4.1/40 = 41/400, 4.3/40 = 43/400, 4.7/40 = 47/400, 4.9/40 = 49/400.

Answer:

D

Step-by-step explanation:

[tex]5(9 + 4) \\ 5(13) \\ 65 \\ prove \: it \: d \: answer \\ 5(9) + 20 \\ 45 + 20 \\ = 65[/tex]

Answer:

lo emos aprendido mucho chicas y chicos xporfor cuidense mucho porque les quiero x xd

Answer:

[tex](2a-b)(2a+b -1 )[/tex]

Step-by-step explanation:

[tex]4a^2-b^2-2a+b[/tex]

[tex](2a+b)(2a-b) -1(2a-b)[/tex]

[tex](2a-b)(2a+b -1 )[/tex]

Answer:

344064

Step-by-step explanation:

hope it is well understood

9514 1404 393

Answer:

  35 cm²

Step-by-step explanation:

You can count the squares, or ...

Any way you do this, there are 35 square, so the area is 35 square centimeters.

Answer:

+4/3

Step-by-step explanation:

-3/4 * -1 = 3/4 then flip it to 4/3

Answer:

4/3

Step-by-step explanation:

the slope of a perpedicular line is the inverse times negative one.

1)the inverse of -3/4 is -4/3

2)-4/3*-1 is 4/3

Answer:

x=13

Step-by-step explanation:

These are corresponding angle and corresponding angles are equal

7x-1 = 8x-14

Subtract 7x from each side

7x-1-7x = 8x-14-7x

-1 = x-14

Add 14 to each side

-1+14 = x-14+14

13 =x

Answer:

A conjecture that can be made is that the line that contains the diagonal from the tip to the vertex of the tail of a dart and the diagonal that joins the fin angles are perpendicular to each other

Step-by-step explanation:

Question; Make a conjecture about the line that contains the diagonal from the tip to the vertex of the tail of a dart and the diagonal that joins the fin angles

Explanation;

We note that a diagonal is a straight line that joins one corner of a polygon with another corner of the polygon from the vertex points of the connected corners

The diagonal that joins the fin angles forms an isosceles triangle at the tail of the dart, and the locus of the line that forms the diagonal from the tip to the tail is a equidistant from the vertex of the fin angles

Therefore, the diagonal from the tip bisects the diagonal that joins the fin angles bisects the base of the formed isosceles triangle while passing through the vertex of the isosceles triangle, it is therefore, perpendicular to the base of the isosceles triangle which is the diagonal that joins the fin angles

A conjecture that can be made is that the line that contains the diagonal from the tip to the vertex of the tail of a dart and the diagonal that joins the fin angles is therefore, that they are perpendicular to each other

Answer:

Quinary - 12310

Binary -  1110111011

Answer:

Quinary= (12310)5

Binary=(1110111011)2

Answer:

15$

Step-by-step explanation:

you need to check how much of e costs and you do that by dividing the price by the amount and than comes up to 1.5 that's for 1 and for 10 it's 15 hope that helps

Answer:

Step-by-step explanation:

(b - c)/b * (b+c)/b  Notice how the second fraction is inverted and multiplied. That's how you handle a 4 tier fraction. Here's a simpler example

[tex]\frac{\frac{2}{3} }{\frac{4}{5} } = \frac{2}{3} * \frac{5}{4}[/tex]

What you get with your problem is

(b^2 - c^2)/b^2

Step-by-step explanation:

1) = {5(x+y)} - 2x

= 5x + 5y - 2x

= 3x + 5y

2)= {2(p×q)} + (p×q)

= (2p×2q)+ p×q

= 4pq + pq

= 5pq

3)= 6a + (8b + 2a)

= 8a + 8b

= 8(a+b)

4)= 3x² + ( x²+7x)

= 4x² + 7x

= x(4x+7)

Answer:

Step-by-step explanation:

72) 5*(x +y) - 2x

  = 5x + 5y - 2x  {Distributive property}

  = (5x - 2x) + 5y    {Combine like terms}

  = 3x + 5y

73) 2*(pq) + pq

   = 2pq + pq     {Combine like terms}

   = 3pq

74) 6a + (8b + 2a)

     = 6a + 2a + 8b   {Combine like terms}

    = 8a + 8b

75) 3*x² + (x² + 7x)

   = 3x² + x² + 7x   {Combine like terms}

   = 4x² + 7x

Answer:

D

Step-by-step explanation:

Answer:

Here is your answer....

Hope it helps.....

Answer:

-3

Step-by-step explanation:

expand the bracket by multiplying everything

inside by 3

after that collect like terms

then solve to come up with -3 as ur answer

Answer:

D: it is the only equation that has strictly positive exponents...

the function is "always going up"

if a function has a negative exponent 2^-x the curve will "decay"

[tex]2^{x^{2} }[/tex] the [tex]x^{2}[/tex] is always positive

Step-by-step explanation:

Answer:

mean = 85, standard deviation = 3.5

Step-by-step explanation:

The empirical rule states that for a normal distribution, 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviation of the mean and 99.7% falls within three standard deviation of the mean.

From the diagram since the shaded are is approximately 95% of the data. Hence 95% falls within two standard deviations of the mean.

σ = standard deviation, μ = mean

Hence; μ ± 2σ = (78, 92)

μ - 2σ = 78       (1);  

μ + 2σ = 92       (2)

Adding equation 1 and 2, gives 2μ = 170

μ = 85

μ - 2σ = 78

85- 2σ = 78

2σ = 7

σ = 3.5

Answer:

i think A is answer you should to do

Answer:

30, half

Step-by-step explanation:

mean of A = (10*5+7*20+2*30+40+4*50+80)/20 = 28.5

mean of B = (2*20+40+5*50+3*60+8*70+80)/20 =57.5

difference =57.5-28.5 =29

mean absolute deviation = (the sum of every data point - mean)/total number

in this case,

MAD = 304/20 = 15.2

Answer:

30 , twice

Step-by-step explanation:

i just did the lesson and got it right

t

Answer:

M = 36 year old

N = 28 years old

Step-by-step explanation:

here,

let the present age of M and N be 'x' and 'y' respectively.

By the first condition,

(x+12) = 3( y - 12)

x+12 = 3y - 36

x = 3y-48 ........ eqn (i)

and

By the second condition,

x= y+8 ........ eqn (ii)

now,

combining both the equations...

x = x

3y-48 = y+8 ( from i and ii )

2y= 56

y = 28

then , if y = 28

soo.. x= y+8

= 28+8

= 36

Answer:

p-$125= reduced price

Step-by-step explanation:

reduced implies that the $125 was SUBTRACTED from the original price.

Answer:

Option 4 .

Step-by-step explanation:

We need to simplify out the given expression . The given expression is ,

[tex]\rm\implies \dfrac{ 12x^4 ( x -3)(x+5)}{30x(x+3)(x+5)}[/tex]

Now see that the term ( x +5) is common in both numerator and denominator . Therefore we can cancel it out . The expression becomes ,

[tex]\rm\implies \dfrac{ 12x^4 ( x -3)\cancel{(x+5)}}{30x(x+3)\cancel{(x+5)}} =\dfrac{ 12x^4(x-3)}{30x(x+3)}[/tex]

Now x⁴ and x can again be cancelled out in numerator and denominator . Similarly we can cancel 12 and 30 by 6 . We have ,

[tex]\rm\implies \dfrac{ 2x^3(x-3)}{5(x+3)}[/tex]

On looking at the provided options , 4th option is correct .

Answer:

Add 25 to each side using the addition property of equality

Step-by-step explanation:

10x − 25 − 3x = 4x − 1

Step 1: 7x − 25 = 4x − 1  Combine like terms

Step 2: 7x = 4x + 24   Add 25 to each side using the addition property of equality

Answer:

a.

f(1)=6; f(n)=6+d(n-1), n>0

Step-by-step explanation:

We are given that

First layer has squares, a=6

Second layer has squares, a2=12

We have to find  an arithmetic explicit formula to determine the number of squares in each layer.

[tex]d=a_2-a_1=12-6[/tex]

nth term of an A.P

[tex]a_n=a+(n-1)d[/tex]

Substitute the value of a

Now, we get

[tex]a_n=6+(n-1)d[/tex]

f(1)=a=6

[tex]a_n=f(n)=6+d(n-1)[/tex]

Hence, option a is correct.

a.

f(1)=6; f(n)=6+d(n-1), n>0

Answer:

f(1) = 6; f(n) = 6 + d(n − 1), n > 0

Step-by-step explanation:

I took the test on flvs and got it right.

100% Guaranteed Correct :)

, Hope this helps

Have a great day!!