Guys please help me with this question

Part (i)

I'm going to use the notation T(n) instead of [tex]T_n[/tex]

To find the first term, we plug in n = 1

T(n) = 2 - 3n

T(1) = 2 - 3(1)

T(1) = -1

The first term is -1

Repeat for n = 2 to find the second term

T(n) = 2 - 3n

T(2) = 2 - 3(2)

T(2) = -4

The second term is -4

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

Part (ii)

Plug in T(n) = -61 and solve for n

T(n) = 2 - 3n

-61 = 2 - 3n

-61-2 = -3n

-63 = -3n

-3n = -63

n = -63/(-3)

n = 21

Note that plugging in n = 21 leads to T(21) = -61, similar to how we computed the items back in part (i).

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

Part (iii)

We're given that T(n) = 2 - 3n

Let's compute T(2n). We do so by replacing every copy of n with 2n like so

T(n) = 2 - 3n

T(2n) = 2 - 3(2n)

T(2n) = 2 - 6n

Now subtract T(2n) from T(n)

T(n) - T(2n) = (2-3n) - (2-6n)

T(n) - T(2n) = 2-3n - 2+6n

T(n) - T(2n) = 3n

Then set this equal to 24 and solve for n

T(n) - T(2n) = 24

3n = 24

n = 24/3

n = 8

This means 2n = 2*8 = 16. So subtracting T(8) - T(16) will get us 24.

Step-by-step explanation:

Area of the rectangle = 9×6 = 54 m²

Area of the path is also 54 m²

so total area of the bigger rectangle is 54+54 = 108 m²

now the ratio of length to width is 9:6 or, 3:2

so, for 108 m²

(3x)(2x) = 108

6x²=108

x²=18

x=3√2

So length = 3x = 9√2 and width = 2x = 6√2

Answer:

D. (-2,-3)

Step-by-step explanation:

substitute the point values of [tex]x[/tex] and [tex]y[/tex] into the equation [tex]y=\frac{1}{2}x-2[/tex]

A. [tex]0=\frac{1}{2}(5)-2[/tex]

   [tex]0=2.5-2[/tex]

   [tex]0[/tex] ≠ [tex]0.5[/tex]

B. [tex]1=\frac{1}{2}(-1)-2[/tex]

   [tex]1=-.5-2[/tex]

   [tex]1[/tex] ≠ [tex]-2.5[/tex]

C. [tex]-1=\frac{1}{2}(3)-2[/tex]

   [tex]-1=1.5-2[/tex]

   [tex]-1[/tex] ≠ [tex]-0.5[/tex]

D. [tex]-3=\frac{1}{2}(-2)-2[/tex]

   [tex]-3=-1-2[/tex]

   [tex]-3=-3[/tex]

I'm pretty sure you are :)

Answer:

okay so given :-

R = x(A+B)

now open bracket =>

R = Ax + Bx

shifting Bx

R - Bx = Ax

so now shift x to lhs and finally we get

A = (R - Bx)/x option d is correct

please brainliest <3

Answer:

x-15

y 42

Step-by-step explanation:

Answer:

A=0

B=0,3

C=9,3

D=9,0

Step-by-step explanation:

Multiplies all the vertices bay scale factor 3/2

Answer:

f(0) =2

Step-by-step explanation:

f (x) = -x + 2

Let x = 0

f(0) = -0+2

f(0) = 2

Answer:

f(0) = 2

Step-by-step explanation:

Substitute x = 0 into f(x)

f(0) = - 0 + 2 = 0 + 2 = 2

Answer:

outliers

explanation:

Answer:

the right answer is

no d (outliers)

Answer:

Step-by-step explanation:

(x+1)(x+3)(x+5), multiply first two parenthesis

(x² +3x +x +3)(x+5), combine like terms

(x² +4x +3) (x+5), multiply the parenthesis

(x³ +5x² +4x² +20x +3x +15), combine like terms

x³ +9x² +23x +15 is in the form ax³ +bx² +cx +d

a=1, b=9, c=23, d=15 are all positive integers

Answer:

A. 90 degrees

Step-by-step explanation:

Look this picture :]

Answer:

y = -3x+9

Step-by-step explanation:

Parallel lines have the same slope

y = -3x+2  

This is in slope intercept form where y =mx+b where m is the slope

The slope is -3

y = -3x+b

Using the point (2,3)

3 = -3(2)+b

3 = -6+b

Add 6 to each side

3+6 = b

9=b

y = -3x+9

Answer:

slope (m) = -3

3= -3(2)+b

b = 9

y=mx+b → y= -3x+9

OAmalOHopeO

Answer: [tex]V=0.0028278\ m^3[/tex]

Step-by-step explanation:

Given

Length of the pipe [tex]l=4\ m[/tex]

Inside diameter of the pipe [tex]d_i=4\ cm[/tex]

Outside diameter of the pipe [tex]d_o=5\ cm[/tex]

Volume of the pipe

[tex]\Rightarrow V=\dfrac{\pi }{4}[d_o^2-d_i^2]\\\\\text{Insert the values}\\\\\Rightarrow V=\dfrac{\pi}{4}[5^2-4^2]\times 10^{-4}\times 4\\\\\Rightarrow V=28.278\times 10^{-4}\ m^3\\\\\Rightarrow V=0.0028278\ m^3[/tex]

Answer:

Size of the original rectangle is 30*20=600

Step-by-step explanation:

Let the length and width of rectangle be x+10 and x. After increasing the dimensions, the new length and width are x+20 and x+10

ATQ, (x+20)(x+10)=2(x+10)(x), x=20.

Answer:

C.The value of a motorcycle decrease by 12% each year

D.Every year, the number of online subscribers to a service is 4 times what it was the previous year

Step-by-step explanation:

A function is said to be exponential if it changes (increases or decreases) by a fixed percentage or proportion over a certain period of time.

From the options given, only options C and D is defined as changing based on a certain percentage. And option D cgbages by a clfixed proportion from the initial value.

The option that represents the exponential function are situation C) and D) and this can be determined by making the mathematical expression of each situation.

Try to make a mathematical expression of the situation given below in order to check which option shows an exponential function.

A) According to the given data, in the first row there are 6 cans, in the second row there are 12 cans, in the third row there are 18 cans, and so on. Now, let 'a' be the total number of rows then, the mathematical expression of this situation is given by:

= 6a

This situation is not representing the exponential function.

B) According to the given data, in the first month there are 20 patients, in the second month there are 40 patients, and so on. Let the total number of months be 'b' then the mathematical expression is given by:

= 20b

This situation is not representing the exponential function.

C) According to the given data, in the first year the value of the motorcycle decrease 12%, in the second month the value decreased by 24% of the initial value, and so on. So, the price of motorcycle decreases exponentially. Therefore, this option is correct.

D) According to the given data, every year, the number of online subscribers to service is 4 times what it was the previous year. The mathematical expression of this situation is:

= [tex]4^x[/tex]

where 'x' is the number of years. Therefore, this option is correct.

For more information, refer to the link given below:

https://brainly.com/question/2263981

Answer:

x= 1/8 is the correct answer

Answer:

1/8

Step-by-step explanation:

7x-x=3/4

6x=3/4

6x/6=3/4÷6

x=1/8

Answer:

It is the last option.

Jordan needs 1 1/2 cups of diced chicken for 3 salads.

To make this easy for you.

1. start on the x axis which is number of salads.

2. Go to the number 3 (of the x axis which is the number of salads)

3. Find your way up to the point marked.

4. see what is your number in the y-axis (in this case it is 1 1/2.

Step-by-step explanation:

I hope it helps!

Answer:

Step-by-step explanation:

On first day , the video was viewed = 320 times .

We are given that Each day since then, the number of views was 25% more than the day before. This means the likes are increasing 1.25 per day .

So, this situation forms G.P.

Where common ratio r = 1.25

First term = f(1) = 320

Formula of nth term in G.P. =

So, nth term of the given situation :

Where f(n) denotes the number of views on nth day .

So, the number of views Vera's video got on the nth day =

Step-by-step explanation:

Answer:

Can you Specify the Question?

Answer:

Step-by-step explanation:

So basically, we would need to divide to the nearest 0.01 or hundredths place. All you would need to do is round from each place which would soon get you to 11,580.00. Simple right!!

I hope this helps!! Have a good rest of your day! :)

Answer:

(12 x 7) feet2

Step-by-step explanation:

formula of area= length times breadth

The expression which describes the area of the bedroom is (12 x 7) square feet. The area is 84 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle is called the area of the rectangle. The rectangle has two sides one is the width and the other is the Length.

Given that Shenandoah's rectangular bedroom is 12 feet long and 7 feet wide.

The area of the rectangle is the product of its width and length.

Area = L x W

The expression for Shenandoah's bedroom area will be written as below:-

Area = 12 x 7

Area = 84 square feet

Therefore, the expression which describes the area of the bedroom is (12 x 7) square feet. The area is 84 square feet.

To know more about the area of the rectangle follow

https://brainly.com/question/25292087

#SPJ2

Answer:

26 is the answer

Step-by-step explanation:

hope this helps you

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

A (4,  2 ) → A' (4, - 2 )

B (7, 0 ) → B' (7, 0 )

C (9, 3 ) → C' (9, - 3 )

A translation of a shift to the left of 3 units is a horizontal shift.

This means subtracting 3 fro the x- coordinate and leaving the y- coordinate

A' (4, - 2 ) → A'' (4 - 3, - 2 ) → A'' (1, - 2 )

B' (7, 0 ) → B'' (7 - 3, 0 ) → B'' (4, 0 )

C' (9, - 3 ) → C'' (9 - 3, - 3 ) → C'' (6, - 3 )

Christopher's distance from his starting point is 3.6 km

Since Christopher initially walks South 5 km and then walks on a bearing of of 036º until he is due east of his starting point.

His distance South, his distance from his starting point and his distance from his 036º bearing, all form a right-angled triangle.

This right-angled triangle with opposite side to the angle 036º, as his distance from his starting point, x and the adjacent side to the angle 036º, as his distance 5 km south.

Since we have both the opposite and adjacent sides of a right-angled triangle,

From trigonometric ratios,

tanФ = opposite/adjacent

tanФ = x/5 km

Now Ф = 036º

So, tan36º = x/5km

x = 5 km(tan36º)

x = 5 km (0.7265)

x = 3.633 km

x ≅ 3.6 km to 1 decimal place.

So, Christopher's distance from his starting point is 3.6 km.

Learn more about bearing here:

https://brainly.com/question/11684993

For a regular polygon with n sides, interior angle

= [(n-2) × 180°]/n

So, interior angle of this regular heptagon shape

= [(7 - 2) × 180°]/7

= (5 × 180°)/7

= 900°/7

= (900/7)°

= 128.571° [approximately]

Answer:

hello,

Step-by-step explanation:

center angle : 360°/7 °

half interior angle=0.5*(180-360/7)=900/14=450/7 = 64 ° +2/7° ≈64.3 °

interior angle= 128°+4/7°≈128.6 °

Answer:

9y+1=32y+1+54

collect like terms, a symbol changes once it crosses the equal to sign =

9y-32y=1+54-1

-23y=54

divide both sides by -23

-23y/-23=54/-23

-23 will cancel -23 to give y

y=54/-23

y=-2.4 or 2 whole number 8/23

Answer: y is -54/23

Step-by-step explanation:

Answer:

Both T+4 and T-4 are the same distance away from 4

T would be the launch time of the rocket...

T - 4 is 4 units of time (seconds)  prior to launch...

T+ 4 is 4 units of time (seconds) after the launch

Step-by-step explanation:

Answer:

The answer would be -2.

Step-by-step explanation:You have to look at where the line is hitting.It has to be perfectly on the corners of the square. The bottom of the y-intercept is always negative and the top is always positive but for the x-intercept the right side is positive and the left side is negative. I hope that helped you!!