Surface Area of Prisms
Can someone show me how to solve and also what the formula is. Please!​

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.

Answer:

4.75t + 7.50b = 790

b = 2t

Step-by-step explanation:

Let t represent the number of tacos that he sold, and let b represent the number of burritos he sold.

4.75t can represent how much money he earned from selling tacos, and 7.50b can represent how much money he earned from selling burritos.

Create an equation that adds these together and sets them equal to 790:

4.75t + 7.50b = 790

Next, create another equation that represents how there were twice as many burritos sold than tacos.

This can be represented by b = 2t.

The system of equations is:

4.75t + 7.50b = 790

b = 2t

Answer:

The equation would be 8h= 128

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

When you divide both sides by 8, you end up with:

16

Answer:

Yusuf is 33 and Ajay is 18

Step-by-step explanation:

Let Y and A stand for the ages of Yusuf and Ajay, respectively.

We are told that:

(1/2)A + 24 = Y [Age of Yusuf is 24 years more than half the age of Ajay]

(A-5)+(Y-5) = 41  [5 years before sum of their ages was 41]

Take the definition of Y in the first equation and use it in the second:

Y = (1/2)A+24 from the first equation

(A-5)+(Y-5) = 41    The second equation

(A-5)+(((1/2)A + 24)-5) = 41  Replace Y with (1/2)A+24

(A-5)+(1/2)A + 24-5 = 41

A-5+(1/2)A + 24-5 = 41

(3/2)A + 14 = 41

(3/2)A = 27

A = (2/3)(27)

A = 18

Ajay is 18 years old

Yusuf is Y=(1/2)(18)+24

Yusuf is 33 years old

====

Check:  Is Yusuf 24 years more than half the age of Ajay?

Ajay = 18, so (1/2)18 = 9.  Add 24 years to get 33.  Yes, this works since Yusuf is 33 years old

Was the sum of their ages = 41 five years ago?

Ajay would have been 13 and Yusuf would have been 28  28+13 = 41  YES

Answer:

A. 90 degrees

Step-by-step explanation:

Look this picture :]

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:

r÷12

Step-by-step explanation:

quotient means division

r÷12

Answer:

144.5 in ^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h  where the b1 and b2 are the lengths of the bases and h is the height

A = 1/2 ( 9.7+24.3) * 8.5

  = 1/2 ( 34)*8.5

   =144.5

Answer:

(28 buses) 932 divided 27 remainder of 14 rounding up to 28.

Step-by-step explanation:

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:

x < -3

Step-by-step explanation:

3x<-9

Divide each side by 3

3x/3 <-9/3

x < -3

Open circle at -3 line going to the left

Answer:

Step-by-step explanation:

3x < -9

Divide both sides by 3

x < - 3

x = {........-5, - 4 ,}

Step-by-step explanation:

According to the fundamentals of Mathematics, as well as corresponding mathematical principles, encompassing trigonometry, are acknowledged to provide the intergenerational definitions for subsequent generations.

Thus far, the radius is equated to half the diameter.

Equation representing the relation between the cost and the weight of the chicken has been given as,

Here, y = cost of the chicken

x = weight of the chicken

By substituting the values of different weights (x) in the given equation we can find the cost of the chicken (y).

For x = 1,

y = 7×1

y = 7

For x = 2,

y = 7×2

y = 14

For x = 3,

y = 7×3

y = 21

For x = 8,

y = 7×8

y = 56

       Therefore, the complete table will be,

Weight (lb),x      1            2             3              8

Cost ($),y          7           14            21            56

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Answer: its for an assignment

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given

(a)

3x + 2y - 8 = 0 ( subtract 3x - 8 from both sides )

2y = - 3x + 8 ( divide the terms by 2 )

y = - [tex]\frac{3}{2}[/tex] x + 4

(b)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{3}{2}[/tex] x + 4 ← is in slope- intercept form

with slope ( gradient) m = - [tex]\frac{3}{2}[/tex] and

(c)

c = 4

That is crosses the y- axis at (0, 4 )

Answer:

x = 46.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp / hyp

sin  54 = x / 58

58 sin 54 =x

x=46.92298

To the nearest tenth

x = 46.9

Answer:

Cạnh huyền=13, cgv1=12, cgv2=5

Step-by-step explanation:

Tam giác ABC

Gọi a là cạnh huyền(đối diện điểm A)

b là cgv đối diện điểm B

c là cgv đối diện điểm C

Theo đề bài: a=b+1 hoặc a=c+1

TH1: a=b+1 ta có hệ pt:

a=b+1                  (1)

b+c=a+4             (2)

[tex]b^{2} +c^{2} = a^{2}[/tex]         (3)

Thế (1) vào (2) ta được: b+c=b+1+4 => c=5

Thế (1) và c=5 vào (3) ta được:  [tex]b^{2} +5^{2} = (b+1)^{2}[/tex]  

<=>  [tex]b^{2} +25=b^{2} +2b+1[/tex]

<=> 2b=24 => b=12

=> a=b+1=12+1=13

TH2: a=c+1 ta có hpt

a=c+1                  (4)

b+c=a+4             (5)

[tex]b^{2} +c^{2} = a^{2}[/tex]         (6)

Tương tự tính được a=13,b=5,c=12

Vậy cạnh huyền=13, 1 cạnh góc vuông=5 và 1 cạnh góc vuông=12

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:

a)sin153°=0.454

cos153°=   -0.891

tan153°=   -0.510

b)sin 204°=  -0.407

cos204°=    -0.914

tan204° =   0.445

c)sin320°=   -0.643

cos320° =  0.766

tan320°=  -0.839

Step-by-step explanation:

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.

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We can simplify the wheel, thinking of it as a simple circle, then using general knowledge about circles, we can solve this.

1) Remember that one rotation of the wheel will be equal to the perimeter of the wheel, and for a circle of radius R, the perimeter is:

[tex]P = 2*3.14*R[/tex]

We know that our wheel has a radius of 5cm, then R = 5cm, we will get:

[tex]P = 2*3.14*5cm =31.4 cm[/tex]

Then one full rotation of the wheel is equal to

2) Not that we know the distance that the wheel does in one single rotation, the total number of rotations needed to do a distance of 50km is equal to the quotient between 50km and the distance that the wheel moves in one rotation.

But first we need to have both values in the same unit system.

Knowin that:

1km = 1000m

1km = 100*1000cm = 100,000 cm

Then 50km = 50*(100,000 cm) = 5,000,000 cm

Now we can solve the quotient:

[tex]\frac{5,000,000cm}{31.4cm} = 159,235.7[/tex]

This means that the wheel needs to do 159,235.7 rotations to move a distance of 50km.

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I'm pretty sure you are :)

Answer:

outliers

explanation:

Answer:

the right answer is

no d (outliers)

Answer:

89.1

Step-by-step explanation:

As the ball bounces, the height lowers due to gravity, Goes down by 50, 40, 32, 26.6. It should continue to go down.

(If im wrong ill edit the answer.)

Answer:

x = 35.0

Step-by-step explanation:

the height is 26√3 since the left one is a 30-60-90 triangle

so to find x

cos(39) = x/26√3

or, x = 26√3×cos(39)

or, x = 35.0

Answered by GAUTHMATH

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:

I think B is correct

Step-by-step explanation:

Because it it shows that -4 is going lesser direction including-4 .

Answer:

First find the slope of the line = (y2 - y1) / (x2 - x1)   where the 2 points are (x1, y1 and (x2, t2).  

Then  substitute the values of  the slope (m) and one of the points   into the point-slope formula

y - y1 = m(x - x1)

Step-by-step explanation:

Find the slope using the slope formula  

Use the slope and one of the points to solve for the y-intercept (b).

One of your points can replace the x and y, and the slope you just calculated replaces the m of your equation y = mx + b. Then b is the only variable left. Use the tools you know for solving for a variable to solve for b.

Once you know the value for m and the value for b, you can plug these into the slope-intercept form of a line (y = mx + b) to get the equation for the line.