for the arthritic sequence 5,9,13,17,21,... how many terms would you need to get to 129

Answer:

9

Step-by-step explanation:

Answer:

[tex]f(n) = \frac{4^n-0.25}{3}[/tex] --- Job offer 1

[tex]g(n) = 16n[/tex] --- Job offer 2

[tex]1 \le n \le 10[/tex]

Step-by-step explanation:

Given

Job offer 1:

Offer = $0.25

[tex]Day 1 = \$1\ Day 2 = \$4\ Day 3 = \$16......[/tex]

Job offer 2:

Daily = $16

Required

Determine the equation for both jobs

For job offer 1:

Considering the pay for day 1, day 2,....

The sequence shows a geometry progression where the payment between subsequent days is a product of 4 by the payment of the previous day.

The sequence can be represented as:

[tex]T_1 = 1; T_2 = 4; T_3 = 16[/tex]

The common ratio (r) is:

[tex]r = \frac{T_2}{T_1} = \frac{4}{1} = 4[/tex]

The sum of n terms is the total salary received in n days.

[tex]S_n = \frac{a(r^n - 1)}{r-1}[/tex]

[tex]S_n = \frac{1 * (4^n - 1)}{4-1}[/tex]

[tex]S_n = \frac{4^n - 1}{3}[/tex]

So, the equation for job offer 1 is:

[tex]f(n) = Offer + S_n[/tex]

[tex]f(n) = 0.25+ \frac{4^n - 1}{3}[/tex]

Take LCM

[tex]f(n) = \frac{0.75 + 4^n - 1}{3}[/tex]

Collect like terms

[tex]f(n) = \frac{4^n - 1+0.75}{3}[/tex]

[tex]f(n) = \frac{4^n-0.25}{3}[/tex]

For job offer 2:

Daily payment of $16 implies that job offer 2 pays 16n for n days.

So:

[tex]g(n) = 16n[/tex]

In both cases: [tex]1 \le n \le 10[/tex]

The cost to bowl a game is $2.5.

Two or more expressions with an Equal sign is called as Equation.

Let g  represent the cost of bowling a game and s represent the cost of renting shoes.

Bill bowled 3 games at a bowling alley and rented shoes, spending a total of $9.00

3g+s=9..(1)

Leann bowled 5 games at a the bowling alley and rented shoes, spending a total of $14.00.

5g+s=14..(2)

Subtract equation 2 from 1

3g+s-5g-s=9-14

-2g=-5

Divide both sides by 2

g=2.5

Hence, the cost to bowl a game is $2.5.

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Answer:

Jeff bought a canoe for $333.75. The sales tax was 5%. What was his total cost?

Step-by-step explanation:

The total cost of jeff  purchase was approximately $351.27.

Answer:

(x+1)²= 49, the answer is B

Step-by-step explanation:

x² + 2x = 48

x² + 2x + (2/2)² -  (2/2)²= 48 --[what we are trying to do is to complete a square by adding (2/2)² -  (2/2)²]

(x+1)²= 49, the answer is B

Answer:

hey I'm pretty sure it's B. (x+2)²=49

Step-by-step explanation:

x²+2x+(2\2)²=48 + (2\2)²

(x+1)²=49

2 over 2 by the power of 2 = 1

Answer:

hi

Step-by-step explanation:

9514 1404 393

Answer:

  9 square units

Step-by-step explanation:

Pick's theorem is a useful relationship in circumstances like these. It tells you the area is ...

  A = i + b/2 - 1

where i is the number of interior points (8), and b is the number of points on the border (4).

The area of this figure is ...

  A = 8 + 4/2 -1 = 9

The area of the polygon is 9 square units.

_____

You can also get there by realizing the bounding rectangle is 4 units square. From that, corner triangles are cut. CW from upper left, those triangles have (base, height) dimensions of (3, 2), (1, 3), (3, 1), and (1, 2). So, the total of their areas is (1/2)(6 +3 + 3 +2) = 7 square units. The shaded area is then 16-7 = 9 square units, same as above.

Answer:

4 months

Step-by-step explanation:

Let

x = number of months

Double Mint Mobile = 100 + 30x

BT&T = 20 + 50x

After how many months will both cell phone plans cost the same?

Equate the cost of both phone plans

Double Mint Mobile = BT&T

100 + 30x = 20 + 50x

100 - 20 = 50x - 30x

80 = 20x

x = 80/20

x = 4 months

Number of months = 4 months

Answer:

Step-by-step explanation:

To figure out the midpoint, you need to plug the coordinates into the midpoint formula.

M (x1 + x2 / 2, y1 + y2/2)

M [ 2 + (-3)/2,  5 + 9/2]

M ( -1/2, 7)

Hey love! <3

Answer:

The area of the following figure would be A = 312cm^2

Step-by-step explanation:

To begin solving for the area of this question we should first calculate the triangles.

The triangles width are 10cm each, and the length for each triangle is 12/2, or 6. Remember the formula for finding the area of a triangle is length times width divided by 2

After calculating all four triangles you should get 30+30+30+30, or 120.

Now, lets calculate the large central rectangle, the formula for this is the basic length times width, so that would equal 192.

Thus, 192+120=312cm^2

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Answer:

the answer is H.

Step-by-step explanation:

Step-by-step explanation:

Parallel

[tex]y = - \frac{2}{5} x + 3[/tex]

Perpendicular

[tex]y = \frac{5}{2} + 4[/tex]

Answer:

Slope of a parallel line: 2/5

Slope of a perpendicular line: 5/2

Explanation:

Parallel lines function

1. y = -2/5x+(R-4)

Perpendicular line function

2. y = 5/2x

Answer:

61 is ur answer

Step-by-step explanation:

Since this was a 90 degree angle you would just subtract 29 from the 90 degrees and get your answer.

Answer:

Step-by-step explanation:

If a number gets increased by scale factor = k

Then k > 1

If the number gets decreased by a scale factor 'k'

Then 0 < k < 1

Let numbers gets increased by the scale factor = 2,

And decreased by the scale factor = [tex]\frac{1}{2}[/tex]

Numbers             Scale up by 2           Scale down by [tex]\frac{1}{2}[/tex]

   0.05                  0.05 × 2 = 0.1             0.05 × [tex]\frac{1}{2}[/tex] = 0.025

    [tex]\frac{1}{2}[/tex]                        [tex]\frac{1}{2}\times 2 = 1[/tex]                      [tex]\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}[/tex]

    7                       7 × 2 = 14                     7 × [tex]\frac{1}{2}[/tex] = 3.5

   13                      13 × 2 = 26                  [tex]13\times \frac{1}{2}=6.5[/tex]

   25                     25 × 2 = 50                 [tex]25\times \frac{1}{2}=12.5[/tex]                

  102                   102 × 2 = 204              [tex]102\times \frac{1}{2}=51[/tex]

Answer: [tex]\$ 713.84[/tex]

Step-by-step explanation:

Given

The price of a chainsaw is [tex]\$539.95[/tex]

The price of each safety chaps is [tex]\$69.95[/tex]

Total price before sales tax

[tex]\Rightarrow C=539.95+2\times 69.95\\\Rightarrow C=\$ 679.85[/tex]

with a tax of 5%, the total cost will be

[tex]\Rightarrow C_t=1.05C\\\Rightarrow C_t=1.05\times 679.85=\$ 713.84[/tex]

Answer:

4.1n

Step-by-step explanation:

Given the equation n – 4.6n – 3.3n + 2.8n , to get its equivalent expression, the following steps must be followed;

Step 1:

Factor out the common variable n

n(1 – 4.6 – 3.3 + 2.8)

Step 2:

Carry out the operation in parentheses;

= n(1+2.8-4.6-3.3)

= n(3.8-4.6-3.3)

= n(3.8-3.3-4.6)

= n(0.5-4.6)

= n(-4.1)

= -4.1n

The equivalent expression is -4.1n

Answer:

Y = 3

X = 2

Step-by-step explanation:

(6x2) = 12

(8x3) = 24

12 + 24 = 36

(6x2) = 12

(5x3) = 15

12 + 15 = 27

Answer:

5 yard

Step-by-step explanation:

Answer:

it a

Step-by-step explanation:

Answer:

A (7)

Step-by-step explanation:

9w = 63

9 x 7 is 63,

9 x 6 = 54,

9 x 8 = 72,

9 x 9 = 81,

Answer:

140 + 96 m

Step-by-step explanation:

There are 4 weeks in 1 month.

Therefore:

Jonny has $50 in a savings account. Each week, he deposits $13 in the account.

$50 + $13 × 4m

The algebraic expression is given as:

50 + 52m

Jonny's brother has $90 in a saving account.

Each week, he deposits $11 in the account.

The algebraic expression is given as:

$90 + $11 × 4m

90 + 44m

An algebraic expression to describe how much money Jonny and his brother will have in their accounts after m months is written as:

Amount Jonny has + Amount his brother has

50 + 52m + 90 + 44m

= 50 + 90 + 52m + 44m

= 140 + 96 m

Answer:

a^2-16

Step-by-step explanation:

you just a.a+a.-4+4.a+4.-4=a^2-16

Answer:

M and N is N and M

Step-by-step explanation:

Answer:

A= 24!

Step-by-step explanation:

just subtract 19 from 43, and that will give you what A equals!

Answer:

24

Step-by-step explanation:

43-19= 24

24+19= 43

Answer:

The sum of the interior angles of a triangle is always 180 degrees. The exterior angle is the angle between any side of a shape, and a line extended from the next side. The sum of an exterior angle and its adjacent interior angle is also 180 degrees.

The relationship between the exterior angle of a triangle and its remote

interior angle is the exterior angle is equal to the sum of the two remote interior angles.

Which is known as the Exterior Angle Theorem.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

In a triangle, the exterior angle is formed when one side of the triangle is extended.

The exterior angle and the two remote interior angles (angles adjacent to the exterior angle on the triangle) form a linear pair, which means they add up to 180 degrees.

More specifically, the exterior angle is equal to the sum of the two remote interior angles.

This relationship is known as the Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

For example, if one of the remote interior angles of a triangle measures 40 degrees, and the exterior angle adjacent to it measures 120 degrees, then the other remote interior angle measures 180 - 40 - 120 = 20 degrees.

Thus,

The relationship between the exterior angle of a triangle and its remote

interior angle is the exterior angle is equal to the sum of the two remote interior angles.

This relationship is known as the Exterior Angle Theorem.

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Answer:

A = 14 mm²

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

Here b = 14 and h = 2 , then

A = [tex]\frac{1}{2}[/tex] × 14 × 2 = 7 × 2 = 14 mm²