A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?

Answer: 1. 4

2. 12

3. 6

4. 8

Step-by-step explanation:

The fifth term is 162 in the geometric sequence.

The geometric sequence defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.

The nth term of a geometric progression is expressed as

Tₙ = arⁿ⁻¹

Where a is the first term, r is the common ratio

A arithmetic sequence is defined as an arrangement of numbers which is particular order.

The formula to find the general term of an arithmetic sequence is,

aₙ = a₁ + (n-1)d

Given data :

First term of sequence geometric (a₁) = 2

The common ratio of geometric (r) = 3

To determine the fifth term of geometric sequence

Let the fifth term of sequence = a₅    

The nth term of a geometric sequence is expressed as :

Tₙ = a₁rⁿ⁻¹

Substitute the values of n = 5, a₁ =2 and r = 3 in the formula,

T₅  = (2)(3)⁵⁻¹  

T₅  = (2)(3)⁴

T₅  = (2)(81)

T₅  = 162

Hence, the fifth term is 162 in the geometric sequence

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Answer: ASA: If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent. SAS: If any two angles and the included side are the same in both triangles, then the triangles are congruent.

Answer:

9x + 22y ≥ 220

x + y ≤ 16

Step-by-step explanation:

First x is number of hours washing cars and y is number of hours tutoring.

He makes $9 per hour on cars, $22 per hour tutoring. So we use variables as substitutes for actual values.

That is 9x + 22y. He can't make less than 220, so use the sign greater or equal to 220.

He also must work no more than 16 hours. Total hours is x+y, and no more than 16 means use the sign less than or equal to.

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The number of hours washing cars and number of hours tutoring, if Blake is working two summer jobs, making $9 per hour washing cars, making $22 per hour tutoring, are 10.2 and 5.85 respectively. The graph is also attached below.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in, 3x + 5 Equals 15, instances.

Given:

Blake is working two summer jobs, making $9 per hour washing cars, making $22 per hour tutoring,

Total working hour = 16

Total money to be earned = $220

Write the equation of the above statement as shown below,

x + y = 16

9x + 22y  = 220

Solve the above equation using a graph,

y = 5.85 and x = 16 - 5.85 = 10.2

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Answer:

45 meters per 30 seconds

Step-by-step explanation:

To figure this question out you first gave to find the unit rate of meters per second by dividing 105 by 70.

105 divided by 70 = 1.5

So Susan can swim 1.5 meters per second.

Then we multiply that amount by 30 to find the number of meters she can swim in 30 seconds.

1.5 x 30 = 45 meters

So, in conclusion, Susan can swim 45 meters per 30 seconds

Answer:

Answer:  69.43 cm

Step-by-step explanation:

Given: Arc length (JK) = 40.5 cm

Central angle ∠ JLK = 210°

Arc length = [tex]\dfrac{x}{360}\times\text{Circumference}[/tex]

[tex]\Rightarrow\ 40.5=\dfrac{210}{360}\times\text{Circumference}\\\\\Rightarrow \text{Circumference} =40.5\times\dfrac{360}{210}\\\\\approx69.43\ cm[/tex]

Hence, Circumference = 69.43 cm

Answer:

The equation of the linear relationship is y = 3x + 2 ⇒ B

Step-by-step explanation:

To solve the question substitute the x in the equation by the x-coordinate of each point to find y, if y equals the y-coordinate of the point, then the point is on the graph of the equation

A.

∵ y = 2x + 3

→ Use the first point (0, 2)

∵ x = 0

→ Substitute x by 0 in the equation

∴ y = 2(0) + 3

∴ y = 0 + 3 = 3

∵ The y-coordinate is 2

∴ The point (0, 2) does not lie on the graph of the relationship

∴ The equation y = 2x + 3 doesn't represent the equation of the relationship

B.

∵ y = 3x + 2

→ Use the first point (0, 2)

∵ x = 0

→ Substitute x by 0 in the equation

∴ y = 3(0) + 2

∴ y = 0 + 2 = 2

∵ The y-coordinate is 2

∴ The point (0, 2) lies on the graph of the relationship

→ Use the second point (1, 5)

∵ x = 1

→ Substitute x by 1 in the equation

∴ y = 3(1) + 2

∴ y = 3 + 2 = 5

∵ The y-coordinate is 5

∴ The point (1, 5) lies on the graph of the relationship

→ Use the third point (3, 11)

∵ x = 3

→ Substitute x by 3 in the equation

∴ y = 3(3) + 2

∴ y = 9 + 2 = 11

∵ The y-coordinate is 11

∴ The point (3, 11) lies on the graph of the relationship

→ Use the fourth point (2, 7)

∵ x = 2

→ Substitute x by 2 in the equation

∴ y = 3(2) + 2

∴ y = 6 + 2 = 8

∵ The y-coordinate is 7

∴ The point (2, 7) doesn't lie on the graph of the relationship

∴ The equation of the linear relationship is y = 3x + 2

Answer:

insta trippy1669

Step-by-step explanation:

Answer:

y = -6x - 39

Step-by-step explanation:

A parallel line will have the same slope so m= -6, but it will have different points.

So we have y= -6x + b and the points are (8,9)

Substitute that in

9 = -6*-8 + b

9 = 48 + b

subtract 48 on both sides

9-48 = 48 - 48 + b

-39 = b

so equation is

y = -6x -39

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Answer:

y=-6x+9

0=-6x+9

6x=9

x=9/3

x=3/2

Given :

Square-based pyramid that has base edges measuring 6 units and lateral edges measuring 5 units.

To Find :

The total area, in square units, of the four triangular faces of a right.

Solution :

We know, area of square based prism is given by :

[tex]A = a^2 + \dfrac{ah}{2}[/tex]

Here, a is the length of square base and h is the height .

[tex]A = 6^2 + \dfrac{6\times 5}{2}\\\\A = 51 \ units^2[/tex]

Therefore, total area in square units is 51.

Answer:

What are the answers?

Step-by-step explanation:

Answer:

friction

Step-by-step explanation:

Consider an object that's not moving, like a chair at rest on the floor. There are two forces acting on it:

• its own weight, pulling it downward

• the normal force, i.e. the floor pushing upward on the chair.

Both of these forces are non-vanishing, but the net force is 0, so the chair remains at rest and its velocity stays at 0.

Answer:

z^2 +2z-15

Step-by-step explanation:

hope this helped

Answer:

D.) obtuse scalene triangle

Step-by-step explanation:

acute triangle: 3 acute angles

right triangle: 1 right angle, 2 acute angles

obtuse triangle: 1 obtuse angle, 2 acute angles

scalene triangle: no congruent sides

isosceles triangle: 2 congruent sides

equilateral triangle: 3 congruent sides

The question is:

"What type of triangle has no congruent sides and one angle that has a measure greater than 90° but less than 180°?"

That means scalene and obtuse.

Answer: D.) obtuse scalene triangle

The triangle is an obtuse scalene triangle, the correct option is D.

A triangle is a polygon with three sides, angles and vertices.

The triangle is classified into various types on the basis of the angle and on the basis of the equality of the length of the sides,

When the measure of all the angles of a triangle is less than 90 degree, it is an acute angle triangle.

When the measure of one of the angle of a triangle is equal to 90 degree, it is a right angled triangle.

When the measure of one of the angle of a triangle is greater than 90 degree, it is called an obtuse angle triangle.

When the measure of all side is different, it is a scalene triangle.

When the two side of a triangle is equal, it is an isosceles triangle.

When all the sides of a triangle is equal, it is an equilateral triangle.

The condition given in the question is triangle has no congruent sides and one angle that has a measure greater than 90° but less than 180°, it is an obtuse scalene triangle.

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Answer:

- 2 feets

Step-by-step explanation:

Given that sea star can be found at an ocean depth of 2 feets ;

An ocean depth of 2 feets can be represented as :

Sea level - depth = 0 - 2 = - 2 feets

Hence, it can be concluded that sea star lives in the ocean

Answer:

You can cancel your investment without wasting a lot of money.

Step-by-step explanation:

Short-term means that you dont have it for a long time, so you could basically wait it out and then cancel.

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Answer:

Short-term investments, also known as marketable securities or temporary investments, are those which can easily be converted to cash, typically within 5 years. Many short-term investments are sold or converted to cash after a period of only 3-12 months. Some common examples of short term investments include CDs, money market accounts, high-yield savings accounts, government bonds and Treasury bills. Usually, these investments are high-quality and highly liquid assets or investment vehicles.

Step-by-step explanation:

Answer:

the equation is in form

y=mx+b where

m=slope

and

b=y-int (the y value for the vertex)

first we look to see what the y value is for the point where x=0 and we can see that it is 5 so b=5

then we look at the slope, slope it the amont of units up then to the side are needed to reach the next point, in this case the line goes up 1 then to the right 1 so the slope is 1/1 (1) so the full equation is

y=x+5

Step-by-step explanation:

Given:

The factory managers decide to to give away [tex]\dfrac{1}{3}[/tex] of [tex]\dfrac{1}{9}[/tex]  of a ton away as samples.

To find:

what fraction of a ton did they give away?

Solution:

According to the question, the factory managers decide to to give away [tex]\dfrac{1}{3}[/tex] of [tex]\dfrac{1}{9}[/tex] of a ton away as samples. So,

[tex]\text{Samples}=\dfrac{1}{3}\left(\dfrac{1}{9}(1\text{ ton})\right)[/tex]

[tex]\text{Samples}=\dfrac{1}{3}\times \dfrac{1}{9}\times (1\text{ ton})[/tex]

[tex]\text{Samples}=\dfrac{1}{27}\times (1\text{ ton})[/tex]

[tex]\text{Samples}=\dfrac{1}{27}(1\text{ ton})[/tex]

So, samples is [tex]\dfrac{1}{27}[/tex] of a ton.

Therefore, they give away [tex]\dfrac{1}{27}[/tex] of a ton as samples.

Answer: The large rectangle boxes all have the property of 2

This is because 2 large boxes are equivalent to 4 and one of the rectangular boxes has to fill in the gap which is the 2  -1 boxes which would make them equivalent to each other.

Answer:

g

Step-by-step explanation:

g

Step-by-step explanation:

Let x be the price of an adult ticket.

Then 0.5x is the price of a child ticket.

We have 2x + 4(0.5x) = £152, therefore 4x = £152 and x = £38.

Hence the price of an adult ticket is £38.

Answer:

Step-by-step explanation:

2a+4c=152

2c=a

4c+2a=152

2c-a=0

Use simultaneous equation

Substitute 2c=a

                  c=a divided by 2 in the first equation and find value of a and c

Answer:

108 degrees

36 degrees

72 degrees

trapezoid

Step-by-step explanation:

Answer:

15.13cm

Step-by-step explanation:

From that above question:

We are told that:

Lateral surface area of a right circular cone : πr√r² + h²

We are give the following parameters:

Lateral surface area = 236.64cm²

Radius = 4.75cm

We are to find the height

Making h the subject of the formula

h = √[(A/r)² - πr²]/π

h = √[(236.64/4.75)²- π ×4.75²]/π

h = 15.12975 cm

Approximately to the nearest hundredth = 15.13cm

Step-by-step explanation:

The equation of the line is y = 1.5x + 3.

Answer:

Step-by-step explanation:

1200x6%(.06)=72

72x4=288

1200+288=1488

1200+72=1272+72=1344+72=1416+72=1488