Match each verbal description of a sequence with its appropriate explicit function.
an= 4 . (2)- 1
an= 3 + 4(n-1)
an = 4+2(n-1)
an = 2 + 3(n-1)
an = 3 . (4)n-1
a, = 2 · (3)9 - 1
an arithmetic sequence with a first term of 2 and a common difference of 3
a geometric sequence with first term of 4 and a common ratio of 2
a geometric sequence with first term of 3 and a common ratio of 4
an arithmetic sequence with a first term of 3 and a common difference of 4

Answer:

B. Tuesday

Step-by-step explanation:

It is the only decrease in price going by the graph

Answer:

Tuesday

Step-by-step explanation:

It went down by the most that day, i.e. from $3.25 to $3.00.

Other days, it did not decrease by as much.

Answer:

The total area of the shape = 4 + 4 + 2 = 10 square units

Step-by-step explanation:

This shape consists of three shape parts.

So, the total area of this shape is the sum of the areas of these shape parts.

1st Part) Finding the area of Right Triangle with base 4 units and perpendicular 2 units

A right triangle with base 4 units and perpendicular 2 units.

Let

'a' be perpendicular side = 2 units

'b' be the base side = 4 units

As

The area of right triangle

[tex]A=\frac{ab}{2}[/tex] ⇒ [tex]\frac{(4)(2)}{(2)}[/tex] = 4 square units

2nd Part) Finding the area of Square with the equal length and width i.e. 2 units

Let  a be the length of any side = 2 units

As the area of square

[tex]A=a^{2} }[/tex]

[tex]A = (2)^{2}=4[/tex] square units

3rd Part) Finding the area of Right Triangle with base 2 units and perpendicular 2 units

A right triangle with base 2 units and perpendicular 2 units.

Let

'a' be perpendicular side = 2 units

'b' be the base side = 2 units

As

The area of right triangle

[tex]A=\frac{ab}{2}[/tex] ⇒ [tex]\frac{(2)(2)}{(2)}[/tex]= 2 square units

Therefore the total area of the shape will be the sum of area of Right Triangle with base 4 units and perpendicular 2 units, area of Square with the equal length and width i.e. 2 and area of Right Triangle with base 2 units and perpendicular 2 units

So,

The total area of the shape = 4 + 4 + 2 = 10 square units

Keywords: area of a shape, area of triangle, area of square

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Answer: y = 3

Step-by-step explanation:

Two lines are said to be parallel if they have the same slope. All we need to do is to find the slope of each line . The formula for finding slope is given as :

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

For the first line

[tex]x_{1}[/tex] = 11

[tex]x_{2}[/tex] = 2

[tex]y_{1}[/tex] = y

[tex]y_{2}[/tex] = 0

substituting into the formula , we have

m = [tex]\frac{0 - y}{2 - 11}[/tex]

m = [tex]\frac{-y}{-9}[/tex]

m = [tex]\frac{y}{9}[/tex]

Also Finding the slope of the second line we have

[tex]m_{2}[/tex] = [tex]\frac{2-5}{-2 - 7}[/tex]

[tex]m_{2}[/tex] = [tex]\frac{-3}{-9}[/tex]

[tex]m_{2}[/tex] = [tex]\frac{1}{3}[/tex]

Since the two lines are parallel , we will equate their slope , that is

[tex]\frac{y}{9}[/tex] = [tex]\frac{1}{3}[/tex]

3y = 9

y = 3

Answer:

A

Step-by-step explanation:

supplementary angles add up to 180

angle cgr and kga are vertical angles so they are equal

that makes the two angles in question add up to 180

Answer:

The correct answer is C. 4 -6

Step-by-step explanation:

Let's solve the operation given, this way:

(7 - 11/) + (-3 + 5/)

7 - 11 - 3 + 5=

12 - 14 = - 2

After resolving the parenthesis, adding and subtracting the result of thhe operation is - 2

The correct answer is C. 4 -6

Answer:

y = - 4x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

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

Here m = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute (- 1, 6) into the partial equation

6 = 4 + c ⇒ c = 6 - 4 = 2

y = - 4x + 2 ← equation of line

x = first angle

y = second angle

z = third angle

x + y + z = 180

The sum of the measures of the second and third angles is twice the measure of the first angle.    ---->       y + z = 2x

The third angle is 12 more than the second.  ---->    z = y + 12

Use substitution to find each variable. Since z is already isolated/by itself, plug it into the other equation

y + z = 2x    Plug in (y + 12) for z

y + (y + 12) = 2x      Simplify

2y + 12 = 2x    Divide 2 on both sides

y + 6 = x          Isolate "y"

y = x - 6         Next you could plug this into z = y + 12, so that z has the x variable

z = y + 12

z = x - 6 + 12

z = x + 6

Now that you have y and z, you can do this:

x + y + z = 180

x + (x - 6) + (x + 6) = 180     Simplify

3x = 180    Divide 3 on both sides

x = 60             Now that you found x, plug it into the other equations to find y and z

y = x - 6

y = 60 - 6

y = 54

z = x + 6

z = 60 + 6

z = 66

x = 60°

y = 54°

z = 66°          [sorry if this is confusing]

PROOF

x + y + z = 180

60 + 54 + 66 = 180

180 = 180

The problem can be solved by setting up and solving a system of equations based on the information given in the problem. Using these equations, we are able to establish a relationship between the angles and thus calculate their individual measures.

To solve this problem, we need to set up and solve a system of equations based on the information provided. We know from the problem that:

First, let's substitute z = y + 12 into the other two equations:

We now substitute x = y + 6 into the equation x + 2y = 168 to find the values of x and y and hence z.

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Answer:

f−1(f(x)) = f(f−1(x)) = x

Step-by-step explanation:

Follow this simple example using the function f(x) = x + 2

f(x) = x + 2

NOw we find the inverse function f^(1)(x).

y = x + 2

x = y + 2

y = x - 2

f^(-1)(x) = x - 2

The inverse function is f^(-1)(x) = x - 2

Now we do the two compositions of functions:

f^(-1)(f(x)) = x + 2 - 2 = x

f(f^(-1)(x)) = x - 2 + 2 = x

Both are equal to x.

Answer: f−1(f(x)) = f(f−1(x)) = x

The expression [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]

We are to prove the relationship;

[tex]f^{-1}(f(x)) = f(f^{-1}(x)) = ?[/tex]

To get the unknown, let f(x) = x - 2

Find its inverse:

Let y = x - 2

Replace y with x;

x = y - 2

y = x+2

Hence [tex]f^{-1}x = x+2[/tex]

Next is to get [tex]f(f^{-1}(x))[/tex]

[tex]f(f^{-1}(x))=f(x+2) = (x+2) - 2\\f(f^{-1}(x))= x\\[/tex]

We can conclude that [tex]f^{-1}(f(x)) = f(f^{-1}(x)) = x[/tex]

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Answers:

These are the three major and pure mathematical problems that are unsolved when it comes to large numbers.

The Kissing Number Problem: It is a sphere packing problem that includes spheres. Group spheres are packed in space or region has kissing numbers. The kissing numbers are the number of spheres touched by a sphere.  

The Unknotting Problem: It the algorithmic recognition of the unknot that can be achieved from a knot. It defined the algorithm that can be used between the unknot and knot representation of a closely looped rope.

The Large Cardinal Project: it says that infinite sets come in different sizes and they are represented with Hebrew letter aleph. Also, these sets are named based on their sizes. Naming starts from small-0 and further, prefixed aleph before them. eg: aleph-zero.

Answer:

Option D: y = 4x + 16

Step-by-step explanation:

Given the line:  y - 1 = 4(x + 3)  ⇒  y = 4x + 13

The slope of the given line = m = 4

The required line is parallel to the given line

So, the slope of the required line = m = 4

So, the general equation of the required line: y = 4x + c

Where c is constant represents y-intercept

To find the value of c, substitute with the point (4,32)

At x = 4 y = 32

∴ 32 = 4 * 4 + c

∴ c = 32 - 16 = 16

∴ y = 4x + 16

The answer is option D: y = 4x + 16

Answer:16 books

Step-by-step explanation:

Final answer:

Julian bought 8 books and received a free book with each purchase, resulting in 16 books altogether by the end of the year.

Explanation:

The question is asking how many books Julian would have altogether if he bought 8 books and received a free book with each purchase this year. To solve this, we need to consider that for every book purchased, he gets an additional book without cost. Therefore, Julian gets 2 books each time he makes a purchase for one book. As he bought 8 books, we simply need to double that amount to account for the free books he received.

To calculate: 8 books purchased × 2 = 16 books altogether.

Julian would have a total of 16 books by the end of the year after his purchases and receiving the complementary books.

Answer: irs

Step-by-step explanation:

Banks give interest on savings accounts to encourage consumers to deposit and retain their money in the bank

Banks give interest on savings accounts to encourage consumers to deposit and retain their money in the bank.

Banks can attract and maintain consumer cash by providing interest, which they can then use to lend to other people or invest in various financial operations.

Paying interest on savings accounts assists banks in maintaining liquidity, generating money, and developing a mutually beneficial relationship.

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Answer:

6

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

First subtract the remainder from 403 to get 390. then divide 390 by 26 to get 15.

The number used by Justin used to divide 403 to get a quotient of 26 with a remainder of 13 is 15.

Division is theartimetic process used to divide a number into equal parts using another number. The sign used to denote division is ÷.

In order to detemine the number used to divide 403, take the following steps:

Subtract 13 from 403 = 403 - 13 = 390

Now divide 390 by 26: 390 / 26 = 15

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Answer:

17k + -13

Step-by-step explanation:

6k + 11k take the + next to the 6k making it say 6k+11

-3 - 10 take the - next to the 10 making it say -3 - 10

Answer: Should Be 0.01

Step-by-step explanation: It’s Asking How Thick it is and never asked when So it would automatically mean from the start therefore it’s 0.01 cm thick

Answer:

g (x) = 2 ^ (x + 2)

Step-by-step explanation:

For this case the transformation of f (x) is given by

g (x) = 2 ^ (x + 2)

To prove it, we must verify that equality is met by replacing the ordered pairs shown in the function g (x)

For (-2,1)

g (-2) = 2 ^ ( -2 + 2)

g(-2)=1

For (-1,2)

g (-1) = 2 ^ ( -1+ 2)

g(-1)=2

For (0,4)

g (0) = 2 ^ ( 0+ 2)

g(0)=4

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Answer:

D

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (8, - 1), thus

y = a(x - 8)² - 1

To find a substitute (0, - 17), the coordinates of the y- intercept into the equation.

- 17 = a(0 - 8)² - 1

- 17 = 64a - 1 ( add 1 to both sides )

- 16 = 64a ( divide both sides by 64 )

a = [tex]\frac{-16}{64}[/tex] = - [tex]\frac{1}{4}[/tex]

y = - [tex]\frac{1}{4}[/tex](x - 8)² - 1 → D

Answer:

25 2/15

Step-by-step explanation:

A = length x width

width is 4 1/6

35 = 4 1/6 x length

solve for length

divide both sides by 4 1/6

35 divided by 4 1/6  or multiply 35 x 6/25 (reciprocal)

210/25

8 10/25 = 8 2/5 is the length

to find perimeter 2xlength + 2xwidth

2 x 4 1/6 + 2 x 8 2/5 = 2 x 25/6 + 2 x 42/5 = 50/6 + 84/5

convert to common denominator and add

use 30 as common denominator

250/30 + 504/30= 754/30

25 4/30 or 25 2/15

Final answer:

To find the perimeter of the rectangle, calculate the length using the given area and width. Then, apply the perimeter formula P = 2l + 2w. The perimeter is approximately 25.1 feet.

Explanation:

Calculating the Perimeter of a Rectangle

To find the perimeter of a rectangle, you need to know both the width and the length of the rectangle. The perimeter is the total distance around the rectangle, which is the sum of twice the width and twice the length: P = 2l + 2w.

The width of the rectangle is given as 4 1/6 feet. To find the length, we can use the provided area of the rectangle which is 35 square feet. The area of a rectangle is found by multiplying the length by the width: A = l × w. Let's call the length 'l'.

First, convert the width to an improper fraction: 4 1/6 = (4 × 6 + 1)/6 = 25/6 feet. Now set up the equation using the area: 35 = (25/6) × l. Solving for 'l' gives us l = (35 × 6)/25 = 210/25 = 8.4 feet.

Now that we have the length, calculate the perimeter using the equation P = 2l + 2w:

P = 2 × 8.4 + 2 × 4 1/6

P = 16.8 + 2 × 25/6

P = 16.8 + 50/6

P = 16.8 + 8.333...

P = 25.133... feet

Therefore, the perimeter of the rectangle is approximately 25.1 feet when rounded to one decimal place.

Answer:

The number is 40

Step-by-step explanation:

Step 1:  To find the number, multiply all of the numbers together

2 * 2 * 2 * 5

40

Answer:  The number is 40

Answer:

40

Step-by-step explanation:

2×2×2×5 = 40

Answer:

Step-by-step explanation:

picture to help

Answer: I can't draw it but i answered

Step-by-step explanation:

To draw a model for 1/6 you would have draw six shapes of any kind. Then you would only fill one of them.

Answer:

Students= 6

Teachers= 2

Step-by-step explanation:

Given: Art museum trip:

           Cost of ticket= $5.5 per teacher and $3 per student.

           Total amount paid= $29.

           Science trip:

           Cost of ticket= $22 per teacher and $11.5 per student.

           Total amount paid= $113.

Lets assume number of teacher be "x" and number of students be "y".

Now, forming an equation for cost of each trip.

we know, total cost= [tex]cost\ of \ each\ ticket \times numbers\ of\ tickets[/tex]

∴Art museum trip, [tex]5.5x+3y= 29[/tex] ---- 1st equation

Science museum trip, [tex]22x+11.5y= 113[/tex] ---- 2nd equation

Next using elimination method to find number teacher and students

[tex]5.5x+3y= 29\\22x+11.5y= 113[/tex]

Multiplying both side of 1st equation by 4

∴ [tex]22x+12y= 116\\22x+11.5y= 113[/tex]

changing sign of 2nd equation on both side and solving it.

∴ [tex]0.5y= 3[/tex]

Dividing both side by 0.5

[tex]y= \frac{3}{0.5}= 6[/tex]

Hence, number of students on field trip was 6.

Subtituting the value of y in 1st equation to find the number of teachers in field trip.

[tex]5.5x+3y= 29[/tex]

⇒ [tex]5.5x+3\times 6= 29[/tex]

⇒ [tex]5.5x+18= 29[/tex]

Subtracting both side by 18

⇒ [tex]5.5x= 11[/tex]

Dividing both side by 5.5

⇒ [tex]x= \frac{11}{5.5}= 2[/tex]

Hence, there were 2 teachers on field trips.

Total of 8 kids came to Taylor's party.

Given is Taylor's 8th birthday and there were 47 presents. Each kid brought 10 presents, except for three kids who brought five presents each and two kids who bought one present each.

Assume that [n] students bought 10 presents. Then, we can write -

3 x 5 + 2 x 1 + 10n = 47

15 + 2 + 10n = 47

10n = 30

n = 3

Total kids = 3 + 3 + 2 = 8

Therefore, total of 8 kids came to Taylor's party.

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Answer:

192

Step-by-step explanation:

20% of 240 is 48

240-48 = 192

Answer:

192

Step-by-step explanation:

20%/100% x 240 =48

His cholesterol level now will be 240 - 48 = 192

Answer: Third option:

Step-by-step explanation:

The equation in Slope Intercept form of a line that does not pass through the point (0,0), which is known as "Origin, is the following:

[tex]y=mx+b[/tex]

Where "m" is the slope of the line and "b" is the y-intercept.

The equation  in Slope Intercept form  of a line that passes through the Origin, is:

[tex]y=mx[/tex]

Where "m" is the slope of the line.

In this case you can observe in the picture attached that the line passes through the point (0,0).

You can also notice that "y" would be the Dependent variable and "x" the Independent variable.

Therefore, the equation of this must have this form:

 [tex]y=mx[/tex]

The only equation that matches with that form, is the one given in the Third option. This is:

[tex]y=2x[/tex]

The linear equation shown in the graph can be written as.

y = 2x

A general linear equation is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

In this graph, we can see that the line intercepts the y-axis at y = 0, so we have:

y = ax

We also can see that the line passes through the point (1, 2), replacing these values in the equation we will get:

2 = a*1

2 = a

Then the linear equation is:

y = 2x

The third option.

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Answer:

Therefore Perimeter of Rectangle ABCD is 4 units

Step-by-step explanation:

Given:

ABCD is a Rectangle.

A(-6,-4),

B(-4,-4),

C(-4,-2), and

D (-6,-2).

To Find :

Perimeter of Rectangle = ?

Solution:

Perimeter of Rectangle is given as

[tex]\textrm{Perimeter of Rectangle}=2(Length+Width)[/tex]

Length = AB

Width = BC

Now By Distance Formula  we have'

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

Substituting the values we get

[tex]l(AB) = \sqrt{((-4-(-6))^{2}+(-4-(-4))^{2} )}[/tex]

[tex]l(AB) = \sqrt{((2)^{2}+(0)^{2} )}=2\ unit[/tex]

Similarly

[tex]l(BC) = \sqrt{((-4-(-4))^{2}+(-2-(-4))^{2} )}[/tex]

[tex]l(BC) = \sqrt{((0)^{2}+(2)^{2} )}=2\ unit[/tex]

Therefore now

Length = AB = 2 unit

Width = BC = 2 unit

Substituting the values  in Perimeter we get

[tex]\textrm{Perimeter of Rectangle}=2(2+2)=2(4)=8\ unit[/tex]

Therefore Perimeter of Rectangle ABCD is 4 units

Answer:

Therefore Perimeter of Rectangle ABCD is 4 units

Step-by-step explanation:

Given:

ABCD is a Rectangle.

A(-6,-4),

B(-4,-4),

C(-4,-2), and

D (-6,-2).

To Find :

Perimeter of Rectangle = ?

Solution:

Answer:

f^-1 (x)=-x-1

Step-by-step explanation:

y=-x-1

x=-y-1

-y=x+1

y=-x-1

Answer:

Part 1) [tex]A=36(\pi-2)\ cm^2[/tex]

Part 2) [tex]P=6(\pi+2\sqrt{2})\ cm[/tex]

Step-by-step explanation:

Part 1) Find the area

we know that

The area of the shape is equal to the area of a quarter of circle minus the area of an isosceles right triangle

so

[tex]A=\frac{1}{4}\pi r^{2}-\frac{1}{2}(b)(h)[/tex]

we have that the base and the height of triangle is equal to the radius of the circle

[tex]r=12\ cm\\b=12\ cm\\h=12\ cm[/tex]

substitute

[tex]A=\frac{1}{4}\pi (12)^{2}-\frac{1}{2}(12)(12)[/tex]

[tex]A=(36\pi-72)\ cm^2[/tex]

simplify

Factor 36

[tex]A=36(\pi-2)\ cm^2[/tex]

Part 2) Find the perimeter

The perimeter of the figure is equal to the circumference of a quarter of circle plus the hypotenuse of the right triangle

The circumference of a quarter of circle is equal to

[tex]C=\frac{1}{4}(2\pi r)=\frac{1}{2}\pi r[/tex]

substitute the given values

[tex]C=\frac{1}{2}\pi (12)[/tex]

[tex]C=6\pi\ cm[/tex]

The hypotenuse of right triangle is equal to (applying the Pythagorean Theorem)

[tex]AC=\sqrt{12^2+12^2}[/tex]

[tex]AC=\sqrt{288}\ cm[/tex]

simplify

[tex]AC=12\sqrt{2}\ cm[/tex]

Find the perimeter

[tex]P=(6\pi+12\sqrt{2})\ cm[/tex]

simplify

Factor 6

[tex]P=6(\pi+2\sqrt{2})\ cm[/tex]

Answer:

36(π-2)cm^2 is area

Perimeter is 6(π+2√2)

Step-by-step explanation:

Answer:true

Step-by-step explanation:

5x-3(2x-4)=

1) solve the parentheses

5x-6x-12=0

2) we just can rest the X

5x-6x=X

3) X-12=0

4) The order of factors does not alter the product

12-X=0

Answer:

True

Step-by-step explanation:

5x − 3(2x − 4)

Expand

5x - 6x + 12

-x + 12

12 - x

( ) are called "parentheses" or "brackets "

Whatever is inside the ( ) needs to be treated as a "package".

So when multiplying: multiply by everything inside the "package".

Multiplying negatives has special rules: a negative times a positive gives a negative, but multiplying two negatives gives a positive:

In that case −3 · -5 = +15 (a positive answer)