Evaluate the following expression if v = 5 and w = -3: 6v - w. Type the number answer only. For example: if the answer was value is 17, then you would type 17 in the blank.

The first four terms of the given sequence are 18, 10, 6, and 4 respectively.

A sequence is an ordered list object which related and connected by a common value.

There are many sequences. They are Arithmetic sequence, Geometric sequence, and so on.

It is given that,

The first term of the sequence is a1 = 18

And the terms of the sequence are related by,

a(n + 1) = (2 + an)/2

For n = 1;

a(1 + 1) = (2 + a1)/2

⇒ a2 = (2 + 18)/2 = 10

For n = 2;

a(2 + 1) = (2 + a2)/2

⇒ a3 = (2 + 10)/2 = 6

For n = 3;

a(3 + 1) = (2 + a3)/2

⇒ a4 = (2 + 6)/2 = 4

Thus, the first four terms of the given sequence are a1 = 18, a2 = 10, a3 = 6, and a4 = 4.

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Answer:

[tex]\large \boxed{\mathrm{B. \ 6}}[/tex]

Step-by-step explanation:

Length AB is similar to length DE.

Scale factor = DE/AB

Scale factor = 12/2

Scale factor = 6

The required Scale factor would be 6 to transform triangle ΔABC to triangle ΔDEF which is the correct option (B).

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.

Length AB is similar to length DE.

Here triangle ΔABC is dilated to form triangle ΔDEF

Length of the side DE = 12

Length of the side AB = 2

As we know scale factor is the ratio of sides in the original image and the image after dilation.

Scale factor = DE/AB

Substitute the values of the length of the side DE and AB,

Scale factor = 12/2

Apply the division operation, and we get

Scale factor = 6

Therefore, the required Scale factor would be 6 to transform triangle ΔABC to triangle ΔDEF.

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Answer:

1.) ( -4, -2 ), ( -6, - 3 )

2.) ( 0, 2 ) , ( 0 , 4 )

Step-by-step explanation:

The inequality sign of >=, the greater than or equal to sign, the upper region will be shaded while for less than sign <, the lower region will be shaded.

Please find the attached file for the solution and the answer.

Answer:

Step-by-step explanation:

Area of a circle = πr²

where

r is the radius

From the question

Area = 6.76 cm²

To find the radius substitute the value of the area into the above formula and solve for the radius

That's

[tex]6.76 = \pi \: {r}^{2} [/tex]

Divide both sides by π

We have

[tex] {r}^{2} = \frac{6.76}{\pi} \\ r = \sqrt{ \frac{6.76}{\pi} } [/tex]

r = 1.46689291

We have the final answer as

radius = 1.47 cm

Hope this helps you

Answer:

GREAT QUESTION!!

Step-by-step explanation:

Bases of exponential functions CANNOT be 1.

It the base was between 0 and 1, .25 for example, then it would be exponential decay, because as x would increase y would decrease.

Just search up exponential decay to see what it looks like, or type in y=.25^x in google search bar.

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Answer:

If the base of the exponent were 1, the function would remain constant. The graph would be a horizontal line. If the base of the exponent were less than 1, but greater than 0, the function would be decreasing.

Step-by-step explanation:

If the base were 1, the function would be constant.

If the base were 1, the graph would be a horizontal line.

If the base were between 0 and 1, the function would be decreasing.

Answer:

The height of the triangular base of the pyramid is s√3/2 units

Step-by-step explanation:

Here in this question, what we are concerned with is to calculate the height of the equilateral-triangle base of the oblique pyramid.

From the question, we are told that the equilateral triangle has a length of a units.

Let’s have a recall on some of the properties of equilateral triangles;

a. All sides are of equal lengths. Meaning side s is the length of all the sides in this case.

b. All angles are equal, meaning they are 60 degree each.

c. Dropping a perpendicular line from the top vertex to the base length will split the equilateral triangle into two right-angled triangles of angles 60 and 30 each.

So to find the height of this triangular base, we can use any of the two right angled triangles.

Kindly recall that the properties of each would be angles 30, 60 and side length s

so to calculate the height h, we can use trigonometric identities

Mathematically, the trigonometric identity we can use is the sine( side length s represents the hypotenuse, while the height h represents the opposite facing the angle 60 degrees)

Thus; we have

Sine of an angle = length of the opposite/length of hypotenuse

sin 60 = h/s

h = s sin 60

In surd form,

sin 60 = √3/2

Thus;

h = s * √3/2 = s√3/2 units

Answer:

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

Step-by-step explanation:

Answer:

A = 62.35 cm²

Step-by-step explanation:

Use the area formula A = [tex]\frac{\sqrt{3}a^2}{4}[/tex], where a is the side length.

Plug in the values:

A = [tex]\frac{\sqrt{3}(12^2)}{4}[/tex]

A = [tex]\frac{\sqrt{3}(144)}{4}[/tex]

A = 62.35 cm²

Answer:

B) 24

D) 48

Step-by-step explanation:

Given:

Two fractions

[tex]\dfrac{1}6 \\and\\\dfrac{3}8[/tex]

To find:

Number that can be chosen as Common denominator such that numerator is also a whole number ?

Solution:

Common denominator for two fractions [tex]\frac{p}{q}[/tex] and [tex]\frac{r}{s}[/tex] is chosen as LCM or multiple of LCM of (q, s).

OR

Common denominator for two fractions is chosen as the Least Common Multiple or multiple of LCM of denominators of the two fractions.

The denominators of the given fractions are 6 and 8.

Let us factorize and try to find the LCM of 6 and 8.

[tex]6 = \underline2 \times 3\\8 = \underline2 \times 2\times 2[/tex]

Common part of the denominators (as underlined) will be taken only once.

So, [tex]LCM = 2 \times 3 \times 2 \times 2 =24[/tex]

Multiples of LCM, 24 = 48

So, the correct answers are:

B) 24 and

D) 48

I have to return 400 notebooks.

Here, we have,

given that,

I order 700 notebooks by accident. I only need 3⁄7 of my order.

To determine how many notebooks you need to return, you can calculate 4/7 of your order, which represents the portion you don't need.

Let's calculate it step by step:

Calculate the number of notebooks you don't need:

4/7 * 700 = 400

we have,

I only need 3⁄7 of my order.

so, i need = 3/7 * 700

                = 300

Subtract the number of notebooks you need from the total order to find the number of notebooks you should return:

700 - 300 = 400

Therefore, you should return 400 notebooks.

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Answer:

Quadrilateral ABCD is a SQUARE

Step-by-step explanation:

When we are given coordinates (x1, x2) and (y1 , y2) for a Quadrilateral, we solve for the sides using this formula.

√(x2 - x1)² + (y2 - y1)²

A (3, 1), B (4, 4), C (7, 5), D (6, 2)

Side AB = A (3, 1), B (4, 4)

√(x2 - x1)² + (y2 - y1)²

= √(4 - 3)² + (4 - 1)²

= √1² + 3²

= √1 + 9

= √10

Side BC = B (4, 4), C (7, 5)

√(x2 - x1)² + (y2 - y1)²

= √(7 - 4)² + (5 - 4)²

= √3² + 1²

= √9 + 1

= √10

Side CD = C (7, 5), D (6, 2)

√(x2 - x1)² + (y2 - y1)²

= √(6 - 7)² + (2 - 5)²

= √(-1) ² + (-3)²

= √1 + 9

= √10

Side AD = A (3, 1), D (6, 2)

√(x2 - x1)² + (y2 - y1)²

= √(6 - 3)² + (2 - 1)²

= √3² + 1²

= √9 + 1

= √10

From the above calculation,

Side AB = √10

Side BC = √10

Side CD = √10

Side AD = √10

Hence, AB = BC = CD = AD

When all the side of a Quadrilateral are the same or equal to each other, it means the Quadrilateral is a square.

Therefore, Quadrilateral ABCD is a SQUARE

Answer:

  d) m - 2 l = - 6; m - l = 5

Step-by-step explanation:

Twice the number of slices on a large pizza is 2l. 6 fewer than that is 2l-6. This is the number on a monster pizza, so we have ...

  m = 2l -6

Subtracting 2l from both sides gives the equation ...

  m -2l = -6 . . . . . matches choice D

Answer:

6n = 1.50

and

13n = 3.12

Step-by-step explanation:

Here in this question, we are interested in writing equations that relate the number of ears of corn sold and the cost.

For Al’s produce stand, let the price per corn sold be n

Thus;

6 * n = 1.50

6n = $1.50 •••••••(i)

For the second;

let the price per corn sold be n;

13 * n = $3.12

-> 13n = 3.12 •••••••••(ii)

To add fractions with different denominators you must find the highest common factor (the highest number they both go into).

For 1 - The highest common factor is 8, 2x4 = 8, 4x2 = 8

now, whatever you do to the bottom, you must do to the top.

So:

3 x 2 = 6 and 5 x 4 = 20

Therefore, your answer would be 6/8 + 20/8

You do that for the rest of them as well, do you get it?

Answer:

    3.  4/15 + 4/5 = 4/15 + 12/15 = (4+12)/15 = 16/15

    5.  2/3  + 7/10 = 20/30 + 21/30  = (20+21)/30 = 41/30

Answer:

12.57

Step-by-step explanation:

The formula to solve the circumference of a circle is:

2 x PI x R (radius)

=> 2 x PI x 2

=> 4 PI or 12.57

Answer:

Step-by-step explanation:

To evaluate the expression substitute the values of a , b , c and d into the above expression

a = - 9

b = - 7

c = 9

d = 3

So we have

2cd + 3ab = 2(9)(3) + 3(-9)(-7)

= 2(27) + 3( 63)

= 54 + 189

We have the final answer as

Hope this helps you

Answer:

0.02

Step-by-step explanation:

Answer:

.02

Step-by-step explanation:

Answer:

JK = 24

Step-by-step explanation:

Δ BKJ and Δ BCA are similar and ratios of corresponding sides are equal, that is

[tex]\frac{JK}{AC}[/tex] = [tex]\frac{BK}{BC}[/tex] , substitute values

[tex]\frac{JK}{40}[/tex] = [tex]\frac{3}{5}[/tex] ( cross- multiply )

5JK = 120 ( divide both sides by 5 )

JK = 24

Answer:

y=-2x+4

x | y

0 | 4

2 | 0

Step-by-step explanation:

Answer:

y^6 - 9y^4 + 27y² - 27

Step-by-step explanation:

(y² - 3) (y^4 - 6y² + 9)

y^6 - 6y^4 + 9y² - 3y^4 + 18y² - 27

y^6 - 9y^4 + 27y² - 27

Answer:

Hey there!

-4/3-4/5

-20/15-12/15

-32/15

Let me know if this helps :)

Answer:

  a. almost 8 years

Step-by-step explanation:

Brenda's expected annual increase in salary is ...

  $63,292 -45,258 = $18,034

If we assume that Brenda's cost of education includes going without 2 years' salary as well as the cost of tuition, her degree's total cost will be ...

  2×$45,258 +15,000 = $105,516

__

Once Brenda starts earning again, she is recovering this cost at the rate of $18,034 per year, so it will take ...

  $105,516/($18,034 /yr) = 5.85 yr

to recover that cost.

Since Brenda spent 2 years in school, from the time she decides to start school until she has recovered her cost, it will be 2 + 5.85 = 7.85 years, almost 8 years.

_____

If Brenda can continue working while going to school, she can recover her tuition cost in about 10 months after graduation.

Answer:

C

Step-by-step explanation:

Answer: The solution of these inequalities are similar because they begin at two, however they are different because in the first inequality two cannot be an answer hence the open circle ⭕️, but the second inequality can have two as a solution hence the closed circle.

Step-by-step explanation:

Answer:

The lateral area of the figure = 480 m²

The surface area = 720 m²

Step-by-step explanation:

By definition, we have;

The lateral area is the area of the vertically facing sides of or the area of the triangular faces of a pyramid

The surface area is the area of the entire surface = Lateral area + The other surface areas of the object

For a pyramid, the surface area =   Lateral area  + Area of base

The figure in the question is a pentagon based pyramid with five triangles on the sides

The lateral area of the figure = 5 × area of the 5 triangles = 5 × Base × Height

The lateral area of the figure = 5 × 12 × 8 = 480 m²

The lateral area of the figure = 480 m²

The surface area = Area of the base + Lateral surface area

Area of the regular pentagon base = 1/2 × Perimeter of the pentagon × Apothem

Perimeter of the pentagon = 5 × 12 = 60 m

Apothem = Perpendicular distance from the pentagon's side to the center = 8.3 m

∴ Area of the regular pentagon base = 1/2 × 60 × 8 = 240 m²

∴ The surface area = 240 +480 =720 m²

The surface area = 720 m²

Answer: 1: Slope 0   Y- Intercept -5

2: Slope 0    Y- Intercept 6

Step-by-step explanation:

Answer:

-1 ( 1/3*1/3*1/3*1/3)

Step-by-step explanation:

-(3)^-4

The exponent is only affecting what is inside the parentheses

-1 * (3) ^-4

We know that a^-b = 1/a^b

-1 * 1/3^4

-1/3^4

-1 ( 1/3*1/3*1/3*1/3)

Answer:

hey hon! 2 liters is equal to 67.628 fluid ounces :) hope you have a nice day.

Answer:

9 dollars per hour

Step-by-step explanation:

36/4=9

Answer:

9

Step-by-step explanation:

4 hours : $36

1 hour : $ x

we need to find x so,

4 hours ÷ 4 = 1 hour

1 : $

since we have divided 4 by 4,

we need to do that to 36 aswell

36  ÷ 4 = 9

1 hour : $9

Answer:

The positive integer factors of 15552 that are perfect squares are;

1, 4, 9, 16, 36, 64, 91, 144, 324, 576, 1296, 5184

Step-by-step explanation:

The positive integer factors of 15552 are;

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 432, 486, 576, 648, 864, 972, 1296, 1728, 1944, 2592, 3888, 5184, 7776, 15552

The perfect square integers are;

1 = 1 × 1

4 = 2 × 2

9 = 3 × 3

16 = 4 × 4

36 = 6 × 6

64 = 8 × 8

91 = 9 × 9

144 = 12 × 12

324 = 18 × 18

576 = 24 × 24

1296 = 36 × 36

5184 = 72 × 72

Therefore, the positive integer factors of 15552 that are perfect squares are;

1, 4, 9, 16, 36, 64, 91, 144, 324, 576, 1296, 5184.

Answer:

0

Step-by-step explanation:

the x after the 10 is literally just 1

so 10 x 1  =10

-10 + 10 = 0

Answer:

[tex]F_{1}[/tex] = 5

Step-by-step explanation:

Given [tex]F_{1}[/tex] is perpendicular to [tex]F_{2}[/tex] then Δ ABC is right

Given [tex]F_{2}[/tex] = [tex]F_{1}[/tex]

Then using Pythagoras' identity in the right triangle

[tex]F_{1}[/tex] ² + [tex]F_{2}[/tex] ² = (5[tex]\sqrt{2}[/tex] )² , that is

2[tex]F_{1}[/tex] ² = 50 ( divide both sides by 2 )

[tex]F_{1}[/tex] ² = 25 ( take the square root of both sides )

[tex]F_{1}[/tex] = 5