Evaluate the expression where x=5 and y =2

The second difference of this quadratic pattern is 2.

The first term of this quadratic pattern is 10.

A sequence of numbers has a quadratic pattern when its sequence of second differences is constant. Therefore,

let the first and fourth term be a and b.

Therefore,

first difference:

1 - a; - 6 - 1 = -7; b + 6; -14 - b;

Second difference:

The second difference is constant . Therefore,

-7  - (1 - a) = -8 + a; b + 6 + 7 = b + 13; -14 - b - b - 6 = -2b - 20;

Therefore,

b + 13 = -8 + a

b  - a = -21

Then,

-2b - 20  = b + 13

-3b = 33

b = 33 / -3

b = - 11

Therefore,

- 11 - a = - 21

-a = -21 + 11

-a = -10

a = 10

Hence, the second difference = b + 13 = -11 + 13 = 2

First term = a

Therefore,

a = 10

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Step-by-step explanation:

70x4=280

12x4=48

48+280=328

Answer:

Step-by-step explanation:

The equation for volume is incorrect. The volume of a cylinder with radius r and height h is πr²h.

volume = π(2b)²(5b+3)

= π(4b²)(5b+3)

= π(20b³+12b²)

The formula for the volume of the given circular cylinder in terms of b is [tex]V = 20b^3 + 12b^2[/tex]

The given expression:

volume of circular cylinder, V = r²h

r = 2b

h = 5b + 3

To find:

To find the volume of the cylinder in terms of b, we will substitute the given values of r and h as follows;

[tex]V = r^2 h\\\\V = (2b)^2 (5b + 3)\\\\simplify \ the \ expression;\\\\V = 4b^2 (5b + 3)\\\\remove \ the \ bracket \ by \ multiplying \ through \ by \ 4b^2\\\\V = 20b^3 + 12b^2[/tex]

Thus, the volume of the cylinder in terms of b is [tex]V = 20b^3 + 12b^2[/tex]

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Answer:

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9[/tex]

Step-by-step explanation:

Given

[tex]tan\theta = 3[/tex]

Required

Find

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)[/tex]

Calculate [tex]tan(\theta + \pi) \ and\ tan(\theta+2\pi)[/tex]

Using tan rule

[tex]tan(\theta + \pi) = \frac{tan\theta + tan\pi}{1 - tan\theta tan\pi}[/tex]

So:

[tex]tan(\theta + \pi) = \frac{tan\theta + 0}{1 - tan\theta *0}[/tex]

[tex]tan(\theta + \pi) = \frac{tan\theta}{1 }[/tex]

[tex]tan(\theta + \pi) = \tan\theta[/tex]

[tex]tan(\theta+2\pi)[/tex]

[tex]tan(\theta + 2\pi) = \frac{tan\theta + tan2\pi}{1 - tan\theta tan2\pi}[/tex]

[tex]tan(\theta + 2\pi) = \frac{tan\theta + 0}{1 - tan\theta *0}[/tex]

[tex]tan(\theta + 2\pi) = \tan\theta[/tex]'

'So:

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)[/tex] [tex]= tan\theta +tan\theta +tan\theta[/tex]

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 3+3+3[/tex]

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9[/tex]

Answer:

45

Step-by-step explanation:

Answer: To get 24

Step-by-step explanation

What you would need to do is first multiply 12 x 5 would come out as 60.

Then from 60 you subtract 17 and 12 to get 5. Divide by the 5 that you just got from 17 and 12 and to get 20. Using the 4 add it to the 20 to get 24.

Answer:

2x + 5y

Step-by-step explanation:

-5x - 10y + 7x + 15y

add the ones with the same variables

-5x + 7x - 10y + 15 y

2x + 5y

and there you have the answer "2x + 5y"

Answer:

$90000

Step-by-step explanation:

From the pie chart,

Let the total annual income =  $y

The percentage of housing = 28 %

The percentage of clothing = 14 %

The combined percentage of housing and clothing = 28+14 = 42 %

If the amount spent on both housing and clothing combined = $ 37800

Therefore,

y(42/100) = 37800

Solve for y

42y = 37800×100

42y = 3780000

y = 3780000/42

y = $90000

Hence, the total annual income is $90000

Answer:

3.87

Step-by-step explanation:

2.58/2=1.29=1/3 pounds

1.29*3=3.87

<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3<3

Answer:

Let's simplify step-by-step.

−2^2 − 13x + 34

= −4 + −13x + 34

Combine Like Terms:

= −4 + −13x + 34

= ( −13x ) + ( −4 + 34 )

= −13x + 30

Answer:

= −13x + 30

Answer:

yes

Step-by-step explanation:

Answer:

.26 cents cheaper a roll

Step-by-step explanation:

to find this you would do 3.64/4 to get the price a roll which is .91

and then you would do 20.80/32 to get the price per roll which is .65

then to get the difference you would do .91-.65 to get .26

Answer:

all the numbers from -3 to 4

Step-by-step explanation:

so it would be,, 8 integers in total.

-3,,-2,,-1,,0,,1,,2,,3,,4

Answer:

6

Step-by-step explanation:

-2 , to 5 on a number line would be 6 apart

-1,1,2,3,4,5

Answer:

Step-by-step explanation:

Using the Excel Formula:

Decision    Variable        Constraint              Constraint

A                     65                          65                         100

B                     80                          80                         80

C                     90                         90                          90

                      14100                    300                        300

= (150 *B3)+(80*B4) +(65*B5)-(100-B3+80-B4+90-B5)*90

Now, we have:

Suppose A, B, C represent the number of units for production A, B, C which is being manufactured

                             A              B                  C                Unit price

Need of X          2                 1                   1                     $20

Need of Y           2                3                  2                    $30

Need of Z           2                2                  3                    $25

Price of  

manufac -      $200          $240            $220      

turing

Now,  for manufacturing one unit of A, we require 2 units of X, 2 units of Y, 2 units of Z are required.  

Thus, the cost or unit of manufacturing of A is:

$20 (2) + $30(2) + $25(2)

$(40 + 60 + 50)

= $150

Also, the market price of A = $200

So, profit = $200 - $150 = $50/ unit of A

Again;

For manufacturing one unit of B, we require 1 unit of X, 3 units of Y, and 2 units of Z are needed and they are purchased at $20, $30, and 425 each.

So, total cost of manufacturing a unit of B is:

= $20(1) + $30(3) + $25(2)

= $(20 + 90+50)

= $160

And the market price of B = $240

Thus, profit = $240- $160  

profit = $80

For manufacturing one unit of C, we have to use 1 unit of X, 2 unit of Y, 3 units of Z are required:

SO, the total cost of manufacturing a unit of C is:

= $20 (1) + $30(2) + $25(3)

= $20 + $60 + $25

= $155

This, the profit = $220 - $155 = $65

However; In manufacturing A units of product A, B unit of product B & C units of product C.

Profit  --> 50A + 80B + 65C

This should be provided there is no penalty for under supply of there is under supply penalty for A, B, C is $40

The current demand is:

100 - A

80 - B

90 - C respectively

So, the total penalty

[tex]{(100 - A) + (80 - B) +(90 - C) } + \$40[/tex]

This should be subtracted from profit.

So, we have to maximize the profit  

[tex]Z = 50A + 80B + 65C = {(100 -A) + (80 - B) + (90 - C)};[/tex]

Subject to constraints;

we have the total units of X purchased can only be less than or equal to 300 due to supplies capacity

Then;

[tex]2A + B +C \le 300[/tex] due to 2A, B, C units of X are used in manufacturing A, B, C units of products A, B, C respectively.

Next; demand for A, B, C will not exceed 100, 80, 90 units.

Hence;

[tex]A \le 100[/tex]

[tex]B \le 80[/tex]

[tex]C \le 90[/tex]

and [tex]A, B, C \ge 0[/tex] because they are positive quantities

The objective is:

[tex]\mathbf{Z = 50A + 80B + 65 C - (100 - A + 80 - B + 90 - C) * 40}[/tex]

A, B, C [tex]\to[/tex] Decision Varaibles;

Constraint are:

[tex]A \le 100 \\ \\ B \le 100 \\ \\ C \le 90 \\ \\2A + B + C \le 300 \\ \\ A,B,C \ge 0[/tex]

Answer:

=15x-7-23+2

=-8x-7+2

=-8x-5

Step-by-step explanation:

Answer:

$196 es el precio del articulo

Answer:

250

Step-by-step explanation:

100 / 22 = 4.54545455

4.54545455 x 55 = 250

Answer: 250

Step-by-step explanation:

Ur welcome

(55x100)/22

Answer:

5

Step-by-step explanation:

Area of right angle Triangle:

6.5 * 9 * 1/2 = 29.25

2nd way to find area:

1/2 * base * height

Since we have area and base:

1/2 * 11.1 * h = 29.25

= 5.27m

= 5m (nearest tenth)

The height h of the roof to the nearest tenth is 5.3 m

Right angle triangle has one of its angles as 90 degrees. The triangles are likewise similar and can be used to find the height h of the roof.

Therefore,

cross multiply

11.1 h = 9 × 6.5

11.1 h = 58.5

divide both sides by 11.1

11.1 h / 11.1 = 58.5 / 11.1

h = 5.27027027027

h = 5.3 m

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Answer:

Step-by-step explanation:

Its c

Answer: The required co-ordinates of the new point are (6, 5).

Step-by-step explanation: Given that the point (-3, 15) undergoes a translation of 9 units right and 10 units down.

We are to find the coordinates of the new point.

We know that

if the point (x, y) undergoes a translation of 9 units right and 10 units down, then its translation rule is given by

(x, y) ⇒ (x+9, y-10).

Therefore, the co-ordinates of he new point are given by

(-3, 15) ⇒ (-3+9, 15-10) = (6, 5).

Thus, the required coordinates of the new point are (6, 5).

Answer:

Scalene. A scalene triangle has three different angles and none of its sides are equal in length

Answer:  The slope describes the change in temperature for every hour after the cold front arrives.

Step-by-step explanation:

Answer:

B is the correct answer

Answer:

-4

Step-by-step explanation:

Answer:

-5, -1.3, 0, and 0.9

Step-by-step explanation:

Answer:

2)-5

3)0

4)0.9

5)-1.3

Step-by-step explanation:

the given inequality tells us that every numbers which are less than 1 are the solution for w

there're only 3 numbers which are less than 1 i.e

Answer:

Option D is the correct answer

Step-by-step explanation:

D. Yes, because it passes the vertical line test.

Answer:

D

Step-by-step explanation:

Just stating the temperature, hope this helps

Answer:

temperature of 10 degrees

Step-by-step explanation:

every other option is negative, like owing $10 means you will have 10 less dollars, a hole 10 feet deep is 10 feet under the ground's surface, so they would be represented by -10. A temperature of 10 degrees is the only positive option :)