Find a₁ for each arithmetic series.Evaluate S₁₅ for the series 3 x+(3 x-2 y)+(3 x-4 y)+ ......

Answer:

Step-by-step explanation:

93959453

In equation (1) the value of y = 3/5 and In equation (2) the value of y = 5/4

In the given statement is

Solve 2x + 5y = -1 for y.

To find the value of y when x= -2

Now, Equation is 2x + 5y = -1 …..(1)

Put the value of x = -2 in eq. 1

2 (-2) + 5y = -1

-4 + 5y = -1

5y = -1 + 4

y = 3/5

Again,  Solve 2xy - x = 3 for y

To find the value of y when x = 2

Now, Equation is : 2xy - x = 3 ….(2)

Put the value of x = 2 in eq. (2)

2(2)y - 2 = 3

4y - 2 = 3

4y = 5

y = 5/4

Hence, In equation (1) the value of y = 3/5 and In equation (2) the value of y = 5/4

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Answer: the original price of the ticket was $42

Step-by-step explanation:

[tex]Let's\ make\ a\ proportion:[/tex]

$44.92 - 107%

     $x   - 100%

[tex]\displaystyle\\x=\frac{44.92*100}{107} \\\\x=\frac{4492}{107} \\\\x=42[/tex]

Answer: 8 dollars and 10 cents

Step-by-step explanation:

5.40 divided by 12 = .45

This means that each juice costs 45 cents

.45x18=8.10

Answer:

$8.10

Step-by-step explanation:

$5.40/12=$0.45 $0.45*18=$8.10

Answer:

$805.32

Step-by-step explanation:

$116.20 + $494.85 + $194.27 = $805.32

He had $805.32 to start.

The total cost of the shirts that the foreign student buy will be 48.71 Krona.

From the information, the person finds a special deal, 7 t-shirts for $07.93, that she would like to purchase for her family.

Therefore, the total cost will be:

= $7.93 / 7 × 5

= $5.66

Therefore, the amount when converted to Krona will be:

= $5.66 × 8.6064

= $48.7

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Answer:

The answer is C "608.313 Krona"

Step-by-step explanation:

Got it right on my quiz.

Check the picture below.

notice, the function namely f(x) or "y", has a hole at (-3 , 2), that means that the values for the range are anything less than 2, but never 2, so 1.1 is ok, 1.99 is also good, 1.999999999999999 is also ok, but never 2, thus y < 2.

Let's also notice, the arrowhead means the graph keeps on going to the left as well as to the bottom.

Answer: The input is a contradiction: it has no solutions

1st step

4m - 4 = 4m

4m - 4 + 4 = 4m + 4

2nd step -

4m = 4m + 4

3rd step -

4m = 4m +4

4m - 4m = 4m + 4 - 4m

4th step -

Combine like terms

0 = 4

Has No Solutions.

Answer:

$1.50

Step-by-step explanation:

there are 5 burgers since 2+3 is five. Divide 7.50 by five. The answer is 1.50.

$1.50

Because 2+3=5 and once you 7.5÷5 it equals 1.5.

Answer:

[tex]1) \: {2}^{3} \\ 2) \: {3}^{6} \\ 3) \: {4}^{4} = 4 \times 4 \times 4 \times 4 = 256[/tex]

(5 , -2)

Step-by-step explanation:

mid point = ( (X1 + X2)/2 , (Y1 + Y2)/2 )

= ( (8 + 2)/2 , (-7 + 3)/2 )

= (5 , -2)

Answer:

Step-by-step explanation:

[tex]\displaystyle\\\frac{10px^2}{3c^2d} \div\frac{5px}{6c^2d^2} =\\\\\frac{10px^2}{3c^2d}*\frac{6c^2d^2}{5px} =\\\\\frac{60c^2d^2px^2}{15c^2dpx^2} =\\\\4d\\\\\\\frac{3}{x+7} \div\frac{8x^2-8x}{x^2+6x-7} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{x^2-x+7x-7} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{x(x-1)+7(x-1)} =\\\\\frac{3}{x+7} \div\frac{8x(x-1)}{(x-1)(x+7)} =\\\\\frac{3}{x+7} \div\frac{8x}{x+7} =\\\\\frac{3}{x+7} *\frac{x+7}{8x} \\\\\frac{3(x+7)}{8x(x+7)}=\\\\\frac{3}{8x}[/tex]

Answer:

4[tex]x^{2}[/tex]

Step-by-step explanation:

1st seperate the equation

[tex]\sqrt{16}[/tex] and [tex]x^{2}[/tex]

square root of 16 is 4, and x squared stays the same, so the equation becomes

4[tex]x^{2}[/tex]

The total amount that you need to pay for the lunch after the sales tax and the tip will be $ 42.85.

We are given that:

The cost of lunch = $ 32

Sales tax = $ 4.45

Tip = 20 %

So, the tip will be calculated by finding the percentage of cost that you are planning to pay has a tip.

Tip = 20 % of $ 32

Tip = 20 / 100 × $ 32

Tip = 0.2 × $ 32

Tip = $ 6.4

Total amount needed to be paid for the lunch = $ 32.00 + $ 4.45 + $ 6.40

Total amount = $ 42.85

Therefore, we get that, the total amount that you need to pay for the lunch after the sales tax and the tip will be $ 42.85.

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The categorization of each variable according to the group of numbers that best captures its values is shown below:

Any integer from 0 to n.

Any number from 0 to h.

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The investor should expect $1716.24375 at the end of 15 years .

Formula for calculation of Simple Interest :

Simple Interest = ( Rate * Principal * no . of years ) / 100 , when no additional investment is made .

Here , principal = $1760.25 , rate = 6.5 , no . of years = 15 .

Substituting values in formula above ,

SI = ( 6.5 * 1760.25 * 15 ) / 100

     = 1716.24375

Hence , the investor should expect $1716.24375 at the end

of 15 years .

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Step-by-step explanation:

or, 55° = (4x - 1)° [ vertically opposite angle ]

or, 55° + 1° = (4x)°

or, 56° = (4x)°

or, 56°/4° = x

or, x = 14°

Therefore the value of x is 14° .

Answer:

(36^7+6^13) is divisible by 7.

Step-by-step explanation:

(36^7+6^13)

First, solve the parentheses and exponents within it.

36^7=36*36*36*36*36*36*36=78364164096

6^13=6*6*6*6*6*6*6*6*6*6*6*6*6=13060694016

Add 78364164096 and 13060694016.

It equals 91424858112.

Divide 91424858112 by 7.

It results in 13060694016.

Hence, yes.

Hope this helps.

The consecutive page no. are 126 and 127.

An example of a run of consecutive integers is 1, 2, 3, 4. Another illustration is 7, 8, and 9. An integer sequence is a set of numbers where each term is one more than the term before it.

Continually following one another, from smallest to greatest, are consecutive numerals. For instance, the sequence of the numerals 1, 2, 3, 4, 5, and so forth.

The next two numbers are (n + 1) and (n + 2) if n is an integer. Take 1 for n as an example. Its subsequent numbers can be read as (2 and 3), or as (1 + 1) and (1 + 2).

let the consecutive page numbers be x and x+1

according to question ,

          x + x + 1 = 253

          2x = 252

            x = 126

so the consecutive page numbers are 126 and 127.

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 The equation that defines the parabola with vertex at the point and focus at (0, 1/2) is

y = 2x²

  The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

  The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

In this case we have the vertex of the parabola at the point (0,0) and the focus at the point (0,  1/2) this is displaced on the y-axis upward, so the parabola is of the form.

y = x²

  Canonical equation

(y - yo) = 4p(x - xo)

Focus:
f = (0, 0 + p)

(y- 0) = 4*0.5(x - 0)²

y = 2x²

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The sum of the given finite series is 2140

Sum notation is used to express long summation into a single formula.

Properties of sum operator:

[tex]\sum\limits^{40}_{n=1} {(3n-8)}=\sum\limits^{40}_{n=1} {3n}-\sum\limits^{40}_{n=1} {8}[/tex]

[tex]=3\sum\limits^{40}_{n=1} {n}-\sum\limits^{40}_{n=1} {8}[/tex]

[tex]=3\sum\limits^{40}_{n=1} {n}-8\times40[/tex]

[tex]=3(1+2+...+40)-8\times40[/tex]

[tex]=3.\frac{40}{2}. (1+40)-320[/tex]

= 2140

Hence, the sum of the given finite series is 2140

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Answer:

(4/3)

Step-by-step explanation:

  1                5

---------  +  --------

  2              6

  1 (3)          5

---------  +  --------

  2(3)          6

  3            5            8

-------  +  -------  =  -------

  6           6             6

  8  ÷  2            4

-------        =     -------

  6  ÷  2             3

I hope this helps!

The expression given by (1/2)⁻¹ is equivalent to 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

(1/2)⁻¹

Taking the negative one exponent gives:

= 2 / 1

Simplifying the equation gives:

= 2

The expression given by (1/2)⁻¹ is equivalent to 2

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Probability that either his partner or the pile have the joker from the deck of 43 cards including one joker ,four players each have 10 cards and 3 cards in a pile is 13/33.

As given,

Total number of cards=43

Number of cards with each players =10

Number of cards in a pile =3

Greg doesn't have joker

Total cards left = 43-10

                       = 33

Probability either his or the pile have the joker = (10 +3)/33

                                                                         = 13/33

Therefore, probability that either his partner or the pile have the joker is 13/33.

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The value of the expression (7 - 1/4 × ✓16)² + (2 - 5)² is 45.

Based on the information given, the expression will be:

(7 - 1/4 × ✓16)² + (2 - 5)²

= (7 - 1)² + (-3)²

= 6² + 3²

= 36 + 9

= 45

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