What is summation notation for the series?
a. -5+2+9+16+ . . . . . . . +261+268

The location of S will be at 9 and ₋19 .

When speaking of a straight line in mathematics, the term "number line" refers to the placement of numbers along some or all of the breadth. Any direction can be used to postpone a number line, which is frequently displayed horizontally.

Given, on a number line R and S are points on the number line.

RS = 5 and R is located at 14.

S is located at = ?

Let x be the coordinate of the point S. Then we have:

14 ₋ x = ±5

x = ± 5 ₋ 14

x = 5 ₋ 14 or ₋5₋14

x = 9 or ₋19

Then the location of point S will be at 9 and -19.

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9/4 cups of hot milk will be used by Chelsea.

As per the given information in question about custard, we know -

For 2/3 cups of sugar, the cups of hot milk required = 1(1/2)

Converting the number of cups of hot milk from mixed fraction to improper fraction -

Number of cups = (2×1 + 1)/2

Number of cups= (2 + 1)/2

Number of cups = 3/2

So, for 1 cup of sugar, the cups of hot milk required will be = (3/2) ÷ (2/3) × 1

Number of cups of hot milk required = (3×3) ÷ (2×2)

Number of cups of hot milk required = 9/4

Hence, for 1 cup of sugar 9/4 cups of hot milk will be used by Chelsea.

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The standard form is 3/2x + y +2 = 0 for line perpendicular to -2 x+3 y=9 through (-1,-3)

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

In an equation, parallel lines have the opposite reciprocal slope. In other words, if a line's slope is a positive fraction, its reciprocal slope is negative.

Here given that  -2 x+3 y=9

can also be written as

y = 2/3x + 3

Here -2/3 is the slope and 3is the y-intercept

To find a parallel line to the following equation, use the opposite reciprocal slope and point, then solve using the point-slope formula.

y - y₁ = m(x - x₁)

We have, m = -3/2 x₁ = -1 and y₁ = -3

y - (-3) = -3/2(x - (-1))

y + 3= -3/2x +1

3/2x + y +2 = 0

We have the standard form 3/2x + y +2 = 0 of a line  perpendicular to y = (2/3)x - 1 through (0,6)

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The perimeter of the given rectangle is (A) 20 units.

The formula of the perimeter of the rectangle: 2(l + b)

Now, substitute values:

Therefore, (A) 20 units are the perimeter of the given rectangle.

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The correct question is given below:
What is the perimeter of the rectangle shown below?

Comparing the functions f(x) = ln (x) and [tex]f^{-1}(x) = e^x[/tex], we can conclude that the domain of [tex]f^{-1}(x)[/tex] is all real numbers and the range is all real numbers greater than 0.

Given function is the logarithmic function f(x) = ln(x).

Now, f(x) has a domain(D) of all real numbers greater than zero and a range(R) of all real numbers.

i.e., f : D → R defined by f(x) = ln(x)

So if an inverse exist for f(x), then, [tex]f^{-1}(x)[/tex] will have R as its domain and D as its range.

i.e.,  [tex]f^{-1}[/tex] : R → D defined by [tex]f^{-1}(x) = e^x[/tex].

Because f( [tex]f^{-1}(x)[/tex] ) = ln([tex]e^x[/tex]) = x, that is the identity function.

So [tex]e^x[/tex] is the inverse of ln(x).

Also, the domain of [tex]f^{-1}(x)[/tex] is all real numbers and the range is all real numbers greater than 0.

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Answer:

Step-by-step explanation:

Based on the number of candy pieces that Mack ate on the first and net day, the number of pieces of candy that he collected on Halloween night was 78 pieces of candy

The total pieces of candy that Mack had left on the next day was:

Number of candy pieces collected - 7 pieces of candy - (10% x Number of candy pieces collected) = 63

To find the number of candy pieces collected:

x - 7 - 10% × x = 63

x - 7 - 0.1x = 63

x - 0.1x = 63 + 7

0.9x = 70

x = 70 / 0.9

x = 77.7

= 78 pieces of candy

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Answer:

-10.08

Step-by-step explanation:

Using order of operations:

[tex] - 17 + (\frac{ - 2.3 + 8.12}{6} ) \times {4}^{2} - 8.6[/tex]

[tex] - 17 + \frac{5.82}{6} \times 16 - 8.6[/tex]

[tex] - 17 + .97 \times 16 - 8.6[/tex]

[tex] - 17 + 15.52 - 8.6[/tex]

[tex] - 10.08[/tex]

The quantities X and Y are proportional as y = rx  then the constant of proportionality r is 1/9.

Firstly, there is proportional relationship.

Two values x  and  y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called constant of proportionality.

WE have been given quantities X and Y are proportional

y = rx

Where r is constant of proportionality.

Then x = 45 and y = 5

Thus,

y = rx

5 = 45r

Now divide by 45 on both side;

r = 5/45

r = 1/9

Therefore, the constant of proportionality r is 1/9.

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The equation of point slope form of (4,6) and (10,30) is -4x + y + 10 = 0.

A straight line is represented using its slope and a point on the line using point slope form. In other words, the point slope form is used to determine the equation of a line whose slope is "m" and passes through the point (x1, y1).

given that

the coordinates points are (4, 6) and (10, 30)

(x1,y1) = (4,6)

(x2, y2) = (10,30)

The formula of point-slope is

(y - y1) = m(x - x1)

Here,

x1 = 4 and y1 = 6 but we don't know the value of

m.

now,find the value of m using the following formula

[tex] m = \frac{(y2 - y1)}{(x2 - x1)}[/tex]

now, substitute the values, we get

[tex]m = \frac{(30 - 6)}{(10 - 4)}[/tex]

[tex]m = \frac{24}{6}[/tex]

m = 4

so, the value of m is 4.

substitute these values into the point-slope formula

(y - 6) = 4(x - 4)

y-6 = 4x - 16

y = 4x -16 + 6

y = 4x - 10

-4x + y + 10 =0

Hence, the equation of point slope form of (4,6) and (10,30) is -4x + y + 10 = 0.

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The value of the expression ( 1/2 )x + ( 1/2 )x + x + 1 is 2x + 1.

A variable, a number, or a mix of numbers, operations, and numbers symbols make up an expression. Two expressions joined by an equal sign form an equation.

A formula called an equation uses the equals symbol (=) to denote the equality of two expressions.

Consider the expression,

1/2x + 1/2x + x + 1

Taking common out,

( 1/2 )x + ( 1/2 )x + x + 1 = ( 1/2) × [ x + x ] + x + 1

( 1/2 )x + ( 1/2 )x + x + 1 = (1/2x) × 2 + x + 1

( 1/2 )x + ( 1/2 )x + x + 1 = x + x + 1

( 1/2 )x + ( 1/2 )x + x + 1 = 2x + 1

Therefore, the value of ( 1/2 )x + ( 1/2 )x + x + 1 is 2x + 1.

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Answer: 41 minutes and 40 seconds

Step-by-step explanation:

1000 meters=1 km

10 km * 1000 meters/1 km=

10 * 1000/1=

10*1000=10000 meters

10000 meters * 1 second/4 meters=

10000 * 1/4=

10000/4=2500 seconds

60 seconds=1 minute

2500 seconds * 1 minute/60 seconds=

2500/60=

(2460+40)/60=

2460/60 + 40/60= 41 minutes and 40 seconds

Answer:

C° = K-273.15

Step-by-step explanation:

The goal is to get C by itself, so subtract 273.15 from both sides.

Answer:

4521 is a rational number because it can be expressed as the quotient of two integers: 4521 ÷ 1.

Step-by-step explanation:

Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers is a rational number

Hope this helps

By elimination, the system of equations, 9a - 3d = 3 and -3a + d = -1, has infinite solutions.

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in a and d, a variable should be eliminated by adding/subtracting the two equations.

Simplifying the first equation by dividing it by -3,

9a - 3d = 3 ⇒ -3a + d = -1     (equation 1)

-3a + d = -1     (equation 2)

Since the simplified equation of the first equation is the same as the second equation, then the two lines are exactly the same or overlapping.

Hence, the system of equations has infinite solutions.

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Answer:

The area of this section of pavement is 800 square feet

Step-by-step explanation:

10 ft times 80 ft = 800 square feet

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The property of real numbers illustrated by the equation  - [ -(x - 10)] = x-10 is Distributive property.

Distributive Property of real number is represented by the expression

a(b+c)=a*b+a*c.

For Example : 3(2+4)=3*2+3*4

                                  =6+12

                                  =18

In the given question ;

LHS  =-[-(x-10)]

First applying distributive property in side "[ ]".            

=  -[-x-(-10)]

= -[-x+10]   

Again applying distributive property , we get

= -(-x)-(+10)

= x-10  =RHS

Therefore , Distributive Property of Real numbers is illustrated by the equation  - [ -(x - 10)] = x-10.

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The height of the tree is 2.22 feet so that the point on the ground is 70 ft from the base of a tree

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

Let h represent the height of the tree. Hence the distance to the top of tree = 3h + 2.

Using Pythagoras theorem:

(3h + 2)² = h² + 70²

9h² + 12h + 4 =  h² + 70²

8h² + 12h - 66 = 0

h = 2.22 feet

The height of the tree is 2.22 feet so that the point on the ground is 70 ft from the base of a tree

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Step-by-step explanation:

(a+b)² = (a+b) × (a+b)

= a(a+b) × b(a+b)

= a² +ab + ba + b²

= a² + b² + 2ab

103² = (100 + 3)²

= 100² + 3² + (2×100×3)

= 10000 + 9 + 600

= 10609

The value of 19 cubes is equal to 6859. The correct option is D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the number is 19. The cube of 19 will be calculated as:-

19³ = 19 x 19 x 19

19³ = 6859

The cube of 19 is calculated by multiplying the number three times. Hence, the cube of 19 is 6859.

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A logarithm is a power that requires a number to be raised to another power.

The logarithmic equation given in the question can be written as

log2(16) =x

We will rewrite this equation in the exponential form by considering the definition of logarithm.

The definition states that,

If x and b are two positive real numbers and the value of b is not equal to 1, then the log of

log b (x)=y is equivalent to by=x

We will convert the given equation according to the above definition,

2x=16

The bases of all the values involved must be identical. So, we will create equivalent expressions in the equation that all have equal bases.

2x=24

Now we have the same bases; the two expressions can only be said equal if the exponents are also equal.

x=4

The variable x is equal to 4.

4

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Step-by-step explanation:

Given that

To find

So, according to the question

From figure we can say that there is present five rectangle of same size.

So far finding the area of this irregular figure we have to find the area of this single rectangle and multiply it by 5 so from that process we can calculate the area of this irregular figure.

Now first we have to learn about the area,

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.

So, we know

The area of one rectangle = l x w

Now, putting the values = 3 x 2 = 6

So,

The area of this irregular figure = 5 ( The area of one rectangle )

                                                   = 5 x 6

                                                   = 30

Answer:

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The remaining scarves he can spend is 4.

A mixture of constants, variables, and operators make up an algebraic expression. Algebraic expressions can be used to accomplish the four fundamental mathematical operations of addition, subtraction, multiplication, and division. Algebraic expression addition and subtraction are quite similar to addition and subtraction of numbers.

Jesse has a total of 47 dollars.

The cost of the new hat is = 19 dollars

The remaining dollars after buying the new hat is 47 dollars - 19 dollars = 28 dollars.

The cost of the scarves is 7 dollars

Thus total scarves for 28 dollars = 28/7 = 4 scarves.

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x<=-4 or x>=-1

A compound inequality is a sentence with two inequality statements joined either by the word “or” or by the word “and.”

“And” indicates that both statements of the compound sentence are true at the same time. It is the overlap or intersection of the solution sets for the individual statements.

“Or” indicates that, as long as either statement is true, the entire compound sentence is true. It is the combination or union of the solution sets for the individual statements. A compound inequality that uses the word “and” is known as a conjunction.

By seeing the graph we can see that there are 2 inequalities. We have to solve them separately

Final answer: x<=-4 or x>=-1

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The quetient is 2x - 5 with no remainder.

Step-by-step explanation:

The give polynomial is   2x² + x - 15

And the given divisor is  (x + 3)

Now, Using divide rule of polynomials

x + 3 ) 2x² + x - 15 ( 2x - 5

         2x² + 6x

        -       -    

____________________

         - 5x - 15

         - 5x - 15

        +       +

__________________

                0

Hence, we get the quotient is 2x - 5 and the remainder is 0

Therefore, The correct answer 2x - 5 with no remainder.

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The equation of the line in slope-intercept form is: y = -4/5x - 8/5.

Using two points on the line, say, (-2, 0) and (3, -4), follow the steps below to find the equation of the line:

Step 1: Find the slope of the line

Slope (m) = (-4 - 0)/(3 -(-2))

Slope (m) = -4/5

Step 2: Find the y-intercept (b)

Substitute m = -4/5 and (x, y) = (-2, 0) into y = mx + b

0 = -4/5(-2) + b

0 = 8/5 + b

0 - 8/5 = b

b = -8/5

Step 3: Substitute m = -4/5 and b = -8/5 into y = m + b

y = -4/5x - 8/5

Thus, the equation of the line in slope-intercept form is: y = -4/5x - 8/5.

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Answer:

m=3/19

Step-by-step explanation:

Answer:

m = 3/19

Step-by-step explanation:

Let's solve your equation step-by-step.

19m = 3

Step 1: Divide both sides by 19.

19m/19 = 3/19

- You might be wondering, why do we need to divide both sides by 19? -

Well, to find m, you need to get it by itself. So by dividing 19m by 19, m stands alone. But again, what we do to one side, we need to do to the other. So 3 must also be divided by 19.

Answer:

m = 3/19

Answer:

-52

Step-by-step explanation:

fill in the x and y values and multiple it and then combine it

The simplified value of the expression given as (29x - 3) + (13y - 17) - (15x + 7) is 14x + 13y  -27

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(29x - 3) + (13y - 17) - (15x + 7)

Open the bracket in the above expression

So, we have

(29x - 3) + (13y - 17) - (15x + 7) = 29x - 3 + 13y - 17 - 15x - 7

Collect the like terms in the above expression

So, we have

(29x - 3) + (13y - 17) - (15x + 7) = 29x - 15x + 13y - 3  - 17  - 7

Evaluate the like terms in the above expression

So, we have

(29x - 3) + (13y - 17) - (15x + 7) = 14x + 13y  -27

Hence, the simplified value of the expression given as (29x - 3) + (13y - 17) - (15x + 7) is 14x + 13y  -27

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Complete question

Evaluate the following expression

(29x - 3) + (13y - 17) - (15x + 7)