Find the sum of each finite arithmetic series. 5+6+7+ . . . . . . +11

The commutative property [tex]\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex] has been proved.

Commutative property:

The commutative property states that the changes the order or position of two numbers while adding or multiplying them does not change the end result.

The general form of commutative property is

A + B = B + A

For example, while adding the number 4, and 5

4 + 5 = 5 + 4 = 9.

Which means both yields the same result.

Given,

Let

[tex]\overrightarrow{a}= < x_1,y_1 >[/tex]

and

[tex]\overrightarrow{b}= < x_2,y_2 >[/tex]

Now we need to prove the commutative property[tex]\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex].

We know that,

"The vectors are defined as an object containing both magnitude and direction. Vector describes the movement of an object from one point to another."

Based on the commutative property,

We have to to apply the value of [tex]\overrightarrow{a}[/tex]and[tex]\overrightarrow{b}[/tex] to the equation,

Then we get,

[tex]\implies\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}[/tex]

=> <x₁, y₁> + <x₂, y₂> = <x₂, y₂> + <x₁, y₁>

While looking at the expression we know that,

Both are equal.

Then the commutative property has been proved.

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The base and height of triangle are 25 and 22 feet.

We are given the relation between base and height of triangle. Let us represent height with h and base with b. The equation relating the two quantities is as follows -

h = b - 3

Now, the area of triangle is given  by the formula -

Area = 1/2 × base × height

Keep the values in formula to find the base of triangle

275 = 1/2 × b × (b-3)

550 = b × (b-3)

b² - 3b - 550 = 0

b² + 22b - 25b - 550 = 0

b (b + 22) -25 (b + 22) = 0

(b + 22) (b - 25) = 0

b = -22 and 25

As the value of base can not be negative, so, the base of triangle is 25 feet.

Calculating height of triangle-

Height = Base - 3

Height = 25 - 3

Height = 22 feet

Hence, the base and height of triangle are 25 and 22 feet.

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Answer: c=-0.01

Step-by-step explanation:

Answer:

875

Step-by-step explanation:

215+200+185+170+155+140+125+110+95+80+65+50+35+20+5+(-10)+(-25)+(-40)+(-55)+(-70)+(-85)+(-100)+(-115)+(-130)+(-145) =875

I'm sure there's an easier way to do this, but if you want a correct answer, here you go. Have a good day!

Answer:

875

Step-by-step explanation:

I think hope it right

1) The mathematical expression that represents this scenario is T = 40/5.

2) The value of T in the equation is $8.

A mathematical expression is a mathematical statement that has two different numbers (known or unknown) and at least one operation.

For instance, an equation is a mathematical equation showing that two variables are equal.

The payment for a subway pass = $55

The number of subway rides = 5

The total amount deducted from the value of the pass = $40

This implies that each subway ride costs = $8 ($40/5)

If T is the cost of a ticket and the total cost incurred for 5 subway rides is $40, therefore T = 40/5.

Thus, the mathematical expression that represents this scenario is T = 40/5.

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Answer: give me the context please

Step-by-step explanation:

Answer:

The large box weighs 18.75 and the small box weights 15.75

Step-by-step explanation:

We are looking to find 2 variables so we will need two equations.

Let l = the large box weight

Let s = the small box weight

7l + 9s + 273                   5l +3s = 141

I want to add these two equations together and have one of the variables be eliminated.  The way both equations are written now, neither variable will drop out.  I see that 9 is a multiple of 3.  If I multiply the second equation all the way through by - 3, the s variable will be eliminated.

-3(5l +3s) -3(141)  Multiple everything by -3

-15l -9s = -423  Now I will add this to the original equation 7l + 9s = 273

7l + 9s = 273

-8l = -150  Divide both sides by -8

l = 18.75  This is the weight of the large box.

Plug in 18.75 to either of the ordinal equations to find the weight of the small box.

5l + 3s = 141

5(18.75) + 3s = 141  Distribute the 5

93.75 + 3s = 141  Subtract 93.75 from both sides

3s = 47.25  Divide both sides by 3

s = 15.75

Check:

Plug in 15.75 for s and 18.75 for l into both of the original equation to see if they equal.

7l + 9s = 273

7(18.75) + 9(15.75) =273

131.25 + 141.75 = 273  Checks

5l + 3s = 141

5(18.75) + 3(15.75) = 141

93.75 + 47.25 = 141

141 = 141 Checks

The simplified form of the expression is -29y - 8

Linear equations are equations that has a linear degree of 1. For instance the expression y =mx + b has a linear degree of 1.

Given the linear equation below:
-7 (3y)+2(-4y+-4)

When solving linear equation, first we will need to expand the expression first.

-7 (3y)+2(-4y+-4)

-21y + 2(-4y) + 2(-4)

Simplify the resulting expression

-21y -8y. - 8

-29y - 8

Hence the simplified form of the expression is -29y - 8

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The solutions of the given polynomial equation p⁴+32=12 p² is p = {-2√2, 2√2, -2, 2}.

The given polynomial equation is:

p⁴+32=12 p²

Subtract both sides by 12 p²

p⁴ + 32 -12 p² = 12 p² 12 p²

p⁴ -12 p² + 32 = 0     ...... (1)

Let x = p², then equation (1) becomes

x² -12x + 32 = 0  

This is a quadratic equation.

Factorize:

   x² -12x + 32 = 0  

⇔ (x - 8 ) (x - 4) = 0

Take:

x - 8 = 0

x = 8

p² = 8

p = ±√8 = ±2√2

Take:

x - 4 = 0

x = 4

p² = 4

p = ±√4 = ±2

Hence the solution is p = {-2√2, 2√2, -2, 2}

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Answer:

y = -1/4 -x/2

Step-by-step explanation:

The solution is attached.

For the given set of inequality, the value of x is 8.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.

Given, the equation is -

x+ 3 > 19 = 3x

⇒ x + 3 > 19 - 3x

Subtracting 3 from bot sides

⇒ x > 16 - 3x

subtracting x from both sides

⇒ 16 - 2x > 0

⇒ x = 8

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Work Shown:

C(x+2) - (x+2)(x-2) = 0

(x+2)(C-(x-2)) = 0

(x+2)(C-x+2) = 0

x+2 = 0 or C-x+2 = 0

x = -2 or x = C+2

If we want one solution only, then we must make C+2 = -2 which solves to C = -4

If C = -4, then x = C+2 = -4+2 = -2 which matches with the first solution mentioned. If C is anything else but -4, then we'd have two different solutions (eg: C = 10 leads to x = C+2 = 12 as the other solution)

Answer:

3

Step-by-step explanation:

if m is the number of months

Beckett: 90 + 25m

Lakota Hills 45 + 40m

so 90 + 25m = 45 + 40m

40m - 25 = 90 - 45

15m = 45

m = 45/15 = 3

The range of each amazon box is 1.6035m

According to the question we have been given that

        height of the conveyer belt = 1.4m

        Speed of the belt = 3m/s

We need to find the range of the amazon box, that is we have to find the distance.

Formula for distance is ,  d = speed * time

We have been given the value of speed we need to find the value of time. For that we will use the formula,

                                     h = [tex]\frac{1}{2} g t^{2}[/tex]

where,         h = height

                   g = acceleration due to gravity = 9.8m/s²

                    t = time

Putting the required value for t we get,

        t = [tex]\sqrt{\frac{2h}{g} } \\[/tex]

          = [tex]\sqrt{\frac{2(1.4)}{9.8} } \\[/tex]

          = √0.286

          = 0.5435 s

Putting the value of time in distance formula we get,

                d = 3 * 0.5435 m

                   = 1.6035 m

Hence the range of each amazon box is 1.6035m

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Answer:

no it is not because natural numbers are whole numbers :)

hope this was helpful!

Answer: 7.5

Step-by-step explanation: 15 ft * 2 in/ft = 30 in18 ft * 2 in/ft = 36 inso area on plan = 30*36 = 1080 in^2on the real size area = 15*18 = 270 ft^2well to compare them change in^2 to ft^2there are 12 in /ftso 144 in^2 per ft^2so1080 in^2 *1 ft^2/144 in^2 = 7.5 ft^2or you could say30 in = 30/12 ft36 in = 3 ftarea = 90/12 ft^2 = 7.5 ft^2 luckily :)

Answer:

Step-by-step explanation:

triangles are similar so:

[tex]\frac{10}{10+14} = \frac{x}{36}[/tex]

24x=360

x=15

The common difference d is 6 and the first term a1 is 20.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.

The formula of Arithmetic progression is

a(n) = a1 + (n - 1)d

given that the two terms of arithmetic sequence,

a3 = 32 and a7 = -8.

now, find the common difference d.

a(n) = a1 + (n - 1)d

Let take a(n) = a7 and a1 = a3.

a7 = a3 + (7 - 3)d

a7 = a3 + 4d

now substitute the values of a6 and a4

-8 = 32 + 4d

-8 + 32 = 4d

d = 24/4

d = 6

so, the common difference d is 6.

then, find the term a1.

take the formula

a(n) = a1 + (n - 1)d

now, substitute a(n) = a3 and d = 6.

32 = a1 + (3-1)d

32 = a1 + 2d

32 = a1 + 2(6)

32 = a1 + 12

a1 = -12+32

a1 = 20.

so, the first term a1 is 20.

Hence, the common difference d is 6 and the first term a1 is 20.

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27.9 cm≤ perimeter ≤28.5cm

The length of the regular hexagon is 4.7cm to 1 decimal place, i.e.,

4.65≤ length≤4.75

As we know the number of sides of a regular hexagon is 6

So the perimeter for the upper bound of length = 6×4.65

                                                                                = 27.9cm

The lower bound of length perimeter = 6× 4.75

                                                              = 28.5cm

Therefore the interval of the perimeter of a regular hexagon is:

27.9cm ≤ perimeter ≤ 28.5cm

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The angle of elevation of the ramp to the nearest degree is 8°

From the information given, we have the following deductions;

The tangent identity is expressed as;

tan θ = opposite/ adjacent

substitute the values

tan θ = 2/ 15

find the ratio

tan θ = 0. 1333

Find the tangent inverse of the value

θ = [tex]tan^-^1(0. 1333)[/tex]

θ = 7. 79 °

θ = 8° in the nearest degree

Thus, the angle of elevation of the ramp to the nearest degree is 8°

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The equation is 24.36 = 5.31 + 5 * x  and the cost of each bag of lemon is $3.81

The given parameters are:

The above means that

Total = Cheese + Bags of lemon * 5

This gives

24.36 = 5.31 + 5 * x

Collect the like terms

So, we have

24.36  - 5.31 = 5 * x

Evaluate the like terms

So, we have

19.05 = 5 * x

Divide through by 5

So, we have

x = 3.81

Hence, the equation is 24.36 = 5.31 + 5 * x  and the cost of each bag of lemon is $3.81

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Answer: x<1

Step-by-step explanation:

add 12 to both sides, divide by 2 on both sides.

Inequality is [tex]p + 31 \ge 85[/tex]

Solution is [tex]p \ge 54[/tex]

===============================================

Explanation:

p = number of pages left to read

31 = number of pages already read

p+31 = total number of pages (unread + read)

This total must be 85 or larger, so that's how we end up with [tex]p+31 \ge 85[/tex]

To solve this inequality, we subtract 31 from both sides to end up with [tex]p \ge 54[/tex] which means Jen still needs to read at least 54 pages.

The correct option is F. 25.

The total number of gallons of gas Amanda will use to travel all the distances is 25.

The amount of between two things, or the state of being far apart, is defined as distance. A five-foot distance between two tables is an example of distance. The difference of the two sides of an issue is an example of distance.

Now, as per the given question;

Amanda plans to drive 160 miles, 235 miles, 185 miles, and 220 miles.

Thus, the total distance ravelled by Amanada is;

= 160 miles + 235 miles + 185 miles + 220 miles

= 800 miles

Amanada's car has the average of 32 miles per gallon of gas.

Thus, the car will cover a total of 32 miles for each gallon of gas.

Thus,

The number of gallon of gas requires = Total distance/(distance travelled for one gallon of gas)

The number of gallon of gas requires = 800/32

The number of gallon of gas requires = 25

Therefore, the gas required to travel a total distance of 800 miles is 25 gallons.

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The eighth term of the given geometric sequence is 256/6561.

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: 2/3, 4/9, 8/27...

As we can observe, each successive term of the geometric sequence is 2/3 of the previous one.

Thus, r = 2/3  and a₁ = 2/3.

The formula used to find the nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]

For n = 8, [tex]a_8=\frac{2}{3}(\frac{2}{3})^7=\frac{2}{3}^8=\frac{256}{6561}[/tex]

Thus, the eighth term of the given geometric sequence is 256/6561.

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Answer:

?

Step-by-step explanation: