An airplane is flying at an airspeed of 490 km/hr in a wind blowing at 50 km/hr toward the southeast. In what direction should the plane head to end up going due east?

Answer:

Step-by-step explanation:

simplify

6/7x + 7= 31

6/7x+7-7=31-7

6/7x=24

6/7x=24/6/7

28

6/7(28)+15-8=31

24+15-8=31

39-8=31

The nearest tenth value of the given expression is a 18.3. the option D is  a correct option.

According to the statement

We have to find that the value of the tenth digit.

So, For this purpose, we know that the

Tenth digit  is the first digit to the right of the decimal point; one out of 10 equal parts of a whole.

From the given information:

14 plus cube root of 81 to the nearest tenth.

Then

the statement become is

[tex]14+(81)^\frac{1}{3}[/tex]

Firstly we have to find the cube root of the number 8 and then have to add 14 number in the out coming answer.

Then

14+ Cube root of 81

Then

14+ 4.32

Then after adding it

18.32

In the nearest tenth value it will become 18.3.

So, The nearest tenth value of the given expression is a 18.3. the option D is  a correct option.

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The constant of variation in  y = (3/2)x is (3/2)

y = kx                           (Where k is the constant)

Here, y = (3/2)x

so k = (3/2)

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.

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Answer:

55 sq ft

Step-by-step explanation:

okay so the are of the lil square is 9 sq ft and the area of the big square is 64 sq ft so j subtract the small from the big

Answer: 55cm ^2

Step-by-step explanation:

Area of a square is A=a^2

Area of small square is 3cm^2 = 9cm^2

Large square has an area of 8cm^2 = 64cm^2

64 - 9 = 55 cm^2

Therefore the remaining area is 55 centimeters squared

Answer: 7

Step-by-step explanation: You can find the mean, or average, of a data set in two simple steps: Find the sum of the values by adding them all up. Divide the sum by the number of values in the data set.

Measure of angle 3 i.e. m∠3 = 130°

The measurement of angle is the degree of that angle or we can also say that the angles are always measured in degree. In geometry, the complete one revolution of four quadrants is of 360 degrees (360°) and divided into total of 360 parts where each part of this represents a degree.

As stated above there are total 360 parts in one revolution thus thus we can find value of particular angle by subtracting the angle from 360 or 180 for a straight line.

In the question,

Let given angle is ∠8.

Given, ∠8 = 50°

Now, according to supplementary angle property

∠8 + ∠6 = 180

50° + ∠6 = 180

∠6 = 130°

As, ∠6 and ∠2 are corresponding angles,

therefore, ∠6 = ∠2 = 130°

Also, ∠2 and ∠3 are vertical opposite angles,

thus, ∠2 = ∠3 = 130°

therefore, ∠3 = 130°

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The complete question is :

Find measures of numbered angle.

a. ∠2

b. ∠3

c. ∠4

The volume of pyramid is 9.16×10⁷ feet³.

We are given the measure of each side of Great Pyramid, which will be it's length and width. Also, we are given height. The formula for calculation of volume of pyramid is -

Volume = (length×width×height)÷3

Keep the values in formula to find the volume of Great Pyramid

Volume = (756×756×481)÷3

Performing multiplication on Right Hand Side of the equation to find the volume of Great Pyramid-

Volume = 274908816÷3

Solving the Right Hand Side of the equation, by performing division, we get the volume of Great Pyramid -

Volume = 9.16×10⁷ feet³

The volume of Great Pyramid is 9.16×10⁷ feet³.

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  955°C is  temperature (in celsius) is the rate constant equal to 0.08857 sec-1.

What is the short definition of activation energy?

The least amount of energy necessary to bring atoms or molecules into a state where they can undergo chemical transformation or physical transport is known as the activation energy .

K = [tex]A . e^{\frac{-Eq}{RT} }[/tex]

logk = logA = Eq/RT

log0.02629 = log5.57 × [tex]10^{10}[/tex] sec-1  -  [tex]\frac{125.6 * 10^{3} }{8.314 * T}[/tex]

                   = log5.57  + [tex]log 10^{10}[/tex]  - [tex]\frac{12.56 * 10^{3 J} }{8.314 * T}[/tex]

                   = log5.57  + 10log10 - 15.10 * 10³ J/T

   -1.5483 = 0.7458 + 10 - 15.10 * 10³/ T

  -1.5483 = 10.7458 - 15.10 * 10²/T

 - 15.10 * 10³/ T   = -1.5483 - 10.7458

   15.10 * 10³ /T = 12.2941

 T = 15.10 * 10³/ 12.2941

       = 1228K

       = 955°C

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Step-by-step explanation:

[tex](x+4)(2x+5)\\\\2x^2+5x+8x+20\\\large\boxed{2x^2+13x+20}[/tex]

Bounce 2 is 2

Bounce 4 is 1/2

Bounce 5 is 1/4

Bounce 6 is 1/8

all of your equivalent heights are correct.

The function g(x)  whose graph is the horizontal shrink of the given graph of  f(x) =5x-6 by a factor (horizontal shrink factor) of 1/4 is  g(x)=5/4 x-6.

As per the question statement, we are supposed to find a function g(x) whose graph is a horizontal shrink of the given graph of f(x) =5x-6 by a factor of 1/4.

Before solving it lets assume f(x)=y

so y =5x-6

Comparing with y= mx+c  where m is the slope

so in y =5x-6  slope is m=5

For applying horizontal shrink by a factor of 1/4 we need to multiply the slope by a factor of 1/4

so new slope [tex]m_{1} =5*\frac{1}{4} =\frac{5}{4}[/tex]

Therefore [tex]g(x) = \frac{5}{4} x -6[/tex]

Therefore the function [tex]g(x)[/tex] whose graph is a horizontal shrink of the given graph of  [tex]f(x) = 5x-6[/tex]  by a horizontal shrink factor of  1/4  is [tex]g(x) = \frac{5}{4} x -6[/tex]

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The slope of the line containing (-3,-5) and (-3,-1) is Infinity.

The slope of a straight line can be written as follows,

m =  [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex]                 equation1

The line is containing the points (-3,3) and (4,3). So, we can write

[tex]y_{2}[/tex] = -1 , [tex]y_{1}[/tex] = -5 , [tex]x_{2}[/tex] = -3 , and [tex]x_{1}[/tex] = -3 .

On substituting the values of variables in equation1, we will get

m = ( (-1)-(-5) ) / ( (-3)-(3) ) = (4/0) = Infinity.

As the slope of a line is Infinity, so we can conclude that the given line is a straight line.

Here:

m = the slope of the line

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.

The slope of the line containing (-3,-5) and (-3,-1) is Infinity.

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Answer:

Step-by-step explanation:

cos(30) x tan (60) + sin (30) = (√3)/2 x √3 + 1/2 = 3/2 + 1/2 = 4/2 = 2

Natalie’s current available balance is $116.07.

To find current available balance, we need to subtract pending deposits/ credits with pending withdrawals/ debits.

Account Balance = Pending deposits / credits – Pending Withdrawals /debits

= $126.02- $97.68 = $28.34

Available Balance = Account Balance + Current Posted Balance

= $28.34 +$87.73 = $116.07

Current Available Balance = $116.07

The balance in checking or demand accounts that is available for use by the client or account holder is known as the available balance. The accessible balance of an account holder may not match the current balance. Any unfinished transactions are often included in the current balance.

Pending Deposit Credits: Pending check deposits that haven't been processed, haven't been credited to your account, or didn't have availability when we got them.

Pending Deposit Debits: Your account is put on hold for the transaction's amount until it is processed.

Hence Natalie’s current available balance is $116.07.

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The inequality that represents the number of nights he can stay in Dallas is 155n+ 99 ≤ 850 (option d).

Here are inequality signs and what they mean:

Since his budget is $850, he can spent a total of $850 or less than $850 on the trip. The sign that would be used to represent this is ≤.

(Total hotel stay cost) + cost of flight ≤. budget

(cost per night x number of hotel stays) + $99 ≤ $850

155n + $99 ≤ 850

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Answer:

Answer is D

Step-by-step explanation:

2 packages of bacon would have to buy for both stores to cost the same.

Given that,
At a store, a carton of eggs costs $2.25 and a package of bacon costs $4.25. At another store, eggs cost $2.75, and bacon costs $4.00. If you were to buy one carton of eggs, how many packages of bacon would you have to buy for both stores to cost the same is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
According to question
WIth the help of arithmetic operators
2.25 + 4.25y = 2.75 + 4.00y
0.25y = 0.50
y = 2

Thus, 2 packages of bacon would have to buy for both stores to cost the same.

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The dimensions of the decks increased by the 11 feet.

According to the statement

We have to find that the length by which we increase the dimensions.

So, For this purpose, we know that the

The Area is the amount of space occupied by a two-dimensional figure.

From the given information:

Ashley has a deck that measures 22 feet by 11 feet. She wants to increase each dimension by equal lengths so that its area is tripled.

Then

The shape of the deck is the rectangle then dimensions is 22 feet by 11 feet.

Then

Area of the deck with the given dimensions =  Length * Breadth

Area of the deck with the given dimensions =  22* 11

Area of the deck with the given dimensions =  242.

Then the dimensions increased by the x

Then

Area of the deck with the given dimensions =  Length * Breadth

Area of the deck with the given dimensions =  (22+x)* (11+x)

Area of the deck with the given dimensions =  242 + 22x+11x+x^2

Area of the deck with the given dimensions =  242 + 33x+x^2

Then according to given details:

x^2 + 33x + 242 = 3*242

x^2 + 33x + 242 = 726

x^2 + 33x = 726 - 242

x^2 + 33x = 484

x^2 + 33x - 484 = 0

After solving

The value of the x become

x = 11 and x = -44

Then second option be neglected.

Then the length increased by the 11 feet.

So, The dimensions of the decks increased by the 11 feet.

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Answer:

44 °

Step-by-step explanation:

In a right triangle such as this

  sin B = opposite leg / hypotenuse

  sin B =   20 / 29

   B = arcsin (20/29) = 44 degrees

Answer:

5/6

Step-by-step explanation:

Get LCD of 30 and add

9/30 + 16/30

25/30

Reduce

5/6

The sum of finite arithmetic series 1+4+7+ . . . . . .+31 is S(11) = 176

The given  arithmetic series is:

      1+4+7+ . . . . . .+31

From the above series, we know that:

The first term, a(1) = 1

The last term, a(n) = 31

The common difference, d = 4 - 1 = 3

Recall the formula to find the nth term of an arithmetic sequence:

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

Substitute a(1) = 1, a(n) = 31, and d = 3:

31 = 1 + (n-1) . 3

31 = 3n - 2

3n = 33

n = 11

In an arithmetic series, the sum of the first n terms is given by:

S(n) = n/2 [ a(1) + a(n) ]

Substitute n = 11, a(1) = 1, and a(n) = 31:

S(n) = 11/2 (1 + 31)

S(11) = 11. 16 = 176

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Answer:

The y-value is 1 less than the square of the x-value,

Step-by-step explanation:

if we follow the letters and convert them into numbers we will get:

y-value=y

1 less than=-1

square of x value=x^2

so

we put the number in order according to the words:

y value=1 less than the square of x

so

y=x^2-1

hope this helps!

The value of the inequality is x > 6

Inequalities are defined as mathematical relations that makes a non-equal comparison between two numbers , elements or expressions.

They are also used to compare two numbers on the number line by their size.

It is an order relationship showing —greater than, greater than or equal to, less than, or less than or equal to

Given the expression;

|1.3x + 7.8| > 0

collect like terms

1. 3x > 0 + 7. 8

1.3x > 7. 8

Make 'x' the subject

Divide both sides by 1. 3

1. x/ 1. 3 > 7. 8/ 1. 3

x > 6

Thus, the value of the inequality is x > 6

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The product of  -2.1. (-3.5) is  7.35

The product of  (-2.1 ) and (-3.5) =  [tex]-2.1\times-3.5[/tex]

                                                    =  7.35

So, the product of (-2.1) and (-3.5) is 7.35.

The quotient is the number which is produced when we perform division operations on two numbers. Fundamentally, it is the result of the division method. There are four primary wordings utilized within the arithmetic division such as divisor, dividend, quotient and remainder.

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Answer:

slope = -4

Step-by-step explanation:

slope = [tex]\frac{y2-y1}{x2-x1}[/tex] = [tex]\frac{-10 - (-2)}{-2 - (-4)}[/tex] = [tex]\frac{-10 + 2}{-2 + 4}[/tex] = [tex]\frac{-8}{2}[/tex] = -4

The value of X in the equation that allows a solution with the values of "a" and "b" is x = 16

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

   We write the given equation

b = 3x + 4a

 and we have the values of the coefficients a and b, and these are:

  We substitute these values in the equation:

b = 3x + 4a

(12) = 3x + 4(-9)     :::: We solve the equation

12 = 3x -36

3x = 12 + 36

3x = 48

x = 48/3

x = 16

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The system of equations, -x + y = -2 and 2x - 2y = 0, has no solution.

A system of linear 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 both equations.

Given two equations in x and y,

-x + y = -2     (equation 1)

2x - 2y = 0     (equation 2)

Rewrite equation 1 as an equation of y and substitute to equation 2.

(equation 1) -x + y = -2     ⇒     y = x - 2

2x - 2y = 0     (equation 2)

2x - 2(x - 2) = 0

2x - 2x + 4 = 0

4 = 0

Since we do not have a definite value for x, and neither will be for y, the system of equation has no solution.

Checking the slope,

(equation 1) -x + y = -2     ⇒     y = x - 2

m = 1

(equation 2) 2x - 2y = 0     ⇒     y = x

m = 1

Since the two equations has the same slopes but different y-intercepts, then these two equations must be parallel with each other.

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