is the relationship between the variables in the table an inverse variation or a direct variation? write an equation to model it.

x= 2 6 7 14
y= 21 7 6 3

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[tex]\quad \qquad \huge \bf \dag \: Answer \: \dag[/tex]

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[tex] \underline{ \large \rm Solution} : [/tex]

[tex]\rm Given : [/tex]

Two equations are -

[tex] \rm Procedure : [/tex]

Considering the equations as (i) and (ii) respectively

From equation (i) -

put this value of y in equation (ii) -

Next thing to do would be to put value of x we got in equation (i) to get y

Values asked are :

[tex] \rightarrow \rm y = - 4[/tex]

[tex] \rightarrow \rm x= - 2[/tex]

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[tex] \large \bf hope \: \: it \: \: helps \: - dabI [/tex]

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The lengths of a,b,c, and d have been derived and expressed in terms of trigonometric ratios below.

As we can see from the figure itself, the value of a = sin θ

This can be written as such because = sin θ = Perpendicular / Hypotenuse

Here, the perpendicular = a and hypotenuse = radius = 1

= sin θ = a

The value of b = tan θ

This is because tan θ = perpendicular/base

Here, the base = radius = 1

= tan θ = b  

The value of c = sec θ

This is because sec θ = Hypotenuse / Base

= sec θ = c

The value of d = cos θ

This is because cos θ = Base / Hypotenuse

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Answer:

2x + 2

Step-by-step explanation:

Combine all the like terms:

-5x + 7x -12 + 14 = 2x + 2

Answer:

2x + 2

Step-by-step explanation:

(- 5x - 12) + (14 + 7x) ← remove parenthesis

= - 5x - 12 + 14 + 7x ← collect like terms

= (- 5x + 7x) + (- 12 + 14)

= 2x + 2

The length of PG if PG' is 0.5 units is; 3 units.

The act or action of enlarging, expanding, or widening : the state of being dilated: such as. : the act or process of expanding (such as in extent or volume)

Here, given that,

Dilation is simply defined as the shrinking or enlarging of an object by a scale factor.

Now, we are told that Line HG is dilated to form a shorter line H'G'.

We are told that the scale factor is 1/6.

Point P is the center of dilation and if PG' is 0.5 units, then we can write the relation as follows;

Length of PG'/Length of PG = 1/6

Thus;

0.5/length of PG = 1/6

Length of PG = 0.5/(1/6)

Length of PG = 4 units

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We spent a total of 40.2 + 24.5+ 37.8 = $102.50

A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator.

Fractions are used to represent the parts of an entity or collection of entities. The components of a fraction are two. The figure at the top of the line is the numerator. It provides information on how many equal sections from the total or collection were taken. The number that appears below the line is the denominator.

We multiply the initial price by the fractions' decimal conversions to determine how much we spent. The quantities are then combined.

You purchased sneakers for $60 and paid 2/3 of that amount, or $0.6666, for a total of $40.20, saving $19.80.

Sweater costs $35 and you paid $7.50 for it, saving you $10.50. 35(0.7)=$24.50.

You paid $45 for a jacket, and since 5/6=0.8333, 45(0.84)=$37.80, you made a $7.20 profit.

We spent a total of 40.2 + 24.5+ 37.8 = $102.50

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The expectation is -$9.6

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes.

Expected winning per ticket :

Σ(X × p(X)) = [(1000 × 1/1000) + (600 × 2/1000) + (300 × 2/1000) + (200 × 5/1000) - price per ticket

= 1 + 1.2 + 0.6 + 1 - 7

= 3.8-7

= -$3.2

Expected winning if 3 tickets are purchased :

3 × (-3.2) = -$9.6

Hence, the expectation is -$9.6

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Slope = (-2 - 4)/(14 - (-1)) = -6/15

Function: This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

A function is a mathematical relation between two sets of values, usually between an input and an output. It can be thought of as a machine that takes a certain input and produces a certain output.

2.7 x 10^3 is about 0.049 times smaller than 5.481 x 10^5.
To determine this, we can divide the two numbers. 5.481 x 10^5 divided by 2.7 x 10^3 equals about 201.593.
This means that 2.7 x 10^3 is about 201.593 times smaller than 5.481 x 10^5. This can also be expressed as 0.049 or 4.9%.

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Answer:

(-1) & 4/3

Step-by-step explanation:

           3x² - x - 4

Sum = -1

Product = 3*(-4) = -12

Factors = -4 and 3       { (-4)*3 = -12 & (-4) + 3 = -1}

3x² - x - 4 = 3x² + 3x - 4x -4 {Rewrite the middle term using the factors}

               = 3x(x + 1) -4(x + 1)

               =(x + 1)(3x - 4)

x + 1 = 0   ;  3x - 4 = 0

     x = -1  ;          3x = 4

                            x = 4/3

[tex]\sf Zeroes \ of \ the \ polynomial \ are \ (-1) \ and \ \dfrac{4}{3}[/tex]

Verification:

         [tex]\sf 3x^2 - x - 4 = 0\\\\Divide \ the \ entire \ equation \ by \ 3\\\\\\\dfrac{3x^2}{3}-\dfrac{x}{3}-\dfrac{4}{3}=0\\x^2 - \dfrac{x}{3}-\dfrac{4}{3}=0[/tex]

       Coefficient of x = sum of the zeroes

                                  [tex]\sf = -1 + \dfrac{4}{3}\\\\=\dfrac{-3}{3}+\dfrac{4}{3}\\\\=\dfrac{1}{3}\\\\[/tex]

Constant = product of the zeroes

               [tex]\sf = (-1)*\dfrac{4}{3}\\\\=\dfrac{-4}{3}[/tex]

Thus verified.

If Shaheen has many triangular piece, each of area 1 sq. Unit and many rectangular piece, each of area 2 sq. Unit  she arranges these to form the given shape then the area of shape is 14 Square Units .

The Area of one triangular piece is given as = 1 Sq . Unit ;

The Area of one rectangular piece is = 2 Sq. Unit ;

From the shape given below ,

we can see that the shape has 4 triangular pieces and 5 rectangular pieces .

So , total area of given shape is ⇒[tex]4\times Area Of Triangle + 5\times Area Of Rectangle ;\\[/tex]

Substituting the values of Area ,

we get ;

[tex]Total Area = 4\times 1 +5\times 2[/tex]

= [tex]4+10[/tex]

= 14 Sq . Units .

Therefore , the area of the given shape is 14 Sq. Units .

The given question is incomplete , the complete question is

Shaheen has many triangular piece, each of area 1 sq. Unit and many rectangular piece, each of area 2 sq. Unit .

If she arranges these to form a shape as shown below, what would be the area of this shape ?

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Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).

A depiction of two equal variables, one on either side of a "equals" sign, is what constitutes an equation in mathematics. To solve common issues, one can use equations. We frequently look for help with pre algebra to overcome obstacles in real life. Basic mathematical concepts are covered in pre-algebra lessons.

Here,

the x-intercepts,

In order to determine the x-intercept(s), put in for y and calculate 4x6y=36.

Make the equation work.

x=9 point form x-intercepts.

x-intercept(s): \s(9,0) (9,0)

the y-intercepts, please.

In order to determine the y-intercept(s), replace with and solve for y=.4(0-)6y=36.

Make the equation work.

To continue, tap.

Point shape y=6 y-intercept(s).

The y-intercept is (0, 6).

Write down the junctions.

x-intercept(s): (9,0)

The y-intercept is (0, 6).

Therefore . the solution of the given problem of equation comes out to be x-intercept(s): (9,0) and y-intercept(s): (0,−6).

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Using the concept of circumference of a circle, the length of the minute hand is 16.5mm.

What is circumference of a circle?

The measurement of the circle's perimeter, also known as the circle's boundary, is called its circumference . The radius of the circle is considered when applying the formula to determine the circumference of the circle.

Circumference of circle(C) = 2πR

where,

R represents the radius of the circle

π is a constant with an approximate value of 3.14

Now, it is given that the tip of a minute-hand travels 103. 62mm in one hour which means that the minute hand moves 360 degrees.

This means that C= 103.62

So, using the concept of circumference of a circle,

C= 2πR

103.62= 2*3.14*R

So, R= 103.62/6.28

R=16.5mm

Hence, the length of the minute hand is 16.5mm.

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Answer:

To find the value of x that makes the expression (4x-6) equal to (8x-6). To do this, you can set the two expressions equal to each other and solve for x:

4x - 6 = 8x - 6

4x = 8x

4x - 8x = 0

-4x = 0

x = 0

So, the value of x that makes (4x-6) equal to (8x-6) is x=0.

Answer:

-4x = -12 Divide each side by '-4'.

Answer:

The answer is 1/4.

I wish you good luck.

Answer: it's hard i thought i could do it but nope dang it

Answer:   B

Step-by-step explanation:   [tex]8x-5x=3x\\3+9=12\\[/tex]

Hope this helps any

Answer:

B. 3x+12

Step-by-step explanation:

8x+3-5x+9

First combine the x. So, 8x-5x=3x

Next combine the 3 and the 9. So, 3+9=12

After you combined like terms your equation now looks like: 3x+12

Hope it helped you.

It is possible for a valid argument to have a false conclusion as long as at least one premise is false.

When the premises are genuine, validity guarantees a true conclusion; when the premises are wrong, validity provides no assurance. Even in a legitimate argument, faulty premises might lead to either a true or erroneous conclusion. In many cases, it was chance rather than reasoning that led to the correct conclusion.

Avoid including: Important evidence or analysis that was not provided in the main body for a stronger conclusion paragraph.Generic closing phrases (for example, “In conclusion…”)Weak remarks that undercut your argument (for example, “There are valid points on both sides of this debate.”)

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Answer: The ship is going to another planet.

Step-by-step explanation:

I hate i-ready,

Your welcome mate

To do 5 choose 3 on calculator, there are many methods including typing the input the mathematical expansion or in scientific calculators according to the model, there is way to represent 5C3.

The notation 5 choose 3 (also known as "5C3" or "5 comb 3") represents the number of ways to choose 3 items from a set of 5 items, also known as the binomial coefficient. It is equivalent to the formula:

5C3 = (5!) / (3! × (5-3)!)

Where "!" denotes factorial, which is the product of all positive integers up to that number.

To calculate 5C3 on a calculator, you can use the above formula and input it as follows:

5!/(3!×(5-3)!)

Most calculators have a button for factorial (symbolized by "!" or "n!"), so you can use that to calculate the factorials in the formula.

For example, on a basic calculator, you can input the following:

5!/(3!×2!)

and then press enter or the "=" button to get the result which is 10.

On some scientific or graphing calculators the notation is different, it could be represented as "comb(5,3)" or "5C3" and you just need to enter it as such.

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If David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. The number of miles that is the airport from his home is 210.

Let d represent the distance that is needed to travel 1 hour

1 hour late decreased to 0.5 hours early = 1.5

Hence,

d/50 + 1.5 = d/35

Simplify

7d + 525 =10d

Collect like terms

525 = 10d - 7d

525 = 3d

Divide both side by 3d

d = 525/3

d = 175

Total number of miles :

Total number of miles = 175 + 35

Total number of miles = 210

Therefore we can conclude that the correct option is C.

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here in equation function, John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.

To create an equation, multiplying and dividing are used to separate constants and variables. In an equation, terms in various forms on each side of the equality sign are equal. John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.To create an equation, multiplying and dividing are used to separate constants and variables.

so we have,

John had paid $8.00 an hour and waits tables

Therefore,

In 29 hours, he earns -

[tex]= 40 X 8\\= 320 $[/tex]

Via tups, he earned 210.50$

So, in total he earns

[tex]= 320 + 210.50\\= 530.50 $[/tex]

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Answer:

y = 3x - 2

Step-by-step explanation:

Answer:

25%  

a half is 50%

a quarter is 25%

Answer: It's option C

Step-by-step explanation:

Well 1 quarter is 25

2 quarters is 50

3 quarters is 75

4 quarters is a dollar

The solutions of the given quadratic equation are 4 and -3/2. Solved using the factoring method to solve a quadratic equation.

what is a quadratic equation?

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation's general form is ax^2 + b*x + c = 0.

where a, b, and c are constant terms and x is the unknown variable.

Here I am using the factoring method to solve a quadratic equation.

Given quadratic equation is

[tex]2x^2 - 5x -12 = 0.[/tex]

By comparing the General form of the quadratic equation we will get

a = 2, b = -5 and c = -12.

2x^2 - (8-3)x - 12 = 0.

2x^2 - 8x + 3x -12 = 0.

2x(x-4) + 3(x-4) = 0

(x - 4) (2x + 3) = 0.

x - 4 = 0 or 2x + 3  = 0

x = 4 or x = -3/2

Given Question is incomplete complete question here:

What are the solutions of the quadratic equation 2x^2-5x-12 =  0?

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Using Pythagoras theorem to solve the right angle triangle, the height of the building is 14.87 feet

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as an equation:

x² = y² + z²

where x is the hypothenuse and y, z are the legs of the right angle triangle.

To determine the height of the building in which the ladder will reach, we have to use Pythagoras theorem for that.

x² = y² + z²

15² = 2² + z²

z² = 15² - 2²

z² = 221

z = √221

z = 14.87 feet

The height is 14.87 feet

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the number of shirts has to be an integer (you can not sell "part" of a shirt) n >= 65

They need at least $1,150

They have already saved $700

They are selling shirts with a profit of $7.00 per shirt

If they sell n number of shirts, they will earn n times $7.00

Since they have already 700, they will earn a total of 700 + 7n

If this quantity has to be equal or greater to 1,150, we can write:

1150 <= 700 + 7n

if we solve this inequality for n:

1150 <= 700 + 7n

1150 - 700 <= 7n

450 <= 7n

450/7 <= n

64.28 <= n

Since the number of shirts has to be an integer (you can not sell "part" of a shirt)

n >= 65

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a) The average rate of change of a function over an interval is the change in the function's output (f(b) - f(a)) divided by the change in the function's input (b - a). So, to find the average rate of change of f over the interval -4 <= x <= 3, we can use the formula:

(f(3) - f(-4)) / (3 - (-4)) = (sqrt(25 - 9) - sqrt(25 - 16)) / (3 - (-4)) = (-2sqrt(7) + 4sqrt(3)) / 7

b) To find the derivative of f(x), we need to use the power rule and the chain rule. The power rule states that the derivative of x^n is nx^(n-1), and the chain rule states that the derivative of f(g(x)) is f'(g(x)) * g'(x).

So, the derivative of f(x) = sqrt 25 - x^2 is:

-2x

c) To find the equation of the line tangent to the graph of f at x = -3, we need to use the point-slope form of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line (which is f'(-3) = -6), (x1, y1) is the point on the graph where the line touches (which is (-3, f(-3)) = (-3, sqrt(25 - 9) = 2sqrt(7))

so we have: y - 2sqrt(7) = -6(x + 3)

d) To check if g(x) is continuous at x = -3, we need to check if the limit of g(x) as x approaches -3 exists and is equal to g(-3).

Since g(x) = f(x) for -5 <= x <= -3 and g(x) = x + 7 for -3 <= x <= 5, we have:

g(-3) = f(-3) = sqrt(25 - 9) = 2sqrt(7)

and the limit of g(x) as x approaches -3 is:

lim x->-3 g(x) = lim x->-3 (x + 7) = -3 + 7 = 4

Since g(-3) = 2sqrt(7) and lim x->-3 g(x) = 4, g(x) is not continuous at x = -3.

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The time taken by Wendy after she learned flying is m/4 minutes or 0.25m minutes.

We will solve this problem with the help of Percentages.

In the concept of percentages, we know that:

100% = 100/100 = 1

75% = 75/100 = 3/4

50% = 50/100 = 1/2

25% = 25/100 = 1/4

In our question, it is given that previously wendy took ‘m’ minutes to commute.

Now she reduced her daily commute by 75% after learning how to fly.

So, our new time = (100-75)% of previous time

= 25% of m minutes

= 25/100 of m minutes = ¼ of m minutes = m/4

So our final answer will be m/4 minutes or 0.25m minutes taken by wendy to commute now.

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Answer: 10.56 cups.

Step-by-step explanation:

1 liter = 4.22 cups; 1.5 liters = 6.34 cups; 2 liters = 8.45 cups; 2.5 liters = 10.56 cups.

Answer:

-2 i think hope this helps

Step-by-step explanation: