A piece of pipe that is 8 feet long is cut into 1/4 ft pieces. How many pieces can be cut from the pipe?

Responses

A 30 pieces

B 28 pieces

C 8 pieces

D 32 pieces

The features of the relation are given as follows:

1. Independent variable: number of weeks.

2. Dependent variable: money saved.

3. Yes, the relationship is linear.

4. The slope is of 40.

5. The domain is: {0, 1, 2, 3, 4, 5, 6, 7}.

6. The range is: {50, 90, 130, 170, 210, 250, 290, 330}.

7. The y-intercept is of $50.

8. The table has no x-intercept.

The output variable is a function of the input, hence the output is the dependent variable and the input is the independent variable.

The input and the output in this problem are given as follows:

In a linear relation, the rate of change of the output relative to the input is constant, and is called slope.

In the context of this problem, the money saved has a constant increase of $40 each week, hence:

The domain is the set containing the input values of the function, hence the number of weeks, as follows:

{0, 1, 2, 3, 4, 5, 6, 7}.

The range is the set containing the output values of the function, hence the money saved, as follows:

{50, 90, 130, 170, 210, 250, 290, 330}.

The y-intercept is the value of y when x = 0, hence, from the table, it is of:

y = 50.

The x-intercept is the value of x when y = 0. From the given table, y never assumes a value of 0, hence the function has no x-intercept.

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The number -32/95 belongs to the set of rational numbers.

Rational numbers may be defined as set of numbers which can be expressed in the form of p/q where q cannot be equal to zero. Irrational numbers may be defined as set of numbers which cannot be expressed in the form of p/q. Rational numbers can be of three types. Positive rational numbers are those in which either both the numerator and denominator are positive, or both are negative. Negative rational numbers are those in which either of numerator or denominator is negative. Zero is also a rational number which can be expressed in the form of p/q. Now, the number -32/95 is expressed in the form of p/q and the numerator is negative, so it is a negative rational number.

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The net worth of the landscaping company is given by:

$187.205.

The net worth of a company or of a person is given by the sum of all assets of the person subtracted by the sum of all debts of the person.

In the context of this problem, the assets, and it's values, of the company are given as follows:

Hence the sum of the assets is given by:

Assets = 48760 + 126790 + 32426 + 20700 + 15640 + 225678 = $469,994.

The debts of the company, with it's values, are given as follows:

Hence the sum of the debts is given by:

Debts = 76400 + 189429 + 16970 = $282,799.

Then the net worth of the company is:

Net worth = Assets - Debt = 469,994 - 282,799 = $187,205.

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2 hours Eugene needs to travel before they are 290 km apart.

Given,

Average speed of Adam = 65 km/h

The average speed of Eugene = 80 km/h

Both travel in the opposite direction

Solution:

Let x be hours taken.

S = d/t

65 x+  80 x = 290

145x = 290

x = 2 hr

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The full sentence relating to the function in the  tabulated data is;

"The x-intercept shows that if Ronald buys only apples, he can buy 12 pounds (lb). The y-intercept shows that if Ronald buys only eaches, he can buy 10 pounds (lbs). Hence the complete sentence."

It is to be noted that in mathematics, a function is an expression, rule, or law that describes the connection between one variable (the independent variable) and another variable (the dependent variable).

Tabular data has the following characteristics: They are made up of rows and columns. A table contains rows and columns and is used to organize everything tabular. Typically, sports statistics are provided in a tabular manner. A table is a type of graphic that arranges data into rows and columns. Tabular data is presented in a table format.

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David gets £2.50 Farooq gets the rest of the money. Let the total sum of the money be x is £8.75.

Therefore,

Let the total sum of the money be x,

David gets 1/6 of x = x/6 = £2.50

⇒ x/6 = £2.50

⇒ x = £2.50 x 6

⇒ x = £15

The total sum of the money = £15

Eva gets 1/4 of x = 1/4 x 15 = £3.75

Farooq gets the rest of the money = x - £3.75 - £2.50

= £15 - £3.75 - £2.50 = £8.75

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Considering the definition of an equation and the way to solve it, if there are 21 students in the club and the T-shirt order costs a total of $187, each T-shirt cost $7.

An equation in mathematics is defined as an equality established between two expressions in which known elements and unknowns or unknown values appear.

The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:

Being "x" the cost of each T-shirt, and knowing that:

the equation in this case is:

21x + 40= 187

Solving:

21x= 187 - 40

21x= 147

x= 147 ÷ 21

x=7

Finally, each T-shirt has a cost of $7.

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If The printing company charges a certain amount for each shirt plus a setup fee of 40$. 21 students in the club and the t-shirt order costs a total of $187,Then each t shirt cost 7.

Two or more expressions with an Equal sign is called as Equation.

Given that, The printing company charges a certain amount for each shirt plus a setup fee of 40$. 21 students in the club and the t-shirt order costs a total of $187,

We need to find how much money dose each t-shirt cost.

Let x be the money for each t shirt.

By given data let us form a equation.

21x + 40= 187

Subtract 40 from both sides

21x=187-40

21x=147

Divide both sides by 21

x=7

Hence the cost each t shirt is 7.

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a= 4

b= - 42

How the given expression is solved ?

[tex]2-\frac{x+2}{x-3} -\frac{x-6}{x+3} \\\\=\frac{2(x^{2} -9)-[(x+2)(x+3)]-[(x-6)(x-3)]}{x^{2} -9} \\\\=\frac{2x^{2} -18-x^{2} -5x-6-x^{2} +3x+6x-18}{x^{2} -9} \\\\=\frac{4x-42}{x^{2} -9}\\\\\text{This is of the form}, \frac{ax+b}{x^{2} -9}[/tex]

Thus, the value of integers a and b are :

a = 4 ; b =- 42

What are integers?

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To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

No, to simplify is to reduce anything to its most basic form without figuring out what the letter 'x' or other letters are. Finding the meaning of the 'x' or other letters is known as solving.

Overview. Making something simpler refers to making it simpler to do or comprehend. Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. We accomplish this by dividing the denominator and numerator by the highest possible number.

It has the same precise meaning. The phrase "expand the brackets" means the same thing as "multiply out the brackets," with the added indication that when we do so, we are multiplying everything inside by everything outside the brackets.

The answer for a is x

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[tex]n-2=10n+42\\n-10n=42+2\\-9n=44\\\frac{-9n}{-9} =\frac{44}{-9} \\n=-\frac{44}{9}[/tex]

Hope this helps.

The value of x is -3.

Given,

[tex]m \angle{DRS}= x+143 \\m \angle{QRS}= 167\\m \angle{QRD}= x+30[/tex]

[tex]m \angle{DRS} +m \angle{QRD} = m\angle{QRS}[/tex]

x+143+x+30 = 167

2x = 167-173

2x = -6

x = -3

We add the two angles in it to find the value of x.

What are angles?

When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.

Angles' Components

Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.

Arms: The angle's two sides are linked at a single end. The arms of an angle are OA and OB.

Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.

The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.

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Answer:

Step-by-step explanation:

Answer:

1. x = -4, y = -5

Chosen strategy was to substitute for y in the second equation since the first equation gives y in terms of x. This gives an equation in x which can be solved for x, then y can be found by substituting for x in the first equation

2.  x = -2, y = -3
Strategy used is to eliminate the x terms by simply adding the equations since the coefficients of x are the same but of opposite signs. Solve for y and use this value to solve for x by substituting in any one equation

3. x = -5, y = 6

Strategy used was to set the RHS of the equations equal to each other since both equations are  equations with y on the LHS. Solve for x then use this value to find y value

4. x = 0, y = 1

Strategy used was to get the y coefficients same but of opposite signs, add the two equations to eliminate the y term, solve for x and then solve for y by substituting x in one of the equations - in this case, the second equation

Step-by-step explanation:

Here is how I would answer this question. Remember there are multiple ways of solving a linear equation of two variables but looking at the equations and from experience, I have chosen the most efficient way (my opinion)

Q1.

y = x - 1     [1]
3x - 4y = 8  [2]

Since we are given y = x - 1 in Eq [1], an obvious strategy is to substitute for y in eqn [2]

=>  3x - 4y

=>  3x - 4(x-1)
=>  3x - 4x - 4(-1) =
=> 3x -4x + 4

=> -1x + 4

=> -x + 4

And we know that eqn [2] has 8 on the RHS

∴   -x + 4 = 8

Subtract 4 from both sides

-x + 4 - 4= 8 -4
-x = 4

Multiply by -1 both sides

x = -4

Substitute for x in equation [1] y = x - 1 to get
y = -4 - 1 = -5

Solution: x = -4, y = -5

Q2
3x + 2y = -12    [1}

-3x + 2y = 0     [2]

Here we can see the coefficients of x are the same but with opposite signs

Adding the two equations will eliminate the x terms and  allow us to solve for y which can be used then to solve for x

Adding [1] and [2] gives

3x + 2y + (-3x + 2y) = -12 + 0

4y = -12

y = -3

Substitute for y in equation [1]

=> 3x + 2(-3) = -12

=> 3x - 6 = -12

=> 3x = -12 + 6  (adding 6 on both sides

=> 3x = -6

x = -2

Solution x = -2, y = -3

Strategy used: Adding both equations to eliminate x terms since x coefficients are same but of different signs

Q3

y = 3x + 21  [1]

y = 2x + 16  ][2]

Since we have two expressions for y in terms of x, set the RHS of equations [1] and [2] to be equal and solve for x

=>  3x + 21 = 2x + 16

Subtract 2x from both sides

=> 3x - 2x  + 21 = 16

=> x + 21 = 16

Subtract 21 from both sides

x = 16 - 21  = -5

Substitute for x in equation [2]
y = 2x + 16

=> y =  2(-5) + 16

y = -10 + 16

y = 6

Solution: x = -5, y = 6

Q4

2x - 7y = -7   [1]

x + y = 1        [2]

We can make the coefficients of one of the variable in both equations the same and either add/subtract as necessary to eliminate one of the variable terms and solve for the other

Multiply [2] by 7 to get
7x + 7 y = 7   [3]

[1] and [3] have y coefficients same but of opposite signs so add [1] and [3] together

2x - 7y + (7x + 7y ) = - 7 + 7

2x + 7x - 7y + 7y = 0

9x = 0

x = 0

Sub for x in [2] x + y = 0 to get

0 + y = 1

or y = 1

Solution: x = 0, y = 1

Strategy used was to get the y coefficients same but of opposite signs, add the two equations to eliminate the y term, solve for x and then solve for y by substituting x in one of the equations - in this case, the second equation

The elevation of the hole after placing the bush in the hole is 93 feet

This is a problem from the unitary method. We can easily solve this problem by following a few steps.

Joel digs a hole at a rate of 35 feet every 10 minutes. So, we have to calculate the rate at 1 min.

Joel digs a hole at a rate of 35 feet every 10 minutes

Joel digs a hole at a rate of 35/10 feet every 1 minute

[ Work done for unit minute = Total work done / total time period ]

Now we have to calculate the total work done for 30 minutes.

For a unit minute work done is 35/10, then for 30 minutes the total work done is, (35/10 × 30 ) feet = 105 feet.

Joel places a bush in the hole that fills exactly 12 feet of the hole.

Therefore, the actual elevation is ( 105 feet - 12 feet ) = 93 feet.

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The titanium has a mass value of 563.75 grams

From the question, the given parameters are

Density of titanium = 4.51 g/cm^3

Volume of benzene = 125.0 cm^3

The mass of the titanium is then calculated using

Density = Mass/Volume

Make Mass the subject of the formula

So, we have

Mass = Volume  x Density

Substitute the known values in the above equation

So, we have the following equation

Mass =125.0 x 4.51

Evaluate the product in the equation

Mass = 563.75

Hence, the mass of the titanium is 563.75 grams

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The possible range of angle x is   x < 44

given data

In △ A B C , A B = 7 , B C = 12 , and m ∠ A B C = 82 ∘

In △ D E F , D E = 7 , E F = 12 and m ∠ D E F = ( 2 x − 6 ) ∘

A C > D F

Solution for angle x is gotten from the clue in A C > D F

This means that angle included by m ∠ A B C = 82 ∘ is greater than the angle included by m ∠ D E F = ( 2 x − 6 ) ∘

We therefore say that

82 ∘ >  ( 2 x − 6 ) ∘

82 + 6 > 2 x

88 > 2 x

divide both sides by 2

88 / 2 > 2 x / 2

44 > x

x < 44 degrees

Hence option g is the correct answer

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Check the picture below.

[tex]sin(31^o )=\cfrac{\stackrel{opposite}{11}}{\underset{hypotenuse}{x}}\implies x=\cfrac{11}{sin(31^o)}\implies {\Large \begin{array}{llll} x\approx 21.4 \end{array}}[/tex]

Make sure your calculator is in Degree mode.

The expansion of the given expressions of exponents are:

22. (b) a²· (a⁰)³ ÷ a¹¹ =  a⁻⁹

22. (f) {(a³a⁴)÷ a⁻³} /{a·((a²a)³)⁴} =  a⁻²⁷

Product rule for exponents state that product of two numbers with same base is given by adding their powers.

That is aⁿ × a ˣ = aⁿ⁺ˣ

Quotient rule for exponents state that the quotient of two numbers with same base is given by subtracting the exponent of denominator from numerator.

That is aⁿ ÷ a ˣ = aⁿ⁻ˣ

Power rule : (aⁿ)ˣ = aⁿˣ

22. (b) a²· (a⁰)³ ÷ a¹¹

       ⇒a²· (a⁰)³ ÷ a¹¹ = a².a⁰ ÷ a¹¹ (using power rule (a⁰)³ = a⁰)

     ⇒a²· (a⁰)³ ÷ a¹¹ =  a²⁺⁰ ÷ a¹¹  ( using product rule a².a⁰= a²⁺⁰ )

     ⇒a²· (a⁰)³ ÷ a¹¹ =  a²÷ a¹¹ = a²⁻¹¹ ( using quotient rule a²÷ a¹¹  =  a²⁻¹¹)

     ⇒a²· (a⁰)³ ÷ a¹¹ =  a⁻⁹

Therefore, expression  a²· (a⁰)³ ÷ a¹¹  is  a⁻⁹

- 22 .(f) {(a³a⁴)÷ a⁻³} /{a·((a²a)³)⁴}

            = {(a³⁺⁴)÷ a⁻³} /{a·((a²⁺¹)³)⁴}    ( using product rule, a³a⁴ = a³⁺⁴  and

                                                               a²a = a²⁺¹)

           ={a⁷÷ a⁻³} /{a·((a³)³)⁴}

          = {(a⁷⁻⁽⁻³⁾} /{a·(a³⁽³⁾)⁴}     ( using quotient rule a⁷÷ a⁻³ = a⁷⁻⁽⁻³⁾ and                                  

                                                   using power rule (a³)³ = a³⁽³⁾)

         =  {a¹⁰} /{a·(a⁹)⁴}  

         =  {a¹⁰} /{a·a³⁶}          ( using power rule (a⁹)⁴ = a⁹⁽⁴⁾ =a³⁶)

        =  {a¹⁰} / {a¹⁺³⁶}          ( using product rule a·a³⁶ = a¹⁺³⁶)

        = { a¹⁰} / {a³⁷}          

       =  a¹⁰ ⁻ ³⁷                  ( using quotient rule a¹⁰ ÷ a³⁷ = a¹⁰ ⁻ ³⁷  = a⁻²⁷)

       = a⁻²⁷

Therefore, expression  {(a³a⁴)÷ a⁻³} /{a·((a²a)³)⁴} is  a⁻²⁷.

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Answer:

the answer is a^-27

Step-by-step explanation:

The value of (f-g)x is x²-2x+2. Therefore, option C is the correct answer.

The given functions are f(x)=x²+1 and g(x)=2x-1.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

We need to find the value of (f-g)(x).

Now, f(x)-g(x)= (f-g)(x)

=x²+1 -(2x-1)

=x²+1-2x+1

=x²-2x+2

The value of (f-g)x is x²-2x+2. Therefore, option C is the correct answer.

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Answer:

15/100×400=60

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

son 60 porque

400/10=40 entonces 40=10% entonces 5% es 20

40+20=60

The actual speed (along the road) of the red car is 81.6 feet per second

What is Pythagoras' theorem?

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem.

Refer to the figure attached.

[tex]z^2=y^2+40^2[/tex]

[tex]z^2=y^2+1600[/tex]

Differentiate with respect to time 't'

[tex]D(z^2)=D(y^2)+D(1600)[/tex]

[tex]2zD(z)=2yD(y)+0[/tex]

[tex]zD(z)=yD(y)[/tex]

Now, y=200,    [tex]z^2=200^2+40^2[/tex] , [tex]z^2=41600[/tex],  [tex]z=203.96[/tex]

D(z)=80.

Substitute the known values into the equation below:

[tex]zD(z)=yD(y)[/tex]

(203.96)(80)=200 D(y)

On simplifying, D(y)=81.6  feet per second

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The actual speed (along the road) of the red car is 81.6 feet per second

What is Pythagoras' theorem?

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' theorem.

Refer to the figure attached.

[tex]z^2=y^2+40^2[/tex]

[tex]z^2=y^2+1600[/tex]

Differentiate with respect to time 't'

[tex]D(z^2)=D(y^2)+D(1600)[/tex]

[tex]2zD(z)=2yD(y)+0[/tex]

[tex]zD(z)=yD(y)[/tex]

Now, y=200,   [tex]z^2=200^2+40^2, z^2=41600,z=203.96[/tex]  

D(z)=80.

Substitute the known values into the equation below:

zD(z)=yD(y)

(203.96)(80)=200 D(y)

On simplifying, D(y)=81.6  feet per second

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Answer:

How do I take 20 % off a price?

Take the original price.

Divide the original price by 5.

Alternatively, divide the original price by 100 and multiply it by 20.

Subtract this new number from the original one.

The number you calculated is the discounted value.

Enjoy your savings!

Step-by-step explanation:

Answer:

6.3

Step-by-step explanation:

Problem

Solution

For this case we can do the following:

We also know that :

Using this property we got:

Now we can distirbute the terms and we got:

4+7i -8 -36 i

And distributing the terms we got:

(7-36)i +(4-8)

-29 i -4

And then our solution would be:

a= -29

b= -4

The distance between you and your friend is changing at the rate of 28 miles per hour after you travel 3 miles.

According to situation,

You are going in east direction with a rate of 16miles per hour and your friend is going towards 12 miles per hour at the rate of 12 miles per hours.

Let us say you cover L distance in east direction and your friend covers B distance in north direction,

Time taken by you to cover 3miles,

Time = Distance L/speed

time = 3/16 hours.

Distance B covered by friend in 3/16 hours,

distance B = speed x time

Distance B = 3/16 x 12

Distance B = 9/4 miles.

As both are going perpendicular to each other,

The distance between you and your friend X can be calculated by the Pythagoras theorem,

X² = L² + B²

Differentiating with respect to time t,

2dX/dt = 2(L)dL/dt + 2(B)dB/dt

As we know,

dL/dt = 16 miles/hour and,

dB/dt = 12 miles/hour,

L = 3 miles,

B = 9/4 miles.

Putting all the values,

2dX/dt = 2(3)(16) + 2(9/4)(12)

dX/dt = 48 + 27

dX/dt = 75 miles per hour.

The distance between you and your friend will change at the rate of 75 miles/hour.

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The most appropriate choice for equation of line in slope intercept form will be given by-

Rate of change is 8 and rate of change represents slope of the line

What is equation of line in slope intercept form?

Equation of line in slope intercept form is written as y = mx +c

m is the slope of the line and c is the y intercept of the line.

The distance between the origin and the point where the line cuts the x axis is the x intercept

The distance between the origin and the point where the line cuts the y axis is the y intercept

Here,

Let the number of classes be x

Total cost of classes = y

Let the equation of line be y = mx + c

Three classes cost $36

Putting x = 3, y = 36

36 = 3x + c .............. (1)

Seven classes cost $68

Putting x = 7, y = 68

68 = 7x + c ............... (2)

Subtracting equation (2) from (1),

4x = 32

[tex]x = \frac{32}{4}[/tex]

x = 8

Putting the value of x in (1)

[tex]3 \times 8 + c = 36\\24 + c = 36\\c = 36 - 24\\c = 12[/tex]

Equation of line is y = 8x + 12

Now coefficient of x in y = mx  + c is the slope of the line and that is the rate of change

so, rate of change is 8 and rate of change represents slope of the line.

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Answer:

Step-by-step explanation:

Given school costs of $36 for 3 classes and $68 for 7 classes, you want to know the rate of change and its meaning.

The "rate of change" in this context is the change in cost for one additional class. It can be found by ...

  rate of change = (change in classes) / (change in cost)

  rate of change = ($68 -$36)/(7 classes -3 classes) = $32/(4 classes)

  rate of change = $8/class

This "rate of change" is the additional cost for the addition of one class. It is the cost per class.

-4 is the numerical value of x which forms part of the coordinates of the points with a slope of -1/4.

Slope is simply expressed as change in y over the change in x.

It is expressed as;

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1( x, 4 )

Point 2( 20, -2 )

To determine the value of x, plug the slope m, x and y values into the slope formula.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

-1/4 = ( -2 - 4 )/( 20 - x )

-1/4 = ( -6 )/( 20 - x )

Cross multiply

-1( 20 - x ) = 4( -6 )

-20 + x = -24

x = -24  + 20

x = -4

Therefore, the numerical value of x is -4.

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The machine make nails at a rate of 8th pounds per hour

From the question, the given parameters are:

The rate in pounds per hour the machine make nails is then calculated as

Rate of making nails = Amount of pounds of nail/Number of time

Substitute the known values in the above equation

So, we have

Rate of making nails = 4th pounds/0.5 hour

Evaluate

Rate of making nails = 8th pounds per hour

Hence, the rate of making nails is 8th pounds per hour

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Answer:

Answer down below!

Step-by-step explanation:

Lets find a point on the graph that we can easily point out to start this problem

We can use the point (0,-3)

From there, we use rise/run to find our answer!

We go up 1 and over 1

Thus, our slope is 1!

Answer:

1

Step-by-step explanation:

slope = rise/run

choose any two points in the graph and count the left/right and up/down to get to that point it's hard to explain u can watch a yt video to completely understand

Answer: 35 = a number

Step-by-step explanation: okay so since the number is being decreased wd know that that is subtraction. so what minus 8=27? well how about we add those two numbers to get the whole? so whats 8+27? 35. Hope this helped

Answer:

Step-by-step explanation:

35