Identity the property of equality that was used for each step

Addition property

Subtraction property

Multiplication property

Division property

Transitive property

Symmetric property

Substitution property

Reflexive property

Distributive property

Step-by-step explanation:

(x + 3) × -7 = -7x - 7×3 = -7x - 21

He has to climb UP 40 feet

Step-by-step explanation:

Answer:

Dinner should cost 250 today.

Step-by-step explanation:

Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

A wheat farmer plows 5 acres of land and collects 135 bushels of wheat

The next day, the farmer plows 8 acres of land and collects 216 bushels of wheat.

Let us create a equation

Bushels/Acres

For first day:

Number of bushels of wheat=135

Number of acres of land=5

135/5=27

Next day:

Number of bushels of wheat=216

Number of acres of land=8

216/8=27

The proportional relation between 1st day and next day is same. It is proportional because the farmer collected 27 bushels for every 1 acre plowed.  

Hence, Yes, it is proportional because the farmer collected 27 bushels for every 1 acre plowed.

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The value of (fоg)(3) = 134.

What is composition of functions?

A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

Consider, the given functions

f(x) = 3x - 1, g(x) = 4x^2 + 9

First to find f(g(x)).

Let,

f(g(x)) = 3(4x^2 + 9) - 1

         = 12x^2 + 27 - 1

f(g(x)) = 12x^2 + 26

Now, to find f(g(3)).

Plug x = 3 in the above equation,

f(g(3)) = 12(3)^2 + 26

         = 12(9) + 26

f(g(3)) = 134

Hence, (fоg)(3) = 134.

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The additive inverse of the matrix A is [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]

From the question, the matrix is given as

[tex]\left[\begin{array}{cc}0&-2&-3&-5\end{array}\right][/tex]

This matrix is given as matrix A

So, we have the following representation

A = [tex]\left[\begin{array}{cc}0&-2&-3&-5\end{array}\right][/tex]

Next, we calculate the required matrix operation

The matrix operation is given as additive inverse of the matrix

This additive inverse of the matrix is calculated by negating each element present in the matrix

i.e. if an element in the matrix is a, the inverse would be -a

Using the above highlights as a guide, we have the following representations

Additive inverse = [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]

Hence, the additive inverse is [tex]\left[\begin{array}{cc}0&2&3&5\end{array}\right][/tex]

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The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9

The equation of the function is given as

f(x) = 3x²

Also, we have

Vertex = (5, 9)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (5, 9)

Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 5)² + 9

This also means that

f(x) = -3(x - 5)² + 9

The -3 is gotten from f(x) = -3x²

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

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The negative amortization at the end of year 1 is $2536.50

For the year 1 there will be still 12% rate of interest going on. There is a negative balance of $200 after payment of 1st month installment.

Thus negative amortization = FV(0.01x12 - 200)

Here 0.01 is the interest per month, 12 is the number of months in a year and -200 is the negative balance in first month

negative amortization = FV(0.01x12 - 200)

The negative amortization at the end of year 1 = $2536.50

The negative amortization at the end of year 5

The loan balance at the end of year 4 = FV(0.13x12x36x800 - 102536)

The loan balance at the end of year 4 = $16132.46

The negative amortization at the end of year 1 is $2536.50

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2089.17 rounded off to nearest tenths(1 decimal place) is 2089.2

2089.17 rounded off to the nearest one is 2089

When you "round to the nearest _____" regardless of what is in the blank the steps are nearly always the same:

Identify which place value you are rounding off a number. The smaller the place value, the more accurate the final result shall be.

Find the next smallest place value, the digit to the right of the place value you're rounding off to. For example, if you want to round to the nearest ten you would have to find the number at the one's place.

If the digit in the next smallest place value is less than five (0, 1, 2, 3, or 4), you leave the digit you want to round off. Any digits after that number become zeros, or drop-offs if they're located after the decimal point. This is called rounding down a number or a sequence of numbers.

If the smallest place value is greater than or equal to five (5, 6, 7, 8, or 9), you increase the value of the digit you're rounding off to by one place (+1). Any remaining digits before the decimal point become zeroes, and any digits that are after the decimal point are dropped. This is called rounding up of numbers.

For example, for rounding off a number 838.274, depending on which place value you'll round to, the final rounded-off answer will vary. Rounding off 838.274:

Rounding off the nearest hundred is 800

Rounding off the nearest ten is 840

Rounding off the nearest one is 838

Rounding off the nearest tenth is 838.3

Rounding off the nearest hundredth is 838.27

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Answer:

Take a look at the attachment...

Hope this helps! :)

1 hour 30 minutes take her to do her homework if she has 30 pages to read and 45 math problems to complete.

What is Unitary Method?

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Karen can read 10 pages and complete 15 math problems in 30 minutes.

So, if she reads 30 pages which is 3 times of 10.

Also, solve 45 maths problem which is 3 times of 15.

So, the time taken to complete 30 pages to read and 45 math problem

= 30 x 3

= 90 minutes

= 1 hour 30 minutes

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Solutions for the given equalities:

m < - 2

y > 5

b > -4

What is inequality in mathematics?

An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.

The given inequalities are

1)              m - 1 < -3

     Adding 3 on both sides, we get

              m - 1 + 3 < -3 + 3

                m + 2 < 0

     Subtracting 2 from both the side, we get

                m + 2 - 2 < 0 - 2

                m < - 2

The graph of this inequality is shown below

2)             -4y < -20

      Dividing by -4, we get

              y > 5

The graph of this inequality is shown below

3)       5 + b > 1

     Subtracting 1 from both the side, we get

            b + 4 > 0

             b > -4

The graph of this inequality is shown below

4)      y = -18

This is a point on a number line, and it can be shown as

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If the number of nickels in a piggy bank is 1 less than twice that of dimes and the total value of the coins is at least $4.35, then the smallest possible number of Nickels and Dimes is 43 and 22, respectively.

As per the question statement, The number of nickels in Bart's piggy bank is 1 less than twice the number of dimes, and the total value of the coins in this piggy bank is at least $4.35,

Then, we are required to determine the smallest possible number of individual coins in the bank.

To answer this question, first we will need to know the monetary values of nickels and dimes, that is,

(1 dime = 10 cents = $0.1), and (1 Nickel = 5 cents = $0.05).

Now let us assume that, there are "x" nickels and "y" dimes in that bank, Then as per the condition that, the number of nickels in Bart's piggy bank is 1 less than twice the number of dimes, we can write an equation with the above assumed two variables, which is, [x = (2y - 1)]...(i)

And as per the other condition that, the total value of the coins in this piggy bank is at least $4.35, we can write another equation, which is,

[(0.1y + 0.05x) = 4.35]

Or, [100(0.1y + 0.05x) = (100 * 4.35)]

Or, [(10y + 5x) = 435]...(ii)

Now substituting eqn (i) in eqn (ii), we get,

[{10y + 5(2y - 1)} = 435]

Or, [(10y + 10y - 5) = 435]

Or, [(10y + 10y) = (435 + 5)]

Or, (20y = 440)

Or, [y = (440/20)]

Or, (y = 22)

Therefore, [x = {(2 * 22) - 1}]

Or, [x = (44 - 1)]

Or, [x = 43]

That is, If the number of nickels in a piggy bank is 1 less than twice that of dimes and the total value of the coins is at least $4.35, then the smallest possible number of Nickels and Dimes is 43 and 22, respectively.

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Graph will shift from(0,0) to (3,4) after the shifting happens due to change in expressions of the parent function.

Graph transformation is the process by which an parent graph, or graphed equation, is changed to produce a variation of the proceeding graph. It's a common type of problem in algebra, specifically the modification in algebraic equations.

The deduced parent function is [tex]\sqrt{x}[/tex]

So, Domain= (0 , ∞)

     Range= (0 , ∞)

Let us take (0,0) as the point and see the shifting of the point with respect to (0,0).

So when function is transformed to √x+3

Function shift from (0,0) to (3,0)

and when function is transformed to [tex]\sqrt{x+3} +4[/tex]

then point shifts to (3,4).

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According to the central limit theorem, the standard deviation of the sample means is a) less than the population standard deviation.

According to the central limit theorem, as long as the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution of the mean will be normal regardless of whether the population has a normal, Poisson, binomial, or other distribution.

The sample means' standard deviation (also known as the standard error of the mean) will be less than the population standard deviation and equal to the population standard deviation divided by the square root of the sample size.

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Using equations, to raise the maximum amount of money, 160 adults and 80 students should attend the theater program on drinking and driving.

An equation is a mathematical statement of the equality of two or more mathematical expressions, using the equation symbol (=).

In this situation, we form a system of equations, to show the maximum number of adults and students allowed for the program.

We also form an objective constraint of inequality to show the limit of the allowed number of people for the program.

Admission fee for adults = $2.00

Admission fee for students = $1.00

The total number allowed in the theater = 240 persons

The ratio of adults to students = 2:1

The sum of ratios is 3

The number of adults = 2x, where, the number of students = x.

2x + x = 240 ... Equation 1

3x ≤ 240 ... Equation 2

If 3x = 240

x = 80

Check:

3x ≤ 240

3(80) ≤ 240

240 = 240

Adults = 160 (2 x 80)

Students = 80 (1 x 80), which meet the second requirement or constraint.

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The probability of choosing a box and picking two quarter coins in a row is 1/108

Probability is the branch concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1. 0 indicates impossibility of the event and 1 indicates certainty.

Probability= sample space / total possible outcome

therefore probability of choosing two quarters in a row = 1/6×1/6= 1/36

The probability of choosing the first box =1/3

Therefore the probability of choosing the first box and picking two quarters In a row is 1/36×1/3= 1/108.

Since box two contain no quarter and box three has only one quarter , the probability of choosing two quarters in a row is 0.

Therefore the probability of choosing a box at random and picking two quarters in a row is 1/108.

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Answer The sequence {an = (−a)n}

Step-by-step explanation:  The sequence {an = (−a)n} is bounded below by −1 and bounded above by 1, and so is bounded. This sequence does not converge, though; since |an − an+1| = 2 for all n, this sequence fails the Cauchy criterion, and hence diverges.

The pressure that would be required to have a flow rate of 62 gal/min is f=86.25

The velocity of the stream is exactly proportional to nozzle pressure. In the given scenario, instead of a stream moving at 80 mph through the fire's super-heated gases, it moves at 60 mph.

The velocity increases as the pressure decreases in a convergent nozzle, but we know that pressure is inversely related to area.

The following formula can be used to compute the flow rate for a given nozzle. Q represents the flow rate. K = Nozzle K factor. P = Nozzle pressure differential. n = Is a constant that is determined by the type of spray pattern.

Given equation is,

f = √120p

Here p denotes the nozzle pressure in pounds per square inch

Also given that p=62 gal/min

f = √120p

Then,

f= √120(62)

f=√7440

f= 86.25

The pressure that would be required to have a flow rate of 62 gal/min is f=86.25

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Answer:

slope = 16/13, increasing

Step-by-step explanation:

solve for the slope

-1.2-(-2.8)/(6.4-5.1)

= 16/13

it's positive meaning it's increasing

1

Step-by-step explanation:

28-28=1 11111111111111111111111111

It will take 12 hours for 15 men to do same job.

How to determine this?

When amount of hour ∝ 1/number of men

When H represent Hour

And M represent the number of men

k to represent the constant

H = k/M as it is inversely proportional

It takes 10 men 18 hours to repair a road

18 = k/10

k = 18 × 10

k = 180

How long will it take 15 men?

When k = 180

H = k/M

H = 180/15

H = 12 hours

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Answer:

Step-by-step explanation: The equation for slope-intercept is y=mx+b

m= slope of the equation, b= y-intercept(what y is when x is zero)

there for the equation is y=5x-5

The actual price of an item is $1371.49.

Given that, the discount percentage is 12.5% and the selling price is $1200.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Let the actual price be x.

Now, x-12.5% of x =1200

⇒ x- 12.5/100 ×x=1200

⇒ x- 0.125x=1200

⇒ 0.875x=1200

⇒ x=1200/0.875

⇒ x=$1371.49

Therefore, the actual price of an item is $1371.49.

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Answer:

Tens:11,410

Ten thousand :10,000

Hundred : 11,400

If water flows into the container at a constant rate of 6 cubic feet per minute, the rate at which the water level rising when the height of the water is 5 feet is; 0.688 ft/min

When we are given an equation that gives the relationship between two or more variables, then by differentiating the equation with respect to time would give us a new equation that involves the rate of change of each of the given variables.

We are given the dimensions of the tank as;

Radius; r = 4 feet

Height; h = 12 feet.

The water in the tank will also have a conical shape.

By similar triangles, we know that;

r/h = 4/12

r = h/3

Now the volume of the water is;

V = ¹/₃πr²h

Put h/3 for r in this volume equation to get;

V = ¹/₃π(h/3)²h

V = (1/27)πh³

Differentiating with respect to time gives;

dV/dt = (3/27)πh²(dh/dt)

We are given;

dV/dt = 6 cubic feet per minute

h = 5

Thus;

6 = (3/27)π(5²)(dh/dt)

dh/dt = 0.688 ft/min

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The decimal that represents the number 4×1+1×1/100+9×1/1000 is given as follows:

4.0119.

A fraction is represented by the division of a term x by a term y, such as in the equation presented as follows:

Fraction = x/y.

The terms that represent x and y are listed as follows:

In this problem, we are given two fractions, and their decimal equivalents are given as follows:

Hence the numeric value of the expression is given as follows:

4×1+1×1/100+9×1/1000 = 4 + 0.01 + 0.0019 = 4.0119.

Which is the decimal number represented by the fraction.

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The word sentence which is used to represent the given inequality

p ≥ 8.9 is a number is at least as large as 8.9.

As given in the question,

Given inequality is equal to :

p ≥ 8.9

In the given inequality sign of greater than and equals to is used.

Explanation for the given word sentences:

Meaning of at least is minimum this much.

At least as large means ( ≥) greater than or equal to

Option is correct.

It represents the symbol (≤ )less than or equal to.

Incorrect option.

It represents the symbol of > greater than only.

Incorrect option.

Therefore, the word sentence which is used to represent the given inequality p ≥ 8.9 is a number is at least as large as 8.9.

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Answer:

Step-by-step explanation:

................ x2