if the federal debt is $24 trillion, and if this debt were divided equally among 300 million people, then how much would each person owe? describe how to estimate mentally the answer to the federal debt problem, and explain briefly why your strategy makes sense.

To solve for x, the equation -fx -g = h is correctly rewritten as x = -h/f - g/f.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given the equation in the question;

-fx - g = h

Solve for x.

To solve for x simply means to make x the subject of the formula or equation.

-fx - g = h

Add g to both side

-fx - g + g = h + g

Negative g and positive g cancels out.

-fx = h + g

Now, divide each term in the equation by the coefficient of x

-fx/-f = h/-f + g/-f

x = -h/f + (-g/f)

x = -h/f - g/f

Therefore, to solve for x, the equation -fx -g = h is correctly rewritten as x = -h/f - g/f.

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The equation describes the relationship between the tangent and secant line segments will be PR · PB = PQ². Then the correct option is B.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The combination of the measurements of the secant section and its outside secant segment is approximately the square of the length of the tangent segment if a tangent section and a secant section are drawn to a circular from an exterior endpoint.

The segment PQ is tangent to the circle at point Q.

The equation describes the relationship between the tangent and secant line segments will be PR · PB = PQ². Then the correct option is B.

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Answer:

31°

Step-by-step explanation:

A bisector splits an angle into two congruent parts.

16,384,000 more people resided in Tokyo

Tokyo population = 34,450,000

Mexico Population = 18,066,000

To find how many more people resided in Tokyo, we subtract =

34,450,000 - 18,066,000 = 16,384,000

What is a good budget for an apartment?

One popular rule of thumb is the 30% rule, which says to spend around 30% of your gross income on rent. So if you earn $2,800 per month before taxes, you should spend about $840 per month on rent.

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All the given options are correct

The variation expression is given as

(2x + 3y) ∝ (x + 5y)

Rewrite as an equation

So, we have

(2x + 3y) = k(x + 5y)

Remove the brackets

So, we have

2x + 3y = kx + 5ky

Collect the like terms

So, we have

kx - 2x = 3y - 5ky

This gives

x(k - 2) = y(3 - 5k)

Divide by both sides by y(k - 2)

x/y = (5k - 3)/(2 - k) --- option (a)

Multiply both sides by y

x = y(5k - 3)/(2 - k) --- option (b)

Express x/y = (5k - 3)/(2 - k) as ratio

x : y = (5k - 3) : (2 - k) --- option (c)

Hence, all the given options are correct

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Answer:

A; x= 8

B; x= -5

C; x= -12

Step-by-step explanation:

a =>  (7x-1)+(15x+5) = 180

22x +4 = 180

22x = 176

x= 8

b=> (x+135)= 130

x= -5

c=> x+60=48

x= -12

The two triangles are congruent because each transformation is a rigid motion. Therefore, option B is the correct answer.

Given that, triangle ABC is reflected in the x-axis, rotated 180°, and translated 2 units to the right and 4 units down to form triangle XYZ.

Reflection is flipping an object across a line without changing its size or shape. Rotation is rotating an object about a fixed point without changing its size or shape. The translation is sliding a figure in any direction without changing its size, shape or orientation.

We know that reflection, rotation and translation in the vertical or horizontal direction are rigid motions.

Rigid motions do not change the size of a polygon so that the two polygons are congruent.

The two triangles are congruent because each transformation is a rigid motion. Therefore, option B is the correct answer.

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Answer:

unfortunately no

Step-by-step explanation:

with ± (plus-minus) sign, you have to work out the two cases.Therefore there're two solutions for this question i.e

[tex]x = \dfrac{ \pm4i}{-2} \implies x _{1} = \dfrac{4i}{-2} \: \: \text{and} \: \: x _{2} = \dfrac{ - 4i}{-2}[/tex]

and this simplifies to [tex]x_1=-2i,x_2=2i[/tex]

We write 5.14*10^5 to convert from 5.14*10^5.

What is scientific notation?

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In the home run derby competition the percent of hits that were home run is: 25.8%

Information about the problem:

To solve this exercise we have to apply the percentage formula:

hits were home (%) = (home runs/ hits) * 100

hits were home (%) = (32/ 124) * 100

hits were home (%) = 0.2580 * 100

hits were home (%) = 25.8%

Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.

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My possible absolute value is -3 ≤ lx - 2l ≤ 3

What is Absolute Value?

The absolute value (or modulus) l x l of a real number x is the non - negative value of x without regard to its sign. For example, the absolute value of 5 is 5 , and the absolute value of -5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.

Now, the question is:

what is a possible absolute value inequality to represent -1≤x≤5

The representation of inequality -1≤x≤5 of  absolute value will be :

-3 ≤ lx - 2l ≤ 3

Now, add 2 to each segment of the system of inequalities to solve for x while keeping the equation  balanced:

-3 + 2 ≤ x -2 + 2 ≤ 3+2

-1 ≤ x ≤ 5

Hence, my possible absolute value is -3 ≤ lx - 2l ≤ 3

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The relation of Kathy that is not a function is: A. {(1, 10), (2, 20), (3, 30)}.

A relation is not a function if there are more than one y-value (range element) that is assigned to one x-value (domain element).

In the first relation, the x-value 1, has three different y-values, 10, 20 , and 30.

However, In the second, third, and fourth relations, each of the x-values has exactly one y-value that corresponds to it. These are all relations that represent functions except the relation in A.

Therefore, the relation of Kathy that is not a function is: A. {(1, 10), (2, 20), (3, 30)}.

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Answer:

Without being able to measure it, it looks like the first on is 45 degrees and the second one is 90 degrees.

Step-by-step explanation:

Do you have a protractor that you can measure them with?

Greetings from Brasil...

Let Ca be the function for Plan A and Cb the function for Plan B.

According to the problem statement, we can conclude that:

where C is the cost and n is the number of videos

Cost that the user will pay for having watched n videos

Ca = cost of Plan A

Cb = cost of Plan B

Is there any point (n) that Ca will be equal to Cb??? Let's equate the functions to check if there is a common point and if there is, what would it be.

Ca = Cb

3n + 8 = 5n

2n = 8

n = 4

In n = 4 we have a condition for the cost that does not matter Ca or Cb.

I will present 2 ways to solve:

1 - building the graph of the functions and observing the points where the Y axis (cost axis) its smaller

2 - assigning 2 points - below n = 4 and above n = 4 - to observe the cost behavior

1 - see attachment

2 - let's choose the points n = 1 and n = 10 (as already said, n=4 does not matter Ca or Cb - meeting point / intersection point)

n = 1

Ca(1) = 3.1 + 8 = 11

Cb(1) = 5.1 = 5

Ca > Cb, then Cb better to the user

n = 10

Ca(10) = 3.10 + 8 = 38

Cb(10) = 5.10 = 50

Ca < Cb, then Ca better to the user

We can come to the following conclusion:

0 < n < 4 → better use Plan B (in this interval the cost to the user will be lower with Plan B)

n = 4 → It doesn't matter to use Plan A or Plan B.

n > 4 → better use Plan A (for n above 4 the cost to the user will be lower with Plan A)

The gathering of x-values determines domain the symbols so one can entire the inequality for the desired area.

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The cost percentage is 3.61 %.

A cost is the worth of money that has been expended in the production or delivery of a good or service and is therefore no longer accessible for use in accounting, retail, research, or accounting.

A percentage is calculated by dividing a value or a number by its sum, then multiplying the result by 100. The percentage calculation formula is ( value / total value) × 100%.

The cost of all ingredients mixed in the stew is $2.76.

The total sales is $435.98.

57 gallons of stew are sold per week.

Therefore, the total sales per week is

= $2.76 × 57 = $157.32

Hence, the cost percentage of food is:

= ( 2.76 × 57 ) / 435.98

= 157.32 / 435.98

= 0.361

= 3.61 %

The cost percentage of the food is 3.61 %.

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There are six slots; first three for letters and the next three for numerals. Each of the slots for letters can be filled in 26 ways; and, each of the slots for numerals can be filled in 9 ways.

Therefore, possible number of license plates = (26 * 26 * 26 * 9 * 9 * 9) = (26^3) * (9^3) = 17576 * 729 = 12812904.

In order to calculate the probability of a compound event A, we use a technique we refer to as "The Slot Method," in which we first calculate the total number of outcomes, n(S), and the total number of successful outcomes, n(A), and then use slots for each of the independent or dependent events that make up the compound event.

In every game you play at a casino, the odds are stacked against you. The chances of winning the top prize when using the maximum coin play range from one in 5,000 to one in approximately 34 million, making slot machine odds some of the worst.

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The approximate radius of the cylinder  is 4.5m

The formula for calculating the surface area of cylinder is expressed as:

SA = 2πr(r+h)

where

r is the radius

h is the height

Given the following parameters

SA = 221.1 square meters

height = 7.8m

Substitute

221.1= 2(3.14)r(r+7.8)

221.1 = 6.28r^2 + 15.6r

Factorize to have

6.28r^2 + 15.6r - 221.6 = 0

On factoring, the value of the radius is 4.5 meters

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Answer:

the answer is A

Step-by-step explanation:

I hope it helps you

Based on the segment addition postulate, we have:

19. AB = 11

20. BD = 43

21. CY = 33

22. CD = 32

23. XC = 11

24. CZ = 44

25. ST = 24

26. AC = 20

Given the following:

AB = BC = CX = YZ

AD = 54

XY = 22

XZ = 33

Applying the segment addition postulate, we would have the following:

19. AB = YZ

YZ = XZ - XY

Substitute

YZ = 33 - 22

YZ = 11

AB = YZ = 11

AB = 11

20. BD = AD - AB

Substitute

BD = 54 - 11

BD = 43

21. CY = XY + CX

CX = AB = 11

Substitute

CY = 22 + 11

CY = 33

22. CD = AD - 2(AB)

CD = 54 - 2(11)

CD = 32

23. XC = AB = 11

XC = 11

24. CZ = CX + XY + YZ

CZ = 11 + 22 + 11

CZ = 44

25. 4x + 12x = 32 [segment addition postulate]

16x = 32

x = 2

ST = 12x = 12(2)

ST = 24

26. 14 + 3x - 4 = 4x + 4 [segment addition postulate]

10 + 3x = 4x + 4

10 - 4 = 4x - 3x

6 = x

x = 6

AC = 4x + 4 = 4(6) - 4

AC = 20

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The result of the given expression is-

[tex]2^3\left(x-\frac{3}{2}\right)^6[/tex]

The amount of times a quantity is multiplied is referred to as its exponent. Power is defined as a number multiplied by itself a certain number of times.

The number that a number is raised in order to define its power as an entire expression is known as its exponent.

Now, consider the following exponent rule;

[tex](x y)^m=x^m y^n, x^{m+n}=x^m x^n, \text { and } \frac{1}{x^n}=x^{-n}[/tex]

Now, according to the question, the given expression is;

[tex]\frac{(2 x-3)^6}{8}[/tex]

Taking 2 common from the numerator;

[tex]\frac{\left[2\left(x-\frac{3}{2}\right)\right]^6}{8}[/tex]

Now, apply the given exponent rule [tex](a b)^m=a^m b^m[/tex] in the above equation.

[tex]\frac{\left[2\left(x-\frac{3}{2}\right)\right]^6}{8}=\frac{2^6\left(x-\frac{3}{2}\right)^6}{8}[/tex]

Apply [tex]a^{m+n}=a^m a^n[/tex] in the above result.

[tex]\begin{aligned}\frac{2^6\left(x-\frac{3}{2}\right)^6}{8} &=\frac{2^{(3+3)}\left(x-\frac{3}{2}\right)^6}{8} \\&=\frac{2^3 \cdot 2^3\left(x-\frac{3}{2}\right)^6}{8} \\&=\frac{8 \cdot 2^3\left(x-\frac{3}{2}\right)^6}{8} \\&=2^3\left(x-\frac{3}{2}\right)^6\end{aligned}[/tex]

Therefore, the simplified form of the given expression is [tex]2^3\left(x-\frac{3}{2}\right)^6[/tex].

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-

The complete question is-

Separate the coefficient from the variable in each expression and write the variable with a negative exponent if it was originally in the denominator.

[tex]\frac{(2 x-3)^6}{8}[/tex]

The exact trigonometric ratios for the angle x is second quadrant.

Given Radian equals to θ = 27π / 4, we need to find all the Trigonometric ratios for the same -

Lets calculate the value of θ first.

We know π equals 180 degree angle and 2π equals 360 degree, hence with each 2π the radian moves back to zero degree. Which means

θ = 27π / 4 can be reduced to θ = 3π / 4

Hence θ = 135 degree which can be represented as below -

As This lies in second quadrant, hence  on x-axis (Value of base , needs to be taken as -1)

sin θ = 1/√2                            cosec θ = √2

cos θ = -1/√2                          sec θ = - √2

tan θ = -1                               cot θ = - 1

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

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Answer:

Step-by-step explanation: The answer is B

The mass of 7m chain = 7 x 2.16 kg = 15.12 kg

It says that 7m of grade 70 tow chain which has a diameter of 3/8'' is required to tow a car.

So length of the chain = 7m

Now given that the weight of the chain = 2.16kg/m

That is weight of 1m of chain = 2.16 kg = mass of 1m of chain

Here, weight corresponds to the mass itself, since both has the same unit 'kilograms(kg)'.

So to find the mass of 7m chain, we need to multiply mass of 1m chain to the length of the chain.

Thus, the mass of 7m chain = 7 x 2.16 kg = 15.12 kg

The question is incomplete. Find the complete question here:

Suppose you need 7m of grade 70 tow chain, which has a diameter of 3/8'' and weighs 2.16kg/m, to tow a car. How would you calculate the mass of this much chain? set the math up. but don't do any of it. just leave your answer as a math expression. also, be sure your answer includes all the correct unit symbols.

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Answer:

y = -3

Step-by-step explanation:

We are given an equation of the line, x=9.

And we want to write another equation of the line that is perpendicular to x=9 and passes through (-6, -3).

There are 3 ways to write the equation of the line:

Any one of these forms would work, but let's use slope-intercept form, as it is the most common way to write the equation of the line.

Perpendicular lines have slopes that multiply to get -1. They are also considered negative and reciprocal. For example, 5 and -1/5 would be the slopes of perpendicular lines.

So, let's find the slope of x=9.

If a line is written like x=9, it means that when it is graphed, it will be a vertical line, and a vertical line has an undefined slope.

As you may know, [tex]\frac{1}{0}[/tex] is also considered to be undefined. This means that the slope of this vertical line can be written as [tex]\frac{1}{0}[/tex].

Now, let's get the reciprocal of this slope (put the value of the numerator on the denominator and vice versa), then add a minus sign after it.

[tex]\frac{1}{0}[/tex] => [tex]-\frac{0}{1}[/tex] => 0

The slope of the line we're writing is 0.

We can replace m in y=mx+b with 0.

y = 0x + b

Now we need to find b.

As the equation passes through the point (-6,-3), we can use its values to help solve for b.

Substitute -6 as x and -3 as y in the equation.

-3 = 0(-6) + b

Multiply.

-3 = b

Replace b with -3 in the equation.

y = 0x - 3

This can also be written as:

y = -3

From the graph of the linear functions, we have that both snowman's will have the same height of 21 inches after 5 hours.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that:

Hence the functions are given as follows:

The functions are graphed at the end of the answer, with A(t) in red and B(t) in blue, and they intersect at (5,21), meaning that both snowman's will have the same height of 21 inches after 5 hours.

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The mistake done by Maya consists in operating the power expression (- 3)³ in a wrong manner.

A procedure of solution is shown and we must check if Maya did all the right steps to get a correct result. We proceed to present our procedure to be compared with that of Maya to find the mistake, that is, the step in which all divergences start.

(a³ - b³) / 5, a = 2, b = - 3    Given      

[2³ - (- 3)³] / 5                      Substitution

[8 - (- 27)] / 5                       Definition of power / Power with negative base

(8 + 27) / 5                          Additive inverse of an additive inverse

35 / 5                                  Definition of addition

7                                          Definition of division / Result

The mistake done by Maya consists in operating the power expression (- 3)³ in a wrong manner.

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All numbers to the equation 2(x-8) + 4x = 6(x-2)-4 are solutions.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given:

2(x-8) + 4x = 6(x-2)-4

On further solving

2x- 16 + 4x = 6x - 12 -4

2x + 4x -6x = -12 -4 +16

6x -6x = 0

6x = 6x

As, both sides are equivalent, all numbers are solutions.

Hence, All numbers are solutions.

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Answer: 1/3

Step-by-step explanation:

It is

Number of gallons of gas would need to travel 874.35 miles 174.034

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

Given:

Gallons Used             Miles Driven

 3333                                663.3

 4444                                 884.4

 4646                                 924.6

From table we can write

3333/663.3 = 5.024

4444/884.4= 5.024

4646/ 924.6 = 5.024

So,  number of gallons of gas would need to travel 874.35 miles

=874.35/5.024

=174.034

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The difference between the real temperature and the apparent temperature is - 30˚F.

What is Subtraction?

Subtraction is an operation which is used to find the difference between two numbers.

Given that;

The temperature outside (real temperature) = 22˚F

The wind chill made it feel like -8˚F.

That is, The apparent temperature = -8˚F

Now,

The difference between the real temperature and the apparent temperature = - 8˚F -  22˚F

                   = - 30˚F

Hence, The difference between the real temperature and the apparent temperature is - 30˚F.

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