two trains, train a and train b weigh a total of 537 tons. train a is heavier than train b. the difference if their weights is 421 tons. what is the weight of each train?

The intermediate step in the form (x+a)2 = b is (x - 8)^2 = 72

From the question, we have the following parameters that can be used in our computation:

x^2 = 16x + 8

Rewrite as

x^2 - 16x = 8

Take the coefficient of x

k = 16

Divide by 2

= 8

Square the quotient

= 64

So, we add 64 to both sides of the equation

So, we have

x^2 - 16x + 64 = 8 + 64

Express as squares and evaluate

(x - 8)^2 = 72

Hence, the intermediate step is (x - 8)^2 = 72

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Answer:The answer to your question “the sensitivity range for an objective function coefficient is the range of values over which the profit does not change.True or False” Is FALSE.

Answer: You will walk 2.795 miles

Step-by-step explanation:

You can solve this using the Pythagorean theorem which is a^2 + b^2 = c^2

Plug in your numbers so you have 2.5^2 + 1.25^2 = c^2

Simplify that down to 6.25 + 1.5625 = c^2

Add   7.8125 = c^2

Find the square root of each of them.   2.795 = c

I don't know how you want me to round the answer so I just did it to the nearest thousandths.

The distance between the student and the mirror is apprοximately 29.41 feet.

Distance is a numerical measurement of hοw far apart or how far away objects or lοcations are from each other. It is a physical quantity that is usually expressed in units such as meters, kilοmeters, miles, οr feet. Distance is a scalar quantity, meaning it οnly has magnitude and nο direction.

To sοlve the problem, we can use the similar triangles prοperty of geometry. Let's denοte the distance between the student and the mirrοr as d. Then, we can set up the follοwing proportion:

(student height + height of mirrοr) / distance frοm student to mirror = height of schοol / distance from mirrοr to school

Plugging in the given values, we get:

(5.1 + 0) / d = 30 / (50 + d)

Simplifying and sοlving for d, we get:

5.1d + 0 = 150

d = 29.41

Therefοre, the distance between the student and the mirrοr is apprοximately 29.41 feet.

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The graph representing the association will be a negative linear association. Then the correct option is C.

The form, direction, confidence, and outliers of an association (relationship) between two quantitative variables can be used to describe it. • A positive association exists when one variable increases as the other dependent variable.

There is no boundary and all the dots are widely dispersed if there is no association. Variational individuals who are part that the dots are close together but not in a straight line.

From the graph, the slope of the best line will be negative.

The graph representing the association will be a negative linear association. Then the correct option is C.

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The measure of angle A is 52 degree.

Vertical angles are angles that are opposite of each other when two lines crosses, they are congruent.

Given that;

Since vertical angles are congruent,

Angle A = Angle B

Plug in the given values

( 7x - 18 ) = ( 6x - 8)

Solve for x

7x - 18 = 6x - 8

7x - 6x = -8 + 18

x = -8 + 18

x = 10

Hence, angle A will be;

Angle A = 7x - 18

Plug in x = 10

Angle A = 7( 10 ) - 18

Angle A = 70 - 18

Angle A = 52°

Therefore, angle A is 52 degree.

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The value of 30000 south korean currency is $25.50.

To convert 30000 South Korean Won to US Dollars, we can use the current exchange rate between the two currencies.

1. First, we need to find the current exchange rate between South Korean Won and US Dollars. As of September 9th, 2021, the exchange rate is 0.00085 USD per 1 South Korean Won.

2. Next, we can multiply the amount of South Korean Won we have by the exchange rate to find the equivalent amount in US Dollars.

30000 South Korean Won * 0.00085 USD/South Korean Won = 25.50 USD

3. Therefore, 30000 South Korean Won is equivalent to 25.50 US Dollars.

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Answer: 28, 30, 32

Step-by-step explanation: The first integer is 28, the second is 30, and the third is 32. The difference from the first integer and the last integer should be 4. x is the first integer, so the equation is:

x+x+2+x+4=90

The first integer plus the second integer(x+2) plus the third integer(x+4) equals 90. Now solve.

x+x+2+x+4=90

3x+6=90

    -6  -6

3x=84

/3   /3

x=28

So the first integer is 28, second is 30, third is 32.

Hope this helps!

Figure ABCD is a square. If AC+BD=56, the length of AX is 28.

Since ABCD is a square, all sides have the same length, let's call it "x".

We know that the sum of the diagonals of a square is equal to twice the length of a side, so AC + BD = 2x.

Therefore, 56 = 2x, and x = 28.

So the length of AX (or any side of the square) is 28 units

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The second graph given in the figure attached below is a correct representation of the given points.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, few points on cartesian plane A = (-2, -3), B = (4, 1)., C = (-2, 3), and D = (0, -1)

The xy pairs of a cartesian point are written in parenthesis as follows: (x, y).

To graph a point, first determine where it lies on the x-axis, then determine where it lies on the y-axis, and lastly plot the intersection of these two axes.

Due to its location at the intersection of the x- and y-axes, the origin of the graph, also known as the point (0, 0), is the center of the diagram.

For point A(-2, -3)

Find the negative 2 on the x-axis and the negative 3 on the y-axis, for instance, to draw the point (-2, -3).

The same will go for the remaining three points.

Therefore, The second graph given in the figure attached below is a correct representation of the given points.

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Answer:

To complete the first set of data so that it has six values and a mean of 21, you can add the following values: 20, 20.5, 20.5, 21.5, 21.5, 21.

The mean of this set is calculated as follows: (20 + 20.5 + 20.5 + 21.5 + 21.5 + 21) / 6 = 21.

To complete the second set of data so that it has six values and a mean of 21, you can add the following values: 20, 21, 21, 21, 21, 22.

The mean of this set is calculated as follows: (20 + 21 + 21 + 21 + 21 + 22) / 6 = 21.

A unit of measurement equal to one thousand meters is called a kilometer.

A kilometre is a length measurement in the metric system that is equivalent to 1000 metres because the word "kilo" implies "one thousand". Longer distances, such those between cities or nations or the duration of a marathon, are frequently measured in kilometers. The lower length units of the metric system, such as meter's, centimeters, and millimeters, can be used to measure shorter distances.

A length measurement in the metric system that is 1,760 yards or 5,280 feet long. A metric capacity unit is one thousandth of a liter. a length expressed as a thousandth of a meter in meters. a common measure of time that is equal to 60 seconds and 1/60 of an hour.

Therefore, the kilometer is equal to one thousand meter's.

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Answer:2y32 is the answer u the graph line and some o f the sqaures to count it

Step-by-step explanation:

In the triangle that we have here cos 42 degrees is equal to sin 48

This was simply solved using the calculator

cos 42 = 0.7431

sin 42 = 0.6691

cos 48 = 0.6691

sin 48 = 0.7431

From the above we can see that the value of cos 42 and sin 48 returned the same digits at 0.7431

Hence the value of cos 42 is sin 48 degrees

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Answer:its 5

Step-by-step explanation: cuz

Answer:

52.40

Step-by-step explanation:

Given that,

Keith's bookshelf has 5 shelves.

He has 262 books.

To find the number of books he can put on each shelf.

 [tex]required \\ number = \frac{Total Books}{Total Shelves}\\\\= \frac{262}{5} = 52.40[/tex]

Hence 52.40 is the right answer.

Answer:

you in BBC FDA's in BBC FDA's in just had not had not had not had on under end

Step-by-step explanation:

no exception

The final payment and amount saved based on the given interest are respectively;

a)  $17697.5 and $1215.12

b) $12377.80 and $562.40

The equation for the interest  is mathematically expressed as:

I = balance*percentage/12

Therefore:

I = 17565.74 * 0.09/12

I = 131.7

The final payment is; F = I + B

F = 131.7 + 17,565.74

F = 17697.5

Amount saved

A.S = (19 * 995.40) - 17697.5

A.S = 1215.12

b) For the loan is paid off with payment 36 with a loan balance of $12,285. 66

I= balance*percentage/12

Therefore:

I = (12,285.66 * 0.09)/12I92.142

I = 92.142

Final payment

F = I + B

F = 92.142 + 12377.80

F = 12377.80

Amount saved

A.S = (13 * 995.40) - 12377.80

A.S = $562.40

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The complete question is;

Doreen Short was looking over the repayment schedule for a loan of $40,000. 00 at 9% for 4 years with a monthly payment of $995. 40.

Find the final payment and amount saved if :

A. ) The loan is paid off with payment 30 with a previous balance of $17,565. 74

B. ) The loan is paid off with payment 36 with a loan balance of $12,285. 66

The distance d between the student and the mirror is given by the similar triangles are d = 10.5 feet

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the triangles be represented as ΔABC and ΔCDE

Now , they are similar triangles

The measure of AB = height of the school = 30 feet

The measure of BC = distance from the school to the mirror = 50 feet

And ,

The measure of DE = height of the student = 6.3 feet

The measure of CD = distance d between the student and the mirror

So , the corresponding sides of similar triangles are in the same ratio

On simplifying the equation , we get

BC / AB = CD / DE

And , 50 / 30 = d / 6.3

Multiply by 6.3 on both sides , we get

d = ( 5/3 ) x 6.3

d = 31.5 / 3

d = 10.5 feet

Hence , the distance d between the student and the mirror is 10.5 feet

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The time it takes is 2 seconds

To find the time that the balloons collided at the highest point, we need to find the vertex of the resulting quadratic function.

First, we can set the two functions equal to each other, since they represent the height of the two balloons at any given time:

-7x^2 + 26x + 3 = -6x^2 + 23x + 5

Simplifying and rearranging terms, we get:

-x^2 + 3x + 2 = 0

Now, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = -1, b = 3, and c = 2.

Plugging in these values, we get:

x = (-3 ± sqrt(3^2 - 4(-1)(2))) / 2(-1)

x = (-3 ± sqrt(1)) / (-2)

Simplifying further, we get:

x = (-3 ± 1) / (-2)

So, x can be either 1 or 2. However, we're only interested in the positive value for x since time cannot be negative.

Therefore, the time that the balloons collided at the highest point is:

x = 2 second

So, the correct answer is: 2.0 seconds

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The probability that Justen wins is 4/9.

The probability that Justen wins is determined by the likelihood that the highest number rolled on the two dice is a 1, 2, 3, or 4. To find this probability, we can first calculate the probability that the highest number rolled is a 5 or 6, which is what would cause Gaberil to win.

The probability of rolling a 5 or 6 on one die is 2/6, or 1/3. The probability of rolling a 5 or 6 on both dice is (1/3) * (1/3) = 1/9.

However, we also need to account for the possibility that one die rolls a 5 or 6 and the other does not.

This can happen in two ways: either the first die rolls a 5 or 6 and the second does not, or the first die does not roll a 5 or 6 and the second does.

The probability of each of these scenarios is (1/3) * (2/3) = 2/9.

So the total probability of Gaberil winning is 1/9 + 2/9 + 2/9 = 5/9.

Since there are only two possible outcomes (either Gaberil wins or Justen wins), the probability of Justen winning is 1 - the probability of Gaberil winning. So the probability of Justen winning is 1 - 5/9 = 4/9.

Therefore, the probability that Justen wins is 4/9.

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The expressions are evaluated below

Expression 1: 4 < 7

Multiplying both sides by 3, 2, 4, and 9 respectively:

3 * 2 * 4 * 9 * (4 < 7)

864 < 1515

Expression 2: 11 > -2

Adding 3 to both sides, then adding 3, then adding (-4) respectively:

3 + 3 - 4 + (11 > -2)

13 > 0

Expression 3: -2 = -2

Subtracting 6 from both sides, then adding 8, then adding 2 respectively:

-2 + 6 + 8 + 2 = -2 + 6 + 8 + 2

14 = 14

Expression 4: -4 < 8

Dividing both sides by -4, then by -2 respectively:

-4/(-4 * -2) < 8/(-4 * -2)

-1/2 < 1

The operations performed on the inequalities in each question did not affect the inequality sig.

The truth of the inequality was also not affected by the operations in all cases.

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The number of moles is given by the equation n = 0.611 moles

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

PV = nRT   be equation (1)

Divide by RT on both sides of the equation , we get

n = PV / RT

Now , when temperature T = 299 K

The value of pressure P = 3 atm

The value of volume V = 5 Liters

The universal gas constant R = 0.0821

Substituting the values in the equation , we get

n = ( 3 x 5 ) / ( 0.0821 x 299 )

On simplifying the equation , we get

n = 15 / 24.5479

n = 0.611 moles

Therefore , the number of moles is 0.611 moles

Hence , the equation is n = 0.611 moles

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The amount of white paint did she use to paint her bedroom walls is 6 21/40 or 6.525 pints.

To find the amount of white paint used, we first need to find the amount of blue paint used. Since 1/4 of the total amount of paint is blue, we can multiply the total amount of paint by its fraction, 1/4, to find the amount of blue paint:
Blue paint = 8.7 pints × 1/4 = 87/40 = 2.175 pints

Now, to find the amount of white paint used, we can subtract the amount of blue paint from the total amount of paint:
White paint = 8.7 pints - 2.175 pints = 261/40 = 6.525 pints

So, Araceli used 6.525 pints of white paint to paint her bedroom walls.

In fraction form, this can be written as 6525/1000 pints, or 6 21/40 pints.

In decimal form, it is simply 6.525 pints.

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The probability of three or fewer heads on four flips of a fair coin is 0.375. This can be determined by calculating the probability of zero, one, two and three heads, which are 0.0625, 0.25, 0.375 and 0.25 respectively. The total of these probabilities is 0.375.

The probability of zero heads on four flips of a fair coin is 0.0625 (1/16).

The probability of one head on four flips of a fair coin is 0.25 (4/16).

The probability of two heads on four flips of a fair coin is 0.375 (6/16).

The probability of three heads on four flips of a fair coin is 0.25 (4/16).

The total probability of three or fewer heads on four flips of a fair coin is 0.375 (1/4).The probability of three or fewer heads on four flips of a fair coin is 0.375. This can be calculated by determining the probability of zero, one, two and three heads. The probability of zero heads is 0.0625, the probability of one head is 0.25, the probability of two heads is 0.375, and the probability of three heads is 0.25. When these probabilities are added together, the total probability of three or fewer heads on four flips is 0.375. This means that the probability of getting three or fewer heads on four flips of a fair coin is 0.375.

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Answer:

$1770.87

Step-by-step explanation:

Formula;    Simple Interest(I) =  P × R × T/100

= $1770.87

Answer:

The value of two numbers if their sum is 12 and their difference is 4 are 8 and 4.

Step-by-step explanation:

I hope this helped