Two steamers leave a port on river at the same time traveling in opposite directions each is traveling 20mph how long will it take for them to be 140 miles apart

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Scale factor that takes triangle ABC to triangle DEF = 2/3

Scale factor that takes triangle DEF to triangle ABC = 3/2

Scale factor = side length of new figure/corresponding side length of original figure.

Given:

Scale factor that takes triangle ABC to triangle DEF = 8/12

Scale factor that takes triangle ABC to triangle DEF = 2/3

Scale factor that takes triangle DEF to triangle ABC = 12/8

Scale factor that takes triangle DEF to triangle ABC = 3/2

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Answer:

$32

Step-by-step explanation:

56+8=64

64/2=32

Answer:

384

Step-by-step explanation:

480x20%=96

480-96=384

Answer: We have m = −3/2 as the slope and b = 150 as the y-intercept.

Step-by-step explanation:

Given data,

The slope of the following line 3x+2y=300

Define Slope :

Slope = (Change in height)/(Change in width) Or: Slope = rise/run. If y represents the vertical direction on a graph, and x represents the horizontal direction, then this formula becomes: Slope = (Change in y)/(Change in x)

The equation of a line presents the relationship between the components of a line in a certain coordinate system. To construct the equation of the line, we must take note of the parameters such as the slope, a point at which the line passes through, and the intercepts.

We solve for the slope, m, and the y-intercept, b, for the given line. We do this by rewriting the expression into the slope-intercept form,

                                y = mx + b

We proceed with isolating y in the given equation.

                                3x + 2y = 300

                                 2y = - 3x + 300

                                  y = (-3x + 300) / 2

                                  y = (-3/2) x + 300/2

                                  y = (-3/2) x + 150

Therefore, we have m = −3/2 as the slope and b = 150 as the y-intercept.

So, slope = -3/2

      b = 150

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The expression is simplified to 1 over c raised to the twentieth power. Option C

The index form of a number can be defined as the number written as an exponential expression.

It is expressed as a single number raised to another number.

Another name for index form is standard form or scientific notation.

Index notation is also a way of representing variables or constants multiplied by themselves a number of times.

Example of index forms are:

a²

b³

c²

From the information given, we have to simplify

(c^4)^−5

Using the rule of indices, we have to multiply the powers

c^-20

Thus, the expression is simplified to 1 over c raised to the twentieth power. Option C

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Answer:

1 over c raised to the twentieth power

Step-by-step explanation:

The teacher will make a decision like this because D. It is easier to compare measurements when using the same unit system.

It should be noted that in this case, the students are measuring the masses of several rocks and they have a scale that can show readings in pounds or kilograms. The teacher requires that they all make their measurements in kilograms.

It should be noted that the teacher will make a decision like this because it is easier to compare measurements when using the same unit system.

Therefore, the correct option is D.

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Answer:600

Step-by-step explanation:

We have, 125% * x = 750

Multiplying both sides by 100 and dividing both sides by 125

we have x = 750 * 100/125

you then get X=600

Answer:x=600

Step-by-step explanation: Multiplying both sides by 100 and dividing both sides by 125

Yes,  the relation is a function.

What does the term "relation function" mean?

What is a relation simple definition?

H={(6, - 2), (5,- 2), (4, -2), (3, - 2), (2, - 2)}

In a function, an x value can never repeat.

This is basically the only rule (that I know of), so, the given values can represent a function.

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Based on the amount deposited by Nancy into the account and the interest it paid, the ending balance after 1 year is $1,220.40

The ending balance of the amount that Nancy deposited which was $1,200 is based on the interest compounded on the amount over the investment year.

The ending balance can be found as:
= Amount deposited x ( 1 + rate) ^ number of years

Solving for the ending balance gives:
= 1,200 x (1 + 1.7%) ^ 1

= 1,200 x 1.017

= $1,220.40

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Answer:

Step-by-step explanation:

Givens

(x - 1)(6x - 5) = 0

Solution

Either one of these can be made into 0 by solving the binomials in the brackets.

x - 2 = 0               Add 2 to both sides

x -2 +2= 0+2       Combine

x = 2

6x - 5 = 0             Add 5

6x -5+5 = 0+5     Combine

6x = 5                   Divide by 6

6x/6=5/6

x = 5/6

Answer

Integer Answer: x = 2

Fractional Answer x = 5/6

The relationships represent proportional relationships and the constant of proportionalities are 5/7 and 12

Does it represent a proportional relationship?

Yes, the graph represents a proportional relationship

This is so because the graph is a linear equation and it passes through the origin

How to find the constant of proportionality (K=Y/X)

On the graph, we have the following point

(X, Y) = (28, 20)

So, we have

K = 20/28

Evaluate

K = 5/7

Here, we have

Y = K * X

This gives

Y = 5/7X

Does it represent a proportional relationship?

Yes, the table represents a proportional relationship

This is so because the table is a linear equation and it has a value (0, 0)

How to find the constant of proportionality (K=Y/X)

On the graph, we have the following point

(X, Y) = (5, 60)

So, we have

K = 60/5

Evaluate

K = 12

Here, we have

Y = K * X

This gives

Y = 12X

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Step-by-step explanation:

x = y - 3

4x = 6y + 10

let's multiply the first equation by -4 and then add both equations :

-4x = -4y + 12

4x = 6y + 10

--------------------

0 = 2y + 22

2y + 22 = 0

2y = -22

y = -22/2 = -11

x = y - 3 = -11 - 3 = -14

The general form of the quadratic function is x² - 2 · x - y + 5 = 0.

In this question we must derive the equation of the parabola in vertex form, whose description is shown below:

4 · p · (y - k) = (x - h)²      (1)

Where:

If we know that (h, k) = (1, 4) and (x, y) = (- 3, 20), then the distance from vertex to focus is:

p = (x - h) / [4 · (y - k)]

p = (- 3 - 1)² / [4 · (20 - 4)]

p = (- 4)² / 64

p = 16 / 64

p = 1 / 4

Then, the equation of the parabola in vertex form is y - 4 = (x - 1)². And now we find the general form of the quadratic formula, that is:

A · x² + B · x + C · y + D = 0          (2)

Then, we proceed to obtain the general form:

y - 4 = (x - 1)²

y - 4 = x² - 2 · x + 1

x² - 2 · x - y + 5 = 0

The general form of the quadratic function is x² - 2 · x - y + 5 = 0.

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The correct option is third graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We have the function

f(x)= |x|

The third graph represent the f(x)= |x|.

This is because the absolute value equations grow at a constant rate.

Also, they are absolute so they are also positive.

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Answer: u have to subtract 78-32  and divide by 100

Step-by-step explanation:

The width of the rectangle, w, is: 19 inches.

The perimeter of a rectangle is the sum of all its four sides which is calculated using the formula:

Perimeter = 2(length + width).

Given:

Perimeter = 144 inches

Width = w inches

Length = 3w - 4 inches

Thus:

2(3w - 4 + w) = 144

2(4w - 4) = 144

8w - 8 = 144

8w = 144 + 8

8w = 152

8w/8 = 152/8

w = 19

Thus, the width of the rectangle, w, is: 19 inches.

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A. The probability that there are exactly 4 pe ople with Type O+ blood in a sample of 10 peopl e.

B. The probability of exactly 3 heads in 6 flips of a coin.

C. The probability that the accumulated annual Yainfall in a certain city next yeay, younded t o the nearest inch, will be 18 inches.

D.The probability that a randomly selected wo man's height is 67 inches or less

So,the correct option is -

D.The probability that a randomly selected wo man's height is 67 inches or less

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The ratios of the food coloring drops that would create the same orange icing are

Ratios are quantitative measures of how much a variable is contained in another.

Ratios show numerical relationships between quantities.

Ratios are expressed as decimals, fractions, and percentages.

The mixture of red coloring = 4 drops

The mixture of yellow coloring = 6 drops

The ratio of red to yellow coloring = 4:6 or 2:3

Choice 1- 2 red:3 yellow = 2:3 (already simplified)

Choice 4- 28 red:42 yellow = 2:3 (when simplified by 14)

Choice 5- 44 red:66yellow = 2:3 (when simplified by 22)

Thus, the ratios of the food coloring drops that would create the same orange icing are Choices 1, 4, and 5.

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The figure 0.12 as given in the task content based on the given data can be interpreted as; the fraction of the books in the library that are how-to books on electronics.

It follows from the task content that the best interpretation of 0.12 is to be determined.

On this note, since three-tenths of the books in the school library are how-to books, and of those, 0.4 deal with electronics;

The statement above therefore means that the fraction of books which are how-to books and deal with carpentry can be evaluated as;

= (3/10) × 0.4

= 0.3 × 0.4

= 0.12.

Ultimately, The figure 0.12 as given in the task content based on the given data can be interpreted as; the fraction of the books in the library that are how-to books on electronics.

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A

Or maybe something else is not sure

The range of a function y = x² + 9 is y ≥ 9

A function is a mathematical expression rule or law that defines the relationship between one variable (dependent variable) and another (independent variable)

The range of a function is the set of output values of that function.

Given the function y = x² + 9, to find the range of the function, we need to find the values of y for which the function is valid.

Making y subject of the formula, we have

x = √(y - 9)

So, the function is valid for √(y - 9) ≥ 0

⇒ y - 9 ≥ 0

⇒ y ≥ 9

So, the range of a function is y ≥ 9

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The dimensions of the rectangle are 8 ft by 5.5 ft.

According to the statement,We have to find that the dimensions of the rectangles.

So, For this purpose, we know that the

A Rectangle may be a four sided-polygon, having all the interior angles adequate 90 degrees.

From the given information:The length of a rectangle is 3 ft but double the width, and therefore the area of the rectangle is 44.

Then

The formula for the world of a rectangle may well be a = L(length) × W(width)A = L × W

Plug in the information:A = 44, L = 2W - 3

b/c but means switch the order before subtracting, W = W

44 = (2W - 3)×W

44 = 2W² - 3W

And then

2W² - 3W - 44 = 0

so,

Factoring: (2W - 11)(W + 4) = 0

2W - 11 = 0 solves to W = 5.5

W + 4 = 0 solves to W = -4

So W = 5.5 and L = 2(5.5) - 3 = 8.

So, The dimensions of the rectangle are 8 ft by 5.5 ft.

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Answer:

$13.08

Step-by-step explanation:

If the price on pump is half the actual price, we just need to double what it says

So

$6.54 x 2 = $13.08

Two ways to do this! There are some more but these are the most intuitive.

Way 1:  Factoring

You can factor this equation into one with parentheses. A way I like thinking of doing this is by seeing if you can split the coefficient of the middle term into the sum of two numbers, which, when multiplied with each other, equal the third term.  To see what I mean, look at the equation you gave.

[tex]x^2 - 18x + 77 = 0[/tex]

[tex]x^2 - 7x - 11x + 77 = 0[/tex]

We notice that when -7 and -11 are multiplied, they equal 77. This means we can factor the equation! As follows:

[tex](x-7)(x-11)=0[/tex]

If you want to see why this works, cross-multiply out [tex](x-7)(x-11)[/tex]. You should see that it is equal to [tex]x^2 - 7x - 11x + 77[/tex].

From here, you should be able to see the solutions are [tex]x = 7, 11[/tex].

Way 2:  Complete the Square

We can do something like this:

[tex]x^2 - 18x + 77 = 0\\x^2 - 18x + 81 = 4\\(x-9)^2 = 4\\x-9 = \pm\sqrt{4}\\x = 9\pm 2\\x = 7, 11[/tex]

Essentially, what we are doing is we are adding / subtracting from both sides of the equation so the left side becomes a perfect square of some term [tex](x-a)[/tex].  From there, we can just solve for [tex]x[/tex].

Hope this helps you, please let me know if anything confuses you.

The monthly payment become $852. Thus , option C is correct option.

According to the statement

We have to find that the monthly repayment.

So, For this purpose, we know that the

The monthly payment is the amount paid per month to pay off the loan in the time period of the loan.

From the given information:

You have decided to buy a new home and the bank offers you a 30 year fixed loan at 5.5% on a balance of $150,000.

Then

we know that the:

Monthly payment = Amount / discount factor

And discount factor = 1-(1+i)^-n / i

Then

M = A*i/1-(1+i)^-n

Where, A=$150000

r=5.5%=0.055

i = 0.555/12

i = 0.004

And t = 30 year

n = 30*12

n = 360

Substitute all the values,

M = 150000*0.004/ 1-(1+0.004)^-360

M = 687.5 / 1-0.192

M = 687.5 / 0.80722

M = 851.7

Approximately, Monthly payment is $852.

So, The monthly payment become $852. Thus , option C is correct option.

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Based on the calculations, Mrs. Mayes spent the least time working on Wednesday.

A fraction can be defined as a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a fraction comprises two (2) main parts and these include the following:

In order to determine when Mrs. Mayes spent the least time working, we would convert the given mixed fractions into a proper fraction and then decimal. Lastly, we would then compare as follows:

Monday = 5 2/5 = 27/5 = 5.4.

Tuesday = 5 5/8 = 45/8 = 5.625.

Wednesday = 5 3/8 = 43/8 = 5.375.

Thursday = 5 4/5 = 29/5 = 5.8.

Based on the calculations above, we can reasonably infer and logically deduce that Mrs. Mayes spent the least time working on Wednesday.

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Complete Question:

The following table shows the amount of time Mrs. Mayes spent word processing each day for four days. On which day did Mrs. Mayes spend the least time working?

The fraction is 12/35.

From the information, it was stated that Manuel does 3/7 of the task while Carlos did 4/5 of what Manuel did.

Therefore, the fraction that was done by Carlos will be:.

= 4/5 × 3/7

= 12/35

The fraction is 12 / 35.

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Answer:

138.18 square yards

Step-by-step explanation:

Assuming the figure is a rectangle because it isn't said that it is otherwise, you would multiply the numbers together and get 138.18 square yards.