Find another point on a line that includes the points (-5, 4) and (4, 1).

Answer:

  21/3100000 ≈ 1/147619

Step-by-step explanation:

You want the scale of a map on which 4.2 cm corresponds to an actual distance of 6.2 km.

The scale of a drawing is the ratio of drawing distance to actual distance. It can be expressed a couple of ways. We can write the given scale as ...

  4.2 cm : 6.2 km

or, we can reduce it to ...

  2.1 cm : 3.1 km

Often, we like to have a single unit of map distance in this ratio, which would make it be approximately ...

  1 cm : 1.47619 km

Another way to write the scale of a map is as a fraction.

  (4.2 cm)/(6.2 km) = (0.042 m)/(6200 m) = 21/3100000

When this is expressed as a unit fraction, the denominator is a repeating decimal with a 6-digit repeat. We can round it to ...

  ≈ 1/147619 . . . . map scale

The scale of the map is ...

  21/3100000 ≈ 1/147619   or   2.1 cm : 3.1 km   or   ≈ 1 cm : 1.47619 km

__

Additional comment

You may need to round the answer to match one of your answer choices.

<95141404393>

Rate Pratap can row in still water is 6.75 and Rate of current is 2.25

Step: 1

Let's y = speed of water and x = his speed of rowing in still water

Speed = Distance/Time (or)

Rate = Distance/Time

Step: 2

he row downstream in 2 hours

Rate in downstream = 18/2

Rate in downstream = 9

i.e.

x + y = 9

x = 9 - y ---(i)

Now, time taken by min to row in upstream = 4 hours

Rate in upstream = Distance/Time = 18/4

Rate in upstream = 4.5

i.e., x-y = 4.5 ---(ii)

Putting the value of x from equation (i) in equation(ii)

9 - y - y = 4.5

9 - 2y = 4.5

9 - 4.5 = 2y

y = 4.5/2

y = 2.25

Putting the value of y in equation (ii)

x - 2.25 = 4.5

x = 4.5 + 2.25

x = 6.75

x = Rate Pratap can row in still water = 6.75

y = Rate of current = 2.25

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After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.

As given in the question,

After flipping a fair coin, when 'H' represents the heads and 'T' represents the tails ,

Number of total outcomes = { H , T }

Total number of outcomes = 2

Number of favourable outcomes to represent heads = 1

Number of favourable outcomes to represent tails = 1

Probability =(Number of favourable outcomes)/ (Total number of outcomes)

Probability of getting heads from the total outcomes is equal to

P(H) = 1 / 2

Probability of getting tails from the total outcomes is equal to

P(T) = 1/2

Therefore, after flipping a fair coin, when 'H' represents the heads and 'T' represents the tails the probability of heads P(H) = 1/2 and probability of tails P(T) = 1/2.

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Answer: 22

Step-by-step explanation:

3 times 5 then add 7

The graph of the  absolute value function is attached below.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

The absolute value measures the distance of a point x to the origin, hence, for example, |-4| = |4| = 0, and has vertex(turning point) at (0,0).

We have to grpah the absolute value function of y = 5x.

Thus, the function is linear function.

The graph of the function is attached below.

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Answer:

9.37

Step-by-step explanation:

twelve surgeons

112.44 / 12 = 9.37

Answer:

$9.37

Step-by-step explanation:

112.44 ÷ 12

The two expressions equivalent to v are:

Here we have the equation:

5*(3a - 1) - 2*(3a + 2) = 3*(a + 2) + v

And we want to find expressions equivalent to v, so to do that, we just need to isolate the variable v in one side of the equation, if we subtract:

3*(a + 2) in both sides we will get:

5*(3a - 1) - 2*(3a + 2) = 3*(a + 2) + v

5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v

That is one of the equivalent expressions, to get the other, we can just simplify the left side.

5*(3a - 1) - 2*(3a + 2) - 3*(a + 2) = v

15a - 5 - 6a - 4 - 3a - 6 = v

Now we can group like terms:

15a - 6a - 3a - 5 - 4 - 6

6a - 15 = v

That is the other equivalent expression to v.

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Answer: base = 23  height = 31

Step-by-step explanation:

Area of triangle = (bh)/2

A = 356.5 cm2

h = b+8

356.5 = (b(b+8)) / 2

2(356.5) = b2 + 8b

0 = b2 + 8b - 713

Use quadratic equation to solve for b (there are on-line quadratic equation solvers, or you can do it manually)

b = -31 , 23

23 is the base    23 + 8 = 31 = height

[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-6)}}} \implies \cfrac{0 +3}{2 +6} \implies \cfrac{ 3 }{ 8 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{ \cfrac{3 }{ 8 }}(x-\stackrel{x_1}{(-6)}) \implies {\large \begin{array}{llll} y +3 = \cfrac{3 }{ 8 } ( x +6) \end{array}}[/tex]

My answer and step by step explanation is provided as an attachment.

The product of the quotient of a and b and the quotient of c and d is ac/bd.

In mathematics, a quotient simply means a quantity produced through the division of two numbers.

From the information, the product of the quotient of a and b and the quotient of c and d.

The product will be:

= a/b × c/d

= ac / bd

The product is ac/bd.

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Answer:

2nd one is the best division

Answer:$12

Step-by-step explanation:

1.75/3= 0.6 (1dp)

0.6 x 20 = 12

Answer:

$11.67

Step-by-step explanation:

3 oranges = 1.75

1 orange = 0.58333333333

20*0.58333333333 = 11.6666667

Answer:

3 * (8 + (n - 1)*x*1/3 ) = 3 * ( 0 )

..

How to find the vertex?

The general form of an absolute value function:

Given function is:

Its vertex is (- 3, - 2), this is our first point to plot, point A.

How to find x-intercepts?

Set y = 0 and solve for x:

So the x-intercepts are ( - 5, 0) and (- 2, 0), points B and C.

Connect the vertex (- 3, - 2) with points ( - 5, 0) and (- 2, 0) and here is your graph.

Answer:

45

Step-by-step explanation:

Number of Latvian footballers(n¹) = 36

Numer of footballers of other nationalities(n²)=36/4=9

Now total number of footballers= n¹+n²= 36+9 =45

According to the trignonmentry of half angles, the value of sin(x/2) is  √(1-5/6)/2, cos(x/2) is √(1+5/6)/2 and the value of tan(x/2) is √11/6/(√(1 + 5/6)

Trigonometry of half angles

Trigonometry of half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° that is half of the standard angle 30° and 22.5° that is the half of the standard angle 45 and so on. So if θ is an angle, then the half angle is represented by θ/2.

Given,

Here we need to find if cos(x)=5/6 , and x is in quadrant I, determine the exact value of each of the following.

sin(x/2), cos(x/2), tan(x/2).

According to the concepts in trigonometry,

We know that the following formulas.

=> sin(x/2) = √(1-cosx)/2

=> cos(x/2) = √(1+cosx)/2

=> tan( x/2)=sin x/1+cosx

Here we know that cos (x) = 5/6

Thus implies that 5 is the opposite and 6 is the hypotenuse, then the adjacent is

Therefore, we can calculate the value of the adjacent a as,

=> a = √(6²-5²)

=> a = √36-25

=> a= √11

Therefore the value of sin x= √11/6

So, the value of sin(x/2)= √(1 - 5/6)/2

And the value of cos(x/2)= √(1 + 5/6)/2

Finally, the value of tan(x/2)=√11/6/(√(1 + 5/6)

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Answer:

Step-by-step explanation:

so if it takes 42 days and 44 days just add them up

42 plus 42 = 82 plus 42=124 plus 42= 166plus 42= 208 plus 42 = 250 plus 42 = 292 plus 42= 334 plus 42= 376 plus 42=418

44 plus 44= 88 plus 44=132 plus 44=176 plus 44 = 220 plus 44= 274 plus 44= 318 plus 44= 362 plus 44=406 plus 44= 450 plus

just keep going

Answer:

100

Step-by-step explanation:

.001*100=.1

Answer:

100 thousandths

Step-by-step explanation:

x=-3.645 and x=1.645 is the solution for the given inequality.

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

The given inequality is

y<x²+2x-6

a=1, b=2, c=-6

x=-b±√b²-4ac/2a

=-2±√2²-4(1)(-6)/2(1)

=-2±√4+24/2=

=-2±√28/2=

=-2+√28/2

=-2+5.29/2

=1.645

and -2-5.29/2

x=-3.645

Hence x=-3.645 and x=1.645 is the solution for the given inequality.

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24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

According to the question,

We have the following information:

The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 65% pure fruit juice.

Now, let's take x pints of 55% pure fruit juice and y pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

So, we have:

x+y = 40

x = 40-y ...(1)

55x/100+80y/100 = 40*65/100

55x+80y = 40*65

Putting the value of x from equation 1:

55(40-y)+80y = 2600

2200-55y+80y = 2600

2200+25y = 2600

25y = 2600-2200

25y = 400

y = 400/25

y = 16 pints

Putting this value in equation 1:

x = 40-y

x = 40-16

x = 24 pints

Hence, 24 pints of 55% pure fruit juice and 16 pints of 80% pure fruit juice will be required to make 40 pints of a mixture that is 65% pure fruit juice.

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The expressions equivalent to 4^10​ are 2^20, 4^4 . 4^6, and  4^4 / 4^-6. Option B, option C, and option E are correct.

Some laws of exponents are:

We need to find all the expressions equivalent to 4^10​.

We will use laws of exponents for all the options one by one.

Option A:

2^5 . 2^2 = 2^(5 + 2) = 2^7

This is not equivalent to 4^10​.

Option B:

2^10 = 2^(2 * 10) = (2^2)^10 = 4^10

This is equivalent to 4^10​.

Option C:

4^4 . 4^6 = 4^(4 + 6) = 4^10

This is equivalent to 4^10​.

Option D:

4^7 . 4^-3 = 4^(7 + (-3)) = 4^4

This is not equivalent to 4^10​.

Option E:

4^4 / 4^-6 = 4^(4 - (-6)) = 4^10

This is equivalent to 4^10​.

So, 2^20, 4^4 . 4^6, and  4^4 / 4^-6 are equivalent to 4^10​.

So, option B, option C, and option E are correct.

Thus, the expressions equivalent to 4^10​ are 2^20, 4^4 . 4^6, and  4^4 / 4^-6. Option B, option C, and option E are correct.

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Answer:

x = y/3 + 4/3

Step-by-step explanation:

Solve for x:

y = 3 x - 4

y = 3 x - 4 is equivalent to 3 x - 4 = y:

3 x - 4 = y

Add 4 to both sides:

3 x = y + 4

Divide both sides by 3:

Answer: x = y/3 + 4/3

Answer:2 years

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is 2 years

The positive difference the  numbers is given as 6.

We are told here that there is a pair of natural numbers whose sum is 52 and whose product is 667. We have to make use of the idea of simultaneous equations to obtain the numbers.

Let the numbers be x and y thus we have;

x + y = 52 ---- (1)

xy = 667 ------ (2)

x = 52 - y ------ (3)

Substituting (3) into (2)

(52 - y)y = 667

52y - y^2 = 667

y^2 - 52y + 667 = 0

Solving the quadratic equation we have;

y=23 or y=29

The difference between the numbers then becomes 29 - 23

= 6

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The expected value for the game is -12.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

The probability of rolling a 2 or 5:

= P(2 or 5)

= 1/6 + 1/6 = 1/3

The probability of not rolling a 2 or 5:

= 1 - 1/3

= 2/3

The expected return:

= (1/3)(36) + (2/3)(-36)

= 12 - 24

= -12

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Answer:

Below

Step-by-step explanation:

Need the drawing but take the two cm measurements and multiply them together then multiply by 4   and then multiply by 4 again to get ft^2

t = d/220 is the equation that shows how many hours (t) a trip takes in terms of the trip's distance (d).

Speed is calculated as follows: speed = distance/time. Calculating the units for speed requires knowledge of the units for both time and distance. Since the distance is measured in meters (m) and the time is recorded in seconds, the units in this example will be meters per second (m/s) (s).

Let the distance be d and the time is t.

The given speed of the train = 220km/hr

Time = d/speed

t = d/220

This is the equation that shows how many hours (t) a trip takes in terms of the trip's distance (d).

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Answer:  t=220/b

Step-by-step explanation: Khan Academy said so

For the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.

When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.

As given in the question,

a. Anita get pay per hour = $9.45

Gross pay received by Anita = $238.61

Deductions :

Federal tax = $28.63

Society tax : $14.79

Medicare : $3.46

State tax : $10.14

Total deduction = $ ( 28.63 + 14.79 + 3.46 + 10.14 )

                          = $57.02

Net pay = Gross pay - total deduction

             = $ ( 238.61 - 57.02 )

             = $ 181.59

Let us consider Anita works for 'h' hours at the rate of $9.45,

9.45h = 238.61

⇒ h = 238.61/ 9.45

⇒ h = 25.25 hours

b. When Anita works for 31 hours

Her gross pay = 31 × 9.45

                       = $ 292.95

Deductions are same

Net pay = $ ( 292.95 - 57.02 )

            = $ 235.93

Therefore, for the gross pay of $238.61 and given deduction Anita's net pay is equal to $181.59 at the rate of $9.45 per hour and she works for 25.25 hours.

When Anita works for 31 hours with the given conditions her gross pay and net pay is equal to $292.95 and $235.93 respectively.

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