The scale on a map is 1:500000
Two towns are 7cm apart on the map
Work out the actual distance between the towns. Give your answer in kilometres

Answer:

The Distributive Law

Step-by-step explanation:

The correct answer of the question is {-1+√61}/ 10 or {-1-√61}/ 10 .

The given quadratic equation is 5 x²+x=3

First, we have to convert the equation in the form

ax² + bx + c = 0, then apply the quadratic formula i.e.

x = {-b±√(b²- 4ac)}/ 2a .

Now,

5 x²+x=3

⇒ 5 x²+ x - 3 = 0

Here, a = 5, b = 1 and c = -3

Now, applying quadratic formula

{-b±√(b²- 4ac)}/ 2a

= {-1±√(1²- 4 × 5 × -3)}/ (2 × 5)

= {-1±√(1 + 60)}/ 10

= {-1±√61}/ 10

= {-1+√61}/ 10 or {-1-√61}/ 10

Therefore the final answer to the given equation is is {-1+√61}/ 10 or {-1-√61}/ 10 .

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The side length of each face of a cube is equal to 2 feet.

We know, Total surface area of a cube = 6a², where a is the side length of the cube.

Here, a = 2 feet

∴ Total surface area of the given cube is equal to

⇒ 6(2)²

⇒ 6(4)

⇒ 24 sq. ft.

∴ Total surface area of the given cube is 24 sq. ft.

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Answer:

y=3

Step-by-step explanation:

Step 1: Cross-multiply.

14/3y+5=3/y

14*y=3*(3y+5)

14y=9y+15

Step 2: Subtract 9y from both sides.

14y−9y=9y+15−9y

5y=15

Step 3: Divide both sides by 5.

5y/5=15/5

y=3

The solution of expression rounded to nearest tenth is -1.1

Rewriting the equation first -

-1.2x = 11.3x + 13.75

Now, shifting 11.3x to other side of the equation and rewriting the equation -

- 1.2x - 11.3x = 13.75

Rewriting the equation according to sign on Left Hand Side

-(1.2x + 11.3x) = 13.75

Performing addition of similar values on Right Hand Side of the equation

-12.5x = 13.75

Solving for the value of x from above mentioned equation -

x = 13.75 ÷ (-12.5)

Performing division to find the value of x

x = - 1.1

The number 1.1 rounded to nearest tenth will be 1.1.

So, the solution of expression rounded to nearest tenth is -1.1

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Lines and mare perpendicular is The same result is obtained by reflecting Q over the Line M as well as rotating Q 180 degrees using the center P.

As a reminder, perpendicular lines are those that cross at a 90-degree angle. Two non-vertical lines are said to be perpendicular when they are in the same plane and intersect at a right angle.

The axes of the coordinate plane, or the horizontal and vertical lines, are simply perpendicular to one another. Additionally, the slopes of the parallel lines have negative reciprocal slopes.

Since Lines L and M are perpendicular lines, or lines that meet at a right angle (90°), rotating Q 180 degrees using the center P has the same result as reflecting Q across Line M.

Q will therefore be identical to reflecting Q over any of the perpendicular lines when rotated 180 degrees from the center.

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Answer:

Step-by-step explanation:

Company A:

The recursive formula is, aₙ=aₙ₋₁+4,000, where a₁=42,000

Company B:

The recursive formula is, aₙ₊₁=(1+0.09) x aₙ, where a₁= 42,000

I'm sure she should go for company B, in the long run, she would make much more money. This is proven because company a is increasing using an arithmetic sequence; based on this all they're doing is adding 4,000. But company B is increasing at a percentage of 9 after a while that can really amount to a lot.

Hope this helps, if you are still confused don't hesitate to ask :))

Josie's pay [tex]a_n[/tex] from company A in the [tex]n[/tex]-th year is given recursively by

[tex]\begin{cases} a_1 = 42000 \\ a_{n+1} = a_n + 4000 & \text{for } n\ge1 \end{cases}[/tex]

while her pay [tex]b_n[/tex] from company B is

[tex]\begin{cases} b_1 = 42000 \\ b_{n+1} = 1.09 b_n & \text{for } n \ge1 \end{cases}[/tex]

From these recurrences, we have

[tex]a_2 - a_1 = 4000[/tex]

[tex]a_3 - a_2 = 4000[/tex]

[tex]a_4 - a_3 = 4000[/tex]

and so on - this is just confirming that the pay from company A increases at flat rate of $4000 each year.

Similarly,

[tex]b_2 = 1.09 b_1 = 45780 \implies b_2 - b_1 = 3780[/tex]

[tex]b_3 = 1.09 b_2 \approx 49900 \implies b_3 - b_2 \approx 4120[/tex]

[tex]b_4 = 1.09 b_3 \approx 54391 \implies b_4 - b_3 \approx 4491[/tex]

and we see here that [tex]b_n[/tex] increases at a larger rate year. In only 2 years of working at company B, Josie would be making more money, and the amount by which her salary increases each year is also increasing.

Assuming Josie hopes to make more money, invest in her future, etc, she should take the offer from company B.

Answer:

21.875%.

Step-by-step explanation:

This is a Binomial Probability Distribution.

Prob (exactly 5 heads) = 8C5(0.5)^5(0.5)^3

= 56 * 3.90625 * 10^-3

= 0.21875

= 21.875%.

[tex]\bold{\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}} = \sqrt[3]{\frac{x}{y} } }[/tex] is the correct form.

We need to find the error in the statement [tex]\bold{\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}} = \sqrt[3]{\frac{xy}{y} } }[/tex]

Starting from LHS of the statement, [tex]\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}}[/tex],

we can cancel the like terms ∛y from the numerator and denominator.

So we get, [tex]\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}[/tex]

Since both of the numerator and denominator has the cubic root, we can combine it.

That is, [tex]\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}[/tex]  = ∛(x/y) is the right answer.

So in this expression  [tex]\bold{\frac{\sqrt[3]{x}}{ \sqrt[3]{y}}\frac{\sqrt[3]{y}}{ \sqrt[3]{y}} = \sqrt[3]{\frac{xy}{y} } }[/tex], y on the numerator is the error.

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Answer:

5/20 is not equivalent to 1/5.

Step-by-step explanation:

We can start by simplifying all of the fractions, by finding numbers we can divide both the numerator and denominator by the same number.

[tex]\frac{3}{15} =\frac{1}{5}[/tex] by dividing by 3.

[tex]\frac{2}{10} =\frac{1}{5}[/tex] by dividing by 2.

[tex]\frac{5}{20} =\frac{1}{4}[/tex] by dividing by 5.

and last but not least

[tex]\frac{15}{75} =\frac{1}{5}[/tex] by dividing by 15.

We can see that 5/20 is the only one that equals to 1/4 when simplified.

Therefore, 5/20 is not equivalent to 1/5.

Hope this helped! Have a great day!

Capella is  1.09 times brighter than Rigel.

In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as  .

[tex]log_ax=N[/tex]

where, a is the base of function or equation

            x =expression or equation

There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations. Some of them are listed below.

Some important formulas of logarithms are :

In the question given here to us,

We use the given formula:

[tex]m_2-m_1= -2.5log\frac{b_2}{b_1} \\[/tex]

Here, m1 = magnitude of Rigel = 0.12

          m2 = magnitude of Capella =0

put the values in eq.

[tex]= > m_2-m_1= -2.5log\frac{b_2}{b_1} \\\\= > - 0.12 = -2.5log\frac{b_2}{b_1}\\\\= > 0.04 = log \frac{b_2}{b_1}\\ \\= > \frac{b_2}{b_1} = 10^{0.04} = 1.09 approx[/tex]

Hence, Capella is  1.09 times brighter than Rigel.

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All the angles of the given triangle are;

∠1 = 41°

∠2 = 85°

∠3 = 95°

∠4 = 85°

∠5 = 36°

∠6 = 49°

∠7 = 106°

We are given different angles. Thus;

∠3 will be equal to 95° because of the definition of vertically opposite angles.

∠4 = 180° - 95° because sum of angles on a straight line is equal to 180°. Thus;

∠4 = 85°

∠2 = ∠4 = 85° because they are both vertically opposite angles.

∠5 = 180° - 144° because sum of angles on a straight line is equal to 180°.  Thus; ∠5 = 36°

∠7 = 180° - (38° + 36°) because sum of angles in a triangle is equal to 180°. Thus; ∠7 = 106°

Sum of angles in a quadrilateral is 360°. Thus;

∠1 = 360 - (90 + 144 + 85)

∠1 = 41°

∠6 = 180 - (90 + 41)

∠6 = 49°

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When calculating time zone differences, you should always add and subtract an hour for each time zone to the west.

A time zone is a region that adheres to a common standard time for social, commercial, and legal activities. Because it is easy for locations in frequent communication to preserve the same time, time zones typically follow the boundaries between countries and their subdivisions rather than rigidly following longitude.

The definition of every time zone is an offset from Coordinated Universal Time. For nearly half of the year, certain regions at higher latitudes observe daylight saving time, which is commonly accomplished by adding an hour to local time in the spring and summer.

It should be noted that the Time Zone gives an overview of current local times around the world. It should be noted that calculating time zones is simple and involves adding or subtracting an hour for every 15 degrees of longitude.

Therefore, when calculating time zone differences, you should always add and subtract an hour for each time zone to the west.

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Based on the Abby, Chantral, Dougie, Kajan, Minh, and Zara being equally fast, the probability that Abby and Chantral will be the first two finishers is 1/15.

The probability that Abby and Chantral will be the first two finishers can be found by the formula:
= Number of successful outcomes where Abby and Chantral will be the first two finishers / Total number of outcomes

Solving gives:

= (21! - 4!) / 6!

= 48 / 720

= 1 / 15

In conclusion, the probability that Abby and Chantral will finish first is 1/15.

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Answer:

4v^2 + 6v + 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Perimeter = 110 in

Area = 490 in²

Answer:

z=120

Step-by-step explanation:

z/12 = 10

multiply both sides by

12 12z/z =

10 x 12

z= 120

Answer:

z=12x10=120

Step-by-step explanation:

hope this helps ˙˚ʚ(´◡`)ɞ˚˙

When a function is plotted, the domain and the range of the function are the x-coordinate and the y-coordinate respectively. The domain and range of the assumed function for Melissa's garden :

x = ( 2, infinity )

p(x) = (0 , infinity )

The function is not given. So, I will give a general explanation to calculate domain and range.

The domain is all possible values the independent variables of a function can take while the range is all possible values the dependent variables of a function can take

Assume the function of Melissa's garden is:

p(x) = x. (x-2)

Start by equating the function to 0

x. (x-2) =0

Split

x=0, x-2=0

x=0 x=2

x will give p(x)  = 0

the length of the garden cannot be 0 or less.

So, the domain of the function is:

x = ( 2, infinity )

p(x) = (0 , infinity )

This means that the domain starts from a value greater than 2 (e.g. 3) and ends at infinity

To calculate the range, we substitute x = ( 2, infinity )  in the function

x=2

p(x) = 2.2-2 =0

So, the range of the function is:

p(x) = (0 , infinity )

This means that the domain starts from a value greater than 0 (e.g. 1) and ends at infinity

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The length of the diagonal is 7.05cm of a square.

The perimeter of the square is 20 cm.

The formula of the perimeter of the square is 4a, where a is the length of the side of the square.

So, 4a = 20

       a = 5

Now we have to find the diagonal of the square.

In a square there is two diagonal, each of equal length

Therefore,

    diagonal = [tex]\sqrt{2}[/tex]a

                    = 1.41 × 5

                    7.05cm

Therefore the diagonal of the square is 7.05cm.

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Answer:

6.51326 is greater than √38

Step-by-step explanation:

6.51326 compared with √39

6.51326 compared with 6.244998

means 6.51326 is greater than √38

The given question represents the commutative property of addition.

Given, (8 + 3) + 11 = 8 + (3 + 11)

According to the commutative property of addition, no matter how the numbers are arranged, the total of two or more numbers remains the same.

The commutative property of addition states that no matter how the numbers are organized, the result of adding or summing two or more numbers will always be the same. The representation of the bracket placement and arrangement in the provided addition problem is referred to as grouping in this context.

The addends can be grouped in several ways without affecting the result, according to the associative feature of addition. Rearranging the addends won't affect the result, according to the commutative property of addition.

Hence the given expression represents the commutative property of addition.

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The best option including the commissions is the Hight tech job.

He was offered a job at high tech and Job at the best computers.

The options are as follows:

The offer that will be best option can be determined as follows:

High tech:

total salary per week = 500 + 5% of 500

total salary per week = 500 + 5 / 100 × 500

total salary per week = 500 + 25

total salary per week = $525

Best Computer:

total salary per week = 400 + 7.5% of 400

total salary per week = 400 + 7.5 / 100 of 400

total salary per week = 400 + 30

total salary per week = $430

Therefore, the best option including the commissions is the Hight tech job.

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The average number of miles she would have to meet her goal will be 2.62 miles each day.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Keilantra plans to pedal her bike 28.8 kilometers each week. She has already written a great deal. assuming she rides for another four days.

Let n be the number of days required more. Then the equation is given as,

⇒ 28.8 / (7 + n)

⇒ 28.8 / 11

⇒ 2.62 km each day

The average number of miles she would have to meet her goal will be 2.62 km each day.

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   The number -√17, expressed as a value or number exponential is -17¹/².

  An exponential number is a mathematical expression and one of the many mathematical operations of reduction, it involves the successive multiplication of a number, it has the form:

aᵇ

Where:

  To convert a root into a exponential we must know the way in which these are related, and it is by means of the following property:

√a = a¹/²

  Now in our case we have -√17 which can be expressed as.

(-1)√17, where 17 = a, then

(-1)17¹/²

-17¹/²

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The common factors of the numbers 18 and 30 is 6

The numbers are given as

18 and 30

Express 18 and 30 as a product of its factors

So, we have

18 = 2 * 3 * 3

30 = 2 * 3 * 5

Multiply the common factors in the above expression

Common factors = 2 * 3

Evaluate the product

So, we have

Common factors = 6

Hence, the common factors of the numbers 18 and 30 is 6

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Inverse of the give function F(x) = √2 x + 1 is F⁻¹(x) = ( x - 1 ) / √2

Given is a function of x, F(x) = √2 x + 1

These question can be solved by following 4 easy steps

Step 1 : Switch the F(x) with the variable y

This implies, F(x) = √2 x + 1 becomes y = √2 x + 1

Step 2 : Interchange the variable x and y in the above obtained equation

This implies, from the equation y = √2 x + 1, we get

x = √2 y + 1

Step 3 : Solve the new obtained equation for y

This implies, we have to simplify the equation by rearranging the terms to get the equation in terms of the variable x.

x = √2 y + 1

=> x - 1 = √2 y

=> √2 y = x - 1

=> y = ( x - 1 ) / √2

Hence we obtain the required equation.

Step 4 : Switch the variable y with F⁻¹(x)

This implies, y = ( x - 1 ) / √2 becomes F⁻¹(x) = ( x - 1 ) / √2

Therefore, we get the inverse of the given function F(x) = √2 x + 1 as F⁻¹(x) = ( x - 1 ) / √2.

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Answer:

x = 4

Step-by-step explanation:

-8x = -x - 28

Move the -x on the right side to the left

-8x + x = -28

-7x = -28

Cross out the negatives

7x = 28

Divide by 7

x = 4

Answer:

[tex]x = 4[/tex]

Step-by-step explanation:

[tex]-8x = -x - 28 \text{ / Add 8x}\\-8x + 8x = -x - 28 + 8x\\\to 0 = 7x - 28 \text{ / Add 28}\\0 + 28 = 7x - 28 + 28\\\to 28 = 7x \text{ / Divide by 7}\\\frac{28}7 = \frac{7x}7\\4 = x[/tex]

Answer: $1875

Step-by-step explanation:Take x as the amount of money you have. 30%=30/100. So, 30/100*x=15. x= 2500. So, 75% of x is 75/100 * 2500 = 1875$

Answer: White rose ratio: 4/12 (simplify) Red rose ratio: 8/12 (simplify)

But you ask for total then red rose so 12/8

Step-by-step explanation: 4+8=12 That is total number of roses. You have 4 white rose so 4 out of 12. Have 8 red rose so 8 out of 12