I hiking trail is 20 km long. Park organizers want to build five rest ops for hikers with one on each end of the trail in the other three spaced evenly between. How much distance will separate successive rest stops

Answer:

10

Step-by-step explanation:

$15.00 / $1.50 = 10

Answer:

[tex]Number\ of\ science\ books=7[/tex]

Step-by-step explanation:

[tex]Let\ number\ of\ science\ books=x\\\\Story\ books=18\\\\2\times science\ books+4=Story\ books\\\\2x+4=18\\\\Subtract\ 4\ from\ both\ the\ sides\\\\2x+4-4=18-4\\\\2x=14\\\\Divide\ both\ sides\ by\ 2\\\\\frac{2x}{2}=\frac{14}{2}\\\\x=7\\\\Number\ of\ science\ books=7[/tex]

Answer:

31.166 repeating

Step-by-step explanation:

Option A:

Difference of cubes

Solution:

Given expression is [tex]27 x^{3}-64[/tex].

27 can be written as [tex]3^3[/tex].

64 can be written as [tex]4^3[/tex].

[tex]27 x^{3}-64=3^3x^3-4^3[/tex]

[tex]27 x^{3}-64=(3x)^3-4^3[/tex]

To find the identity to rewrite the given expression:

Option A: Difference of cubes

[tex]27 x^{3}-64[/tex] can be rewritten as [tex](3x)^3-4^3[/tex].

That means the difference of two cubes.

So, it is true.

Option B: Difference of squares

[tex]27 x^{3}-64[/tex] cannot be written as square terms.

So, it is false.

Option C: Sum of cubes

[tex]27 x^{3}-64[/tex] cannot be written as sum of cubes.

So, it is false.

Option D: Pythagorean Triples

[tex]27 x^{3}-64[/tex] cannot be written as Pythagorean Triples.

So, it is false.

Hence difference of cubes if the correct answer.

Answer:

So the factors and multiples of 42 are 1, 2, 3, 6, 7, 14, 21, 42

Step-by-step explanation:

Factors are what you can multiply to get a number and a multiples are what you get after multiplication. We can determine the factors of 42. The multiples of 42 are:

[tex]1 x 42= 42[/tex]

[tex]2 x 21= 42[/tex]

[tex]3x 14 = 42[/tex]

[tex]6 x 7 = 42[/tex]

So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The multiples of 42 are 1,2,3,4,5,6 etc

So common multiples and factors are 1, 2, 3, 6, 7, 14, 21, 42

In the equation 6 X 7 = 42, 6 and 7 are factors and 42 is the multiple. Factors are numbers that can be exactly multiplied to get another number, while a multiple is a number that can be divided evenly by another number. Hence, the relationship between factors and multiples is inherently interconnected.

In the equation 6 X 7 = 42, 6 and 7 are the factors, and 42 is the multiple. Factors are numbers you can exactly multiply together to get a another number, in this case 6 and 7 are factors of 42 because when multiplied together, they equal 42. On the other hand, a multiple is a number that can be divided by another number without leaving a remainder, so 42 can be evenly divided by 6 or 7, making it a multiple of those numbers. The relationship between factors and multiples can be seen as two sides of the same coin - factors are what you multiply together to get a multiple.

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Answer:

x[tex]\leq[/tex]38

Step-by-step explanation:

bring back the x and the 38 with a space between to decide on the symbol put back i the less than sign between both terms then put a line underneath to form the symbol less than or equal to.

Answer:

The swimming pool will contain approx [tex]8243\ gal[/tex] of water.

Step-by-step explanation:

Given the swimming pool is in a cylindrical shape.

And the dimensions are [tex]20\ feet[/tex] diameter with a height of [tex]3.5\ feet.[/tex]

Also, [tex]1\ ft^3 =7.5\ gal[/tex]

First, we will find the volume of the swimming pool.

The swimming pool is in cylindrical shape.

So, the volume would be [tex]\pi r^2h[/tex]

The height [tex](h)[/tex] is given as [tex]3.5\ feet.[/tex] To calculate radius [tex](r)[/tex] we will divide the diameter by two.

The radius of the cylinder would be [tex]\frac{20}{2}=10\ feet[/tex]

Plug these values in the formula we get,

[tex]\pi r^2h\\=\pi\times 10^2\times 3.5\\=3.14\times 100\times 3.5\\=1099\ ft^3[/tex]

Now, it is given [tex]1\ ft^3 =7.5\ gal[/tex]

So, [tex]1099\ ft^3 =1099\times 7.5\ gal=8242.5\ gal[/tex]

The swimming pool will contain approx [tex]8243\ gal[/tex] of water.

To find the volume of the cylindrical pool, calculate the radius, then use the formula for the volume of a cylinder, finally convert the volume to gallons. The cylindrical swimming pool can contain approximately 8267 gallons of water.

Step-by-step explanation:

From the looks of it, it seems that you're factoring out the greatest common factor. I gotcha covered.

The square boxes are the biggest common factors in those equations. Hopefully, this helps!

Answer:

a

Step-by-step explanation:

Answer:

1 1/8

Step-by-step explanation:

1/8 of 9

Of means multiplication

1/8 x 9

= 9/8

= 1 1/8

Answer:

1) 3 (6y+7) (2y−7)

2) 12y2+28y−49

3) 36y2+168y+147

4) 36y2−84y−147

5) 3(6y+7)(2y−7)

Answer:

49.4

Step-by-step explanation:

Round up, since the 8 [tex]\geq[/tex] 5

Answer:

cost of a chicken $7.25

cost of a duck $4.25

Step-by-step explanation:

Let c represent chickens and d represent ducks

50 chicken + 3 ducks = $550 ➡ 50c + 30d = $550

44 chicken + 36 ducks = $532 ➡ 44c + 36d = $532

Now find the difference of equations

(50c + 30d) - (44c + 36d) = $550 - $532

6c - 6d = $18

6×(c-d) = $18 divide both sides by 6

c - d = $3 Now we can use this information to find the cost of a chicken and duck

50c + 30d = $550

c - d = $3 multiply second equation by 30

30 × (c-d) = $3 ➡30c - 30d = $30

Now add this new equation we found to the very first equation

30c - 30d + 50c + 30d = $550 + $30 (-30d will eliminate 30d)

80c = $580 divide both sides of the equation by 80

c = $7.25

We know that c - d = 3 so now replace c by $7.25 the price we just found

$7.25 - d = $3

$7.25 - $3 = d

$4.25 = d

Answer:

See diagram and explanation

Step-by-step explanation:

A number on the right is greater than a number on the left on the number line.

Mark numbers 2 and 3 on number line (number 3 is to the right from number 2, because 3 > 2).

Divide the unit segment  between numbers 2 and 3 into 8 equal parts (this segment is the unit segment because the distance between 3 and 2 is 1).

Each such part represents [tex]\frac{1}{8}[/tex] of the segment.

Mark the number [tex]2\dfrac{1}{8}[/tex] next to the right from 2 (you have to take 2 and 1/8).

Answer:

No, a 24 square centimeter rectangle is smaller than a 24 square inch rectangle

Step-by-step explanation:

we know that

[tex]1\ in=2.54\ cm[/tex]

so

Convert in^2 to cm^2

[tex]24\ in^2=24(2.54)^2=154.8\ cm^2[/tex]

so

[tex]24\ cm^2 < 154.8\ cm^2[/tex]

therefore

[tex]24\ cm^2 < 24\ in^2[/tex]

A 24 square inch rectangle is larger than a 24 square centimeter rectangle due to unit conversion.

No, a 24 square inch rectangle is larger than a 24 square centimeter rectangle.

To compare rectangles of different units, we need to convert the units to the same measurement. Since 1 inch is equal to 2.54 centimeters, a square inch is larger than a square centimeter.

Therefore, a 24 square inch rectangle has a greater area than a 24 square centimeter rectangle.

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{1}{2}[/tex] and c = 4, thus

y = - [tex]\frac{1}{2}[/tex] x + 4 ← equation of line

Answer:

-8y = -9x - 5

y = (9/8)x + 5/8

Step-by-step explanation:

y-int 5/8

The y-intercept of the given line equation 9x – 8y + 5 = 0, is 5/8, which is obtained by rearranging the equation into the slope-intercept form.

The subject pertains to finding the y-intercept of a line from a given equation, which is a topic in Algebra.

The equation given is 9x – 8y + 5 = 0. First, we need to rearrange the equation into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Arranging the equation, we get: -8y = -9x -5, which simplifies further to y = 9/8x + 5/8. So, the y-intercept of the line is 5/8.

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Answer:

this expression is not factorable

Step-by-step explanation:

Answer:  

Step-by-step explanation:

you need to divide 10 by 2/3.

Katty has 10/1 tanks of gas fuel in his truck. He uses 2/3 of it each day.

81k^2 - m^2 factors to

(9k + m)(9k - m)

Prove this by FOILing.

First - 81k^2

Outer - (-9km)

Inner - 9km

Last - (-m^2)

Put it into equation form

81k^2 - 9km + 9km - m^2

And combine terms to get the original equation,

81k^2 - m^2.

⭐ Answered by Hyperrspace (Ace) ⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius! ⭐

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

(9k+m) X (9k - m)

Step-by-step explanation:

81[tex]k^{2}[/tex] - [tex]m^{2}[/tex]

= (9k)^2 - (m)^2 ( taking the square roots)

=(9k+m) (9k - m)

here we have applied the rules of a^2 - b^2 = ( a+b) ( a -b)

here 9k is taking as a and m is taking as b

thus you get your answer.

hope it helps.

Answer:

45 divided by 9 equals 5

Step-by-step explanation:

Answer: The speed of the faster lane is 800 km/hour and the slower plane is 600 km/hour

Step-by-step explanation:

The speed of the faster plane is 800 km/h and the speed of the slower plane is 600 km/h.

The given parameters:

Distance traveled by both planes, d = 3600 km

The distance traveled by both planes is the same;

d = u(t + 1.5) ---(1)

d = (v - 200) (t + 1.5)

3600 = vt + 1.5v - 200t  - 300  

d = vt  ----(2)

3600  =  vt

[tex]v = \frac{3600}{t}[/tex]

[tex]3600 = \frac{3600}{t} t \ +\ 1.5 (\frac{3600}{t} ) \ - \ 200 t - 300\\\\3600 = 3600 + \frac{5400}{t} - 200t - 300\\\\300 = \frac{5400}{t} - 200t\\\\300t = 5400 - 200t^2\\\\200t^2 +300t - 5400 = 0\\\\2t^2 + 3t- 54= 0\\\\(2t - 9)(t + 6)= 0\\\\t = 4.5 \ \ or \ \ -6 \ \\\\t = 4.5 \ hours[/tex]

The speed of the faster plane is calculated as;

[tex]v = \frac{3600}{t} \\\\v = \frac{3600}{4.5} \\\\v = 800 \ km/h[/tex]

The speed of the slower plane is calculated as follows;

[tex]u = v- 200\\\\u = 800 - 200\\\\u = 600 \ km/h[/tex]

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Answer:

$26

Step-by-step explanation:

$6.75 - $7

$3.75 - $4

2 adults = 7x2= $14

3 children = 4x3= $12

$14 + $12 = $26

The answer is D. $26.

Answer:

[tex]x=6\\ \\y=-6[/tex]

Step-by-step explanation:

Given the system of two equations:

[tex]\left\{\begin{array}{l}-4x-2y=-12\\ \\4x+8y=-24\end{array}\right.[/tex]

Add these two equations (left side add to left side and right side add to right side):

[tex]-4x-2y+4x+8y=-12+(-24)\\ \\-2y+8y=-12-24\\ \\6y=-36\\ \\y=-6[/tex]

Substitute [tex]y=-6[/tex] into the first equation:

[tex]-4x-2\cdot (-6)=-12\\ \\-4x+12=-12\\ \\-4x=-12-12\\ \\-4x=-24\\ \\x=6[/tex]

Answer:

x =(-5-√57)/2=-6.275

Step-by-step explanation: