A pulley is used to pull a boat to the dock. The rope is attached to the boat 7 feet below the level of the pulley. What is the distance from the boat to the dock when the rope is 25 feet long?

Answer:

80 m/s

Explanation:

Given:

i) initial velocity (as starts from rest) = 0 m/s

ii) acceleration:  4 m/s²

iii) distance travelled: 800 m

Formula required:

(final velocity)² - (initial velocity)² = 2 × acceleration × distance

Now solve:

v² - 0² = 2 × 4 × 800

v² = 6400

v = √6400

v = 80 m/s

The simplest radical form of the expression is [tex]\mathbf{40 ^{2/3}x^{{10}/{3}}y^2}[/tex].

When we have indices in the form [tex]\mathbf{ax^{2/3}}[/tex], we are going to find the cube root of the (ax)². This can be mathematically expressed as:

[tex]\mathbf{=(\sqrt[3]{ax})^2 }[/tex]

From the given information:

[tex]\mathbf{=(8x^55y^3)^{2/3}}[/tex]

[tex]\mathbf{=(\sqrt[3]{8x^55y^3} } )^2[/tex]

[tex]\mathbf{=(\sqrt[3]{40x^5y^3} } )^2[/tex]

[tex]= (\sqrt[3]{40x^5} \times \sqrt[3]{y}^3)^2[/tex]

[tex]\mathbf{= 40 ^{2/3}x^{{5*2}/{3}}y^2}[/tex]

[tex]\mathbf{= 40 ^{2/3}x^{{10}/{3}}y^2}[/tex]

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Answer:

[tex] - \infty < x < \infty [/tex]

Step-by-step explanation:

Kyles's monthly repayment on the television based on hire purchase agreement is R229

The monthly repayment is the amount paid monthly with interest on a particular loan or to recover from debt.

From the given information:

Thus

principal amount left to be repaid = 5600 - 840 = 4760

Using the formula:

[tex]\mathbf{M=\dfrac{P( \dfrac{r}{12}) (1+\dfrac{r}{12})^n }{(1+\dfrac{r}{12})^n - 1}}[/tex]

[tex]\mathbf{M=\dfrac{4760( \dfrac{0.14}{12}) (1+\dfrac{0.14}{12})^{24} }{(1+\dfrac{0.14}{12})^{24} - 1}}[/tex]

M = R228.54

M ≅ R229

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The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is C.

The Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

 [tex](a+b) > c\\(b+c) > a\\(c+a) > b[/tex]

Given the length of the two sides of the triangle, therefore, we can write the inequalities,

8 + 5 > x  ⇒   13 > x

8 + x > 5  ⇒  x > - 3

5 + x > 8  ⇒  x > 3

Now, as per the inequality the value of x can lie between 3 to 13, but as the side needs to be greatest, therefore, the value of x will be 12.

Hence, the correct option is C.

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Answer:

12in

Step-by-step explanation:

By using a system of equations, we will see that the solution is:

x = 25, y = -50, z = -15

We can write this as a system of equations:

4x + 2y - z = 15

x + y - z = -10

-3x - y + z = 60

Notice that if we add the second and third equations, we get:

(x + y - z) + (-3x - y + z ) = -10 + 60

-2x = 50

x = 50/-2 = -25

So we already got the value of x. Replacing that in the second equation we et:

25 + y - z = -10

Isolating y we get:

y = -10 - 25 + z = z - 35

Now we can replace that in the first equation:

4x + 2y - z = 15

4*25 + 2*(z - 35) - z = 15

100 + z - 70 = 15

z = 15 - 100 + 70 = -15

And using:

y =  z - 35 = -15 - 35 = -50

Then the soution to the matrix equation is:

x = 25, y = -50, z = -15

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By using the listing method, the number of possible uniforms that Brilliant Spa can choose from is equal to 9 uniforms.

In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.

From the information provided above, we have the following points:

By using the listing method, a list of all the elements in this data set is given by:

List = {(yellow, black), (yellow, blue), (yellow, white), (red, black), (red, blue), (red, white), (green, black), (green, blue), (green, white)}

Number of possible uniforms = 9 uniforms.

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Answer:

y=mx+c

Step-by-step explanation:

if any one of them have this form it's the linear function

The height of the tree is 9 meters

This is the angle the line of sight makes with the horizontal.

Analysis:

The line of sight , the shadow length and height of tree form right angled triangle.

Let the height of tree be h

so that, tan 24 = h/20

h = 20 tan 24

h = 20(0.445) = 8.9m = 9m

In conclusion, the height of the tree is 9m.

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Answer:

  x/5

Step-by-step explanation:

The revenue from sales is the product of the selling price of the ticket and the number of tickets sold.

__

If n represents the number of tickets sold, then the revenue from selling tickets for £5 each will be ...

  (n)(£5) = £x

Dividing by the coefficient of n will given the number of tickets sold:

  n = £x/(£5) = x/5

The number of tickets sold is x/5.

Answer:

Add 3 to both sides

Property: Addition property of equality

Step-by-step explanation:

Action: Add 3 to both sides.

⇒ x - 3 =               12

(cancel out)+ 3     + 3

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

     x    =        15  

The property used:

→ equation is true and the same #is added to each side the resulting equation is true. for any #s a,b,c,if a=b then a+c=b+c.

Answer:

ok no problem

i am here to give knowledge

Answer:

[tex]q^2-2q+1[/tex]

Step-by-step explanation:

[tex](q-1)^2=(q-1)(q-1)[/tex]

Distribute: [tex]q^2-q-q+1[/tex]

Solve: [tex]q^2-2q+1[/tex]

Hope this helped! Have a great day/night! :)

The solution to the equation [tex]\frac{2x}{x - 1} - \frac{2x -5}{x^2 - 3x + 2} = \frac{-3}{x -2}[/tex] is (b) there is no solution.

The equation is given as:

[tex]\frac{2x}{x - 1} - \frac{2x -5}{x^2 - 3x + 2} = \frac{-3}{x -2}[/tex]

Factorize the quadratic numerator

[tex]\frac{2x}{x - 1} - \frac{2x -5}{(x - 1)(x - 2)} = \frac{-3}{x -2}[/tex]

Multiply through by (x - 1)(x - 2)

2x(x - 2) - (2x -5) = -3(x - 1)

Expand

2x² - 4x - 2x + 5 = -3x + 3

Collect like terms

2x² - 4x - 2x + 3x + 5 - 3 = 0

Evaluate the like terms

2x² - 3x + 2 = 0

Using a graphical tool, the above equation has no real solution

Hence, the solution is (b) there is no solution.

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The true equation will be f(6) = 0. Then the correct option is C.

A statement, principle, or policy that creates the link between two variables is known as a function.

The function f(x) is given by the set of ordered pairs.

{(1,0), (–10,2), (0,6), (3,17), (–2,–1)}

Then the function can be written as

f(abscissa) = ordinate

Then the function will be

f(0) = 6

Then the correct option is C.

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Answer:

f of 0 = 6

Step-by-step explanation:

Edge

Answer:

130

Step-by-step explanation:

can't have a 4 in units so carry over

The next whole number after 123 in base four is 130.

The entire amount of digits employed in a specific number system is referred to as the base of that system. The [0, b -1] range is occupied by the digits of the base "b" number system. The radix of a number system is another name for this base of the number system.

Given, A number in base four, 123.

Now, In base four there are 4 numbers they are 0, 1, 2, 3.

the next whole number in the number (123)₄ will be (130),

As after adding 1 to the unit digit it will become 'zero' and 1 will carry over.

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Step-by-step explanation:

a complicated way to say "the probability to roll a number that is less or equal to 5".

and that is

5 desired cases over 6 total cases, and that means

5/6 = 0.833333333...

Answer:

1.equilateral

2.isosceles

3.isosceles

4.isosceles and right

5.scalene

6.scalene and right

7.isosceles and right

8.isosceles

9.equilateral

Answer:

$213.84

Step-by-step explanation:

Think of a rectangle. In the case the length is 6 meters and the width is for meters. To be able to find the area of this rectangle, you need to multiply the length by the width. 6 multiplied by 4 is 24. In the equation it tells you that 1 square meter is $8.91, so now you are trying to figure how much 24 square meters would cost. To figure this out, you will need to multiple 24 by $8.91 giving you $213.84.

Hope this helps.

Sum of two interiors=Exterior

[tex]\\ \rm\Rrightarrow 39+6x+11=11x-10[/tex]

[tex]\\ \rm\Rrightarrow 6x+50=11x-10[/tex]

[tex]\\ \rm\Rrightarrow 60=5x[/tex]

[tex]\\ \rm\Rrightarrow x=12[/tex]

Answer:

3y-15

Step-by-step explanation:

(y-7)3=3y-21

3y-21+6=3y-15

Answer:

the heart rate increases for 6 minutes, remains constant for 19 minutes ,and then gradually decreases for 5 minutes

Blocks would he need on the 12th step of the pattern is 34.

The correct option is A

A series is the cumulative sum of a given sequence of terms.

Given:

We can write the series as follows:

1,4,7,10,13,.......

First term =1

common difference= 4-1=3

Using Arithmetic series

[tex]a_{12}\\[/tex]= a+11d

    =  1 +11*3

    = 1+33

    = 34.

Hence, 34 blocks need on 12th step.

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Answer:

whats the solution you looking at?

Step-by-step explanation:

4 can be greater than 1 by number wise but also 4 could be -4 or 4 could not add up to the full amount of w for like if you have 4 2 by 2s and 2 16 by 16s 4 would be smaller

Usando el teorema fundamental de conteo, se encuentra que 132 maneras diferentes de otorgar las medallas.

Es un teorema que establece que si hay n cosas, cada una con [tex]n_1, n_2, \cdots, n_n[/tex] formas de hacer, cada cosa independiente de la otra, el número de formas en que se pueden hacer es:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

En este problema:

Así, el número de maneras diferentes en que se pueden otorgar las medallas es dado por:

[tex]N = n_1 \times n_2 = 12 \times 11 = 132[/tex]

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Answer: (-12, 0) and (6, 0)

Step-by-step explanation:

The equation of the parabola is of the form

[tex]y=a(x+3)^2 + 405[/tex]. To find a, we can substitute in the coordinates (0,360).

[tex]360=a(0+3)^2 + 405\\\\360=9a+405\\\\-45=9a\\\\a=-5[/tex]

So, the equation is [tex]y=-5(x+3)^2 + 405[/tex]. Setting this equal to 0,

[tex]-5(x+3)^2 + 405=0\\\\5(x+3)^2 = 405\\\\(x+3)^2 = 81\\x+3=\pm 9\\\\x=-12, 6[/tex]

So, the x-intercepts are (-12, 0) and (6, 0).

Answer:

Interest rate is a proportion of a loan rewarded as interest to the borrower, usually expressed as an annual percent of the current loan.

Answer:

See below

Step-by-step explanation:

An interest rate is basically a percentage of principal charged by the lender for the use of its money, and it is paid via simple interest (usually in an annual period). That principal is the amount of money loaned.

For example, you may have seen a 1.5% annual interest rate, or something like that. This means that if your principal was $5000, let's say, you would have to pay $5000 * 0.015 = $75 in interest per year.

Answer:

tha nks

Step-by-step explanation:

The sentence which best describes the interval [-2, 1] is; The function is decreasing on the interval [-2, 1].

From the given table, we see that from the interval of -2 to 1 we see that the value of y constantly decreased with each value.

This is because the differences where 12, 6 and 1.5. Thus, it is clear that the values of y constantly reduces with each corresponding values of x.

Thus, the function is decreasing on the interval [-2, 1].

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The cost per unit actually comes down to 0.8$per unit.

We have given that,

The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.

The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.

Overtime wages were required to produce at levels above 25,000 units.

A cost is an expenditure required to produce or sell a product or get an asset ready for normal use.

The cost of production per unit of the item produced is 1$ as long as the total units produced are less than 2500.

If more than 2500 units are produced then the cost per unit actually comes down to 0.8$per unit.

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