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The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

x² - 6x - 27 = 0

Adding 27 to both sides:

x² - 6x - 27 + 27 = 0 + 27

x² - 6x = 27

Adding to both sides the square of half the coefficient of x, that is 9:

x² - 6x + 9 = 27 + 9

(x - 3)² = 36

taking square root of both sides:

√(x - 3)² = √36

x - 3 = ±6

x = 3 ± 6

x = 3 + 6 or; x = 3 - 6

x = 9; or x = -3

The solution to the Raoul's equation x² - 6x - 27 = 0 is x = 9; or x = -3

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The cost of packaging the box of chocolates per weight unit is;  ¹/₄x²/(x + 2)

We are given the cost of packing the box as;

C(x) = ¹/₄x²

where;

x is the number of chocolates

We are told that a box can never have fewer than 3 chocolates.

Now, the weight of a box of chocolates is given by; W(x) = x + 2

Thus, cost per unit weight is;

C(x)/W(x) = ¹/₄x²/(x + 2)

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Answer:

It should be 7.

Step-by-step explanation:

If y = 4 multiply 2 by 4 equals eight, then you have 8x-8=48. Do the opposite of subtraction to both sides the 8 cancels on the left side add 8 to 48 you get 56 now all you have to is get x by it self to get that do the opposite of multiplication divide both sides by 8 and you should get 7.

Answer:

hope you can understand

Answer:

3m²n⁴

Step-by-step explanation:

Given :

⇒ [tex]\sqrt[4]{81m^{8}n^{16} }[/tex]

=============================================================

Solving :

⇒ [tex]\sqrt[4]{81}[/tex] × [tex]\sqrt[4]{m^{8} }[/tex] × [tex]\sqrt[4]{n^{16} }[/tex]

⇒ [tex]\sqrt[4]{3^{4} }[/tex] × [tex]\sqrt[4]{(m^{2})^{4} }[/tex] × [tex]\sqrt[4]{(n^{4})^{4} }[/tex]

⇒ 3 × m² × n⁴

⇒ 3m²n⁴

Answer:

f(x) = -1/2x + 1

Step-by-step explanation:

y intercept is +1

For slope, used points on the graph (2,0) and (0,1)

m= y2-y1/x2-x1

= (1-0)/(0-2)

= -1/2

Answer:

Step-by-step explanation:

there is a 50/50 chance of getting a chocolate cupcake. :P

The first step that we need to take before attempting to solve the problem is to understand what the problem is asking us to do and what they are giving us to help solve the problem.  Looking at the problem statement they are asking for us to determine the probability that a point will randomly be plotted in the shaded region.  We are not given much of anything else which means that we will need to use our own numbers.

The picture that was provided has a square with four equal circles inside right next to each other.  Therefore, we can say that each side of the square is going to be 2 units which causes the diameter of the circle to be half that or 1 unit.  We can go even further and determine that the radius is going to be 0.5 units for each circle.  Let's determine the area of all the shapes.

Area of the square

Area of a circle

The area that we got from the circle only gives us the area for one of the circles so we need to multiply the number by four to give us the total area of the circles.

Total area of the circles

Now that we determined the area of both the square and the circles we can move onto the part of finding the probability of a point randomly landing on a circle.

Determine the probability

However, now that we have determined what the probability, looking at the answer options we can see that all of the are in percentages.  So let's convert our probability into a percentage.

Convert to percentage

Therefore, looking at the options given, the option that would best fit this choice would be option B, about 80%.

Answer:

slope = [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, - 9 ) and (x₂, y₂ ) = (12, 6 )

m = [tex]\frac{6-(-9)}{12-2}[/tex] = [tex]\frac{6+9}{10}[/tex] = [tex]\frac{15}{10}[/tex] = [tex]\frac{3}{2}[/tex]

Answer:

Option D graph

Step-by-step explanation:

x - 4 ≥ - 1

add 4 to both sides, x - 4 + 4 ≥ - 1 + 4

x ≥ 3

so x is greater than or equal to 3

- equal to means closed dot at 3

- greater than means arrow to the right of 3

Answer:

[tex]\frac{1}{13}[/tex]

Step-by-step explanation:

Probability is the number of favorable outcomes divided by the number of total outcomes. The total outcomes are all the situations that could possibly happen. There are 52 cards in the deck, so there are 52 total outcomes. Next, the favorable outcomes are the outcomes we want. In this case it is drawing a 6. There are four 6's in a deck of cards: 6 of hearts, 6 of spades, 6 of diamonds, and 6 of clubs. This means there are 4 favorable outcomes.

We can write the probability as a fraction: [tex]\frac{favorable-outcomes}{total-outcomes}[/tex], so we can get [tex]\frac{4}{52}[/tex]. Since both 4 and 52 are divisible by 4, the fraction can be simplified to [tex]\frac{1}{13}[/tex].

Answer:

1/13

Step-by-step explanation:

that's the answer to the question

Answer:

radius = √13

Step-by-step explanation:

Forming the equation :

(x - h)² + (y - k)² = r²

Solving :

The first rational expression simplifies to (m - 1).

The second rational expression simplifies to (m - 2) / m.

The third rational expression simplifies to (m - 2) / (m - 1).

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.com

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

(m² - 2m + 1) / (m - 1)

(m² - 2m + 1) / (m - 1)

= (m - 1) / 1

= m - 1

The first rational expression simplifies to (m - 1).

(m² - 3m + 2) / (m² - m)

(m² - 3m + 2)

= (m - 1)(m - 2)

(m² - m)

= m(m - 1)

So,

(m² - 3m + 2) / (m² - m)

= (m - 2) / m

The second rational expression simplifies to (m - 2) / m.

(m² - m - 2) / (m² - 1)

(m² - m - 2)

= (m - 2)(m + 1)

(m² - 1)

= (m - 1)(m + 1)

So,

(m² - m - 2) / (m² - 1)

= (m - 2) / (m - 1)

The third rational expression simplifies to (m - 2) / (m - 1).

Thus,

The first rational expression simplifies to (m - 1).

The second rational expression simplifies to (m - 2) / m.

The third rational expression simplifies to (m - 2) / (m - 1).

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The complete question.

Match each rational expression to its simplest form.

(m² - 2m + 1) / (m - 1)

(m² - 3m + 2) / (m² - m)

(m² - m - 2) / (m² - 1)

Options:

(m - 2) / m

(m - 1)

(m - 2) / (m - 1)

Answer:

the cost of the chair is 175.

Step-by-step explanation:

if the chair is x, the table will be 5x

now,

the equation formed will be,

5x+x = 1050

on solving,

6x= 1050

x= 1050÷6

x= 175

therefore, the cost of the chair will be x= 175.

and the cost of the table will be 5x= 5×175 = 875.

Because x is the number of boxes in the shipment, we conclude that the correct option is "the maximum weight allowed in a shipment"

Remember that for a function f(x), the y-intercept is given by f(0).

In this case, the graph represents the amount of allowed weight remaining in a shipment depending on the number of boxes of screws included.

Then the variable x represents "the number of boxes of screws in the shipment".

So when x = 0, there are no boxes.

Then the y-intercepts represents the remaining weight when there are no boxes of screws, which would be all the allowed weight on the shipment.

The correct option is:

"the maximum weight allowed in a shipment"

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Answer:

A

Step-by-step explanation:

the maximum weight allowed in a shipment

Answer:

q→p

Step-by-step explanation:

The converse of p→q is q→p.

which means If q ,then p.

[tex]\begin{cases} u=6i-2j\\\\ v=-3i+7j \end{cases}\qquad \begin{cases} < 6~~,~~-2 > \\\\ < -3~~,~~7 > \end{cases} \\\\[-0.35em] ~\dotfill\\\\ u-v\implies < 6~~,~~-2 > ~~ - ~~ < -3~~,~~7 > \\\\\\ < 6-(-3)~~,~~-2-7 > \implies < 6+3,-9 > \implies < 9,-9 > \implies 9i-9j[/tex]

Answer:

The answer is origin

Answer: orgin

Step-by-step explanation:  orgin

The quantity of pure antifreeze that must be added to 2 quarts of a 20% antifreeze solution to obtain a 60% antifreeze solution 2 quarts

How to solve equation?

You have 2 quarts of 20% antifreeze.

(100%)x + (20%)2 = 60%(x + 2)

100x + 40 = 60(x + 2)

100x + 40 = 60x + 120

100x - 60x = 120 - 40

40x = 80

x = 80/40

x = 2 quarts

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Answer:

4

Step-by-step explanation:

do distributive property first. -7 * 6 and -7 * 3

now you should have -42+21m = 26 + 4m

subtract 4m to the other side 21m-4m=17m

then add 42 to the other side which would give you 68

17m=68

17 divided by 17 =1

68 divided by 17=4

Answer:

I think the letter B is a good idea for me to do the same as oneroure and I have a module that I can use to make sure that I have the right to use the periodic table to find the element name and its symbol then calculate the total amount of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between the rows of the main crop between thank you

Answer:

230 degrees

Step-by-step explanation:

draw a horizontal line from x and use congruent rule to have a full 360 degree circle. You can now subtract 60 and 70 from 360 degrees leaving you with 230 degrees as x

Answer:

4 radians

Step-by-step explanation:

[tex]s = \theta r[/tex]

[tex]20 = 5 \theta[/tex]

[tex] \theta = 4[/tex]

Answer:

20%

Step-by-step explanation:

Take the amount of rent and put it over the total amount of money to find  the percent

800/4000 =.2

Change to percent form by multiplying by 100

.2 * 100 = 20%

a.0+3

b.3

c.3-4

d.-1

....................

The quotient of 552/58 is 276/29.

The quotient of a number is the result or the outcome when you divide two numbers together.

From the given information, the quotient of [tex]\mathbf{\dfrac{552}{58}}[/tex] is can be determined by dividing both the numerator and the denominator by (2):

i.e.

[tex]\mathbf{=\dfrac{276}{29}}[/tex]

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Answer:

A person bought three lots for $22,000 net each and divided them into four lots of equal frontage. The lots were then sold for $18,000 each. What was the approximate percentage of gross profit? 9%The initial investment was $66,000 (3 lots at $22,000 each).