if x+[tex]\frac{1}{x}[/tex]=[tex]\sqrt{11}\\[/tex], find the value of [tex]x^{3}[/tex]+[tex]\frac{1}{x^{3}}[/tex]

Answer:

See below!

Step-by-step explanation:

Let the two numbers be x and y

x + y = 66 ----------------(1)

2x = y + 15

2x - y = 15 ---------------(2)

Add both equations

x + y + 2x - y = 66 + 15

x + 2x = 66 + 15

3x = 81

Divide both sides by 3

Put x = 27 in Eq. 1

27 + y = 66

Subtract 27 to both sides

y = 66 - 27

[tex]\rule[225]{225}{2}[/tex]

Answer:

The first option.

Step-by-step explanation:

The graph starts very negative and ends very positive. Not sure how else to explain it.

Graph of the system of inequality is a solid line and a portion of area is shaded which satisfy the condition of the inequality.

What is inequality?

When left hand side is not exactly equal to the right hand side of an equation then it is known as inequality. For system of inequality, there are four types of inequalities <, >, [tex]\le[/tex], and [tex]\ge[/tex].

Using following steps anyone can graph the inequality:

1. Get y alone on one side of a linear inequality in two variables (like x and y) before graphing it. Then, take into account the associated equation that was created by switching the inequality sign for an equality sign. This equation has a line as its graph.

2. The graph is a dashed line if the inequality is strict ( < or >). The graph is a solid line if the inequality is not strict ([tex]\le[/tex] or [tex]\ge[/tex] ).

3. The last step is to choose a point that is not on either line (typically (0, 0) is the simplest) and determine whether or not these coordinates fulfil the inequality. If so, shade the portion of the half-plane that contains that point. If not, shade the opposite half-plane.

Hence, the graph of the system of inequality is a solid line and a portion of area is shaded which satisfy the condition of the inequality.

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Answer:

33,000

Step-by-step explanation:

0.33 x 10^5 is 33,000

The number of sugar cups will be equal to 7.5 cups.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that the ratio of flour to sugar is 2 cups to 3 cups. The number of cops for flour is 5.

The number of sugar cups will be calculated as,

F / S = 2 / 3

5 / S = 2 / 3

S = ( 5 x 3 ) / 2

S = 7.5 cups

Therefore, the number of sugar cups will be equal to 7.5 cups.

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There is no sufficient evidence to support that the population mean is less than 165.

What is mean ?

The average of a set of values is referred to as the mean in statistics and math. The simple arithmetic mean, geometric mean, and harmonic mean are some of the methods that can be used to calculate the mean. The simple arithmetic mean involves adding the numbers together and dividing the result by the number of observations.

From the given data

183, 152, 178 , 157 , 194 , 163 , 144 , 114 , 178 , 152 , 118 , 158

Mean = 157.5833

Standard deviation s = 24.39

  n = 12

Null hypothesis  [tex]H_{0}[/tex] : μ = 165

Alternative Hypothesis [tex]H_{1}[/tex] = μ < 165

Level of significance ∝ = 0.05

degree of freedom (df) = n - 1

                                (df) = 12 - 1

                                (df) = 11

critical value [tex]t_{0.05 , 11}[/tex] = -1.796 (left - tailed)

Test - statistics (t) = ( mean - μ ) / ( s / √n)

                         (t) = -1.053

p - value = 0.1574

p - value > Significance level (∝)

 0.1574 > 0.05

We fail to reject the null hypothesis

Critical value [tex]t_{0.05 , 11}[/tex] = -1.796

                   |[tex]t_{0.05 , 11}[/tex]| = 1.796

|test - statistics| < |critical value|

1.053 < 1.796

We fail to reject the null hypothesis

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Answer:

2 hours and 24 minutes

Step-by-step explanation:

If each worker does 100 each hour than 5 workers do 500 in 2 hourse leaving 100 left so then you 2 hours aka 120 minutes divided by 5 = 24 so it all adds to be 2 hours 24 minutes

Answer:

depends on how long u need it for

Step-by-step explanation:

The equation that represents how many grams of the compound will remain after 4 hours is A(4) = 380 *(1 - 12.1%)⁴

From the question, we have the following parametersa:

Mass = 380 grams

Rate of decay= 12.1% per hour

These parameters can be represented using the following exponential equation

A(n) = A *(1 - r)ⁿ

Where

n = number of hours = 4

A  = Initial mass = 380

r = rate of decay = 12.1%

Substitute the known values in the above equation, so, we have the following representation

A(4) = 380 *(1 - 12.1%)⁴

Hence, the equation is A(4) = 380 *(1 - 12.1%)⁴

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When we have two sides and the angle between them, we have "SAS." Calculate the unknown side using the Law of Cosines, then find the lesser of the other two angles using the Law of Sines, and finally find the final angle by adding the three angles together to make 180 degrees.

The two triangles are congruent if we can demonstrate that two sides and the included angle of one triangle are congruent with two sides and the included angle of another triangle.

Triangles are considered congruent by SAS if their two sides match those of the other triangle's corresponding two sides, and if their included angles are parallel in both triangles.

Hence we get the required answer.

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Answer:

Answer is attached as a photo. I will be honest I am not familiar with a calculus problem being set up that way. I am guessing that is what they are looking for...

Step-by-step explanation:

The upper bound of the given function is 20 while the lower bound of the given function is -8.

A certain kind of relationship called a function binds inputs to essentially one output.

In other words, the function is a relationship between variables, and the nature of the relationship defines the function for example y = sinx and y = x +6 like that.

As per the given function,

-2 ≤ f(x) ≤ 5

At the upper bond, f(x) = 5

[tex]\int\limits^{3}_{-1} {f(x)} \, dx[/tex] = [tex]\int\limits^{3}_{-1} {5} \, dx[/tex]

⇒ 5(3 + 1) = 20

At the lower bond f(x) = -2

[tex]\int\limits^{3}_{-1} {f(x)} \, dx=\int\limits^{3}_{-1} {-2} \, dx[/tex]

⇒ -2(3 + 1) = -8

Hence "The upper bound of the given function is 20 while the lower bound of the given function is -8".

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Answer:

8 cards per chip

Step-by-step explanation:

So 32:4 is the ratio.

Divide by 4 to get 8 cards per chip.

The amount they earn from the sale of candy canes as required is; $6.75.

It follows from the task content that the amount earned by Raven and Tyler as in the task content is to be determined.

Since they sell their cups of hot chocolate for $2.25 in which case they sold 11 cups.

However, the question requires that the amount which they earn from the sale of candy canes is to be determined.

Therefore, since each candy cane is sold for $0.75, it follows that the amount earned on 9 candy cones is;

= 9 × $0.75

= $6.75

Ultimately, the amount earned from the candy canes is; $6.75.

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Answer:

x less than or equal to -2

Step-by-step explanation:

I believe that's the answer

Answer:

  x < -2

Step-by-step explanation:

You want the domain of a function graphed as a curve with an open circle at x=-2, which is the right end of the curve.

The domain is the horizontal extent of the graph. It is the set of values for which the relation is defined.

The open circle at (x, y) = (-2, 0) means that point is not part of the graph. All x-values to the left of that point have corresponding y-values, so the extent of the graph can be said to be ...

  x < -2

The domain of the relation is x < -2.

The expression that represents the total number of miles Hayden biked is A. 5 × (3 + 3 + 2 1/4)

It is important to note that an expression simply refers to mathematical statements which have at least two terms which are then related by an operator. In this case, they contain either numbers, variables, or both.

In this case, since Hayden rode his bike 5 times and each time he biked a 3 mile path, a 2 mile path, and a 2 1/4 mile path. Then in this situation, the expression will be:

= 5 × (3 + 3 + 2 1/4)

In conclusion, the correct option is A.

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The example of a complex fraction is the fraction that consisting fraction on the numerator or denominator or both, that is 4 / (1/6)

The simple fraction consist of both numerator and denominator as whole number. The term on the top is the numerator and the term on the bottom is called the denominator

The complex fraction is defined as the fraction that consisting fraction on the numerator or denominator or both

The example of the complex fractions are

4 / (1/6)

Here the numerator is the 4 and it is a whole number. The denominator is 1/6 that is a fraction

Therefore, the example of a complex fraction is 4 / (1/6)

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The value of x in the considered inequality's solution set is given by -10.

What is  inequality ?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

We have;

3(x - 4) ≥ 5x + 2

By solving;
3(x - 4) ≥ 5x + 2

3x - 12 ≥ 5x + 2

Adding -3x-2 on both sides we get ;

-12-2 ≥ 5x-3x

-14 ≥ 2x

Dividing both sides by 2,we get;

-14/2 ≥ 2x/2

-7 ≥ x

x ≤ -7

As a result, any numbers that are less than or equal to -7 comprise the solution set for this inequality.

There is currently only the value -10 in the solution set because -10 ≤ -7.

As a result, the value of x in the collection of solutions to the inequality under consideration is provided by -10.

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Answer:

Great than 10, but less than 100

Step-by-step explanation:

Make 700% a decimal by dividing by 100

700/100 = 7

7 = 5 = 35

700% of 5 is 35.

Answer:Greater than 10 but less than 100

Step-by-step explanation

700% of 5 = 35

35 is greater than 10

but less than 100

hope this helps

Answer: 23/5 = 4 3/5

20/12 = 1 8/12 = 1 2/3

3 3/4 = 15/5

4 7/15 = 67/15

18/8 = 2 2/8 = 2 1/4

45/18 = 2 9/18 = 2 1/2

8 3/10 = 83/10

1 11/12 = 33/12

Step-by-step explanation:

The slope of the line that passes through (2,4) , (9,10) is 6/7

From the question, the points are given as

(2,4) , (9,10)

Rewrite the above points properly

So, we have the following ordered pairs

(x, y) = (2,4) and (9,10)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (2,4) and (9,10)

Substitute the known values in the above equation

So, we have the following equation

Slope = (10 - 4)/(9 - 2)

Evaluate

Slope = 6/7

Hence, the slope of the line is 6/7

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If triangle RST is an acute triangle, then m∠S must be less than 90°.

What is Acute Traingle?

A form of triangle called an acute triangle has acute angles at each of its three internal angles. Triangles with sharp angles are also known as acute triangles. Acute triangles have different side lengths, but their interior angles are always less than 90°.

In light of the foregoing, if triangle RST is an acute triangle,

then,

∠R , ∠S and ∠T, all are less than 90.

A triangle that is equilateral and has all three interior angles equal and less than 90 degrees, or angles that are all 60 degrees, is an example of an acute triangle.

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Answer:

$300

Step-by-step explanation:

S = amount of $$ Shivani currently has

Y = ... Yamini currently has

1. If Shivani gives 60 to Yamini, the amounts with both will be equal:
   S - 60 = Y + 60

2. if Yamini gives 20 to Shivani, the amount with Shivani would become twice the amount left with Yamini: 2(Y-20) = S+20

3. Simplify both equations and solve the system:

   S = Y + 120
   S = 2Y - 60

   Y + 120 = 2Y - 60  ⇒  Y = 180

   S = 180 + 120 = 300

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

Work Shown:

x = price of the TV before the discount

20% of x = 0.20x = discount, aka amount saved

x - 0.20x = 0.80x = price after discount

0.80x = 240

x = 240/0.80

x = 300

The TV was $300 before the discount.

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

Check:

20% of 300 = 0.20*300 = 60 dollars is the amount saved

300-60 = 240 is the price after the discount, which matches the given info. The answer is confirmed.

Answer:

34°

Step-by-step explanation:

34° is the the compliment of 56°

complementary angles can add upto 90°

56 + 34 = 90

90° - 56° = 34°

or

56° + x = 90°

-56 -56

x = 34°

Name of the angle = acute angle 34°<90°

0° - 90° = acute angles

90° - 180° = obtuse angles

By using Unitary method it can be calculated that

4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint

 1 quart of blue paint is mixed with  [tex]3\frac{1}{3}[/tex] quarts of white paint

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

a) Here, Unitary method will be used

Blue Paint                   White Paint

(Quart)                          (Quart)

[tex]1\frac{1}{2}[/tex]                                     5

[tex]1\frac{1}{5}[/tex]                                     4

1                                        [tex]3\frac{1}{3}[/tex]

5 quarts of white paint is mixed with [tex]\frac{3}{2}[/tex] quarts of  blue paint

1 quart of white paint is mixed with [tex]\frac{3}{2} \times \frac{1}{5}[/tex] quarts of blue paint

4 quarts of white paint is mixed with [tex]\frac{3}{2} \times \frac{1}{5} \times 4[/tex] quarts of blue paint

4 quarts of white paint is mixed with [tex]\frac{6}{5}[/tex] quarts of blue paint

4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint

Again

[tex]\frac{3}{2}[/tex] quarts of blue paint is mixed with 5 quarts of white paint

1 quart of blue paint is mixed with  [tex]5 \div \frac{3}{2}[/tex] quarts of white paint

1 quart of blue paint is mixed with  [tex]\frac{10}{3}[/tex] quarts of white paint

1 quart of blue paint is mixed with  [tex]3\frac{1}{3}[/tex] quarts of white paint

c) Finally

  4 quarts of white paint is mixed with [tex]1\frac{1}{5}[/tex] quarts of blue paint

   1 quart of blue paint is mixed with  [tex]3\frac{1}{3}[/tex] quarts of white paint

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21⁰

sin0=opp/hyp

sin0=5/14

0=(sin^-1)5/14

0=21⁰

The standard form of the complex numbers ( 7 − 5 i ) ⁢ ( 2 + 3 i ) is

Complex numbers are numbers that are represented of the form a + ib

a and b are real numbers. a is the real part and b is in the imaginary part

i = √-1

Opening up the parenthesis by multiplication  

( 7 − 5 i ) ⁢ ( 2 + 3 i )

= 14 +21i - 10i -15i^2

where i^2 = -1

= 14 +21i - 10i -15 * -1

= 14 +21i - 10i +15

= 29 + 11i

The equation is equal to 29 + 11i

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The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation (or zeros or roots of a polynomial function). The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials. A polynomial doesn't need to have rational zeros.

Rational root theorem, also called rational root test, in algebra, theorem that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, the leading coefficient (the coefficient of the highest power) must be divisible by the denominator of the fraction and the constant term (the one without a variable) must be divisible by the numerator.

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