8. (5 points) Simplify. Write the final form with no fractions. cos(x) tan(x).csc(x)

Step-by-step explanation:

let's do the operations :

6(2x - 7) - 3 = 12x - 21

12x - 42 - 3 = 12x - 21

-45 = -21

that is never true, no matter what values for x we come up with.

and therefore, there is no solution.

Answer:

x = 10935/59048 = 0.185

Step-by-step explanation:

27 = 3^3

(27)^2 = (33)^2 = 36

Answer:

Step-by-step explanation:

are the what???

The inverse of the function y = log₀.₅ x is f⁻¹ (x) = (0.5) ˣ.

We are given the function:

y = log₀.₅ x

We need to find the inverse of the function.

First we will find the value of x in terms of y.

The logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.

We can write it as:

(0.5)^ y = x

x = (0.5) ^ y

now, the inverse of the function will be:

f⁻¹ (x) = (0.5) ˣ

Therefore, the inverse of the function y = log₀.₅ x is f⁻¹ (x) = (0.5) ˣ.

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The classification of the compounds according to their functional class: A | Aldehyde

B | Alcohol

C | Ketone

D | Amine

Compound A contains a carbonyl group (C=O) bonded to two alkyl groups (R-). This is the general structure of an aldehyde. Aldehydes are characterized by their strong, sweet odor.

They are also very reactive, and can be used to make a variety of other compounds, such as esters and carboxylic acids.

Compound B contains an oxygen atom (O) bonded to two alkyl groups (R-). This is the general structure of an alcohol. Alcohols are characterized by their ability to dissolve other polar compounds, such as water. They are also used in a variety of products, such as solvents, cleaners, and fuels.

Compound C contains a carbonyl group (C=O) bonded to a propyl group (CH3CH2CH2-) and an amino group (NH2). This is the general structure of a ketone.

Ketones are characterized by their strong, sweet odor. They are also very reactive, and can be used to make a variety of other compounds, such as esters and carboxylic acids.

Compound D contains a nitrogen atom (N) bonded to three alkyl groups (R-). This is the general structure of an amine. Amines are characterized by their basic properties. They are also used in a variety of products, such as pharmaceuticals, plastics, and fertilizers.

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The inverse of the matrix A is:

| -5  2 |

|   3 -1 |

To find the inverse of a matrix using row reduction, we can use the following algorithm:

1. Write the matrix A next to the identity matrix I, separated by a vertical line to obtain the augmented matrix [A|I].

2. Apply row operations to transform the left side of the augmented matrix into the identity matrix I. Perform the same row operations on the right side of the augmented matrix to obtain the inverse matrix A^-1.

3. If the left side of the augmented matrix cannot be transformed into I, then A does not have an inverse.

Let's apply this algorithm to find the inverse of the matrix A:

```

| 1  2 |

| 3  5 |

```

We first write the augmented matrix [A|I]:

```

| 1  2 | 1  0 |

| 3  5 | 0  1 |

```

Next, we perform row operations to transform the left side of the augmented matrix into I:

R2 - 3R1 -> R2

```

| 1  2 | 1   0 |

| 0 -1 | -3  1 |

```

-R2 -> R2

```

| 1  2 | 1    0 |

| 0  1 | 3   -1 |

```

-2R2 + R1 -> R1

```

| 1  0 | -5   2 |

| 0  1 | 3   -1 |

```

We have now transformed the left side of the augmented matrix into I, so the right side is the inverse matrix:

```

| -5  2 |

|  3 -1 |

```

Therefore, the inverse of the matrix A is:

```

| -5  2 |

|   3 -1 |

```

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The question requires to find out how long it will take a hiker to make a complete circuit around the triangular trail with an average walking speed of 2 m/s.

The triangular hiking trail is given in the diagram below; The distance around the trail is the sum of all the three sides of the triangle. To find the length of each side of the triangle, we will apply the distance formula. Distance Formula The distance formula between two points (x₁, y₁) and (x₂, y₂) in a plane is given by;\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)For example, the length of side AC can be calculated as follows;\(AC=\sqrt{(20-0)^2+(10-0)^2}\)\(AC=\sqrt{(20^2+10^2)}\)\(AC=\sqrt{400+100}\)\(AC=\sqrt{500}\)\(AC=22.36\text{ m}\)Similarly,

The length of the other two sides can be calculated as follows; AB = 14.14 mBC = 20 m The perimeter of the triangle is the sum of all the three sides. P = AB + BC + AC P = 14.14 + 20 + 22.36 P = 56.5 m Hence, it will take a hiker more than 100 minutes to make a complete circuit around the triangular trail. Answer: More than 100

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If a lab class conducts a 1000 trial scattering probability experiment. nine marbles were used on a 47.20 cm wide board. The number of hits recorded were 615, the diameter of the marbles is approximately 4.1 cm.

Assuming that the experiment was conducted with the same conditions (e.g. speed, direction) for each trial, we can estimate the diameter of the marbles using the scattering probability and the size of the target area.

The scattering probability is the ratio of the number of hits to the total number of trials. In this case, the scattering probability is:

P = 615/1000 = 0.615

This means that, on average, 61.5% of the marbles that were aimed at the board hit one of the target marbles.

The target area is the area of the board divided by the number of targets. The area of the board is the product of its width and height, which we don't know. However, we can assume that the height of the board is much larger than the diameter of the marbles, so that the height does not significantly affect the scattering probability.

Therefore, we can estimate the target area by dividing the width of the board by the number of targets:

A = 47.20 cm / 9 = 5.2444 cm^2

The target area is the area of one target marble, assuming they are all the same size. The area of a circle is given by:

A = π (d/2)^2

where d is the diameter of the circle.

Solving for d, we get:

d = √(4A/π) = √(4 × 5.2444 cm^2 / π) ≈ 4.1 cm

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now, that radical expression above is just the simplification of a longer expression, and that could have been many really, but off the many, this would be one that simplifies like so

\(\boxed{4\sqrt[4]{65610}~~ - ~~3\sqrt[4]{146410}} \\\\[-0.35em] ~\dotfill\\\\ 4\sqrt[4]{(6561)(10)}~~ - ~~3\sqrt[4]{(14641)(10)}\implies 4\sqrt[4]{(9^4)(10)}~~ - ~~3\sqrt[4]{(11^4)(10)} \\\\\\ 4(9)\sqrt[4]{10}~~ - ~~3(11)\sqrt[4]{10}\implies 36\sqrt[4]{10}~~ - ~~33\sqrt[4]{10}\implies 3\sqrt[4]{10}\)

Answer:

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

If CE=7x+4, then x+3+(8x-9)=7x+4

x+3+8x-9=7x+4

Combine like terms: 9x-6=7x+4

Isolate x to one side: 2x-6=4

add 6: 2x=10

divide by 2: x=5

check your work;plug x into both equations

5+3=8, 8(5)-9=31....8+31=39

7(5)+4=39

For part a, we know that b = ac - 1. We can rewrite this equation as ac = b + 1. So, all vectors of the form (a, b, c) can be written as (a, b, (b + 1)/a).

For part b, we are given that c = 0. So, all vectors of the form (a, b, 0) can be written simply as (a, b, 0).
For part c, we are given that ab = 7. So, all vectors of the form (a, b, c) for which ab = 7 can be written as (a, b, 7/a).
a. All vectors of the form (a, b, c), where b = a c 1:
These vectors are represented as (a, a*c + 1, c). To create such a vector, you can choose any values for 'a' and 'c', and then calculate the value of 'b' by using the given formula (b = a*c + 1).
b. All vectors of the form (a, b, 0):
These vectors are represented as (a, b, 0). To create such a vector, you can choose any values for 'a' and 'b', and the third component 'c' will always be 0.
c. All vectors of the form (a, b, c) for which a b = 7:
These vectors satisfy the condition a*b = 7. To create such a vector, you can choose any values for 'a' and 'b' that satisfy this equation (for example, a=1 and b=7, or a=7 and b=1), and then choose any value for 'c'. The resulting vector will be of the form (a, b, c).

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The correct choice is within your skills and abilities.

Once you get to determine things you are capable of and things you are not capable of, you will be able to concentrate on your strengths more. This will in turn produce big results as compared to if you opted to concentrate on your weaknesses.

It will also result in no or less time wasted in doing what you are less capable of.

Its almost close to impossible to be able to do everything. Each person is gifted in a certain area or skill or capability. We are all different and that's okay.

Its so important to concentrate in the areas you are more comfortable with. This will help you much with improving your skills and abilities.

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Answer:

Step-by-step explanation:

a you just had to say a

Answer:

x=6 and y=−6.

Step-by-step explanation:

Let's solve your system by elimination.

−4x−2y=−12; 4x+8y=−24

−4x−2y=−12

4x+8y=−24

Add these equations to eliminate x:

6y=−36

Then solve 6y=−36 for y:

6y=−36

y = -6

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

−4x−2y=−12

Substitute −6 for y in−4x−2y=−12:

−4x−(2)(−6)=−12

−4x+12=−12(Simplify both sides of the equation)

−4x+12+−12=−12+−12(Add -12 to both sides)

−4x=−24

x = 6

Answer:

4

Step-by-step explanation:

You can cut it 4 ways to obtain equal parts on both sides. It's along the same as the symmetry of a square.

The valid C identifiers from the given options are (b) travel time, (d) number, (f) inchesinonecentimeter, (g) monthly pay, and (h) first.

In C programming, identifiers are names used to identify variables, functions, and other entities. They must follow certain rules to be considered valid. Here's an analysis of each option:

(a) firstc prog: Invalid identifier because it starts with a number, which is not allowed in C.

(b) travel time: Valid identifier because it consists of alphabetic characters and spaces are allowed.

(c) 3feetinayard: Invalid identifier because it starts with a number, which is not allowed in C.

(d) number: Valid identifier because it consists of alphabetic characters.

(e) cpp assignment: Invalid identifier because it contains a space, which is not allowed in C.

(f) inchesinonecentimeter: Valid identifier because it consists of alphabetic characters.

(g) monthly pay: Valid identifier because it consists of alphabetic characters and spaces are allowed.

(h) jack'shomework: Invalid identifier because it contains an apostrophe, which is not allowed in C.

To summarize, the valid C identifiers from the given options are (b) travel time, (d) number, (f) inchesinonecentimeter, (g) monthly pay, and (h) first.

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The permanent life insurance amount per thousand is; $17.76

Life insurance is defined as a product offered by insurance companies that provides for a tax-free benefit in the event of the death of the policy insured. It is usually used to provide a lump some of money that covers the basic living expenses for a family.

Now, we are told that;

Annual Premium = $1332

Face value = $75000

Now, the permanent life insurance amount per thousand is;

PLI per thousand = Annual Premium/(Face Value/1000)

PLI per thousand = 1332/(75000/1000)

= $17.76

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a. Hence in first case, if the distribution is normal, Probability is 0.0077 that the sample mean hardness for a random sample of 16 pins is at least 51

b. In second, Probability is 0 that the sample mean hardness for a random sample of 44 pins is at least 51.

The mean is one of the measures of central tendency used in statistics. The average of the specified collection of numbers is what is referred to as mean. It indicates the data set's values that are distributed equally. The three most popular methods for determining central tendency are the mean, median, and mode.

To find the mean, tally up all the values listed on a datasheet, then divide that total by the total number of values. When all the values are organized in ascending order, the median is the value that falls in the middle of the data. The number in the list that is repeated a maximum number of times is the mode.

a)

Y ~ N ( µ = 50 and σ = 1.6 )

P ( Y > 51 ) = 1 - P ( Y < 51 )

Standardizing the  value

Z = ( Y - µ ) /( σ / √(n))

Z = ( 51 - 50 ) /( 1.6 / √ ( 15 ) )

Z = 2.4206

P (  ( Y - µ ) /( σ / √ (n)) > ( 51 - 50 ) /( 1.6 / √(15) )

P ( Z > 2.42 )

P ( Y > 51 )  = 1 - P( Z < 2.42 )

P ( Y  > 51 )  = 1 - 0.9923  ( from the Z table)

P ( Y   > 51 )  = 0.0077

b)

P ( Y > 51 )  =1 - P ( Y < 51 )

Standardizing the  value

Z = ( Y - µ ) /( σ / √(n))

Z = ( 51 - 50 ) /( 1.6 / √ ( 43 ) )

Z = 4.1

P (  ( Y - µ ) /( σ / √ (n)) > ( 51 - 50 ) / ( 1.6 / √(43) )

P ( Z > 4.1 )

P ( Y > 51 )  =1 - P ( Z < 4.1 )

P ( Y > 51 )  = 1 - 1

P ( Y > 51 )  = 0

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The perimeter of triangle is 66.24 units.

What is triangle?

In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane

Main body:

according to question :

c = 28

let the vertices be A,B,C

∠A= 30°

by using trigonometric ratios,

BC/ AB = sin30°

AB = C = 28

BC/28 = sin30°

BC = 28*sin30°

BC= 28*(1/2)

BC = 14

similarly

AB /CA = cos 30°

28/CA = √3/2

CA = 28*√3/2

CA = 14/√3

CA = 24.24

Hence , perimeter = AB +BC +CA = 28+14+24.24

                              =66.24 units

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Changing the coefficient of x to 6 changes the meaning of expression as 5 is added to 6 times x

Solution:

Given that number 2 in the expression 5 + 2x is called the coefficient of x

We are asked to find what happens when changing the coefficient to 6 change the meaning of the expression

In the expression,

5 + 2x

This means 5 is added to 2 times x or 5 is added to twice of x

Number 2 is called coefficient of x

When we change this coefficient to 6, the expression becomes,

5 + 6x

So now the meaning of expression becomes,

5 is added to 6 times x

So changing the coefficient of x changes the meaning of expressionStep-by-step explanation:

Answer:

Between the edges of the first two triangles there is a ratio. To find this ratio, you need to ratio one edge of a small triangle to one edge of a large triangle. So 5/30=6/36=8/48=1/5. The ratio we want to find is 1/5 or 5.

The length of BC in this problem is given as follows:

BC = 3.6.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The similar triangles for this problem are given as follows:

ABC and ADE.

Hence the proportional relationship for the side lengths is given as follows:

3/5 = BC/6.

Applying cross multiplication, the length BC is given as follows:

BC = 6 x 3/5

BC = 3.6.

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Answer:

x = 55, y = 70, z = 125

Step-by-step explanation:

125 and x are adjacent angles and are supplementary, then

x = 180 - 125 = 55

The triangle is isosceles ( 2 congruent sides ) thus the base angles are congruent, both 55

The sum of the 3 angles in the triangle = 180° , thus

y = 180 - (55 + 55) = 180 - 110 = 70

55 and z are adjacent and supplementary, so

z = 180 - 55 = 125

Answers:

x = 55

y = 70

z = 125

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

Explanation:

The tick marks indicate those two lines are the same length. We have an isosceles triangle. One base angle is x. The other missing base angle is also x, which is adjacent to angle z. The base angles of any isosceles triangle are always congruent.

Since the 125 and x degree angle form a straight line, they must add to 180

x+125 = 180

x = 180-125

x = 55

We can use this to find y

x+x+y = 180 .... three angles of any triangle always add to 180

2x+y = 180

2(55)+y = 180 .... plug in x = 55

110+y = 180

y = 180-110

y = 70

And,

x+z = 180

55+z = 180 ... plug in x = 55

z = 180-55

z = 125

Answer:

The answer is x = \(\frac{-5}{3}\).

Step-by-step explanation:

First, we expand the brackets. Therefore:

\(2x+6 = -4x+(-4)\)

\(2x+6 = -4x -4\)

Then, we separate the like terms:

\(2x+4x = -4-6\)

Then we add the like terms up and solve for x:

\(6x = -10\)

Therefore:

\(x = \frac{-10}{6}\)

which, simplified, is:

\(x = \frac{-5}{3}\).

Answer:

83 degrees

Step-by-step explanation:

We can use the consecutive angle theorem to find the the value of x.

We can do that by doing 5x+10.5+6x+10 = 180

After simplifying, we get 11x+20.5=180

Subtract 20.5 on both sides and you get 11x=159.5.

Divide by 11 on both sides and you get x=14.5

Now we can use opposite angle theorem and set angle N and angle T equal.

That means we could write 5x+10.5 = m<T

We can substitute 14.5 for x and we get 72.5+10.5 = m<T

Simplify and you get 83 = m<T

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

Hope this helps!

The proportion EF/DF = BC/AC is true. Hence, option A is the accurate answer to this question.

We are given that the two triangles ΔABC and ΔDEF are similar.

According to the definition of a similar triangle, we know that the ratio of the corresponding sides is proportional and the corresponding angles are always congruent.

Since ΔABC and ΔDEF are similar, this implies that -

∠A corresponds to ∠D,

∠B corresponds to ∠E, and

∠C corresponds to ∠F.

Thus we can say -

EF/DF = BC/AC

AB/DF = DE/AC

AB/EF = DE/BC

Only option A satisfies the condition. Hence, the proportion EF/DF = BC/AC is true.

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The complete question is -

The triangle abc and triangle def are similar. Which proportion must be true?

Answer:

For a decimal 0.3333(it goes on forever)

Step-by-step explanation:

It is 0.3333 because that's the closest to a third you can get

Answer:

There are many like 2/6, 3/9, 4/12, 5/16 and so on.

Step-by-step explanation:

a) The luminosity of Alpha Centauri A is 3.817 × \(10^26\)Watts.

b) The light bulb must be placed at a distance of 1.9×\(10^17\)m away.

a) To calculate the luminosity of Alpha Centauri A, we can use the inverse square law for light. This law states that the luminosity of a light source is equal to the apparent brightness divided by 4π times the square of the distance. The apparent brightness of Alpha Centauri A is given as 2.7×\(10 ^−8\)Watts/m2 and its distance is 4.4 light-years, which is equal to 4.05 × \(10^16\)m. Thus, the luminosity of Alpha Centauri A is equal to 2.7 × \(10^-8\)Watts/m2 divided by (4π ×(4.05 × \(10^16\) m)2), which is equal to (4π×(4.05 × \(10^16\)m)2) Watts.

b) To calculate the distance at which a light bulb must be placed in order to have the same apparent brightness as Alpha Centauri A, we can again use the inverse square law for light. This time, we will use the given luminosity of the light bulb (100 Watts) and the given apparent brightness of Alpha Centauri A (2.7 × \(10^-8\)Watts/m2). Rearranging the equation, we get the distance equal to the square root of (100 Watts divided by 4π times 2.7 × \(10^-8\)Watts/m2), which is equal to 1.9 ×\(10^17\)m. Thus, the light bulb must be placed at a distance of1.9 × \(10^17\)m away in order to have the same apparent brightness as Alpha Centauri A in our sky.

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