Trigonometry Question:
Find all solutions on the interval [0,2π)
12sin^2(x)+cos(x)-6=0

The elementary row operation that will reduce the x–element in row 2 to 0 in this matrix is -2R1 + R2

The complete question is added as an attachment

The matrix is given as:

1   1    1       12

2  1    0     14

2  0   3      19

Rewrite as:

x   y    z      

1   1    1       12

2  1    0     14

2  0   3      19

So, the x-element of the second row is

x = 2

When the first row is multiplied by negative 2 and added to the second row, the x-element of the second row is reduced to 0

This is represented as;

-2R1 + R2

i.e.

-2(1   1    1       12)

+   2  1    0     14

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

    0  -1   -2    -10

Hence, the elementary row operation that will reduce the x–element in row 2 to 0 in this matrix is -2R1 + R2

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[tex] \sqrt{112x {}^{6}y {}^{3} {z}^{5} } \\ \sqrt{(2 {}^{4} \times 7 )x {}^{6}y {}^{2}yz {}^{4} z } \\ 2 {}^{2}x {}^{3} yz {}^{2} \sqrt{7yz} [/tex]

Events A and B are dependent (option B).

Dependent events are events that can occur together. If event A occurs then event B would occur. In a standard deck of cards, cards that are hearts are red in colour. If a heart card is picked, then it would be red in colour.

Independents events are events whose occurrence do not depend on each other. They are random events.

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I'll go for the third option. It seems sensible to having a balance in estimating provided data, even though that may not always be the case.

Hope this helps!

Answer:

6450.35/90.85 = 71 yards.

Step-by-step explanation:

These are some of the ways you can make 15 by adding three numbers together.

The first way is doing  6+6+3.There are some more ways to do it too.

2nd way is 6+4+5.

3.   1+6+6

4.   5+5+5

Answer:  $34.32

Step-by-step explanation: We first calculate the price of the dress that was on sale. 30% of 35 is 35/10 x3. This is equal to 3.5x3 which is 7+3.5 = 10.5 We subtract this from 35 to get $24.5. So, the dress cost $24.5. Next 1/2 of 17 is 8.5. In total, the items cost $24.5+$8.5 = $33. Then, there is a 4% sales tax we have to add on to 33. 1% of 33 is 33/100 which is 0.33. This time 4 is 1.32. 33+1.32 is 34.32.

The number of bags of candy and cookies sold by the drama club is 4 and 10 respectively

let

The equation:

8.50x + 4.50y = 79

y = x + 6

Substitute x = y + x into

8.50x + 4.50y = 79

8.50x + 4.50(x + 6) = 79

8.50x + 4.50x + 27 = 79

8.50x + 4.50x = 79 - 27

13x = 52

x = 52/13

x = 4

Recall,

y = x + 6

y = 4 + 6

y = 10

Therefore, the number of bags of candy and cookies sold by the drama club is 4 and 10 respectively.

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[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ V=562\\ r=5 \end{cases}\implies 562=\cfrac{\pi (5)^2 h}{3}\implies 1686=25\pi h \\\\\\ \cfrac{1686}{25\pi }=h\implies 21.47\approx h[/tex]

Answer:

1 hour

Step-by-step explanation:

[tex]\begin{array}{ccll} \$&messages\\ \cline{1-2} 5 & 100\\ 9.55& x \end{array} \implies \cfrac{5}{9.55}~~=~~\cfrac{100}{x} \\\\\\ 5x=955\implies x=\cfrac{955}{5}\implies x = 191[/tex]

The number of text messages that can be sent with $9.55 is 191.

Given that, it cost Taub $5.00 to send 100 text messages.

We need to find how many text messages did she send if she spent $9.55.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. The proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let the number of text messages she sent with $9.55.

Now, 5:100::9.55:x

⇒5x=955

⇒x=955/5

⇒x=191

Therefore, the number of text messages that can be sent with $9.55 is 191.

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The value of tanθ = ±∞ or tanθ = ±√(7/5)

The question is a trigonometric equation

A trigonometric equation is an equation that has unknowns that contain trigonometric ratios.

Given the trigonometric equation 7cosec²θ - 9cot²θ = 7, we require tanθ.

So, 7cosec²θ - 9cot²θ = 7

using the trigonometric identity 1 + cot²θ = cosec²θ.

Substituting this into the equation, we have

7cosec²θ - 9cot²θ = 7

7(1 + cot²θ)² - 9cot²θ = 7

7(1 + 2cot²θ + cot⁴θ) - 9cot²θ = 7

7 + 14cot²θ + 7cot⁴θ - 9cot²θ = 7

14cot²θ + 7cot⁴θ - 9cot²θ = 7 - 7

14cot²θ + 7cot⁴θ - 9cot²θ = 0

7cot⁴θ + 14cot²θ - 9cot²θ = 0

7cot⁴θ + 5cot²θ = 0

Factorizing out cot²θ, we have

cot²θ(7cot²θ - 5) = 0

⇒ cot²θ = 0 or 7cot²θ - 5 = 0

⇒ cotθ = ±√0 or 7cot²θ = 5

⇒ cotθ = ±0 or cot²θ = 5/7

⇒ cotθ = ±0 or cotθ = ±√(5/7)

⇒ 1/tanθ = ±0 or 1/tanθ = ±√(5/7)

⇒ tanθ = ±1/0 or tanθ = ±√(7/5)

⇒ tanθ = ±∞ or tanθ = ±√(7/5)

So, the value of tanθ = ±∞ or tanθ = ±√(7/5)

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Answer: [tex]\Large\boxed{2}[/tex]

Concept:

Here, we need to know the idea of the PEMDAS method.

PEMDAS is an acronym for the order of operations.

Solve:

Given expression

[tex]\dfrac{3^3~-~13}{11~-~2^2}[/tex]

Simplify the exponents

[tex]=\dfrac{27~-~13}{11~-~4}[/tex]

Simplify by subtraction

[tex]=\dfrac{14}{7}[/tex]

Simplify the fraction

[tex]\Large\boxed{=2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

[tex]let \: the \: number \: be \: denoted \: by \: p \\ five \: times \: a \: number = 5p \\ square\: of \: a \: number = p {}^{2} [/tex]

[tex] \gamma - p {}^{2} = 5p - p {}^{2} [/tex]

Answer:

16 square units

Step-by-step explanation:

You find the area by multiplying the base times the height.  The base or horizonal length is 4.  You get this from the ordered point x (4,0).  The x coordinate 4, tells us that the point x is 4 spaces to the right of zero, so the length or base is 4.

The height is also 4.  You get this from the point S (2,4)  The y coordinate of 4 tells you how high up the point is.

4 x 4 = 16

Answer:

20%

Step-by-step explanation:

We can start by finding out how much the price of the television was reduced by.

250 - 200 = 50

Now, we need to know what percent of 250 is 50? Let x represent the percent of 250 that is 50. Using this, we can set up an equation:

[tex]x\%\times 250=50[/tex]

Notice that a percentage can also be written as that number over 100.

[tex]\frac{x}{100}\times250=50[/tex]

[tex]\frac{250x}{100}=50[/tex]

Reduce the fraction (250 and 100 have a common factor of 10)

[tex]\frac{25x}{10}=50[/tex]

Reduce the fraction again (25 and 10 have a common factor of 5)

[tex]\frac{5x}{2}=50[/tex]

Multiply both sides by two

[tex]5x=100[/tex]

Divide both sides by 5

[tex]x=20[/tex]

Therefore the price of the television was reduced by 20%.

The possible value of y are 16, 32 and 64

The table above is an exponential table.

Therefore, let's confirm the ratio of the y axis.

8 / 4 = 2

4 / 2 = 2

Therefore, the other y axis can be gotten as follows:

y = 8 × 2 =  16

y = 16 × 2 = 32

y = 32 × 2 = 64

y = 64 × 2 = 128

Therefore, the possible value of y are 16, 32 and 64

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Step-by-step explanation:

Since you haven't provided any functions, I can answer this question generally as to what the function would look like.

So when a polynomial has an even degree, then the two end behaviors will go in the same direction, and when it has an odd degree, then the two end behaviors will be in opposite directions. When a polynomial has a positive leading coefficient the right side will go towards infinity, and if a polynomial has a negative leading coefficient the right side will go towards negative infinity.

So let's look at the information:

As x approaches negative infinity, y approaches positive infinity.

Just given this we can't really say anything about the polynomial since we have to relate this to the right end behavior, or as x approaches infinity, so let's look at that.

As x approaches positive infinity, y approaches negative infinity.

This means that as x increases, y decreases, so that means the leading coefficient is negative. Since we know both end behaviors, and they're opposite (one y-value goes to negative infinity, and the other positive infinity), that means the polynomial is an odd degree.

So this means the polynomial will look something like this:

[tex]ax^n+bx^{n-1}+cx^{n-2}...[/tex]

where the leading coefficient "a" is negative and the degree of the polynomial (degree of leading coefficient) will be odd.

Answer:A

Step-by-step explanation:

edge 2023

Answer:

58, 66, 79, 84, 87 (see explanation for the exact answer)

Step-by-step explanation:

{58, 66, 79, 84, 87}

minimum = 58

lower quartile = 66

median = 79

upper quartile = 84

maximum = 87

Answer + Step-by-step explanation:

58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87

The data set is in order then :

the minimum = 58

The maximum = 87

Determining the median :

first ,we notice that the data set has an even number (14) of numbers

Then

The median is the average of the two central values of the data set :

the two central values are the 7th and 8th numbers:

[tex]\text{median} =\frac{79+79}{2} =79[/tex]

Determining the lower quartile  :

The lower quartile is the median of the set :

58, 60, 65,  67 , 68, 72, 79

this set has an odd number (7) of values

Then

The central value is 67

Therefore

The lower quartile is 67

Determining the upper quartile  :

The upper quartile is the median of the set :

79, 80, 81,  82  , 86, 86, 87

this set has an odd number (7) of values

Then

The central value is the 4th number which is 82

Therefore

The upper quartile is 82

Interquartile range :

82 - 67 = 15

177.8 centimeters.

The shortest distance between the tip of the cone and its rim:

cos θ= base/Hypotenuse

cos 77°=[tex]\frac{40}{H}[/tex]

[tex]0.22495=\frac{40}{H}[/tex]

[tex]H=177.8[/tex]

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The shortest distance between the tip of the cone and its rim exits 51.11cm.

If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.

Cos 38.5 = 40 / x

Solving the value of x, we get

Multiply both sides by x

[tex]$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x[/tex]

[tex]$\cos \left(38.5^{\circ}\right) x=40[/tex]

Divide both sides by [tex]$\cos \left(38.5^{\circ}\right)$[/tex]

[tex]$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]

simplifying the above equation, we get

[tex]$x=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]

x = 51.11cm

The shortest distance between the tip of the cone and its rim exits 51.11cm.

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Answer:

1/4

Step-by-step explanation:

Change is y (f9x) over the change in x.

Look at the f(x) column.

What is the change from -2 to -1?  1

What is the change from -1 to 0? 1

What is the change from 0 to 1? 1

What is the change from 1 to 2? 1

We see that this change is constant.  It is always 1.

Look at the x column.

What is the change from -8 to -4? 4

What is the change from -4 to 0? 4

What is the change from 0 to 4? 4

What is the change from 4 to 8? 4

We see that the change is constant.  It is always 1.

When we put this change the form a/b we get 1/4

The constant in the expression represents that the company earned  85 billion dollars in 2008.

The expression given in the question is known as a quadratic function. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. The graph of a quadratic function is a curve called a parabola. Parabolas may curve upward or downward

An example of a quadratic function is ax² + bx + c

Where: a,b, c are real numbers not equal to zero

c = constant.

The constant in this question is 85. It is the amount earned in 2008

Here are the options:

The company earned  85 billion dollars from 2008 to 2018

The company earned  85 billion dollars in 2008

The company earned 14  billion dollars from 2008 to 2018.

The company earned  14 billion dollars in 2008.

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Answer:

dave needs 3/5

Step-by-step explanation:

Step-by-step explanation:

what is the question ?

what problem needs to be solved ?

is it to find the ratio between fruit and nuts ?

then remember, a ratio is a fraction.

so, the ratio fruit : nuts is

1/5 / 1/3 = 1×3 / 5×1 = 3/5 or 3 : 5

or is it about any fraction problems and we need to bring them to the same denominator to add our compare them ?

to compare the 1/5 cup of fruit with the 1/3 cup of nuts, the smallest common multiple of 5 and 3 is 15. so we need to bring all to .../15.

how to make 15 out of 5 ? by multiplying 5 by 3. and we need to do this on the top of the fraction as well to keep the original value of the fraction.

1/5 = 1/5 × 3/3 = 3/15.

and with the same line of thinking :

1/3 = 1/3 × 5/5 = 5/15.

so, when mixing 1/5 cup of fruit with 1/3 cup of nuts, we get 3/15 + 5/15 = 8/15 cup of trail mix.

here you can clearly see the ratio again : 3/15 : 5/15 = 3:5

the first solution to get only full cups of trail mix is

3 cups of fruit and 5 cups of nuts = 8 cups of trail mix.

anything less will always end up with parts of cups (since 3/5 can't be simplified anymore).

Answer:

The correct answer is 2 [tex]\frac{2}{5}[/tex].

Step-by-step explanation:

To get this answer, we first have to add the numerators.

We can easily say that 4 + 8 = 12

That leaves us with the improper fraction, [tex]\frac{12}{5}[/tex].

To make this fraction proper, we must first find out how many times 5 can go into 12.

5 can go into 12 two times which leaves us with 2 left over from the numerator.

Now all that's left to do is add 2 (the amount of times 5 can go into 12) and [tex]\frac{2}{5}[/tex] (the left over fraction) to get the answer 2[tex]\frac{2}{5}[/tex].

Hope this helps:) Goodluck!

See attached images for the graph.

The radius of cylinder = 6 meter

The height of cylinder = 11 meter

According to the question,

Surface area of the cylinder = 640.56 m²

Let the height of the cylinder = x meters

Let the radius of the cylinder = (x-5)meters

Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)

640.56 = 2 (3.14) (x-5) (x)

640.56/(6.28) = x² - 5x

x² - 5x =102

x² - 5x - 102 =0

using quadratic equation, [-b±√(b² - 4ac)]/2a.

b = -5; a=1; c=102

x =[-(-5) ±√(-5)² - 4(1)(102)]/2

= [5 ± √433]/2

x = 11 and -7

since x=-7 neglect negative value, we get x=11.

The height of the cylinder is 11 meters

The radius of the cylinder is (11 - 5) = 6 meters.

Hence, The radius of cylinder = 6 meter.

The height of cylinder = 11 meter.

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Answer:

Step-by-step explanation:

The radius of cylinder = 6 meter

The height of cylinder = 11 meter

According to the question,

Surface area of the cylinder = 640.56 m²

Let the height of the cylinder = x meters

Let the radius of the cylinder = (x-5)meters

Formula for surface area of cylinder = 2πrh ( where 'r' is the radius of the cylinder and 'h' height of the cylinder)

640.56 = 2 (3.14) (x-5) (x)

640.56/(6.28) = x² - 5x

x² - 5x =102

x² - 5x - 102 =0

using quadratic equation, [-b±√(b² - 4ac)]/2a.

b = -5; a=1; c=102

x =[-(-5) ±√(-5)² - 4(1)(102)]/2

= [5 ± √433]/2

x = 11 and -7

since x=-7 neglect negative value, we get x=11.

The height of the cylinder is 11 meters

The radius of the cylinder is (11 - 5) = 6 meters.

Hence, The radius of cylinder = 6 meter.

The height of cylinder = 11 meter.

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Answer:

x>-3

Step-by-step explanation:

7x+18>-3

transpose 18 to the other side to group the like terms

7x>-3-18

7x>-21

You divide bother sides by a 7 to get the value of x

7x/7>-21/7

therefore x>-3

The probability of the frequency of an event in repeated trials under comparable circumstances is a statistical analysis.

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

Finding the distribution hidden in your data is the aim of a statistical analysis. What do you mean by the distribution that lies underlying my data? "The distribution of your data describes the peaks and valleys of its characteristics in relation to a target population.

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The angles and lengths of each of the given triangles are;

5) m∠B = 57.52°

6) B = 70.81°

7) AB = 55.43 Km

8) AC = 39.06 ft

The cosine rule is expressed as;

c = √[a² + b² - 2ab(cos C)]

5) Using cosine rule;

BC = √[21² + 13² - 2(21*13)(cos 91)]

BC = 24.89

Using sine rule, we can find angle B as;

21/sin m∠B = 24.89/sin 91

sin m∠B = (21 * sin 91)/24.89

sin m∠B = 0.8436

m∠B = sin⁻¹0.8436

m∠B = 57.52°

6) Using cosine rule;

14² = 11² + 13² - 2(11*13)(cos B)]

196 = 121 + 169 - 286(cos B)

cos B = (121 + 169 - 196)/286

cos B = 0.3287

B = cos⁻¹0.3287

B = 70.81°

7) Using cosine rule;

AB = √[24² + 36² - 2(24*36)(cos 134)]

AB = 55.43 Km

8) Using cosine rule;

AC = √[21² + 26² - 2(21*26)(cos 112)]

AC = 39.06 ft

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