Use basic trigonometric identities to simplify the expression: 2 sin (x) cos (x) sec (x) csc (x) = ?

Answers

Answer 1

Answer:

[tex]2sin(x)*cos(x)*sec(x)*csc (x)=2[/tex]

Step-by-step explanation:

Remember the identities:

[tex]sec(x)=\frac{1}{cos(x)}\\\\csc(x)=\frac{1}{sin(x)}[/tex]

Ginven the expression:

[tex]2sin(x)*cos(x)*sec(x)*csc (x)[/tex]

You need to substitute [tex]sec(x)=\frac{1}{cos(x)}[/tex] and [tex]csc(x)=\frac{1}{sin(x)}[/tex] into it:

[tex]2sin(x)*cos(x)*sec(x)*csc (x)=2sin(x)*cos(x)*\frac{1}{cos(x)}*\frac{1}{sin(x)}[/tex]

Now, you need to simplify.

Remember that:

[tex]\frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d}[/tex]

And:

[tex]\frac{a}{a}=1[/tex]

Then, you get:

[tex]=\frac{2sin(x)*cos(x)}{cos(x)*sin(x)}}=2[/tex]


Related Questions

What is the slope if the line x+3y = 10

Answers

Answer:

the slope is -1/3

the Y intercept is 10/3

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

We want to get the equation in slope intercept form (y=mx+b)  where m is the slope and b is the y intercept

x+3y = 10

Subtract x from each side

x-x+3y = -x+10

3y = -x+10

Divide each side by 3

3y/3 = -1/3x +10/3

y = -1/3x +10/3

The slope is -1/3 and the y intercept is 10/3

An object is translated by (x - 2, y - 6). If one point in the pre-image has the coordinates (-3, 7), what would be the coordinates of its image? (-5, 1) (-1, 13) (-1, 7) (-9, 5)

Answers

Answer:

B. (-1,13)

Step-by-step explanation:

Given translation

(x,y)→(x-2,y-6)

moves point 2 units to the left and and 6 units down.

If a point after this translation has coordinates (-3,7), then its preimage has coordinates (-1,13) (translate the image point 2 units to the right and 6 units up to get preimage point).

Answer:

(-5,1)

Step-by-step explanation:

A small pie factory needs to ship 360 pies a day to stay profitable. 180 pies are baked every 3 hours. Of the baked pies, 20% go directly to freezer storage and 80% are loaded on a truck for delivery. Find the constant of proportionality for the number of pies baked and loaded on a truck for delivery. A.48 B. 60 C. 96 D. 144

Answers

Answer:

Constant of proportionality should be 48.

Step-by-step explanation:

Given that a small pie factory needs to ship 360 pies a day to stay profitable. 180 pies are baked every 3 hours. Of the baked pies, 20% go directly to freezer storage and 80% are loaded on a truck for delivery.

Now we need to find about what is the constant of proportionality for the number of pies baked and loaded on a truck for delivery.

Number of baked pies = 180

Number of pies loaded on truck for delivery = 80% of baked pies

= 0.80(180)= 144 in 3 hours.

So number of pies loaded per hour = 144/3= 48

Hence constant of proportionality should be 48.

7x+(2x+7)=9x+7 show work

Answers

it is true 9x=9x

7x+(2x+7)=9x+7

7x+2x+7=9x+7

-7. -7

7x+2x=9x

9x=9x

What is the value of h when the function h(x)=x^2−8x+14 is converted to vertex form?

Answers

Answer:

h=4

Step-by-step explanation:

The given function is

[tex]h(x)=x^2-8x+14[/tex]

We add and subtract the square of half the coefficient of x.

[tex]h(x)=x^2-8x+(\frac{-8}{2})^2-(\frac{-8}{2})^2+14[/tex]

[tex]h(x)=x^2-8x+(-4)^2-(-4)^2+14[/tex]

The first three terms forms a perfect square trinomial

[tex]h(x)=(x-4)^2-16+14[/tex]

[tex]h(x)=(x-4)^2-2[/tex]

We now compare to the vertex form;

[tex]h(x)=a(x-h)^2+k[/tex]

We have h=4

What is the value of log13

Answers

log 10=1,

log 2= 0.3010, and  

log 3= 0.4771.

From these values, we can find many other log values.  

log 5 = log 10 - log 2 = 0.699

log 0.5 = 0–log 2 = -0.301

log 1.5 = log 3 - log 2 = 0.1761

log 2.5 = log 5 - log 2 = 0.398

To find log of any number y:

Express y as (10^m)*(2^n)*(3^p)*(1+x).

Approximate log(1+x) as

(0.4343)*(x-x^2/2+x^3/3)

Or 0.4353*(x-x^2/2)

log y =

m + 0.3010*n + 0.4771*p + (0.4353)*(x-x^2/2+x^3/3)

To find log 13

13=2^2*3*(1+1/12)

log 13

= 2*0.3010 + 0.4771 + (0.4353)*(1/12 - 1/288+1/5184)

= 0.6020 + 0.4771 + 0.034847

= 1.1139

can someone help me with this?​

Answers

V=ABh

S=a +b+c

————-

2

=83.5

Information about how the students at vista view High school got to school this morning is shown in the table out of all 252 twelfth graders rode in a car to school

Answers

We can actually deduce here that the 114 rode in a car to school out of 252 twelfth graders.

Please, note that the question is incomplete.

What is information?

Information actually refers to the available facts and structured data that is given or learnt. Information is very important to achieve and acquire certain knowledge.

Below is the complete question:

Information about how the students at Vista View High School got to school this morning is shown in the table. A 6-column table has 4 rows. The first column has entries Tenth grade, eleventh grade, twelfth grade, Total. The second column is labeled Walk with entries 104, blank, 99, 314. The third column is labeled Bicycle with entries 8, 10, blank, blank. The fourth column is labeled Bus with entries 96, 72, 28, 196. The fifth column is labeled Car with entries blank, 88, blank, 276. The sixth column is labeled Total with entries 282, blank, 252, 815. Out of all 252 twelfth graders, how many rode in a car to school?

A.11

B. 74

C. 111

D. 114

So, in order to find the number of twelfth graders that actually rode in a car, we will have:

Number of twelfth graders that rode in a car = total number of twelfth graders - those that walked - those that rode bicycles - those that went with bus.

Where:

Total number of twelfth graders = 252

Those that walked = 99

Those that rode bicycles = 11

Those that went with bus = 28

Therefore, the number of twelfth graders that rode in a car = 252 - 99 - 11 - 28 = 252 - 138 = 114.

Those that rode in a car = D. 114

We see that out of the information given, one can actually see that 114 rode in a car to school.

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A sculptor creates an arch in the shape of a parabola. When sketched onto a coordinate grid, the function f(x) = –2(x)(x – 8) represents the height of the arch, in inches, as a function of the distance from the left side of the arch, x. What is the height of the arch, measured 3 inches from the left side of the arch?

Answers

The correct answer is:  D) 30 inches

Explanation:

We know that x represents the distance in inches from the left side of the arch. Using 3 for x, we have:

f(3) = -2(3)(3-8)

f(3) = -2(3)(-5)

f(3) = -6(-5)

f(3) = 30

Therefore, the correct answer is 30 inches! Thank you for your inquiry, your welcome for the answer and explanation!

The correct answer is:  D) The height of the arch, measured 3 inches from the left side of the arch 30 inches

What is the height?

In math, height can be defined the vertical distance from the top to the base of the object. It is measured in cm, inches, meters, etc.

We know that x represents the distance in inches from the left side of the arch. Using 3 for x, we have:

f(3) = -2(3)(3-8)

f(3) = -2(3)(-5)

f(3) = -6(-5)

f(3) = 30

Therefore, the correct answer is 30 inches

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a number is chosen at random from 1 to 50 find the probability of selecting factors of 36​

Answers

Answer:

9/50 or 18%

Step-by-step explanation:

The factors of 36 are-

123469121836

That's 9 factors. 1-50 means that it is a 9 out of 50 chance, or 80%.

When a number is chosen at random from 1 to 50 the probability of selecting factors of 36 is 2/50​.

What is probability?

Probability is the ratio that shows us how likely an event will occur from a given set of events.

We can find the required probability below:

The factors of 36 are:

36 = 2*2*3*3

Therefore the factors of 36 are 2 and 3.

Total number of factors = 2

Total number of numbers from 1 to 50 = 50

The probability of selecting factors of 36​ = P(selecting factors of 36)

= 2/50

The probability of getting a factor of 36 when a number is chosen at random is 2/50.

Therefore, we have found that when a number is chosen at random from 1 to 50 the probability of selecting factors of 36​ is 2/50.

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The 2 ft side length of the scale drawing corresponds to a side length of 120 feet for the actual skate park. What is the scale factor?

Answers

Answer:

The scale factor is [tex]\frac{1}{60}[/tex]

Step-by-step explanation:

we know that

The scale factor is equal to the ratio between the side length of the scale drawing to the corresponding side length in the actual

so

[tex]\frac{2}{120}=\frac{1}{60}[/tex]

Answer:

1/60

Divide

Step-by-step explanation:

PLZZZZZZZZZZZZZ HELP I NEED TO PASS THIS TEST I WILL GIVE BRAINLIST ANSWER TO WHO ANSWERS IT RIGHT

A statue has the shape of a square pyramid. The side length of the square base is 20 feet. The slant height of the monument is 16 feet. What is the height of the monument? Enter your answer, rounded to the nearest tenth of a foot, in the box.

____

|___| ft

Answers

Answer:

[tex]b=12.5[/tex] ft

Step-by-step explanation:

From this description we can draw this diagram

Now we can use the Pythagorean theorem to find the height.

[tex]10^2+b^2=16^2\\\\b^2=256-100\\\\b=\sqrt{156}[/tex]

This square root is equal to

[tex]b=12.489[/tex]

Which rounds to

[tex]b=12.5[/tex] ft

If the half-life of K-40 is 1.3 billion years and if a sample rock found on an island is estimated to be 1 billion years old, what percentage of the original parent K-40 would be present in the rock? Round your numerical values to the hundredths decimal place.

Answer Choices

(A) 76.92%
(B) 1.3%
(C) 58.67%
(D) 99.99%

Answers

For this case, we must make a rule of three, to find the percentage of the k-40 found in the sample found.

1.3 ----------> 100%

1 -------------> x

Where "x" represents the percentage of k-40 present in the sample found.

[tex]x = \frac {1 * 100} {1.3}\\x = 76.9230[/tex]

Rounding off we have:

76.92%

ANswer:

Option A

The percentage of parent K-40 remaining in the rock is calculated as 76.92% of the original K-40.

Percentage of parent K-40 remaining in the rock:

Calculate the number of half-lives: 1 billion years / 1.3 billion years = 0.7692 or about 0.77 half-lives.

Use the formula[tex](1/2)^n[/tex] where n is the number of half-lives to find the percentage remaining: [tex](1/2)^0.77[/tex]  ≈ 0.76.

Convert to a percentage for the original K-40 remaining in the rock: 0.76 * 100% ≈ 76.92%.

How to draw 30/4 in to an mix number

Answers

7 1/2

Divide 30 by 4 to get 7 with a remainder of 2. This means the answer is 7 2/4.Simplify the fraction. 2/4 is the same as 1/2, so the answer is 7 1/2.

divide 30 by 4. you’ll get 7 remainder:2 take the whole number you got:7 take the remainder:2 (that will be ur numerator) then take the divisor:4

you’ll get 7 2/4

(simplest form is 7 1/2)

Indicate in standard form the equation of the line through the given points P(0,-4), Q(5,1)

Answers

bearing in mind that

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf P(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Q(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-4)}{5-0}\implies \cfrac{1+4}{5}\implies \cfrac{5}{5}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-4)=1(x-0)\implies y+4=x \\\\\\ y=x-4\implies -x+y=-4\implies \stackrel{\textit{standard form}}{x-y=4}[/tex]

Find the fifth roots of 32(cos 280° + i sin 280°)

Answers

Answer:

The fifth root is 2[cos(56°) + i sin(56°)]

Step-by-step explanation:

* To solve this problem we must revise De Moiver's rule

- In the complex number with polar form

∵ z = r(cosФ + i sinФ)

∴ z^n = r^n(cos(nФ) + i sin(nФ))

* In the problem

- The fifth root means z^(1/5)

- We can put 32 as a form a^n

∵ 32 = 2 × 2 × 2 × 2 × 2 = 2^5

∴ z = 2^5[cos(280°) + i sin(280°)]

* Lets find z^(1/5)

[tex]*z^{\frac{1}{5}}=[2^{5}]^{\frac{1}{5} } (cos(\frac{1}{5})(280)+isin(\frac{1}{5})(280)[/tex]

[tex]*(2^{5})^{\frac{1}{5}}=2^{5.\frac{1}{5}}=2[/tex]

∴ z^(1/5) = 2[cos(56) + i sin(56)]

* The fifth root of 32[cos(280°) + i sin(280°)] is 2[cos(56°) + i sin(56°)]

 

if i have 67 apples and eat 34 and times it by 12 how much do i have?

Answers

67 - 34 = 33 (Since you ate 34 apples)

33*12 = 33*10 + 33*2 = 330 + 66 = 396

396 apples.

Help with number four plz!!!!!!

Answers

Answer:

Yes

Step-by-step explanation:

First we'll find the number of total bars of soap.

8 + 8 + 11 = 27

Is 27 divisible by 27?

Yes because 27 / 3 = 9

So you could rearrange the soaps to have 9 bars in each basket.

The points (4, 1) and (x, -6) lie on the same line. If the slope of the line is 1 what is the value of x?

A -3
b 3
c 9
d 11

Answers

Answer:

x=9

Step-by-step explanation:

The Slope is given by the following equation

m= (y2-y1) / (x2-x1)

Where x2=4, x1=x, y2=1, y1=-6, m=1 by requirements of this problem

Developing the equation we have this:

[tex]1=\frac{1-(-6)}{4-x}[/tex]

Which leaves to the following equation

[tex]5=4-x[/tex]

Resulting that x=9

HELP IM ‍♀️ CONFUSED WILL GIVE BRAINLIEST AND 10 points CAN SOMEONE HELP WITH MY HOMEWORK QUESTIONS

Answers

Answer:

1 3/4

Step-by-step explanation:

8.25-6.5

Answer:

I believe it is B

Lowest- 6 1/2 inches

Tallest- 8 1/4 inches

6 1/2-8 1/4= 1 3/4

I am sorry if this is wrong.

how do you do the problem?
3x - 8y= 32
-x + 8y= -16

Answers

Answer:

  (8, -1)

Step-by-step explanation:

We note that the coefficients of y are opposites, so when we add these equations, the y-terms will cancel:

  (3x -8y) +(-x +8y) = (32) +(-16)

  2x = 16 . . . . simplify

  x = 8 . . . . . . divide by 2

  -8 +8y = -16 . . . substitute into the second equation

  -1 +y = -2 . . . . . divide by 8

  y = -1 . . . . . . . . add 1

The solution is (x, y) = (8, -1).

_____

Comment on systems of equations

There are formulas for the solution of a system of equations like this. However, we are taught several methods that can be used instead of the formulas. One of my favorite is graphing, now that graphing calculators and apps are available on-line and on your local smart device. Other ad hoc methods include "elimination" or "addition", and "substitution." Using these methods can often save steps over using a formula, which is partly why they're taught.

Can some body help me with number 12 it’s due tomorrow.

Answers

Answer:

Mean = 51.375

Mode = 55,44

Step-by-step explanation:

add all the numbers up and divide by 8

find the most repeating numbers.

Answer:

Mean: 51.375

Median: 51.5

Mode: 44, 55

Hope This Helps!  Have A Nice Day!!

explain very simple ans very easy

Answers

Answer:

That would be 132/396

Step-by-step explanation:

the 132 is the part of the fraction and the 396 is the rest of the fraction.

Answer:

33 and 2/3 percent

Step-by-step explanation:

132x100 divided by 132+396 = 33.33

Please help and thank you

Answers

Answer:

C

Step-by-step explanation:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\ \\ y_2-y_1=m(x_2-x_1) \\ \\ -y_1=-y_2+m(x_2-x_1) \\ \\ y_1=y_2-m(x_2-x_1)[/tex]

Answer:

C

Step-by-step explanation:

Given

m = [tex]\frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }[/tex] ( cross- multiply )

y₂ - y₁ = m(x₂ - x₁) ( subtract y₂ from both sides )

- y₁ = m(x₂ - x₁) - y₂

Multiply through by - 1

y₁ = - m(x₂ - x₁ ) + y₂, thus

y₁ = y₂ - m(x₂ - x₁ ) → C

Identify the equation that represents the line of best fit on this scatter plot.
30 POINTS

Answers

[tex]y=\frac{5}{7} x+2[/tex]

How?

The way you find it is easy. +2 means go up 2y. 5 is y too, so you do 2+5=7. Now go 7 positive x. The answer is this.

Hope this helped:)

Answer:

C. [tex]y=\frac{5}{7}x+2[/tex].

Step-by-step explanation:

We have been given a scatter plot. We are asked to find the equation of line of best fit.

First of all, we will find slope of line of best fit using points [tex](0,2)[/tex] and [tex](7,7)[/tex].

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-2}{7-0}[/tex]

[tex]m=\frac{5}{7}[/tex]

We can see that y-intercept of line of best fit is 2.

We will write our equation in slope intercept form [tex]y=mx+b[/tex], where,

m = Slope,

b = The y-intercept.

Upon substituting [tex]m=\frac{5}{7}[/tex] and [tex]b=2[/tex] in slope-intercept form, we will get:

[tex]y=\frac{5}{7}x+2[/tex]

Therefore, the equation of line of best fit for given scatter plot is [tex]y=\frac{5}{7}x+2[/tex] and option C is the correct choice.

Convert to an expression using radical notation.
x1/3

Answers

[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^{\frac{1}{3}}\implies \sqrt[3]{x^1}\implies \sqrt[3]{x}[/tex]

Triangle JKL is a right triangle. What is the length of JK?

Answers

Answer:

[tex]H.2\sqrt{2}\ cm[/tex]

Step-by-step explanation:

Hello, I think I can help you with this

To solve this you can use the Pythagorean theorem, which states

in a right triangle:

[tex]side\ length^{2}+side\ length^{2}=hypotenuse^{2} \\[/tex]

the hypotenuse is the longest length of the triangle, in this case JK

Step 1

Let

side1= 2 cm

side2= 2 cm

hypotenuse=unknown=JK

isolate the hypotenuse from the equation

[tex]side\ length^{2}+side\ length^{2}=hypotenuse^{2}\\hypotenuse=\sqrt{side\ length^{2}+side\ length^{2}}[/tex]

It's a distance, we'll only take the positive root

put the values into the formula

[tex]hypotenuse=\sqrt{side\ length^{2}+side\ length^{2}} \\hypotenuse=\sqrt{(2\ cm)^{2}+(2\ cm)^{2}}\\hypotenuse=\sqrt{4\ (cm)^{2}+4\ (cm)^{2}}\\hypotenuse=\sqrt{8\ (cm)^{2}} \\hypotenuse=\sqrt{4\ (cm)^{2}*2} \\hypotenuse=\sqrt{4\ (cm)^{2}} \sqrt{2}\\hypotenuse=2\sqrt{2}\ cm[/tex]

the length JK is

[tex]2\sqrt{2}\ cm[/tex]

have a good day

The scatter plot shows the height and weight of football
players on a team.
How many football players weigh less than 70 kilograms?
Enter your answer in the box.

Answers

the answer is two football players weigh less than 70 kilograms

Answer:

Less than 2 players.

Step-by-step explanation:

Given that the scatter plot shows the height and weight of football

players on a team.

WE have to find the number of players who weigh less than 70 kgs.

In the graph of scatter plot we find tha when y<70, there are 2 points in the graph.

Hence only two players in football weight less than 70 kgs.

:0Need Help Please!!!!

Answers

Answer:

v = ( D/ 2Z )

Step-by-step explanation:

Equation given : D = 2ZV

In order to find V, we will have to divide both sides by 2Z

: V = D/2Z

I really need help please

Answers

Answer:

the answer is C

Explanation:

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