please show work along with answer:
[tex] \frac{1 + \tan(x) }{1 + \cot(x) } [/tex]

Answers

Answer 1

Hello,

[tex] \dfrac{1+tan(x)}{1+cotg(x)} = \dfrac{1+ \frac{sin(x)}{cos(x)} }{1+ \frac{cos(x)}{sin(x)}} \\\\ = \dfrac{cos(x)+sin(x)}{cos(x)*( \frac{sin(x)+cos(x)}{sin(x)} } )\\\\ = \dfrac{sin(x)}{cos(x)} \\\\ \boxed{=tan(x)}\\\\ [/tex]

Related Questions

5.95, 5.90, 5.85, 5.80, 5.75, 5.75, 5.75, 5.65, 5.65, 5.65, 5.55, 5.55, 5.55, 5.55, 5.55, 5.55
The men's pole vault finals' scores for the 2004 Olympic games in Athens are shown. Is the mean a good descriptor of this set?

Answers

yes, the mean is a good descriptor because there is no outliers...if there would have been outliers, then the median would have been a better descriptor

Answer:

Step-by-step explanation:

Yes because their are no outlier

At the movie theatre, child admission is $5.40 and adult admission is $9.20 . on thursday, twice as many adult tickets as child tickets were sold, for a total sales of $785.40 . how many child tickets were sold that day

Answers

33 child tickets were sold that day.

adult tickets = a
child tickets = c

9.2a + 5.4c = 785.4
a = 2c

Substitute a into the first equation
9.2(2c) + 5.4c = 785.4
Simplify
18.4c + 5.4c = 785.4
Combine like terms by adding
23.8c = 785.4
Divide both sides by 23.8 to isolate the variable c
c = 33

PLEASE HELP!!!!!!!!!!!
Susan makes 5 fruit cups for the picnic.In each cup,she has 5 strawberries and 3 kiwi. Joanna uses the same number of total fruits to make her strawberry and kiwi fruit cups,but she uses 4 cups. In each cup she uses 8 strawberries.
How many are in each fruit cup Joanna makes?

Answers

For every One cup that Susan makes she has five strawberries and three kiwis. For every 1 cup that Joanna makes, there are eight strawberries. So now we have to figure out how many kiwi that are in her cup. So if there are eight strawberries we were going to add one for the kiwi and that will be nine. So for Joanna she uses eight strawberries and nine kiwis

which natural phenomenon is the best example of periodic behavior

Answers

The high temperature for a given city

Answer: The answer is the number of hours of daylight each day.

Step-by-step explanation: We are to give the best example of a natural phenomenon of periodic behavior.

A periodic behavior means the behavior which repeats itself in equal intervals of time or periods. Since we are talking about a natural phenomenon, so the rotation of earth around the sun can be an example.

In other words, we can say the number of hours of daylight each day will be the proper example, because the sun gives light for almost same number of hours each day.

Thus, the natural phenomenon is the number of hours of daylight each day.

How many permutations of three items can be selected from a group of six? use the letters a, b, c, d, e, and f to identify the items, and list each of the permutations of items b, d, and f?

Answers

Number of permutations of 3 items can be selected from a group of 6
= 6P3
= \frac{6!}{3!}
= \frac{6 x 5 x 4 x 3!}{3!}
= 6 x 5 x 4
= 120

There are 120 permutations.

Permutations of items b, d and f is the different arrangement using these 3 letters & they are
bdf, bfd, dbf, dfb, fbd, fdb

The number of permutations of 6 items that can be selected from a group of 6 is; 120 ways.

List of permutations of items b,d and f is; bdf, bfd, dbf, dfb, fdb, fbd

Permutations and selection

The permutation required can be evaluated as follows;

6P3

6!/3!

6× 5× 4 × 3!/3!

= 6×5×4 = 120 ways.

The List of permutations of items b,d and f is;

bdfbfddbfdfbfdbfbd

Answers

Let x be the score of the 3rd quiz,, then the average score will be:
(83+91+x)/3, which = (174+x)/3. but this average should be greater or equal to 85 and smaller or equal to 90:

85 ≤ (174+x)/3 ≤ 90
1st multiply all terms with 3 → 255 ≤(174+x) ≤ 270
2nd subtract 173 from all terms → 255-174 ≤174-174+x ≤270-174
81 ≤ x ≤ 96

Using the approximation 3.14 for pi, what is the radius of a circle with circumference 28.3 m?

Answers

Using π ≈ 3.14, the radius of a circle with circumference 28.3 m is approximately 4.5 meters.

Step 1:

Write down the formula for the circumference of a circle.

The formula for the circumference (C) of a circle is given by:

[tex]\[ C = 2 \pi r \][/tex]

Step 2:

Substitute the given value for the circumference into the formula.

Given [tex]$C = 28.3$[/tex] m, we use the approximation [tex]$\pi \approx 3.14$[/tex]:

[tex]\[ 28.3 = 2 \times 3.14 \times r \][/tex]

Step 3:

Solve for the radius (r).

Divide both sides of the equation by [tex]$2 \times 3.14$[/tex]:

[tex]\[ r = \frac{28.3}{2 \times 3.14} \][/tex]

Step 4:

Calculate the value of (r).

[tex]\[ r = \frac{28.3}{6.28} \][/tex]

[tex]\[ r \approx 4.5 \text{ m} \][/tex]

So, the radius of the circle with a circumference of 28.3 m, using the approximation [tex]$\pi \approx 3.14$[/tex], is approximately 4.5 meters.

A ladder is leaned against a building. the bottom of the ladder is 11 feet from the building. the top of the ladder is 19 feet above the ground. what is the slope of the ladder?
b. what does the slope of the ladder mean in the real world?
c. if the ladder were set closer to the building, would it be harder or easier to climb? explain in terms of the slope of the ladder.

Answers

A ladder is leaned against a building. the bottom of the ladder is 11 feet from the building. the top of the ladder is 19 feet above the ground.

a. what is the slope of the ladder?

slope = rise / run = height / base = 19 feet / 11 feet = 19 /11

b. what does the slope of the ladder mean in the real world?

The slope is the inclination of the ladder. The higher the slope the more leaned is the ladder.

c. if the ladder were set closer to the building, would it be harder or easier to climb? explain in terms of the slope of the ladder.

if the ladder were closer to the building the base would be lower and the heigth would be higher, so the slope would be higher, which means that the ladder would be steeper, therefore harder to climb.

Given that the rise and run of a ladder are 19 feet and 11 feet respectively:

a. Slope of the ladder = 19/11 = 1.7

b. Slope = inclination of the ladder

c. The slope will be steeper and difficult to climb if the ladder was set closer to the wall of the building.

Recall:

Slope = vertical distance along a line / horizontal distance = rise/run

a. run = 11 feet

rise = 19 feet

Slope of the ladder = [tex]\frac{rise}{run} = \frac{19}{11}[/tex] = 1.7

b. The slope of the ladder refers to the inclination of the ladder to the wall.

c. If the ladder was set close to the wall of the building, the more steeper the slope would be. This would make it difficult to climb compared to a gentle slope.

In summary, given that the rise and run of a ladder are 19 feet and 11 feet respectively:

a. Slope of the ladder = 19/11 = 1.7

b. Slope = inclination of the ladder

c. The slope will be steeper and difficult to climb if the ladder was set closer to the wall of the building.

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A certain oxyacid is derived from the oxyanion so3(-2). the formula for the oxyacid is which

Answers

To make this anion into a complete acid, then this must be added with Hydrogen ion H+. So the chemical equation looks like:

H+ + SO3(2-) --> ?

Now to balance it:

H+ + SO3(2-) --> H2SO3

Answer:

H2SO3

Answer:

H2SO3-

Step-by-step explanation:

what is the answer for 4x-9=k solve for x

Answers

4x - 9 = k

4x - 9 (+9) = k (+9)

4x/4 = (k+9)/4

x = (k+ 9)/4

hope this helps

Kristen lives directly east of the park. The football field is directly south of the park. The library sits on the line formed between Kristen’s home and the football field at the exact point where an altitude to the right triangle formed by her home, the park, and the football field could be drawn. The library is 2 miles from her home. The football field is 8 miles from the library.

Answers

Final answer:

Using Pythagoras theorem, we can find that the library is approximately 7.746 miles from the football field, which forms a right-angled triangle with Kristen's home and the park.

Explanation:

This problem is a classic example of use of Pythagoras theorem in right-angle triangle. Here, the distances of Kristen's home, the park, and the football field form a right-angle triangle, with the distance from the park to the library acting as the altitude of the triangle. To find the distance from the library to the football field, we can use the relation:

[tex]\text{(Hypotenuse)}^2 = \text{(Base)}^2 + \text{(Perpendicular)}^2[/tex]

According to the problem, The library is 2 miles from her home (Base), The football field is 8 miles from the library (Hypotenuse). So the distance from the library to the football field can be calculated as:

[tex]\text{Perpendicular} = \sqrt{(\text{Hypotenuse})^2 - (\text{Base})^2} = \sqrt{(8\text{ miles})^2 - (2\text{ miles})^2} = \sqrt{60} \approx 7.746 \text{ miles}[/tex]

So, the library is approximately 7.746 miles from the football field.

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What is the simplest form of this?

Answers

(2x - 1)² + 1

Rewrite the equation without the "²" sign.

(2x - 1)(2x - 1) + 1

Simplify.

(4x² - 2x - 2x + 1) + 1

Simplify.

4x² - 4x + 2

~Hope I helped!~

The measures of the interior angles in a polygon are consecutive integers. the smallest angle measures 136 degrees. how many sides does this polygon have?

Answers

Other than writing an iterative computer program to determine this answer, it can be done manually.
Using N as the number of sides of a polygon, (N-2)180 = number of degrees of an N-sided polygon. The range from 180 up to 1260 for a 9 sided polygon.
Starting with 136 and adding consecutive numbers to it, the answer turns out to be a 9 sided polygon of 1260 degrees.

What is the difference between 150.2 and 146.4?

Answers

3.8 Is the difference.

The bottom of a ladder must be placed 4 feet from a wall. the ladder is 12 feet long. how far above the ground does the ladder touch the wall? round your number to the nearest tenth.

Answers

Pythagorean theorem

a^2+b^2=c^2

c=12

a=4

16 + b^2 = 144

b^2 = 128

b = 11.3

There are 11.3 feet far above the ground does the ladder touch the wall.

What is Pythagoras theorem?

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

The bottom of a ladder must be placed 4 feet from a wall. the ladder is 12 feet long.

Now, Let the length of the ladder above the ground does the ladder touch the wall = x

Hence, We get;

x² = 12² - 4²

x² = 144 - 16

x² = 128

x = √128

x = 11.3 feet

Thus, the length of the ladder above the ground does the ladder touch the wall = 1.3 feet

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Which expression represents the phrase, "one fifth the sum of 14 and a number"?

a) 15(14+x)
b) 15(14)+x
c) 15+14+x
d) 15x+14

Answers

Let

x--------> the number

we know that

1) the phrase, "the sum of 14 and a number"

represent the expression --------> [tex](14+x)[/tex]

and

2) the complete phrase, "one fifth the sum of 14 and a number"

represent the expression --------> [tex]\frac{1}{5}(14+x)[/tex]

therefore

the answer is

[tex]\frac{1}{5}(14+x)[/tex]

Noelle has 5/6 of a yard of purple ribbon and 9/10 of a yard of Pink ribbon. How mucho ribbon does se have altogether?

Answers

Well you need to find a common denominator which 30 is the closest one. 5/6 becomes 25/30, 9/10 becomes 27/30. 27/30+ 25/30 = 52/30. To simplify that you divide by 2 to get 26/15. It is no longer divisible to a whole number after that point.

Two geometric figures that are identical in shape, although not necessarily the same size, are called ____.

Answers

They are called similar.

They are called similar Similar if they are the same shape and size they are congruent.

The expression 6s2 represents the surface area of a cube with edges of length s. what is the cube's surface area when s = 8?

Answers

That would actually be 6*s^2
area = 6 * 8^2
area = 6 * 64
area = 384

If you triple a number and add 11 you get 200 what is the number

Answers

You can set up a simple algebraic equivalent to find a number equivalent to 200 after being multiplied by 3 and added 11 to.

3x+11=200
3x=189
x=63

Had to edit! Realized what I had done wrong

Well let's work backwards to find out! Okay so subtract 11 from 200 (because you added 11) then you got 189 know and then you would divide the number by 3 (because you tripled it) so 189÷3=63 so let's try it with 63.

63 tripped is 189, 11 added to 189 is 200

So know know that it works we know it's our answer. 63

PLEASE HELP ME!!!! 20 PNTS!!!!!

Simplify the expression:
[tex] \frac{ \sqrt{ - 16} }{(3 - 3i) + (1 - 2i)} [/tex]
A.
[tex] \frac{ - 20 - 16i}{9} [/tex]
B.
[tex] \frac{8 + 4i}{15} [/tex]
C.
[tex] \frac{8 - 4i}{15} [/tex]
D.
[tex] \frac{ - 20 + 16i}{41} [/tex]

Answers

[tex]\frac{\sqrt{-16}}{(3-3i)+(1-2i)}\\\\\frac{4i}{4-5i}*\frac{4+5i}{4+5i}\\\\\frac{4i(4+5i)}{(4-5i)(4+5i)}\\\\\frac{16i+20i^{2}}{16+20i-20i-25i^{2}}\\\\\frac{-20+16i}{16+25}\\\\\\\frac{-20+16i}{41}[/tex]

A line has slope 56 and y–intercept −3. Which answer is the equation of the line? y=−3x+5/6 y=5/6x−3 y=3x+5/6 y=5/6x+3

Answers

Answer:

The answer is the second one for sure y=5/6x−3.

Step-by-step explanation:

The equation of the line is y = (5/6)x - 3 which is the correct answer would be option (B).

What is the equation?

The term "equation" refers to mathematical statements that have at least two terms with variables or integers that are equal.

We have been given a line that has a slope of 5/6 and a y-intercept is -3.

Let the required line of the equation would be as

y = mx + c

Where m is the slope of the line

We have given the y-intercept is -3 which means the x-coordinates will be zero.

Substitute the value of x = 0 and y = -3 in the above equation to get c.

⇒ -3 = m(0) + c

⇒ -3 = c

The slope of the line m = 5/6 which is given in the question,

Substitute the value of m = 5/6 and c = -3 in the equation y = mx + c

⇒ y = (5/6)x - 3

Therefore, the equation of the line is y = (5/6)x - 3.

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Can someone clearly explain and workout Q20? Much appreciated

Answers

What we do is take half of the x coefficient, which in this case is 4. So take half of 4 to get 2. Then square 2 to get 2^2 = 4.

We will add and subtract 4 to the expression so that things don't change. It's effectively the same as adding zero.

Once this happens, you rearrange terms and factor.

x^2 + 4x + 3
x^2 + 4x + 3 + 0
x^2 + 4x + 3 + (4-4)
(x^2 + 4x + 4) + 3 - 4
(x^2 + 4x + 4) - 1
(x+2)^2 - 1

Answer: (x+2)^2 - 1

The slope of a line is -3. Find the slope of a line that is perpendicular to this line.

A.-3
B.-1/3
C.1/3

Answers

The slope of a line is -3
perpendicular lines, slope is opposite and reciprocal
so the slope of a line that is perpendicular to this line will be 1/3

answer
C.1/3

Please help! What is the solution of 4|x-3|-8=8?

A) x=-1 or x=7
B) x=19/4 or x=7
C) x=-1 or x=19/4
D) x=3/4 or x=19/4

Answers

It is A) x=-1 or x=7

A random sample of n = 4 scores is obtained from a population with a mean of m = 80 and a standard deviation of s = 10. if the sample mean is m = 90, what is the z-score for the sample mean

Answers

I'm just guessing but maybe its 11.

How would I solve 2x - 3 = x + 2?

Answers

2x-3=x+2
. -x -x
1x -3=2
+3 +3
1x=5

1x divide by 1x, 5 divide by 1x
Which will be:
X=5

Answer: 2x-3=x+2

. -x -x

1x -3=2

+3 +3

1x=5

1x divide by 1x, 5 divide by 1x

Which will be:

X=5

Which of the following rational numbers is equal to 2 point 8 with bar over 8 ? twenty two over nine, twenty four over nine, twenty six over nine, twenty eight over nine

Answers

just to remove ambiguities, the bar over the expression means it's repeating itself to infinity.

[tex]\bf 2.888\overline{8}\impliedby \textit{now say, let's make }x=2.888\overline{8} \\\\\\ \textit{and multiply it by 10, to move over the 8 to the left} \\\\\\ \begin{array}{llll} 10x&=&10\cdot 2.888\overline{8}\\ &&28.88\overline{8}\\ &&26+2.888\overline{8}\\ &&26+x \end{array}\implies 10x=26+x \\\\\\ 9x=26\implies x=\cfrac{26}{9}[/tex]

notice, the idea being, you multiply it by 10 at some power, so that you move the "recurring decimal" to the other side of the point, and then split it with a digit and "x".

now, you can plug that in your calculator, to check what you get.

Final answer:

The rational number that equals to 2.8 (a decimal number that has repeating 8), from the options given, is twenty six over nine (26/9) because when converted to decimal it gives 2.89, which is closest to 2.8

Explanation:

The question is asking which rational number is equal to 2.8 where the bar over the number indicates that it is repeating. The dot over the 8 implies that the number is actually 2.8888..., where the 8 is repeated indefinitely. So we need to find which fraction out of your given options: twenty two over nine, twenty four over nine, twenty six over nine, twenty eight over nine, equals to this decimal number.

To convert these fractions to decimal form:

22/9 = 2.44,
24/9 = 2.67,
26/9 = 2.89,
28/9 = 3.11

By comparing these values, we can see that twenty six over nine (26/9) is the decimal equivalent to 2.8 as it gives us 2.89 which is closest to it.

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7t + 4 is less than or equal to 3t

Answers

-7t-3t would be -4t
4 is less than or equal to -4t
Divide 4from -4
-1 is less than or equal to t

I don't see no choices for this question but I can tell u that greater than, less than, and equal to ALL SHARE THE SAME RESULT which is -1.

Here is my work for if 7t + 4 < 3t:

4 < 3t - 7t
4 < -4t
t < -1

Even if u do greater than, less than, or equal to it would all have the same answer, it would be t < -1, t > -1, and t = -1. Either way u do it, it will still have the same answer so in terms u can say answer is both or all of the above.

Anyone? I’m so stuck

Answers

A = 180-110 = 70

angle A is 70 degrees

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please show work along with answer:[tex] \frac{1 + \tan(x) }{1 + \cot(x) } [/tex]

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please show work along with answer:
[tex] \frac{1 + \tan(x) }{1 + \cot(x) } [/tex]