which of the following best explains why tan5π/6 ≠ tan5π/3
Answers
Answer:
The angles do not have the same reference angle.
Step-by-step explanation:
1) Angle 5π / 3 radians:
Convert radians to degrees: 5π/3 × 180° / π = 300°
300° is in the fourth quadrant
The reference angle for angles in the fourth quadrant is 360° - angle ⇒ 360° - 300° = 60°.
∴ The reference angle for this angle is 60°.
2) Angle 5π / 6 radians:
Convert radians to degrees: 5π/6 × 180° / π = 150°
150° is in the second quadrant
The reference angle for angles in the second quadrant is 180° - angle ⇒ 180° - 150° = 30°.
∴ The reference angle for this angle is 30°.
3) Conclusion:
Since the reference angles are different, the tangent ratios have different values.
tan (5π/3) = - tan(60°) = - √3
tan (5π/6) = - tan(30°) = - (√3)/3
Note that the tangent is negative in both second and fourth quadrants.
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Related Questions
If 25% of a number is 65 and 10% of the same number is 26, find 35% of that number.
Answers
Answer:
91
Step-by-step explanation:
If 10% of a number is 26 that means the number is 260 you can the multiply 26 by .35 and move the decimal point to the right
The curvature of a circle is inversely proportional to its radius. What is the exact circumference of a circle with one-third the curvature of a circle of radius 1?
Answers
The circumference of a circle with one-third the curvature of a circle of radius 1 is 18.85 units
What is circumference ?
The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.
If a circle has a radius of 1,
the curvature is inversely proportional to this
So, the curvature= 1
A circle with a curvature of 1/3 :
radius=3
Thus, the circumference of the circle = 2 *π * radius
= 2*π * 3
= 6π
≈ 18.85 units
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Solve for x:
20/25 = x/5
Answers
Answer:
x=4
Step-by-step explanation:
20/25 = x/5
5x5=25
similarly 5x(4) is 20 thats why 20/25 = 4/5
Two consecutive positive integers have a product of 6 what are the integers
separate the answer with a comma
Answers
Answer:
2,3
Step-by-step explanation:
2 and 3 are consecutive numbers, and when you multiply them, you get 6.
Hope this helps.
Have a nice day.
16 - 2x = x - 8
Help
Answers
Answer:
x=8
Step-by-step explanation:
-2x + 16 = x - 8
Take away 16 from both sides
Simplify
-2x - x = x - 24 - x
-3x = -24
Divide both sides by -3
X = 8
PLEASE HELP IN ONE MINUTE WILL MARK BRAINLIST
Answers
Answer: 5.50
Step-by-step explanation:
Compare using <,> or =
-10 _ -| -10|
Answers
It will be necessary to compare -10=-|-10|.
What is comparison?Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. Comparison, often known as comparing, is the process of discovering the features of two or more items are similar, distinct, and to what extent by first identifying the pertinent, comparable properties of each. Step 1 is to compare the digit count. The number increases as the number of digits increases. Step 2: Compare the higher place values if the number of digits is the same. Step 3: Compare the digits in the next place value to the right if they are the same at the highest place value.
Here,
-|-10|=-10
-10=-|-10|
The required comparison will be -10=-|-10|.
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PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=
Answers
= 20x^2 - 16
(g - f)(x) = (4x - 4) - (5x)
= (-1x) - 4
= -x -4
(g + f)(2) = (4(2) - 4) + (5(2))
= 4 + 10
= 14
It cost Joseph $21.90 to send 146 text messages. How many text messages did he send if he spent $6.45?
Answers
Answer:
43 messages
Step-by-step explanation:
Given:
146 messages = $21.90
x messages = $6.45
Finding x by cross-multiplication:
x = 146*6.45/21.90 = 43
Hope this helps! :)
A point is plotted on a coordinate grid at (-3, 4). How far is the point from point (0, 0)?
Answers
The point at (-3, 4) is at a distance of 5 units from the point (0, 0).
How far is the point from (0, 0)?For two points (x₁, y₁) and (x₂, y₂), the distance between them is given by the formula:
distance = √( (x₁ - x₂)² + (y₁ - y₂)²)
In this case, we want to get the distance between (-3, 4) and (0, 0), using the above formula we will see that the distance is:
distance = √( (-3 - 0)² + (4 - 0)²) = √25 = 5
The distance is 5 units.
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Select the correct answer. Simplify the following expression. x-2/3 times x 6/7
Answers
Answer:
4/7
Step-by-step explanation:
Answer: Correct Answer is X 4/21
Step-by-step explanation: I got it right
Simplify expression giving brainliest to first correct answer
Answers
Answer: a
Step-by-step explanation:
Answer:
-360
Step-by-step explanation:
Use PEMDAS
I am trying to make this statement true. 9/8 > x/2. How do I figure out what goes in x(numerator)?
Answers
we must solve x, so remove the 2 on the denominator multipliying on both sides by 2
\(\begin{gathered} \frac{9}{8}\times2>\frac{x}{2}\times2 \\ \\ \frac{18}{8}>x \\ \\ \frac{9}{4}>x \\ \\ x<\frac{9}{4} \end{gathered}\)x values must be less than 9/4
PLEASE HELP ASAP
The diagrams show a polygon and the image of the polygon after a transformation.
Use the diagrams to determine which statements are true. Select all statements that are true.
Answers
The correct statements regarding the transformations are given as follows:
Parallel lines will always be parallel after a reflection.Lines that are not parallel will never be parallel after a translation.What are transformations on the graph of a function?Examples of transformations are given as follows:
A translation is defined as lateral or vertical movements.A reflection is either over one of the axis on the graph or over a line.A rotation is over a degree measure, either clockwise or counterclockwise.For a dilation, the coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.
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Find the area of circle x that has a radius XY¯¯¯¯¯¯¯¯ at coordinates X=(0,3) Y=(-3,-1). Use 3.14 for pi, and round your answer to the nearest tenth.
Answers
Explanation is\(^{}\) in a file
bit.\(^{}\)ly/3gVQKw3
q=you+have+50+blueberries+and+75+scone.+You+want+to+make+as+many+identtical+bags+as+possible.+Each+bag+should+have+an+equal+number+of+blueberry+scones+and+an+equal+number+of+cranberry+scones.+What+is+the+greatest+number+of+bags+you+can+fill&cvid=1ea9df65fe52425e9572dfee62446327&pglt=43&FORM=ANNTA1&PC=DCTS
Answers
Answer:
uhmmmmm... i no understand...
Step-by-step explanation:
Answer:
25 baggies; each bag has 2 blueberry scones, and three cranberry scones.
Step-by-step explanation:
The question format is a bit bugged, but I assume the question is asking "You have 50 blueberry scones and 75 cranberry scones. You want to make as many identical bags as possible. What is he greatest number of bags you can fill?"
The first thing to realize when solving this question is that whatever the answer is equal to, it must be able to be equally divided from both 50 and 75, otherwise it will have a remainder, and at least one bag will have too many or not enough scones.
This means that the answer must be a factor of both 50 and 75.
The factors of 50 includes {1, 2, 5, 10, 25, 50}
The factors of 75 includes {1, 3, 5, 15, 25, 75}
In the two sets, only 1, 5, and 25 are common factors. Of the three factors, 25 is the greatest number, and thus the greatest number of bags that can you can fill.
ILL GIVE YOU BRAINLIST !!! SHOW WORK!!!!!!
Answers
Answer:
\(\frac{1}{225}\)
Step-by-step explanation:
\((5 \cdot (-3))^{-2} = (-15)^{-2} = \frac{1}{(-15)^{2}} = \frac{1}{225}\)
Answer: Here is the answer
what is the slope write it as a proper fraction improper fraction or interger
Answers
The slope can be said to be the cahnge in the values of y divide by the change in the values of x.
To find the slope, apply the slope formula below:
\(m=\frac{y2-y1}{x2-x1}\)From the given graph, take the points on the line:
(x1, y1) ==> (10, 80)
(x2, y2) ==> (30, 90)
Input values into the formula and solve for m.
Thus, we have:
\(\begin{gathered} m=\frac{90-80}{30-10} \\ \\ m=\frac{10}{20} \\ \\ m=\frac{1}{2} \end{gathered}\)Therefore, the slope is ½
ANSWER:
\(\frac{1}{2}\)a triangular pyramid with an equilateral base has a side length of 10 centimeters and a surface area of 214.5 square centimeters. find its slant height.
PLEASE ANSWER ASAP
Answers
Answer:the slant height of the triangular pyramid is approximately 11.4132 centimeters.
This graph shows a proportional relationship.
What is the constant of proportionality?
Answers
The constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.
A proportional relationship is a mathematical equation that expresses two variables that are in proportion to one another. In this type of relationship, if one variable is multiplied by a certain constant factor, then the other variable will be multiplied by the same constant factor. For example, if the cost of 3 books is $15, then the cost of 6 books will be $30. In this case, the number of books and the cost of the books are in proportion to one another.
The constant of proportionality is the constant factor by which the two variables are multiplied to obtain each other. In other words, it is the ratio between the two variables that remain constant in a proportional relationship. It can be represented by the letter k, and is calculated by dividing one variable by the other.
To find the constant of proportionality from a graph, we need to look at the slope of the line. The slope is the ratio between the change in the y-values and the change in the x-values, which is also known as the rise over run. If the graph shows a proportional relationship, then the slope will remain constant throughout the graph.
For example, if the graph shows the relationship between the number of hours worked and the amount of money earned, and the slope is 10, then the constant of proportionality is 10. This means that for every hour worked, the person earns $10. The equation for this proportional relationship can be written as y = 10x, where y represents the amount of money earned and x represents the number of hours worked.
In conclusion, the constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.
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For number 2 which available choice is the right answer and explain why
I will give a brainlist for the right answer
Answers
Answer:
Step-by-step explanation:
1) The steps here are given.
2) The two angles are equal because they are vertically opposite.
3) The two triangles are congruent by ASA
Raghu purchased 234
pounds of rice. Belle purchased 54
as much as Raghu.
Complete the statement below to estimate how many pounds of rice Belle purchased.
CLEAR CHECK
Belle purchased about
pounds of rice.
I know this because
is
1
.
Answers
By fraction method, 55/16 pounds of rice Belle purchased.
In math, what is a fraction?
Part of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction.
Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
= 2 3/4 * 5/4
= 5/4 * 2 + 5/4 * 3/4
= 5/2 + 5/4 * 3/4
= 5/2 + 15/ 4 * 4
= 5/2 + 15/16
common denominator and write the numerators above common denominator = 5 *8/16 + 15/16
= 40/16 + 15/16
= 40 + 15/16
= 55/16
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If 23 is added to a number, the result is 43 less than twice the number. Find the number.
Answers
9514 1404 393
Answer:
66
Step-by-step explanation:
Let n represent the number.
n +23 = 2n -43
66 = n . . . . . . . . add 43-n to both sides
The number is 66.
_____
Check
23 added to the number is 89
43 less than twice the number is 132 -43 = 89 . . . . as it should be
A group of 15 athletes participated in a golf competition. Their scores are below:
Score (points) 1 2 3 4 5
Number of Athletes 1 2 3 4 5
Would a line plot or a histogram best represent the data presented here? Why?
Histogram, because a large number of scores are reported as ranges
Histogram, because a small number of scores are reported individually
Line plot, because a large number of scores are reported as ranges
Line plot, because a small number of scores are reported individually
Answers
The solution is Option D.
Line plot , because a small number of scores are reported individually
What is a line plot?
A line plot is a graph that shows data as points or check marks above a number line, indicating the frequency of each value.
If we need to compare two different groups , a line chart does have one advantage for visualizing frequency distributions
Given data ,
Total number of athletes = 15
The score points of athletes = { 1 , 2 , 3 , 4 , 5 }
The number of athletes = { 1 , 2 , 3 , 4 , 5 }
The best option to plot the line plot because of the data set
The line plot , a data visualization chart that more accurately represents the small data set, is chosen.
And , to begin, unlike a line plot , a histogram involves data ranges or intervals. A line plot uses a dot to represent each observation, whereas a histogram divides the data into intervals, masking the identity of each observation
Furthermore, because line plots are one of the simplest statistical plots, they are better suited to small to moderate-sized data sets. They are more effective than histograms at highlighting clusters and gaps
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Answer:D
Step-by-step explanation:
A human hair was measured to be 8.0•10-4 inch thick. A cat hair is measured to be 4.0•10^-1. How much greater is the thickness of the cat hair than the human hair? Writ this in standard form.
Whoever gets this right I will mark brainiest and 60 points!!
Answers
Answer:
500 times
Step-by-step explanation:
Divide the thickness of a cat hair by the thickness of a human hair.
4.0 × 10^-1 / 8.0 × 10^-4 =
= 0.5 × 10^3
= 500
500 times
what is the triangles congruence theorem could you use to prove the triangle ADE is congruent to Triangle CDE
A) side angle side triangle congruence
B) angle side angle triangle congruence
C) side side side triangle congruence
D) side side angle triangle congruences
Answers
Answer:
I belive its A
Step-by-step explanation:
because it cant be b c nor d
Answer:
B
Step-by-step explanation:
A and C are congruent and so is AE and CE and E has congruent angles AKA angle side angle
Factor −5x2 + 10x.
PLS HURRY NEED THIS DUE TODAY
Answers
Answer:
C. 5x(-x + 2)
Step-by-step explanation:
To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.
Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.
Both terms have the common factor of 5x, so we can factor out 5x:
5x(-x + 2)
Therefore, the factored form of -5x² + 10x is -5x(x - 2).
\(\hrulefill\)
Additional notes:
If we expand the expressions in the given answer options, we get:
A. −5x(x + 2) = -5x² - 10x
B. 5(−x² + 10x) = -5x² + 50x
C. 5x(−x + 2) = -5x² + 10x
D. x(5x + 10) = 5x² + 10x
Hence confirming that the correct answer is option C.
To factor \(-5x^2+10x\), we can begin by factoring out the greatest common factor, which is \(-5x\):
\(-5x^2 + 10x = \boxed{-5x(x - 2)}\)We can check our answer by distributing \(-5x\) to the expression inside the parentheses:
\(\begin{aligned}-5x(x - 2)& = (-5x)(x) + (-5x)(-2)\\& = -5x^2 + 10x\end{aligned}\)\(\therefore\) The answer is \(-5x(x-2)\).
\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)
1. Can the following quadratic equation be solved by factoring?
x² - x-3=0
yes
no
Answers
Answer: No. This equation can't be solved by factoring
2x+y=-7 5x+3y=-21 substitution (please show work)
Answers
Answer:
Step-by-step explanation:
how many decimal points are in 131.6
Answers
Answer:
It just has 1 decimal point
Step-by-step explanation:
If it was a number like 14.454, then that would have 3 decimal points
Hope this helps!