1/[tex]\sqrt{3}[/tex] is the exact trigonometric ratios for the angle x whose radian measure is given.
What are trigonometric ratios?Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.
Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.
The right triangle's three sides are as follows:
Hypotenuse (the longest side)Perpendicular (opposite side to the angle)Base (Adjacent side to the angle)sin(4π/3) = sin(π + π/3)
= - sin(π/3)
= - [tex]\sqrt{3}[/tex]/2
CSC(4π )/3) = csc(π + π /3)
= - csc(π /3)
= - 2/[tex]\sqrt{3\\[/tex]
cos(4π /3) = cos(π + π /3)
= - cos(π /3) = - 1/2
sec(4 π /3) = sec(π + π/3)
= - sec(π /3) = - 2
tan(4π )/3) = tan(π + π /3)
= tan(π/3) = [tex]\sqrt{3}[/tex]
Cot (4π/3 )= cot(π + π/3)
= Cot π/3 = 1/[tex]\sqrt{3}[/tex]
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The inverse of f(x)=9x^2
Given function:
f(x) = 9x²Let the inverse is y = f⁻¹(x).
Swap x and y in the given function and solve for y:
x = 9y²y² = x/9y = √(x/9)y = √x / 3The inverse of the given function is:
f⁻¹(x) = √x / 3Answer:
f-¹(x) = √(x)/3
Step-by-step explanation:
Now we have to,
→ find the inverse of f(x)=9x²
Then the inverse function will be,
→ f(x) = 9x²
→ y = 9x²
→ 9y² = x
→ y² = x/9
→ y = √(x/9)
→ [ y = √(x)/3 ]
Hence, the inverse is √(x)/3.
A regular hexagon is divided into 6 congruent triangles. If the perimeter of the hexagon. is 48 centimeters, what is the height of each triangle?
A 4 \mathrm{~cm}
B 4 \sqrt{3} \mathrm{~cm}
C 6 \sqrt{3} \mathrm{~cm}
D 8 \mathrm{~cm}
E 8 \sqrt{3} \mathrm{~cm}
Answer:Your answer would be E
Step-by-step explanation:8 times 6 would be 48
The measure of height of each triangle will be 4√3 cm. Then the correct option is B.
What is the perimeter of the regular polygon?All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.
P = (Side length) x n
A regular hexagon is divided into 6 congruent triangles. If the perimeter of the hexagon is 48 centimeters.
Then the Side length of each triangle will be given as,
48 = (Side length) x 6
Side length = 8 cm
Then the measure of the height of each triangle will be calculated as,
tan 60° = h / (8 / 2)
√3 = h / 4
h = 4√3 cm
The measure of height of each triangle will be 4√3 cm. Then the correct option is B.
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try these using the above pattern, find the value of the following. (i) 73 – 63 (ii) 123 – 113 (iii) 203 – 193 (iv) 513 – 503
The value of the given question by using the above pattern is (i)127, (ii)397, (iii)1141, (iv)7651.
What do you mean by pattern?In the real world, in artificial design, or in abstract concepts, a pattern is a regularity. As a result, a pattern's components repeat in a predictable way. Any of the senses can directly witness patterns, which are types of patterns made of geometric shapes and frequently repeated like wallpaper designs. On the other hand, abstract patterns in science, math, or language might only be visible through analysis. In actuality, direct observation entails recognizing visual patterns, which are common in both nature and art. Natural visual patterns are frequently chaotic, hardly ever precisely repeat, and frequently contain fractals. Spirals, meanders, waves, foams, tilings, fissures, and patterns produced by rotational and reflective symmetries are examples of natural patterns.
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What is the value of the expression 3 -4?
Answer:
-1
Step-by-step explanation:
3 - 4 = -1
When dealing with subtraction, you must be very careful with the order you place your numbers in. Let alone, subtraction is important in real-world situations, so just something to help. :)
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A cell phone company charges an initial price of $500 for a new phone and then $60 each month after the purchase. if c (t) is a rational function that represents the average monthly cost of owning the cell phone, what is the range of the function? (2 points) r: (0, 500) r: (60, 560) r: ℠r: (−[infinity], [infinity])
The range of the given function is: (500, ∞).
What is the range of a function?The collection of potential output values for a function is known as its range.
Now,
Given:
Initial price of the cell phone = $500Monthly charge = $60Let 't' be the number of months. Then, the function C(t) can be calculated as:
C(t) = 500 + 60t
For range:
The minimum value will be when t = 0, i.e., when no charge has been charged by for each month.
Thus, C(0) = 500 + 60(0)
=> C(0) = 500
The maximum value will be when t = ∞, i.e., for infinite number of months.
=> C(∞) = 500 + 60(∞)
=> C(∞) = 500 + ∞
=> C(∞) = ∞
Thus, the range of the function will be: (500, ∞).
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Write an
inequality that represents the
temperatures (in degrees Fahrenheit)
of the interior of the iceberg.
-20°C to
-15°C
The inequality representation can be expressed as: -4 < x < 5
Representation of real number into inequality.An inequality is a mathematical connection that exists between two expressions and may be expressed by one of the following:
"greater than >" "less than < ""less than or not equal to ≤: "greater than or equal to" ≥:From the given expression, the conversion of °C to F is estimated by using the formula:
(°C × 9/5) + 32
For -20°C , we have:
= (-20°C × 9/5) + 32
= -4 F
For -15°C, we have:
= (-15°C × 9/5) + 32
= 5 F
Therefore, this can be represented in inequality form as: -4 < x < 5.
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Rewrite: [tex]15\frac{1}{6}[/tex]% as a decimal. Round to the nearest thousandths.
Answer:
15.17
Step-by-step explanation:
Multiply whole number by denominatorAdd product to the numeratorDivide the sum by the denominatorRound your number to the neaests thousandthSelect the correct answer. What is this expression in simplified form? 2√2-7√18 OA 18√5 OB. 84√2 OC. 84 OD. 14sqrt6
The expression in simplified form is -19√2
How to write this expression in simplified form?The expression is given as:
2√2 - 7√18
Express 18 as 9 * 2
So, we have:
2√2 - 7√18 = 2√2 - 7√(9 * 2)
Take the square root of 9
2√2 - 7√18 = 2√2 - 7 * 3√2
This gives
2√2 - 7√18 = 2√2 - 21√2
Evaluate the difference
2√2 - 7√18 = -19√2
Hence, the expression in simplified form is -19√2
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Grace has read 2 chapters in each of her 9 books. How many chapters has read in all
Answer:18
Step-by-step explanation:2*9=18 hope this helps
Answer:
18 chapters have been read in total.
Step-by-step explanation:
How many lines appear in a square
Answer: 4?
Step-by-step explanation:
Pls help I dont get this
Answer:
Step-by-step explanation:
3+9(5)
8
2 is equal to
Answer:768
Step-by-step explanation:
I NEED HELP FAST PLEASE‼️‼️
SIMPLIFY TO SIMPLEST FORM‼️
Answer:
1/2
Step-by-step explanation:
-put 3/8 and 3/4 side-by-side.
-keep 3/8
-change the division sign to a multiplucation sign
-flip 3/4 to 4/3
-multiply
I don't get this, I would be happy if someone helped me.
Answer:
Step-by-step explanation:
(5/8 + 6/8)/(-4/6 - 5/6)
(11/8)/(-9/6)
(11/8)*(-6/9)
= -66/72 = -11/12
Answer:
11/12
Step-by-step explanation:
5/8 + 3/4 = 1 3/8
-2/3 - 5/6 = 1 1/2
1 3/8 divided by 1 1/2 = 11/12
What is the distance between -6 2/3 and 4 1/3 on a number line, in units?
Select ALL that apply.
The distance between the points = |-6 2/3 - 4 1/3| = |-20/3 - 13/3| = |-33/3| = |-11| = 11 units.
How to Find the Distance between Two Points on a Number Line?The distance between two points on a number line is the absolute difference between their coordinates.
Given the following points are on a number line:
-6 2/3 and 4 1/3
The distance between the points = |-6 2/3 - 4 1/3|
The distance between the points = |-20/3 - 13/3|
The distance between the points = |(-20 - 13)/3|
The distance between the points = |-33/3| = |-11|
The distance between the points = 11 units.
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(PLEASE HELP) -5 - (-5/3)
Answer:
steps
-5-5(-5/3)
=-5-(-25)
=10/3
=3 1/3
Step-by-step explanation:
What is 943,158,670.3491 rounded to the 100 millions? PLEASE ANSWER ASAP!
Answer:
I believe the answer is 943,158,670.349
Step-by-step explanation:
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!
9. Royanne determined that it cost her $.75 a day to make her own lunch
for school. If she ate in the cafeteria, lunch would cost $2.25. In five days,
how much money would Royanne save by bringing her own lunch to
school?
O $5.50
O $7.50
$9.50
a train is travelling at a speed of 90 miles per hour. the driver of the train plans on maintaining this speed for the next 120 miles, plus or minutes 15 miles. find the minimum and maximum numbers of hours the train will travel at that speed.
The minimum and maximum numbers of hours the train will travel at that speed are 1.17 and 1.5
How to find the minimum and maximum numbers of hours the train will travel at that speed?The given parameters are
Speed = 90 miles per hour
Current speed = next 120 miles, plus or minutes 15 miles.
Let the time travelled be x
So, we have the following equation
Speed * Time = Distance
This gives
|90x - 120| =15
Remove absolute bracket
90x - 120 = ±15
Add 120 to both sides
90x = 120 ±15
This gives
90x = (120 - 15, 120 + 15)
Evaluate
90x = (105, 135)
Divide by 90
x = (1.17, 1.5)
Hence, the minimum and maximum numbers of hours the train will travel at that speed are 1.17 and 1.5
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What is the slope of the line that passes through the points (1,-6) and (-2,-8) ?
We can conclude that the slope of the line is (-2, -3).
What do we mean by the slope?The slope of a line indicates its steepness. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).The formula of slope: y₂ - y/x₂ - x₁
Put the values in the formula as follows:
y₂ - y/x₂ - x₁-8 - (-6)/-2 -1-2/-3Therefore, the slope of the line is (-2, -3).
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from the top of a 160-ft lighthouse, the angle of depression to a ship in the ocean is 26°. how far is the ship from the base of the lighthouse? (round your answer to the nearest foot.)
The distance of ship from the base of the lighthouse is 328.54m, as found with the help of angle of depression.
What is Angle Of Depression?The angle of depression is the angle formed by the horizontal line and the horizontal line's observation of the item. When we know the angles and the distance of an object from the ground, it is primarily utilized to find the distance between the two objects.Given:
Height of lighthouse = 160 feetAngle of depression = 26°To find: Distance of ship from the base of the lighthouse.
Finding:
Let 'x' be the distance of the ship from the base of the lighthouse and θ be the angle of depression.
Then, tanθ = [tex]\frac{160}{x}[/tex]
=> x = [tex]\frac{160}{tan26}[/tex]
=> x = [tex]\frac{160}{0.487}[/tex]
=> x = 328.54m
Hence, The distance of ship from the base of the lighthouse is 328.54m, as found with the help of angle of depression.
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1. Find the value of two numbers if their sum is 12 and their difference is 4.
Answer:
8 and 4
Step-by-step explanation:
Answer:
8+4
Step-by-step explanation:
8-4 is equal to 4 and 4+8 is equal to 12
Question 38.
Write the first six terms of the arithmetic sequence with the first term, a1 = 240, and common difference, d= 24.
The first six terms are a1 = ,a3= , a4= ,a5= , and a6= .
[tex]a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360[/tex]
7. The top of a tree is 35 feet above ground level. The roots reach down 22 feet below ground
level. What is the difference between the top of the tree and the bottom of the roots?
Answer:
57?
Step-by-step explanation:
35-(-22)
Pls show steps on how u got the answer and thank u
Answer:
A=3
Step-by-step explanation:
-7a+28=7
subtract 28 from both sides to eliminate it from the first side
-7a=-21
Two negatives equals a positive
7a=21
divide both sides by 7
a=3
two vertices of an obtuse triangle are $(6,4)$ and $(0,0)$. the third vertex is located on the negative branch of the $x$-axis. what are the coordinates of the third vertex if the area of the triangle is 30 square units?
Since the third vertex is located on the negative branch of the x-axis, the coordinates of the third vertex of this triangle is equal to (-15, 0).
The types of triangle.In Geometry, there are different types of triangle based on the length of their sides and angles, and these are;
Equilateral triangleScalene triangleIsosceles triangleObtuse triangleRight-angled triangleHow to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this formula:
Area = 1/2 × b × h
Where:
b is the base area.h is the height.Note: The height of this triangle is the y-axis of (6, 4).
Substituting the given parameters into the formula, we have;
Area = 1/2 × b × h
30 = 1/2 × b × 4
2b = 30
b = 30/2
b = 15 units.
Since the third vertex is located on the negative branch of the x-axis, the coordinates of the third vertex of this triangle is equal to (-15, 0).
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Complete Question:
Two vertices of an obtuse triangle are (6,4) and (0,0). The third vertex is located on the negative branch of the x-axis. What are the coordinates of the third vertex if the area of the triangle is 80 square units?
The image of the point (2, -3)under a translation is (1, -6)Find the coordinates of the image of the point (9, -5)under the same translation.
The image of the point (2, -3)under a translation is (1, -6). the coordinates of the image of the point (9, -5)under the same translation is (9,-8).
With the aid of mirror-related concepts, we will first build a diagram of the image position in order to determine the coordinates of the image location. We will use trigonometry to determine the necessary coordinates after sketching the diagram.
Without needing to change its orientation, a translation relocates an item from its original location on the coordinate grid.
An illustration of a transformation is translation. A transformation is a technique for moving or repositioning a shape.
Image of the point (2,-3)
under the translation (2,-6)
2+a=2
a=2-2
a=0
-3+b=-6
b=-6+3
b=-3
By applying the translation (x+0,y-3) to (9,-5)
(9+0,-5-3)
(9,-8)
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Ethan works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commision on top of his base salary equal to 25% of his total sales for the week. How much would Ethan make in a week in which he made $1250 in sales? How much would Ethan make in a week if he made xx dollars in sales?
Ethan makes in a week = $812.5
Given :
Total sales for the week = $1250
a guaranteed salary = $500
paid a commission on top of his base salary (Percentage commission) = 25%
Time and work problem:
Work Done = Time Taken × Rate of Work
Rate of Work = 1 / Time Taken
Time Taken = 1 / Rate of Work
If a piece of work is done in x number of days, then the work done in one day = 1/x
Total Wok Done = Number of Days × Efficiency
Efficiency and Time are inversely proportional to each other
X:y is the ratio of the number of men who are required to complete a piece of work, then the ratio of the time taken by them to complete the work will be y:x
Solution :
Amount of commission earned = 25% of $1250
= 25/100 × $1,250
= 0.25 × 1250
= $312.5
Total earnings = Base salary + Amount of commission earned
= $500 + $312.5
= $812.5
Ethan makes in a week = $812.5
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Which relation is a function?
Can someone help me please?!!!
Answer:
The second one is a function.
Step-by-step explanation:
The other 3 have one-to-many mappings.
For example the first relation has 1 mapping to 2, 3, 4 and 5.
HELP ME PLEASE!!!!
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.
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WITH QUESTION A!
Answer:
Cohesion and Adhesion. The complementary action of these two forces allows water to rise in a narrow capillary tube such as the xylem tissues of plants.
Step-by-step explanation:
Cohesion: the water molecules attract each other and are responsible for the surface tension of water.
Adhesion: the water molecule is also able to attract other non-water molecules. This allows water to be able to ‘cling’ to the sides of a capillary tube.
The complementary action of these two forces allows water to rise in a narrow capillary tube such as the xylem tissues of plants.
please let me know if you need a deeper/ more complex explanation, i am always happy to help :)