The value of cot(x/2) is -3.73
What are trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given that, Csc(x) = -2
Since,
cscx = 1/sinx
Therefore,
1/sinx = -2
sinx = -1/2
sinx = -sin30°
x = -30°
Therefore,
cot (x/2) = cot(-15)
= -1/tan15
= -3.73
Hence, the value of cot(x/2) is -3.73
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Find the equation of the linear function represented by the table below in slope-intercept form.
x y
1 0
2 2
3 4
4 6
Answer:
y = 2x -2
Step-by-step explanation:
y = mx + b
We need the slope (m) and the y-intercept (b) to write the eqation.
The slope is the change in y over the change in x. We can see from the table that the y is changing by 2 as the x changes by 1
So the slope is 2/1 which is the same as 2
The slope (m) is 2.
The y-intercept is the place where the line crosses the y axis. It is at the point (0,b). When x is zero, what is y? If we follow the patter and move to the number before x is 1, we get x = 0. That means that we have to move back 2 units of the y's. That would be -2. So the y-intercept is the point (0,-2).
The y-intercept (b) is -2
y = 2x - 2
The total price for 7 movie tickets is $71.40. If each ticket costs the same amount, how much does one movie ticket cost?
Answer:
Each ticket costs: $10.20
Step-by-step explanation:
If all 7 tickets together add up to 71.40, you cna find the price of one by dividing.
Take 71.40 and divide that by 7
71.40 / 7 = 10.2
the receipt you are using indicate that a mixture should be heated to a temperature of 132F.The mixture is currently at 109F. how many more degrees d does the mixture need to be heated
The mixture must be heated an amount of 23 °F to reach a temperature of 132 °F.
How much must the receipt be heated to be at recommended temperature?
Temperature is the measure of how "hot" a system is. Physically speaking, temperature is closely related to atomic and molecular motion within a system. In this problem we find a mixture that must be at a certain temperature, higher than its real one.
Therefore, the amount required to increase the temperature of the mixture is defined by following subtraction:
ΔT = R - r
Where:
ΔT - Temperature difference, in degrees Fahrenheit.r - Real temperature, in degrees Fahrenheit.R - Expected temperature, in degrees Fahrenheit.If we know that r = 109 °F and R = 132 °F, then the temperature difference is:
ΔT = 132 °F - 109 °F
ΔT = 23 °F
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Drag tiles to the boxes to form correct pairs. Not all tiles will be used. Determine each segment length in right triangle ABC.
The value each segment length in right triangle ABC are AD = 6 units, BC = 4 units, AB = 4√3 units and BD = 2√3 units
How to determine each segment length in right triangle ABC?Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles
Since AC = 8 and CD = 2.
Thus, AD = AC - CD = 8 - 2 = 6 units
sin 30° = BC/AC
0.5 = BC/8
BC = 0.5 × 8
BC = 4 units
AB = √(8²-4²) (Pythagoras theorem)
AB = 4√3 units
BD = √(4²-2²) (Pythagoras theorem)
BD = 2√3 units
Therefore, drag the value of each segment length in the box accordingly
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very important please help
The given angle 2.59 radian into degree is 148.40°.
What is radian and degree?
While a radian is another unit of measurement that is used to measure angles, a degree is a unit of measurement that is used to measure circles, spheres, and angles. The radian, or one pi radian, is only half the diameter of a circle, which has 360 degrees, or its entire area.
Given:
The angle in radian is 2.59.
We have to convert this angle into degree.
Since, the formula to convert angle θ from radian to degree is,
Radian = [tex]\frac{180}{\pi }[/tex] degree
= 2.59 x (180/π)
= 148.40°
Hence, the given angle 2.59 radian into degree is 148.40°.
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A reservoir in the shape of a right circular cylinder is to contain 79,200 L of water. If the radius of the cylinder is 3 m, find its height.
Please find attached herewith the solution of your question.
Answer: 2.8 m
Hope it helps.
If you have any query, feel free to ask.
What is the square root of 6,7,8,9, and 10?
The square root of the numbers are 2. 45, 2. 65, 2. 82, 3 and 3. 16 respectively.
What is square root?The square root of a number is described as the factor that when multiply by itself would give the original
It is represented with the symbol, "√".
To determine the square root of a number is to find the opposite of the square of that same number.
It is also described as the number having the value of its power or exponent as 1/2
From the information given, we have to determine the square root of the numbers, we have;
a. √6
The square root of the number is 2. 45
b. √7
The square root of the number is 2. 65
c. The square root of 8
√8 = 2. 82
c. The square root of 9
√9 = 3
d. The square root of 10
√10 = 3. 16
Hence, the square root is the opposite of squaring the number
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Answer:
a) 2.45b) 2.65c) 2.82d) 3e) 3.16Step-by-step explanation:
i think this is right ans. of your question.......-2x-3y=48 and 7x+3y=21
Answer:
Step-by-step explanation:
2424242424242424hhj
The graph of f(x) = |x| − 2 has an x-intercept at ???
A- (0,0)
B- (0,-2)
C- (-2,0)
D- (2,2)
√((1 - CSC² y) (COS²y-1))
The simplified trigonometric expression [tex]\sqrt{(1 - \csc^2{(y)}){(\cos^2{y} - 1)}}[/tex] is given as follows:
[tex]\sqrt{(1 - \csc^2{(y)}){(\cos^2{y} - 1)}} = \cot{y}\sin{y}[/tex]
How to simplify the trigonometric expression?The trigonometric expression for this problem is defined as follows:
[tex]\sqrt{(1 - \csc^2{(y)}){(\cos^2{y} - 1)}}[/tex]
Then trigonometric identities are used to simplify the radicands of the rational expression.
The identity that uses the cossecant squared is given as follows:
csc²(y) = 1 + cot²(y).
Hence:
1 - csc²(y) = -cot²(y).
The identity that uses the cosine squared is given as follows:
sin²(y) + cos²(y) = 1.
Hence:
cos²(y) - 1 = -sin²(y).
Then the expression can be simplified as follows:
[tex]\sqrt{(1 - \csc^2{(y)}){\cos^2{y} - 1}} = \sqrt{-cot^2{y} \times -\sin^2{y}}[/tex]
As the product of two negative numbers is positive, we have that:
[tex]\sqrt{cot^2{y}sin^2{y}}
Taking the square root of each squared term, the simplified expression is given as follows:
cot(y)sin(y).
Missing InformationThe problem asks for the simplified expression.
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The equation of line 1 is shown.
v=-3x-1
Click to show whether each line, represented by their
equations, is parallel to line I, perpendicular to line 1, or neither
(Or just look at picture) lol
x = 3y perendicular to l
y = -3x parallel to l
y = 3x + 2 neither
x -3y = -6 perpendicular to l
6y = 2x + 10 perpendicular to l
What is Slope ?A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks.
One approach for determining a line's slope from a graph is to use the formula immediately after knowing the coordinates of two points that are on the line. Let's assume that the coordinate values for the two spots are unknown. Therefore, we also have another way to determine the slope of the line. This approach entails attempting to determine the tangent of the angle formed by the line and the x-axis.
The line is
y = -3x -1
slope is -3 by slope intercept form
The line x = 3y
or y = (1/3)*x
slope is 1/3
we know for a line perpendicular to a given line slope should be -1/m so the slope will be (1/3)
so, x = 3y is perpendicular
y = -3x have slope -3 so it is parallel
y = 3x + 2 slope is 3 so neither
x - 3y = -6
or , y = (1/3)*x + 2 , so slope is (1/3) so perpendicular to line
And
6y = 2x + 10
here slope is 1/3 so perpendicular to line.
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Information
500 customers contacted a company today.
Phone
250 Customers
Webchat
4x Social Media
Email
III)
50% of Phone
Social Media
Question
Adjust the pie chart to represent the source of customer contacts.
G
Pie graphs can be used to display percentages of an entire group and depict percentages at a certain moment. Customers contacted via the web = x(let) then.as a result, customers contacted online (chart = x = 100), 25 customers were reached by social media, or x/4
What purpose does a pie chart serve?Pie charts can be used to show percentages for the whole group or for a specific time period.
In contrast to bar and line graphs, pie charts do not show changes over time.
The following pages provide descriptions of the various pie chart elements.
Since the slices of a pie chart represent different parts of the whole, their sum must always equal 100%.
Number of customers overall = 250 clients were contacted via email for every 500 customers contacted via phone, or 50% of phone contacts.
=(50÷100)×250
=125
Customers reached via social media
= total customers + 250 + 125 + x+1 = 500 x+1
=125 × 5
T=125
x=100.
Customers contacted via the web = x(let) then.
as a result, customers contacted online (chart = x = 100)
25 customers were reached by social media, or x/4
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Help please I forgot how to do this cuz I’m in geometry but they give us algebra questions to practice with sometimes
Answer:
y = - 2x - 1--------------------------------------
As per table we see:
The y-coordinates decrease at a rate of - 2, it is representing the slope of the line.To find the y-intercept we add 2 to the value of y = - 3 when x = 1, it will represent y = - 1 at x = 0.
The slope-intercept form is:
y = mx + b, where m is the slope, which is - 2 and b is the y-intercept, which is - 1.After plugging in the values of m and b the line becomes :
y = - 2x - 1ABCD is a quadrilateral in which angle A equal 86, angle C equal 110, and angle D equal 40. The angle ABC is bisected to cut the side AD at E. fine angle AEB
Using the given information, the measure of angle AEB is 62
Calculating the measure of an angleFrom the question, we are to determine the measure of angle AEB
From the given information, we have that
Angle A = 86°
Angle C = 110°
Angle D = 40°
First, we will calculate the measure of angle B
A + B + C + D = 360°
86 + B + 110 + 40 = 360 (Sum of angles in a quadrilateral)
B + 236 = 360
B = 360 - 236
B = 124
∴ Angle ABC = 124
Then,
Angle ABC is bisected
Therefore,
Angle AEB = 1/2 × 124
Angle AEB = 62
Hence, angle AEB is 62
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(Look at picture) ty btw
The correct statements regarding the linear function G(t) = 10 - 2t are given as follows:
Initially, the tank has 10 gallons of gasoline.
The rate of consumption is of 2 gallons per hour.
The slope of G(t) represents the fuel consumption of the vehicle.
The t-intercept represents the time it takes for the vehicle to run out of gas.
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
The linear function is defined as follows:
G(t) = 10 - 2t.
In which the variables are:
G(t) is the amount of gasoline that the car has after t hours.
t is the time in hours.
The slope and the intercept are presented as follows:
Slope of -2: 2 gallons are consumed each hour.
Intercept of 10: The initial fuel in the car is of 10 gallons.
The t-intercept is:
10 - 2t = 0
2t = 10
t = 5.
Which is the time it takes for the car to run out of fuel.
Missing Information
The options are given by the image shown at the end of the answer.
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What is the equation of the line in slope-intercept form that passes through point (0, −2) and is parallel to the line y = -1/2 + 6? Show all necessary steps.
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mc + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x + 6 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes , then
slope of parallel line = - [tex]\frac{1}{2}[/tex]
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = - [tex]\frac{1}{2}[/tex] x - 2 ← equation of parallel line
Indefinite Integral and Chain Rule
The travelled distance functions for the particle is the integral equation [tex]\Delta s = \int\limits^{t = 3}_{t = 0} {|t^{3} - 3 \cdot x^{2} + 2\cdot x|} \, dt[/tex]. (Correct choice: C)
How to define a definite integral associated to the distance travelled by a particle
In this problem we find the case of a particle whose velocity is defined by cubic function v(t) = t³ - 3 · t² + 2 · t and we are asked to find its travelled distance, that is the distance traveled by the particle along its path. Since travelled distance is a scalar, then we must apply the following definition:
[tex]\Delta s = \int\limits^{t = b}_{t = a} {|v(t)|} \, dt[/tex]
Where:
v(t) - Velocity of the particle.a - Initial time.b - Final time.Δs - Travelled distance.Therefore, the travelled distance function is shown below:
[tex]\Delta s = \int\limits^{t = 3}_{t = 0} {|t^{3} - 3 \cdot x^{2} + 2\cdot x|} \, dt[/tex]
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Lucy paid $3.20 for 4 pounds of coffee beans. How much did she pay for each pound of coffee beans?
At the 2006 Winter Olympics in Torino, Italy, US speed skater Apolo Ohno took the gold medal for the 500m sprint by completing the course in 41.935 s. What was his average speed for this event in m/s.
The average speed of Apolo Ohno, in the sprint in the Winter Olympics in 2006, given the time taken to complete the course, was 11. 92 m /s
How to find the average speed ?A body's average speed is the mean value of its speed for a certain time period. The average speed formula is necessary because a moving body's speed vary over time instead than remaining constant. Even though the speed changes, we can still use the total time and total distance numbers, and with the help of the average speed calculation, we can determine a single value that represents the entirety of the motion.
Given the distance that Apolo Ohno had to sprint and the time he completed the course in, his average speed in the event was :
= 500 m / 41. 935 s
= 11. 92 m /s
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HELPP!!!!!!
shipping 2 large boxes and 3 small boxes cost 49$. shipping a large box costs 2$ more than shipping a small box. what is the price of shipping a large box?
Answer: I'm guessing this is addition.
Shipping 1 large box would be $51. Shipping 2 large boxes would be $54 dollars.
Step-by-step explanation: I don't know if you wanted addition or multiplication but the answer I gave is addition
How many square feet of outdoor carpet will we need for this hole?
The area of a outdoor carpet is 42 square feet.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
In the given figure, the outdoor carpet consist two triangles and one rectangle.
Here, rectangle measures length=11 ft and width = 3 ft, small triangle has base= 2 ft and height =3 ft and large triangle has base= 4ft and height =3 ft.
So, area of rectangle is 11×3 = 33 square ft
Area of small triangle = 1/2 ×Base×Height
= 0.5×2×3
= 3 square feet
Area of large triangle = 1/2 × 4×3
= 6 square feet
Total area = 33+3+6
= 42 square feet
Therefore, the area of a outdoor carpet is 42 square feet.
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Please helpp :,)
Use the graph to answer the questions on this quiz.
Over which of the following approximate interval(s) is the price decreasing?
▢ 4 < x < 6
▢ 6 < x < 10
▢ 0 < x < 4
▢ 10 < x < 16
Answer: I believe it is
4 < x < 6
10 < x < 16
A textbook store sold a combined total of 447 sociology and math textbooks in a week. The number of math textbooks sold was 57 less than the number of sociology textbooks sold. How many textbooks of each type were sold?
If a textbook store sold a combined total of 447 sociology and math textbooks in a week. The number of textbooks of each type that were sold is: 195 Math textbooks, 138 Sociology textbooks.
How to find the number of textbook that were sold?Let x represent the number of math textbooks
Let y represent the number of sociology
Altogether bookseller sold 447 math and sociology textbooks
Hence,
x + y = 447
Since the number of sociology textbooks sold was 57 less than the number of math books sold.
So:
y = x - 57
Substitute for y in the equation
x + y = 447
x + (x - 57) = 447
2x - 57 = 447
Combine like terms
2x = 447 -57
2x = 390
Divide both side by 2x
x = 390/2
x = 195 (Math textbooks)
y = x - 57
y = 195 -57
y = 138 ( Sociology textbooks)
Therefore 195 and 138 textbooks were sold.
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18. If x=2, find the value of q in the equation 3x-4=x+q. A. 8 D.-1 B.I C.0
The value of q in the equation 3x-4=x+q when x=2 is 0.
We can find the value of q in the equation 3x-4=x+q by solving for q:
First, we can substitute the given value of x (x=2) into the equation:
3(2)-4=2+q
Simplifying:
6-4=2+q
2=2+q
Now we can subtract 2 from both sides of the equation:
q = 0
So, the value of q in the equation 3x-4=x+q when x=2 is 0.
Answer: q = 0
Step-by-step explanation:
3x - 4 = x + q
2x - 4 = q
Substitute x = 2 in the equation,
2 x 2 - 4 = q
q = 0
Therefore, the correct answer is 0.
ANYONE GOOD AT MATH!? PLEASE HELP!!
The values of g(g(4)) = 0 and f(f(3)) = - 3.
Equation of Parabola:A portion of the right cone known as a parabola is one that runs parallel to the generating line on one side of the iconic figure. The parabola is likewise a quadratic connection, much like the circle, however, unlike the circle, either 'A' or 'B' will be squared, but never both.
Here we have
Equation of parabola f(x) = x² - 2x - 3 and line g(x) = x - 2
Here we need to find g(g(4)) and f(f(3))
To find g(g(4)) take x = 4
g(4) = 4 - 2 = 2
=> g(g(4)) = g(2) = 2 - 2 = 0
Therefore, g(g(4)) = 0
To find f(f(3)) take x = 3
f(3) = 3² - 2(3) - 3 = 9 - 9 = 0
f(f(3)) = 0² - 2(0) - 3 = - 3
Therefore,
The values of g(g(4)) = 0 and f(f(3)) = - 3.
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Given a set A={1,2,3,4,5,6,7}
Define a relation induced by the partition of set A and that partition must contain of at least 3 subsets.
Given a set A={1,2,3,4,5,6,7}, a relation induced by the partition of set A is
(1,2,3) -> {1,2,3}, (4,5) -> {4,5}, (6,7)-> {6,7}
What is a set?Generally, A set comprises elements or members that may be mathematical objects of any sort, including numbers, signs, points in space, lines, other geometric forms, variables, or even other sets. A set is a mathematical formula for a collection of various things.
A relation induced by a partition of a set is a relation that defines a way of grouping elements in the set into subsets, called "blocks" or "cells". In this case, the set
A={1,2,3,4,5,6,7}
can be partitioned into at least 3 subsets. For example, one possible partition is
A={1,2,3}, {4,5}, {6,7}.
The relation induced by this partition is a relation that assigns to each element in one of the 3 subsets, i.e.
(1,2,3) -> {1,2,3}, (4,5) -> {4,5}, (6,7)-> {6,7}
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32 2 8. David and John Share $455 in Ratio OF respectively. 28 B How much money does John get . ?
The amount that John gets is given as follows:
$364.
How to obtain the amount that John gets?The amount that John gets is obtained applying the proportions in the context of this problem.
The ratio between the amounts that David and John gets is given as follows:
2:8.
Meaning that relative to the total amount, the fractions are given as follows:
David: 2/10 = 1/5.John: 8/10 = 4/5.The total amount is given as follows:
$455.
Hence the amount that John gets is given as follows:
4/5 x 455 = $364.
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Dominic fills some jars with chutney that
he has made.
Each jar weighs 230 g when it is empty
and can contain 300 cm³ of chutney.
8 full jars of chutney weigh a total of
5.68 kg.
Calculate the density of the chutney, in
g/cm³.
If your answer is a decimal, give it to
1 d.p.
Answer:
1.6 g/cm³
Step-by-step explanation:
230g = 0.23 kg
0.23 kg x 8 = 1.84 kg
So, the weight of chutney in the 8 jars is 5.68kg - 1.84kg = 3.84kg or 3840g.
So, 1 jar weight is 3840g/8 or 480g of chutney.
Density = 480/300 or 1.6 g/cm³
Answer:
2.36
Step-by-step explanation:
5.68 kg into grams = 5680 and 300*8 is 2400
5680/2400 is 2.36
[tex]x^{2} +5x-14[/tex]
[tex] \sf {x}^{2} + 5x - 14 \\ \sf {x}^{2} - 2x + 7x - 14 \\ \sf x(x - 2) + 7(x - 2) \\ \sf \: (x - 2)(x + 7) = 0 \\ \sf \: x = 2 \: and \: x = - 7[/tex]
Chi has $13.30 in dimes and quarters. The number of dimes is three more than four times the number of quarters. How many of each are there?
Answer:
To solve this problem, we will use the following steps:
Step 1: Let's assume that the number of quarters is x, and the number of dimes is y
Step 2: We know that the number of dimes is three more than four times the number of quarters, so we can write the equation: y = 4x + 3
Step 3: We also know that Chi has $13.30 in dimes and quarters. Since dimes are worth $0.10 and quarters are worth $0.25, we can write the equation: 0.25x + 0.10y = 13.30
Step 4: Now we have two equations with two unknowns, we can substitute one equation into another to find the value of x and y.
y = 4x + 3
0.25x + 0.10(4x + 3) = 13.30
0.25x + 0.40x + 0.30 = 13.30
0.65x = 13
x = 20
Step 5: We can substitute the value of x in one of the equation, to find the value of y
y = 4(20) + 3
y = 83
Final Answer: Chi has 20 quarters and 83 dimes.
Note: We can check our solution by multiplying the number of quarters by $0.25 and the number of dimes by $0.10 to check if the total money is $13.30 which is true.
