Answers
Answer:
D. tan x
Explanation:
Given the trigonometric expression:
\(\frac{\tan x \cdot \sec x}{\csc x} \cdot \cot x\)Now, the expression can be rewritten in the form below:
\(\begin{gathered} \frac{\tan x\cdot\sec x}{1}\times\frac{\cot x}{\csc x}\frac{}{} \\ \begin{equation*} =\tan x\times\frac{\sec x}{\csc x}\cdot\cot x \end{equation*} \\ =\frac{\sin(x)}{\cos(\text{x})}\times\frac{\cos x}{\sin x}\times\frac{\sec x}{\csc x}\text{ where }\begin{cases}\tan x=\frac{\sin x}{\cos\text{ x}} \\ \cot x=\frac{cosx}{sinx}\end{cases} \\ =\frac{\sec x}{\csc x} \\ =\frac{1}{\cos x}\div\frac{1}{\sin x} \\ =\frac{1}{\cos x}\times\sin x \\ =\frac{\sin x}{\cos x} \\ =\tan x \end{gathered}\)The expression is equivalent to tan x.
Option D is correct.
Related Questions
(−2, 5), slope = -4 slope intercept form
Answers
____________________________________________
Slope-Intercept Form - Solution and Explanation
____________________________________________
Hello! So...
We are given the following to convert:
Convert into Slope-Intercept Form
(-2, 5), slope = -4
____________________________
1. Compute the line equation y = mx + b for slope. In this case, our slope (m) equals -4, and passes through (-2, 5).
____________________________
2. Determine the y-intercept. In this case, b = -3.
____________________________
3. Now, construct the line equation (y = mx + b), where m = -4 and b = -3. Then, you will have your converted solution in Slope-Intercept Form.
Slope-Intercept Form:
\(y=-4x-3\)
___________________________________________
Hope this helps! If not, feel free to comment on the matter and I will see what else I can do to assist your further. However, if this does help, lmk! Thanks and good luck!
1. When the net is folded into the rectangular prism shown beside it, which letters will be on the back and bottom of the rectangular prism?
(The letter on the back will be D.
The letter on the bottom will be E.)
(The letter on the back will be A.
The letter on the bottom will be D.)
(The letter on the back will be C.
The letter on the bottom will be A.)
(The letter on the back will be D.
The letter on the bottom will be C.)
Answers
When the net is folded into the rectangular prism
The letter on the back will be A.The letter on the bottom will be D.How to determine the position of the lettersA rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. Another name for it is a cuboid.
Applying science of vision to see technical details in the prism, seeing letter B on the top means that D will be on the bottom.
the side we face will be C while the bac will be A
on the other side, the left end not showing is E and this make up all the part of the prism
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Aris and Josiah are reading a 50-page book for their ELA class. Aris wants to know what page Josiah is reading. Josiah gives her two hints: 1. The product of the two page numbers he can see is 930. 2. The page he is reading is an odd numbered page.
Answers
Answer:
31
Step-by-step explanation:
Let x and (x + 1) be the page numbers Josiah can see
Hint 1: x(x + 1) = 930
⇒ x² + x = 930
⇒ x² + x - 930 = 0
Using quadratic formula,
\(x = \frac{-b\pm\sqrt{b^2 -4ac} }{2a}\)
a = 1, b = 1 and c = -930
\(x = \frac{-1\pm\sqrt{1^2 -4(1)(-930)} }{2(1)}\\\\= \frac{-1\pm\sqrt{1 +3720} }{2}\\\\= \frac{-1\pm\sqrt{3721} }{2}\\\\= \frac{-1\pm61 }{2}\\\)
\(x = \frac{-1-61 }{2}\;\;\;\;or\;\;\;\;x= \frac{-1+61 }{2}\\\\\implies x = \frac{-62 }{2}\;\;\;\;or\;\;\;\;x= \frac{60 }{2}\\\\\implies x = -31\;\;\;\;or\;\;\;\;x= 30\)
Sice x is a page number, it cannot be negative
⇒ x = 30 and
x + 1 = 31
The two pages Josiah can see are pg.30 and pg.31
Hint 2: The page he is reading is an odd number
Out of the pages 30 and 31, 31 is an odd number
Thereofre, Josiah is reading page 31
1, 3, 9, 27, 81, 243, ?
Find pattern
Answers
Answer:
You're multiplying each of those numbers by 3.
Step-by-step explanation:
1 * 3 = 3
3 * 3 = 9
9 * 3 = 27
27 * 3 = 81
81 * 3 = 243
Each number is multiplied by 3.
1 x3=3 -> 3x3=9 -> 9x3=27 -> 27x3=81 and so on.
Happy to help; have a great day! :)
The sum of two numbers is 48. One number is 4 less than the other. Find the numbers.
Answers
Answer:
=26
=22
Step-by-step explanation:
\( \: \: \: x+x-4=48 \\ = 2x - 4 = 48 \\ = 2x = 48 + 4\\ = 2x = 52 \\ = x = 26 \\ \: \: \: \: \: \: \: \: \:= x - 4 = 26 - 4 = 22\)
HELP PLEASE!!!!!! Anaya bought a sweater that was on sale. The sweater originally cost $34.50 but was purchased for $27.60. What percentage of the original price was the discount?
Answers
Answer: 80%. Hope this helps, please consider making me Brainliest.
Step-by-step explanation:
To find the percentage, divide the sale cost by the original cost:
27.60/34.50
Let's multiply both sides by 10 to make the operation easier:
27.6/34.5 ( I eliminated the zero's because they kind of have no use) -->
276/345, now solve:
276/345 = 0.8
0.8 = 80%
The percentage is 80%.
NEED HELP ASAP!!
Which equations represent exponential growth?
Which equations represent exponential decay?
Drag the choices into the boxes to complete the table.
Exponential Growth:
Exponential Decay:
y = 1700(1.25)^t
y =240(1/2)^t
y = 4000(1.0825)^t
y = 1.5(10)^t
y = 12,000(0.72)^t
y = 8000(0.97)^t
Answers
Answer:
Growth: y = 1700(1.25)^t, y = 4000(1.0825)^t, y = 1.5(10)^t
Decay: y =240(1/2)^t, y = 12,000(0.72)^t, y = 8000(0.97)^t
Step-by-step explanation:
In an exponential equation, growth and decay are determined by the factor you are multiplying by exponentially. If it's under 1 you're basically exponentially dividing the initial value. Over 1 and you are increasing the value.
Write an equation that represents the relationship between the number of buckets filled, , in hours.
Answers
1)
y = bucket fill
x = time in hours
This is the relationship because 1 hour = 1 filled bucket, the relationship is 1 : 1.
Equation
y = x
2) The rate is 1 bucket/hour
k = 1 bucket/hour
use functional notations to describe the function displayed to the right.
Answers
Examining the table the functional notation is in the second option which is f ( x ) = x^2
How to determine the functional notations of the tableThe table represents functions of input variables and the output variables.
The functional notation represents the relationship between the input and out variables
comparing the values and the function
f ( x ) = x^2
at x = -3 ⇒ f ( -3 ) = (-3)^2 = 9
at x = 0 ⇒ f ( 0 ) = (0)^2 = 0
at x = 1 ⇒ f ( 1 ) = (1)^2 = 1
This shows that f ( x ) = x^2 is the correct option
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OMG PLEASE I BEG I NEED HELP 5th grade math
Answers
Answer: A
Step-by-step explanation:
Volume= LxWxH so we get 20x28x24 as given.
Volume= 13,440 which is the volume of the box given. ANd so if the box is 10,500cubic inches, we subtract to find the difference.
13,440-10,500= 2,940 Cubic Inches
Option A
Answer:
Part A: 13440 cubic inches.
Part B: A - 2940 cubic inches.
Step-by-step explanation:
The volume of the box = 24x20x28 = 13440 cubic inches.
The problem tells us that his gift is 10,500 cubic inches. So subtract that from the volume of the box.
13440-10500 = 2940 cubic inches. The answer is A.
Find the volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0). Slices perpendicular to the x-axis are semicircles. Enter answer using exact values.
Answers
The volume of the solid whose base is a triangle with vertices (0,0), (0,3), and (5,0) is 25π/12 cubic units.
What is a triangle?
A triangle is a closed geometric shape that is formed by connecting three line segments. These line segments are called sides, and the points where they meet are called vertices. A triangle has three sides, three angles, and three vertices.
To start, let's graph the triangle to get a better understanding of the problem:
(0,3) *
|\
| \
| \
| \
| \
(0,0) *-----*-----> x
(5,0)
The height of this slice is given by the line from the point (x,0) to the point (0,3), which has equation y = 3/5 * x + 0. The radius of the semicircle is half the height of the slice, which is given by the equation r = 3/10 * x.
The area of a semicircle is πr²/2, so the volume of this slice is:
V(x) = π * (3/10 * x)² / 2 * dx
To find the total volume of the solid, we need to integrate this expression over the range of x values that covers the entire base of the solid, which is from x=0 to x=5:
V = ∫₀₅ π * (3/10 * x)² / 2 dx
V = π/20 * ∫₀₅ x² dx
V = π/20 * [x³/3] from 0 to 5
V = π/20 * (5³/3)
V = π/4 * (25/3)
V = 25π/12
Therefore, the volume of the solid is 25π/12 cubic units.
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What is the gradient of the blue line
Answers
Answer:
Up 2 to the right 1
Step-by-step explanation:
that would be i think
The side of a triangle are in the ratio 4:4:3 what kind of triangle is it (b) calculate the smallest angle of the triangle to the nearest degree
Answers
The smallest angle of the equilateral triangle is 60 degrees
If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.
To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.
For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:
Smallest angle \(= \frac{180}{3} = 60\)\) degrees.
Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).
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On a ferris wheel, Sarah observes that it takes 45 seconds for her chair to complete a full revolution. Her chair is 30 feet from the axle of the ferris wheel.
To the nearest hundreth, Sarah's angular velocity is _____ radians per minute.
Answers
Answer:
The angular velocity is 8.38 radians per minute
Step-by-step explanation:
From the question,
It takes 45 seconds to complete a full revolution,
That is, 1rev/45secs
First, we will convert this to revolutions per minute (rev/min)
1rev/45secs = \(\frac{1 revolutions}{45 seconds} \times \frac{60seconds}{1minute}\)
= 4/3 rev/min
Now, we will convert this to radians per minute (rad/min)
1 revolutions = 2π rad
4/3 rev/min = \(\frac{\frac{4}{3} rev}{min} \times \frac{2\pi rad}{1 rev}\)
= 8.38 rad/min
Hence, the angular velocity is 8.38 radians per minute
Graph the line with slope -3 passing through the point (1,-5)
Answers
The equation of the line in the standard form exists 3x - y = 2.
What is the equation of a line?The equation of a line is a representation of a line on an x-y plane that illustrates the relationship between x and y for each point on the specific line. When x and y are variables and a, b, and c are constants, a line has the standard form ax + by = c.
Y = mx + b is the slope-intercept form of a line, where x and y are variables, m is the line's slope, and b is the line's y-intercept.
The one-point formula reads: y - y₁ = m(x - x₁). to describe the equation of a line traveling through the point (x1, y1) and having a slope of m.
We are asked to graph a line with a slope = -3, passing through the point (1, -5).
We use the one-point formula to determine the equation of this line, with slope m = -3, (x₁, y₁) = (1, -5).
Substituting these values in the equation y - y₁ = m(x - x₁), we get
Let the equation be y - -5 = -3(x - 1)
simplifying the equation, we get
y = -3x + 3 - 5
y = -3x - 2
3x - y = 2
The equation of the line in the slope-intercept form exists y = -3x - 2
The equation of the line in the standard form exists 3x - y = 2.
We draw the locations (1,-5) (because it is obvious that the line goes through this location) and (0, 2) (since the y-intercept is at 2 and the line passes through the point (0, 2)) in order to graph this line. We draw a line connecting these places, then we expand it on both sides to create the necessary line.
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Finde the value of x in the proportion ( 5x+ 1 ):3 =(2x +2): 7(6 x) = (4x) :7
Answers
In the proportion (5x + 1):3 = (2x + 2):7, the value of x is -1/29.
In the proportion (6x):(4x) = 7, there is no value of x that satisfies the proportion.
To find the value of x in the given proportions, let's solve them one by one:
(5x + 1) : 3 = (2x + 2) : 7
To solve this proportion, we can cross-multiply:
7(5x + 1) = 3(2x + 2)
35x + 7 = 6x + 6
Subtracting 6x from both sides and subtracting 7 from both sides:
35x - 6x = 6 - 7
29x = -1
Dividing both sides by 29:
x = -1/29
Therefore, the value of x in the first proportion is -1/29.
(6x) : (4x) = 7
To solve this proportion, we can simplify the left side:
6x / 4x = 7
Dividing both sides by 2x:
3/2 = 7
This equation is not true, as 3/2 is not equal to 7.
Therefore, there is no value of x that satisfies the second proportion.
In summary, the value of x in the proportion (5x + 1) : 3 = (2x + 2) : 7 is -1/29, and there is no value of x that satisfies the proportion (6x) : (4x) = 7.
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Which of the following could be the value of x in the equation x^2 - 21 = 100 Choose all the correct answers
Answers
How to solve your problem
x^{2}-21=100
Quadratic formula
Factor
1
Move terms to the left side
x^{2}-21=100
x^{2}-21-100=0
2
Subtract the numbers
x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0
x^{2}\textcolor{#C58AF9}{-121}=0
3
Use the quadratic formula
x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
x^{2}-121=0
a=\textcolor{#C58AF9}{1}
b=\textcolor{#F28B82}{0}
c=\textcolor{#8AB4F8}{-121}
x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}
4
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Add zero
Multiply the numbers
x=\frac{\pm 22}{2}
5
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x=\frac{22}{2}
x=\frac{-22}{2}
6
Solve
Rearrange and isolate the variable to find each solution
x=11
x=-11
The monthly profit for a company that makes decorative picture frames depends on the price per frame. The company determines that the profit is approximated by f(p)= -80p + 3440p -36,000, where p is the price per frame and f(p) is the monthly profit based on that price.
Requried:
a. Find the price that generates the maximum profit.
b. Find the maximum profit.
c. Find the price(s) that would enable the company to break even.
Answers
Answer:
a. $21.50
b. $980
c. $25 and $18
Step-by-step explanation:
a. The price that generates the maximum profit is
In this question we use the vertex formula i.e shown below:
\((-\frac{b}{2a}, f(-\frac{b}{2a} ))\\\\\)
where a = -80
b = 3440
c = 36000
hence,
P-coordinate is
\((-\frac{b}{2a}, (-\frac{3440}{2\times -80} ))\\\\\)
\(= \frac{3440}{160}\)
= $21.5
b. Now The maximum profit could be determined by the following equation
\(f(p) = 80p^2 + 3440p - 36000\\\\f($21.5) = -80(21.5)^2 + 3440(21.5) - 36000\\\\\)
= $980
c. The price that would enable the company to break even that is
f(p) = 0
\(f(p) = -80p^2 + 3440p - 36000\\\\-80p^2 + 3440p - 36000 = 0\\\\p^2 -43p + 450 = 0\\\\p^2 - 25p - 18p + 450p = 0\\\\p(p - 25) - 18(p-25) = 0\\\\(p - 25) (p - 18) = 0\)
By applying the factoring by -50 and then divided it by -80 and after that we split middle value and at last factors could come
(p - 25) = 0 or (p - 18) = 0
so we can write in this form as well which is
p = 25 or p = 18
Therefore the correct answer is $25 and $18
Please answer this correctly without making mistakes
Answers
Answer:
1540 cm³
Step-by-step explanation:
V= blh= 14 cm * 22 cm * 5 cm = 1540 cm³
Answer:
1540 cm³
Step-by-step explanation:
This is because the formula for volume is l*w*h so 5*22*14 is 1540
brainliest please
Given the set S = {a, b, c, d}, answer the following.
(a) How many one-element subsets does S have?
(b) How many two-element subsets does S have?
(c) How many three-element subsets does S have?
(d) How many four-element subsets does S have?
(e) How many zero-element subsets does S have?
(f) How many subsets does S have?
(g) If
n(S) = k,
how many subsets will S have?
Answers
Answer:
Step-by-step explanation:
6.(03.02) Write a situation in which positive and negative numbers are used to describe values that have opposite meaning. What does 0 represent in this situation you created?
Answers
Possible Answer 1:
Positive values represent elevations above sea level, while negative values are elevations below sea level. For example, a building may be +100 or simply 100 feet high. Another example: going scuba diving could lead the diver to reach a elevation of -10 meters. The value 0 is the exact location of sea level itself. In other words, if your elevation is 0, then you are at the surface of the water.
==========================================================
Possible Answer 2:
Often in money, loans and borrowing happens. If so, then we use negative numbers to indicate debt. If someone has a bank balance of say -10 dollars, then they owe the bank $10. Positive values mean that they don't owe the money and it's entirely theirs to spend however they want. A balance of 0 means they neither have money, nor do they owe anyone.
==========================================================
Possible Answer 3:
Let's say we define negative distance to mean that you walk some amount to the left (to match up with the fact the negative x values point left). So for instance, we could say the number -14 indicates you walked 14 feet to the left. Positive values on the other hand will mean you walk some amount to the right. Drawing an x axis number line is very recommended. The value 0 indicates that no walking has occurred at all.
==========================================================
Of course, when you write your answer, it should be in your words only. Those answers posted above are just a springboard to get you started.
The radius of a circle is increasing at a rate of 6 centimeters per minute. Find the rate of change of the area when the radius is 4 centimeters.
Answers
Answer:
The rate of change is of of the area when the radius is 4 centimeters \(48\pi\) square centimeters.
Step-by-step explanation:
Area of a circle:
The area of a circle of radius r is given by:
\(A = \pi r^2\)
Implicit derivative:
To solve this question, we have to derivate implictly the equation as a function of t. Thus:
\(\frac{dA}{dt} = 2\pi r \frac{dr}{dt}\)
The radius of a circle is increasing at a rate of 6 centimeters per minute.
This means that \(\frac{dr}{dt} = 6\)
Find the rate of change of the area when the radius is 4 centimeters.
This is \(\frac{dA}{dt}\) when \(r = 4\). Thus
\(\frac{dA}{dt} = 2\pi r \frac{dr}{dt} = 2\pi(4)(6) = 48\pi\)
The rate of change is of of the area when the radius is 4 centimeters \(48\pi\) square centimeters.
Determine the slope and y-intercept of a line that passes through the points (2, 4) and (–4, 1).
m = [ A. –2.5 , B. –1.5 , C. 0.5 ]
b = [ A. 3, B. 7, C. 9 ]
Answers
Answer:
hhhhhhhhhhhhiiiiiiiii
The general form of the equation of a circle is a X squared plus BY squared plus 3X plus 3Y plus Z equals zero wear a equals B does not equal zero is the circle has a radius of three units in the center lies on the Y axis, which set of values of a B C,D and E my correspond to the circle
Answers
The set of values that corresponds to the circle with a radius of three units and the center lying on the Y axis is:
A = 1, B = 1, C = 0, D = 3, E = 0.
The general equation of a circle is given by:
x^2 + y^2 + 2gx + 2fy + c = 0
In this case, since the circle has a radius of three units and the center lies on the Y axis, we can deduce the following information:
The center of the circle lies on the Y axis, which means the x-coordinate of the center is zero.
The radius of the circle is three units, which means the distance from the center to any point on the circle is three units.
Using the information above, we can substitute the values into the general equation to solve for the corresponding values:
Substituting the x-coordinate of the center (zero) into the equation, we have:
0^2 + y^2 + 2g(0) + 2fy + c = 0
y^2 + 2fy + c = 0
Since the center lies on the Y axis, the x-coordinate is zero, so the term with x (2gx) becomes zero.
Substituting the radius of the circle (three) into the equation, we have:
(3)^2 = 9
Therefore, the equation becomes:
y^2 + 2fy + c = 9
Comparing this equation with the general form of the circle equation, we can deduce the values of A, B, C, D, and E as follows:
A = 1 (coefficient of x^2)
B = 1 (coefficient of y^2)
C = 0 (constant term)
D = 3 (coefficient of x)
E = 0 (coefficient of y)
Hence, the set of values that corresponds to the circle is A = 1, B = 1, C = 0, D = 3, and E = 0.
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You inherit $50,000 from crazy aunt Millicent, but it goes into a trust, where it earns 5.25% interest compounded quarterly for 7 years. Then you can have the money. How much will you get?
ASAP please help
Answers
After 7 years, you will have approximately $72,821.87 in the trust.
To find how much will you get?We can use the formula for compound interest to calculate the balance in the trust after 7 years:
A = P*(1 + r/n)^(n*t)
Where
A = the balance after 7 yearsP = the principal amount ($50,000)r = the annual interest rate (5.25% = 0.0525)n = the number of compounding periods per year (4, since the interest is compounded quarterly)t = the time in years (7 years)Plugging in the values, we get:
A = $50,000*(1 + 0.0525/4)^(4*7)
A = $72,821.87
Therefore, after 7 years, you will have approximately $72,821.87 in the trust.
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Evaluate the expression?-2 (1/6) 4 (2/3)
Answers
we have the following:
\(-2\cdot\frac{1}{6}\cdot4\frac{2}{3}\)therefore:
\(-\frac{2\cdot1\cdot4\cdot2}{6\cdot3}=-\frac{16}{18}=-\frac{8}{9}\)therefore, the answer is -8/9
Which value of x makes this equation true?
–5(r = 20) 35
Answers
Answer:
r = -140
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable. Not sure if this was the answer you were looking for.
An equation for the difference between the time is 38.4 - a= 9.59. The others time was
Answers
Answer:
Presumably the "others time" is the quantity \(a\), which is 28.81
Step-by-step explanation:
Let's solve for \(a\) from
\(38.4-a=9.59\)
Adding \(a\) gives
\(a+9.59=38.4\)
Then subtracting 9.59 gives
\(a=38.4-9.59=28.81\)
there are 30 cupcakes in a tin. 16 of the cupcakes are iced of which 3 contain walnuts. 5 cupcakes are neither iced nor contain walnuts. work out the probability that the cupcake picked at random contains walnuts
Answers
The probability that the cupcake picked at random contains walnuts is given as follows:
0.4 = 40%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:
30.
The number of cupcakes with walnuts is given as follows:
3 that are also iced.30 - (16 + 5) = 9 that are not iced.Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:
p = (3 + 9)/30
p = 12/30
p = 0.4.
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Identify the coefficient in the algebraic expression 4ac-3
4
-3
3
4ac
Answers
Answer:
4
Step-by-step explanation:
4 is the coefficient because its infront of the variable