csc² x (1 + sin²x) = cot²x
Answers
Answer:
The given equation is:
Csc² x (1 + sin²x) = cot²x
To prove this equation, we will start with the left-hand side of the equation and simplify it using trigonometric identities.
LHS: Csc² x (1 + sin²x)
= 1/sin²x * (1 + sin²x) [Using the identity csc²x = 1/sin²x]
= 1 + sin²x/sin²x
= 1 + 1/cos²x [Using the identity sin²x + cos²x = 1]
= (cos²x + 1)/cos²x
= cot²x [Using the identity cot²x = cos²x/sin²x]
Therefore, LHS = RHS, which proves the given equation.
Related Questions
8. What is the value of x in the diagram?
A
E
429
B
49
D
32°C
Answers
Answer:
D. \(10^{\circ}\)
Step-by-step explanation:
Let the measure of minor arc \(AE\) be \(\alpha\) and the measure of minor arc \(BD\) be \(\beta\).
Using the secant-secant theorem, \(\frac{\alpha-\beta}{2}=32 \implies \alpha-\beta=64^{\circ}\).
By the inscribed angle theorem, \(\alpha=84^{\circ}\).
Thus, \(\beta=20^{\circ}\).
By the inscribed angle theorem, \(x=10^{\circ}\).
Two hens can lay 2 eggs in 2 minlutes if that is the maximum speed how many hens can lay 500 eggs in 500 minutes
Answers
To determine how many hens are needed to lay 500 eggs in 500 minutes, we divide 500 eggs by the number of eggs laid by each hen in 500 minutes. In this case, 500 eggs divided by 250 eggs per hen equals 2 hens.
So, you would need two hens to lay 500 eggs in 500 minutes at their maximum speed.
jackson and julie are babysitters
Answers
Answer:UwU
Step-by-step explanation:
Answer:
kfjnenowkn jcnj dnonojneqfou
Step-by-step explanation:
HELP I HAVE 10 MIN
Which of the following is a unit fraction?
10/19
1/5
8/15
1/17
Answers
Answer: 1/5 & 1/17
Step-by-step explanation:
In math, a unit fraction can be defined as a fraction whose numerator is 1. So, the only 2 answers would be 1/5, and 1/17.
Hope this helps.
Answer:
1/17 and 1/5
Step-by-step explanation:
a unit fraction is a fraction whose numerator is 1
Please help I dont understand how to get the length of segment DF
Answers
the measure of the angle will be 70°.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.An isosceles triangle in geometry is one with at least two sides that are of equal length. Both having exactly two sides of equal length and having at least two sides of equal length are acceptable specifications, with the latter version containing the equilateral triangle as an exception.
The sum of all angle of triangle = 180
The given triangle two angles are given 44° and 68°
The other angle is 180° - (44+68) = 180 - 110 = 70°
Hence the measure of the angle will be 70°.
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What Is the volume of a rectangle and circle 6x12x7
Answers
Answer:
504 i think
Step-by-step explanation:
8. What is the slope of the line?
A. 0
B. 1
C. Infinity
D. Undefined
Answers
Because y=2 is a horizontal line, there is no rise
Answer:
0.
Step-by-step explanation:
The slope of the line is defined as the change of elevation of the line (\(\frac{rise}{run}\)).
In this case, there is no change in the slope as the line continues across (0 , 2), meaning that the slope of the line is 0.
If the slope of the line is 1, then the line will have (rise 1/run 1), meaning that it will have a linear slope. (See attached image).
Vertical lines have infinite slope, and so can also be called undefined as it moves neither left or right, giving it no run.
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PLEASE HELP THIS IS HARD
Answers
The Area of the shaded portion is: 72 square inches
What is the Area of the shaded region?The formula for the area of a triangle is given by the formula:
Area = ¹/₂ * base * height
Now, to get the area of the shaded portion, we will get the area of the larger triangle and subtract the area of the smaller one from it.
Thus:
Area of larger triangle = ¹/₂ * 17 * 13 = 110.5 square inches
Area of smaller triangle = ¹/₂ * 11 * 7 = 38.5 square inches
Thus:
Area of shaded portion = 110.5 square inches - 38.5 square inches
Area of shaded portion = 72 square inches
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what is the value of 2(c+1) = 10
Answers
Answer:
c=4
Step-by-step explanation:
2c+2=10
2c=8
c=4
2c+2=10
take away two from both sides and you’ll get:
2c=8
divide both sides by 2 and you’ll get:
c=4
The model shows the expression 21 + 9. Which expression is equivalent to this sum? O 317+3) 0 31+ 3 0 3+7+3 O 763+3)
Answers
Given data:
The given expression is (21+9).
The given expression can be written as,
\((21+9)=3(7+3)\)Thus, the first option is correct.
Evaluate the expression below when x = 6 and y = 2. 6x2y3
Answers
Answer:
I think that the answer is 432.
Step-by-step explanation:
6x2y3.We have x as 6 and y as 2.So we replace them with their numbers.
We'll have 6*6*2*2*3 which will give us 432. I HOPE THIS HELPS.
Prove that C2 with a square of length 10x+1 with x being 0
Answers
Assuming that C2 is a circle with a circumference of 2, and x is equal to 0, then the square with a length of 10x+1 would have a length of 1.
In this case, the statement to prove would be: "The circle C2 with a square of length 1 (circumscribed around the circle) has an area greater than or equal to the area of the circle."
To prove this statement, we can use the formula for the area of a circle (A = πr^2), where r is the radius of the circle. We know that the circumference of C2 is 2, so we can find the radius using the formula for the circumference of a circle (C = 2πr):
2 = 2πr
r = 1/π
Substituting this value of r into the formula for the area of a circle, we get:
A = π(1/π)^2
A = 1/π
Therefore, the area of C2 is 1/π.
Next, we need to find the area of the square with a length of 1. The formula for the area of a square is A = s^2, where s is the length of a side. In this case, the length of a side is 1, so the area of the square is:
A = 1^2
A = 1
Comparing the area of the circle and the area of the square, we have:
1/π ≥ 1
Since π is approximately 3.14, we can see that 1/π is greater than 1. Therefore, the circle C2 with a square of length 1 (circumscribed around the circle) has an area greater than the area of the square.
Therefore, we have proven that C2 with a square of length 10x+1 (where x is 0) has a circle with an area greater than the area of the square.
If every 2 cm on a scale drawing is equal to 7 feet in real life, which lines on the drawing would be greater than 21 feet in real life? Select all that apply. A) 7 cm B) 5 cm C) 9 cm D) 12 cm
Answers
The correct answers are A) 7cm, C) 9cm and D) 12cm
Define the Conversion of units?The process of changing a given quantity that is expressed in one unit of measurement to another unit of measurement that is equivalent in value is referred to as conversion of units.
If every 2 cm on a scale drawing is equal to 7 feet in real life, then we can use proportions to find out which lines on the drawing would be greater than 21 feet in real life.
Let x be the length of a line on the scale drawing in centimeters. Then, we can set up the following proportion:
⇒ \(\frac{2cm}{7 feet} = \frac{x cm }{yfeet}\)
where y is the length of the line in real life. Solving for y, we get:
⇒ \(y = \frac{7 feet} {2cm} *x\)
⇒ \(y = 3.5 x feet\)
If we put x = 2cm (given) then, y = 7 feet
For y = 21 feet, the value of x = 6cm.
Therefore, any line on the scale drawing that is greater than 6cm in length corresponds to a length greater than 21 feet in real life.
So, the lines on the drawing that are greater than 21 feet in real life are:
A) 7cm, C) 9cm, D) 12cm
Therefore, the correct answers are A) 7cm, C) 9cm and D) 12cm
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In August Maria’s clothing store sold 1547 shirts with the ratio of short sleeve to long sleeve shirt being 9:8. how many short sleeve shirts were sold
Answers
The number of short sleeves that Maria sold is 819.
What is ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them.
In this case, Maria’s clothing store sold 1547 shirts with the ratio of short sleeve to long sleeve shirt being 9:8.
The number of short sleeves will be:
= Ratio for short sleeve / Total ratio × Total number of clothes
= 9 / (8 + 9) × 1547
= 9/17 × 1547
= 819
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The table shows the price for different numbers of cupcakes:
Answers
Answer:
Ok what are we supposed to do?
Step-by-step explanation:
Problem
(a) Expand and simplify \((x^2+2)^2\)
(b) Hence fully factorise \(x^4+4x+3\)
Please do not give me irrelevant answers.
Answers
Answer:
a)
\((x^{2} + 2)(x^{2} + 2)\\x^{4} + 2x^{2} + 2x^{2} + 4\\= x^{4} + 4x^{2} + 4\\\)
b)
\((x +1)(x + 1)(x^{2} -2x +3) = (x + 1)^{2} (x^{2} -2x +3)\)
whats the magnatude of the vector,(2,-2)? round your answer to the nearest hundredth, if necessary
Answers
Magnitude of the given vextor :
\( \sqrt{(2 ){}^{2} + ( - 2) {}^{2} } \)\( \sqrt{4 + 4} \)\( \sqrt{8} \)\(2 \sqrt{2} \)\(2 \times 1.41\)\(2.82\)Kwame is given the graph below.
Which of the following best describes the graph?
a quadratic equation with differences of 1, then 2, then 4, ...
an exponential function with a growth factor of 2
a quadratic function with a constant difference of 2
an exponential function with growth factors of 1, then 2, then 4, ..
Answers
The best description of the graph is "a quadratic function with a constant difference of 2."
A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.
In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.
On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.
Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.
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Help! Will give brainliest to first correct answer.
Answers
Answer:
a) 7n
b) n+7
c) n -7
d). \(\frac{n}{7}\)
Step-by-step explanation:
All you have to do for this question is look at the key words. These will help you find the correct answers.
Product = multiplication (x)Sum = addition (+)Difference = subtraction (-)Quotient = DivisionPLS PLS PLS PLSSSSS HELPPP
Answers
Answer:
The regular bottle holds 9 fl oz of sun screen
Step-by-step explanation:
75% of 12 = 9
Noah invested $890 in an account paying an interest rate of 4 5/8% compounded
annually. Riley invested $890 in an account paying an interest rate of 5 1/4%
compounded continuously. To the nearest hundredth of a year, how much longer
would it take for Noah's money to triple than for Riley's money to triple?
Answers
Answer:
3.37 years
Step-by-step explanation:
\text{Rate 1: }4\tfrac{5}{8}\%=4+5/8=
Rate 1: 4
8
5
%=4+5/8=
\,\,4.625\%\rightarrow 0.04625
4.625%→0.04625
\text{Rate 2: }5\tfrac{1}{4}\%=5+1/4=
Rate 2: 5
4
1
%=5+1/4=
\,\,5.25\%\rightarrow 0.0525
5.25%→0.0525
890\text{ tripled is }2670
890 tripled is 2670
\text{Calculate Tripling Time for Noah}
Calculate Tripling Time for Noah
\overline{\phantom{\text{Calculate Tripling Time for Noah}}}
Calculate Tripling Time for Noah
\text{Compounded Annually:}
Compounded Annually:
A=P(1+r)^t
A=P(1+r)
t
A=2670\hspace{35px}P=890\hspace{35px}r=0.04625
A=2670P=890r=0.04625
Given values
2670=
2670=
\,\,890(1+0.04625)^{t}
890(1+0.04625)
t
Plug in values
2670=
2670=
\,\,890(1.04625)^{t}
890(1.04625)
t
Add
\frac{2670}{890}=
890
2670
=
\,\,\frac{890(1.04625)^{t}}{890}
890
890(1.04625)
t
Divide by 890
3=
3=
\,\,1.04625^t
1.04625
t
\log\left(3\right)=
log(3)=
\,\,\log\left(1.04625^t\right)
log(1.04625
t
)
Take the log of both sides
\log\left(3\right)=
log(3)=
\,\,t\log\left(1.04625\right)
tlog(1.04625)
Bring exponent to the front
\frac{\log\left(3\right)}{\log\left(1.04625\right)}=
log(1.04625)
log(3)
=
\,\,\frac{t\log\left(1.04625\right)}{\log\left(1.04625\right)}
log(1.04625)
tlog(1.04625)
Divide both sides by log(1.04625)
24.2989=
24.2989=
Calculate Tripling Time for Riley
Compounded Continuously:
A=Pe^{rt}
A=Pe
rt
A=2670\hspace{35px}P=890\hspace{35px}r=0.0525
A=2670P=890r=0.0525
Given values
2670=
2670=
\,\,890e^{0.0525t}
890e
0.0525t
Plug in
\frac{2670}{890}=
890
2670
=
\,\,\frac{890e^{0.0525t}}{890}
890
890e
0.0525t
Divide by 890
3=
3=
\,\,e^{0.0525t}
e
0.0525t
\ln\left(3\right)=
ln(3)=
\,\,\ln\left(e^{0.0525t}\right)
ln(e
0.0525t
)
Take the natural log of both sides
\ln\left(3\right)=
ln(3)=
\,\,0.0525t
0.0525t
ln cancels the e
\frac{\ln\left(3\right)}{0.0525}=
0.0525
ln(3)
=
\,\,\frac{0.0525t}{0.0525}
0.0525
0.0525t
Divide by 0.0525
20.9259=
20.9259=
How much longer for Noah to triple:
24.2989-20.9259
24.2989−20.9259
3.373
3.373
8 more than negative 10
Answers
8 is greater than -10, because 8 is farther to the right than -10 in a number line.
how do you find the value of f(-5) for the function
f(x)=3x^2-2x+5
Answers
Answer: 90
Step-by-step explanation:
f(x) = 3x^2-2x+5
f(-5) = 3 x (-5)^2 - 2(-5) + 5
f(-5) = 3 x (-5)^2 - 2(-5) + 5
f(-5) = (3x25) +10 + 5
f(-5) = 75 + 15
f(-5) = 90
To find the value of f(-5) for the given function , we just need to put the value of x ( which is -5) in the given function. Let's do it!
\( \purple{\frak{\implies f(x) = 3x^2-2x+5}} \\ \)
\( \sf \implies f(-5) = 3 \times (-5)^2 - 2(-5) + 5 \\ \)
\( \sf \implies f(-5) = 3 \times (-5)^2 - 2(-5) + 5 \\ \)
\( \sf \implies f(-5) = (3\times 25) +10 + 5 \\ \)
\( \sf \implies f(-5) = 75 + 10+5\\ \)
\( \purple{\frak{ \implies f(-5) = 90} }\\ \)
Henceforth, the value of the function is 90.What is 5 - 6 1/6
Please help thanks!
Answers
Answer:
-1 1/6
Step-by-step explanation:
just use your calculator
Answer:
-1 1/6
Step-by-step explanation:
used a calculator
Amanda wants to play a game in which each player gets4 cards. She has a total of 11 cards. How many people can play? How many cards will be remaining?
Answers
Based on the total cards that Amanda has and the number of cards that each player gets, the number of people who can play are 2 people and 3 cards will be remaining.
How to find the number who can play?Amanda has a total of 11 cards that will have to be shared to the players to play the game.
Out of this 11, players need to get 4 cards. The number of complete players who can play are therefore:
= 11 / 4 cards per player
= 2.75 players
= 2 players
The number of cards remaining:
= 11 - (4 x 2 players)
= 11 - 8
= 3 cards
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Solve the absolute value equation and enter the solution in set notation.
|2X-3|-7=0
Answers
Answer:
{ x : x = -2 U x = 5 }
Step-by-step explanation:
| 2x - 3 | - 7 = 0
Add 7 to both sides: | 2x - 3 | = 7
So either 2x - 3 = 7
2x = 10
x = 5
Or -(2x - 3) = 7
-2x + 3 = 7
-2x = 4
x = -2
{ x : x = -2 U x = 5 }
It is assumed that the test results for a class follow a normal distribution with a mean of 78 and a standard deviation of 36. If you know that a student's grade is greater than 72, what is the probability that it is greater than 84
Answers
Answer: 0.4337
Step-by-step explanation:
Let X represents the test results for a class that follow a normal distribution .
Given: Mean \(\mu=78\), Standard deviation \(\sigma=36\)
Then, the probability that it is greater than 84 will be
\(P(X>84)=P(\dfrac{X-\mu}{\sigma}>\dfrac{84-78}{36})\\\\=P(Z>0.167)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.167)\\\\=1-0.5663=0.4337\ [\text{By p-value table}]\)
Hence, the required probability = 0.4337
Determine the value of x in the figure below:
x = 3
x = 1.7
x = 5
x = 4
Answers
Hello!
x = the intersection
5x + 3 = 2x + 15
5x - 2x = 15 - 3
3x = 12
x = 12/3
x = 4
Answer: X=4
Step-by-step explanation: 5x + 3 and 2x + 15 are congruent. sub tract 3 from each side, 5x and 2x + 12 are equal. Subtract 2x from each side, 3x and 12 are equal. Divide each side by 3 and get X=4
if x-y = 8 and xy=5 , find x^2 + y^2
Answers
Answer:
x² + y² = 74
Step-by-step explanation:
given
(x - y) = 8 ( square both sides )
(x - y)² = 8² ← expand left side using FOIL
x² - 2xy + y² = 64 ← substitute xy = 5
x² - 2(5) + y² = 64
x² - 10 + y² = 64 ( add 10 to both sides )
x² + y² = 74
Multiply the following using the vertical multiplication method:
Answers
Answer: A) 3x⁴ - x³ + 3x² + 18x + 4
Step-by-step explanation:
Vertical Multiplication is the same with polynomials as it is for numbers.
How would you multiply 1 2 3
x 4 5
You would multiply the top row by 5, shift everything one space to the left and multiply everything by 4, and then add those values.
We do the same for polynomials.
3x² + 5x + 1
x² - 2x + 4
4(3x² + 5x + 1) --> 12x² + 20x + 4
-2x(3x² + 5x + 1) --> -6x³ - 10x² - 2x
x²(3x² + 5x + 1) --> 3x⁴ + 5x³ + 1x²
Sum: 3x⁴ - 1x³ + 3x² + 18x + 4