Drag the tiles to the boxes to form correct pairs
Match the identities to their values, taking these conditions into consideration: sin X = pi2/2 cos y = -1/2 angle x is in the first quadrant, and angle
y is in the second quadrant.
What is the value of sin(x + y)?
- (2 + √3)
√3-2
-(√6 + √2)/4
What is the value of tan(x - y)?
What is the value of cos(x + y)?
(√6-√2)/4
What is the value of tan(x + y)?
Answers
The correct matches are sin (x+y) = (√6-√2) / 4, tan(x-y) = √3-2, cos(x+y) = -(√6+√2) / 4 and tan(x+y) = -(2+√3)
Given that, sin x = √2/2, and cos y = -1/2,
Finding sin y and cos x,
Therefore,
sin y = √3/2
cos x = √2/2
Therefore, tan x = √2/2 / √2/2
tan x = 1
Also,
tan y = -√3/2 / 1/2
tan y = -√3
Now,
1) sin (x+y) = sinx·cosy + cosx·siny
= √2/2×(-1/2) + √2/2×√3/2
= (√6-√2) / 4
∴ sin (x+y) = (√6-√2) / 4
2) tan(x-y) = tan x - tan y / 1 + tanx tany
= 1 + √3 / 1 - √3 = √3-2
∴ tan(x-y) = √3-2
3) cos(x+y) = cos (x) cos (y) − sin (x) sin (y)
= √2/2 × (-1/2) - √2/2 × √3/2 = -√2/4 - √6/4
= -(√6+√2) / 4
∴ cos(x+y) = -(√6+√2) / 4
4) tan(x+y) = tan x + tan y / 1 - tanx tany
= 1-√3 / 1 +√3 = -2 - √3 = -(2+√3)
∴ tan(x+y) = -(2+√3)
Hence, the correct matches are sin (x+y) = (√6-√2) / 4, tan(x-y) = √3-2, cos(x+y) = -(√6+√2) / 4 and tan(x+y) = -(2+√3)
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Related Questions
A cell phone which regularly sell for Ghana cedi 450.00 is on sale for 40% off how are much would you pay for the phone
Answers
You would pay Ghana cedi 270.00 for the phone during the sale.
To calculate this:
40% of Ghana cedi 450.00 is 0.40 x 450 = Ghana cedi 180.00
Subtracting this discount from the original price gives:
Ghana cedi 450.00 - Ghana cedi 180.00 = Ghana cedi 270.00
Let f = <12, 2> and v= <2, 4>. Find 4f - 6v.
Answers
4f - 6v is equal to the vector <36, -16>.
To find 4f - 6v, we need to perform scalar multiplication on both vectors and then subtract the result.
Scalar multiplication of a vector by a scalar k is simply multiplying each component of the vector by k. For example, if we have the vector <a, b>, then k times that vector would be <ka, kb>.
Using this definition, we can find:
4f = 4<12, 2> = <48, 8>
6v = 6<2, 4> = <12, 24>
So, 4f - 6v = <48, 8> - <12, 24> = <36, -16>
Therefore, 4f - 6v is equal to the vector <36, -16>.
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A basket contains four red apples and an unspecified number of green apples. Four apples are randomly selected. What is the smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent?
Answers
The smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent is 4000.
What is Probability?Probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 meaning that the event is impossible and 1 meaning that the event is certain. Probability theory is widely used in the analysis of statistical data, such as in the study of the behavior of populations or financial markets.
To calculate the smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent, we must first calculate the probability of not finding any green apples. This can be done by finding the probability of selecting four red apples from the basket. With four red apples and an unspecified number of green apples, the probability of selecting four red apples is 4/N, where N is the total number of apples in the basket.
To find the smallest number of green apples, we must set the probability of selecting four red apples equal to 0.001 and solve for N. This gives us:
N = 4/0.001
Therefore, the smallest number of green apples that makes the probability of finding at least one green apple among the four at least 99.9 percent is 4000.
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Help me
Find Area of ABCD ?
Answers
Answer:
63.67
Step-by-step explanation:
nice one, this got me thinking some time
The graph shows g(x), which is a transformation of f(x) =|x|. Write the function rule for g(x). Write you're answer in the form a|x-h|+k, where a, h, and k are integers or simplified fractiins.
g(x) =_______
WILL GIVE BRAINLIEST.
Answers
Answer: g(x)= -|x|
.
Step-by-step explanation:
a|x-h|+k
> this form shows the shifts, stretches and reflections
> If there is a h or k, the vertex has shifted to (h, k)
> "a" is your stretch
> if there is a - in front, the function has been refected
The image you gave is facing upside down so it's been reflected. There has been no other changes the (h, k) is (0,0) and there has been no stretch
g(x)= -|x| just put a negative in front to show reflection.
An element with a mass of 600 grams decays by 29.5% per minute. To the nearest minute, how long will it be until there are 2 grams of the element remaining?
Answers
It takes 16 minutes until there are 2 grams of the element remaining.
Given that, an element with a mass of 600 grams decays by 29.5% per minute.
Remaining element is 2 grams.
According to the question,
600(1-29.5%)ˣ=2
600×0.705ˣ=2
0.705ˣ=2/600
0.705ˣ=0.00333
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
x=log(0.00333)/log(0.705)
x=16.35
x≈16
Therefore, it takes 16 minutes until there are 2 grams of the element remaining.
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Find sin([tex]\frac{5\pi }{12}[/tex]) using sum and difference identity.
Show all work
Answers
The solution of the sine function sin(5π/12) is (√6 + √2)/4.
As per the sum and difference identity for sine, which states:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
To find sin(5π/12), we can express it as the sum or difference of two angles whose sine values we know.
One possible way is to use the fact that:
5π/12 = π/4 + π/6
So we have:
sin(5π/12) = sin(π/4 + π/6)
Using the sum identity, we get:
sin(π/4 + π/6) = sin(π/4)cos(π/6) + cos(π/4)sin(π/6)
We know that sin(π/4) = cos(π/4) = √2/2 and sin(π/6) = 1/2, so we can substitute:
sin(π/4 + π/6) = (√2/2)(√3/2) + (√2/2)(1/2)
simplify the expression:
sin(π/4 + π/6) = (√6 + √2)/4.
Therefore, sin(5π/12) = sin(π/4 + π/6) = (√6 + √2)/4.
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let x=13^1/4. rewrite the equation in the box, replacing 13^1/4 with x
Answers
Rewriting the equation for x gives[tex]x = \sqrt[4]{13}[/tex]
Rewriting the equation for xFrom the question, we have the following parameters that can be used in our computation:
x = 13^1/4
To rewrte the equation for x, we introduce radicals
By pronounciation, x = 13^1/4 means that the value of x is 13 raised to the power of 1/4 i.e. the fourth root of 13
When rewritten, we have
[tex]x = \sqrt[4]{13}[/tex]
Hence, the solution is [tex]x = \sqrt[4]{13}[/tex]
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each value to the correct expression.
22
0
5
8
27
1+5.2 + (1 + 3)² ←
4 + 8(+2)
0.25 4³1
15
Reset
Next
Answers
The value matched to the correct expression is
1 + 5 = 6
2 + (1 + 3)² = 18
4 + 8(2) = 20
4³ = 64
Matching each value to the correct expression.From the question, we have the following expression that can be used in our computation:
1 + 5
2 + (1 + 3)²
4 + 8(2)
4³
Evaluating the expressions, we have
1 + 5 = 6
2 + (1 + 3)² = 18
4 + 8(2) = 20
4³ = 64
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Twice the difference of a number and is 2equal to8 . Use the variable y for the unknown number.
Answers
The answer of the given question based on the equation is , the unknown number is 6.
What is Equation?An equation is the mathematical statement that asserts equality of the two expressions. It typically consists of the two expressions separated by equal sign " = ". The expressions can include variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation. Solving an equation involves finding the value(s) of the variable(s) that make the equation true.
The statement can be translated into an equation as follows:
2(y - 2) = 8
Simplifying the equation, we can distribute the 2 on the left-hand side:
2y - 4 = 8
Then, we can add 4 to both sides to isolate the variable:
2y = 12
Finally, we divide both sides by 2 to solve for y:
y = 6
Therefore, the unknown number is 6.
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Use the table below to calculate the expected value of a mega ball ticket. Remember, the expected value is the expected winnings/loses over many trials. Which means, your solution will be the expected outcome per ticket if you were to buy every possible combination of numbers (all 302,575,350 of them). After calculating the expected value of a ticket, use the information you have calculated to calculate how much the grand prize needs to be in order to break even (have an expected value of $0). When calculating this, don’t forget to deduct the cost of the ticket ($2.00) from any winnings.
Match 5 + Megaball (1/302575350) Prize 40000000
Match 5 (24/302575350) Prize 1000000
Match 4 + Megaball (325/302575350 Prize 10000
Match 4 (7800/302575350) Prize 500
Match 3 + Megaball (20800/302575350) Prize 200
Match 3 (499300/302575350) Prize 10
Match 2 + Megaball (436617/302575350) Prize 10
Match 1 + Megaball (3399723/302575350) Prize 4
Match 0 + Megaball (817712/302575350) Prize 2
Not a Winner (297842418/302575350) Prize 0
Answers
In order for the expected value of a mega ball ticket to be zero, the grand prize needs to be at least $4,105,724.49.
What is value?The term "value" can have different meanings depending on the context in which it is used. Generally, value refers to the worth or usefulness of something, often measured in terms of money, time, or other resources.
According to given information:To calculate the expected value of a mega ball ticket, we need to multiply the probability of winning each prize by the value of that prize, and then sum up the products:
Expected value = (1/302575350) x $40,000,000 + (24/302575350) x $1,000,000 + (325/302575350) x $10,000 + (7800/302575350) x $500 + (20800/302575350) x $200 + (499300/302575350) x $10 + (436617/302575350) x $10 + (3399723/302575350) x $4 + (817712/302575350) x $2 + (297842418/302575350) x $0
Expected value = $0.65444
This means that if you were to buy every possible combination of numbers (all 302,575,350 of them), the expected value of a ticket would be $0.65444.
To calculate the amount the grand prize needs to be in order to break even, we need to set the expected value equal to zero and solve for the prize:
0 = (1/302575350) x (Prize - $2.00) + (24/302575350) x ($1,000,000 - $2.00) + (325/302575350) x ($10 - $2.00) + (7800/302575350) x ($500 - $2.00) + (20800/302575350) x ($200 - $2.00) + (499300/302575350) x ($10 - $2.00) + (436617/302575350) x ($10 - $2.00) + (3399723/302575350) x ($4 - $2.00) + (817712/302575350) x ($2 - $2.00) + (297842418/302575350) x ($0 - $2.00)
Simplifying this equation, we get:
0 = (1/302575350) x Prize - $0.01359
Solving for the prize, we get:
Prize = $0.01359 x 302575350
Prize = $4,105,724.49
Therefore, in order for the expected value of a mega ball ticket to be zero, the grand prize needs to be at least $4,105,724.49.
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5.1: Math Talk: Distribution
Distribute each expression mentally.
5(x + 3)
x(x − 3)
(x + 4) (x + 2)
(x - 5)(x - 5)
2500 2015)
monly updates belles
istisq sal 919dT szil v
Answers
The equation is solved and the distribution property is given by
a) A = 5x + 15
b) B = x² - 3x
c) C = x² + 6x + 8
d) D = x² - 10x + 25
Given data ,
Let the equation be represented as A
Now , the value of A is
a)
A = 5 ( x + 3 )
On simplifying the equation , we get
A = 5 ( x ) + 5 ( 3 )
A = 5x + 15
b)
B = x ( x - 3 )
On simplifying the equation , we get
B = x ( x ) - x ( 3 )
B = x² - 3x
c)
C = ( x + 4 ) ( x + 2 )
On simplifying the equation , we get
C = ( x + 4 ) ( x ) + ( x + 4 ) ( 2 )
C = x² + 4x + 2x + 8
C = x² + 6x + 8
d)
D = ( x - 5 ) ( x - 5 )
On simplifying the equation , we get
D = ( x - 5 ) ( x ) + ( x - 5 ) ( -5 )
D = x² - 5x - 5x + 25
D = x² - 10x + 25
Hence , the equations are solved
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find the missing area.
Answers
EVENTS A AND B ARE MUTUALLY EXCLUSIVE. FIND THE MISSING PROBILITY.
EVENTS A AND B ARE MUTUALY EXCLUSIVE. FINDTHE MISSING PROBALITY P(B)=1/5,P(A OR B)=3/4, P(A)=?
Answers
A and B are mutually exclusive events, so PA) is 11/20.
Given that, P(B)=1/5 and P(A or B)=3/4.
For mutually exclusive events A and B
That is, P(A or B) = P(A) + P(B)
Here, 3/4 = P(A)+1/5
P(A)=3/4 - 1/5
P(A)=(15-4)/20
= 11/20
Therefore, P(A)=11/20
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pls answer this!!!
worth 30 points
find the circumference of a circle with d=97cm diameter
round to 3 significant figures
Answers
The circular is around 305 cm in circumeference.
The circumference of a circle is given by the formula:
C = πd
where d is the diameter of the circle.
Substituting d = 97 cm and using the value of π to be 3.14159, we get:
C = πd
C = 3.14159 × 97 cm
C ≈ 304.731 cm
Rounding this to 3 significant figures, we get:
C ≈ 305 cm
Therefore, the circumference of the circle is approximately 305 cm.
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I need help with this question
Answers
After 6 years, the investment is whort $4,051.97
How much will be invest be whort after 6 years?We know that this can modeled by an exponential equation of the form:
y = A*(1 + r)^x
Where A is the initial amount and r is the rate at which the investement grows (in decimal form)
Then we can write the equation as:
y = 2700*(1 + 0.07)^x
Where x is the number of years.
Then after 6 years, the investment is whort:
y = 2700*(1 + 0.07)^6 = 4,051.97
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HELP, 50 POINTS PLEASEEEEE
Which of the following equations represents a line that passes through the points (-5,4) and (10,14)
|. y = 6/5x -2
||. 6x+5y=-10
I'll give you brain crown thingy if you get it right PLEASE
Answers
The equation of the line is determined as; y = (2/3)x + 22/3.
What is the equation of line that passes through the point?
The general equation of line is written as;
y = mx + b
Where;
m is the slope of the line b is the y intercept.The slope is calculated as;
m = (y₂ - y₁) / (x₂ - x₁)
m = (14 - 4 ) / (10 + 5)
m = 10/15
m = 2/3
The y intercept is calculated as;
y = mx + b
4 = 2/3(-5) + b
4 = -10/3 + b
b = 4 + 10/3
b = 22/3
The equation of the line is determined as;
y = (2/3)x + 22/3
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i need help wit dis question may someone pls help plsss
Answers
For 15 feet below the sea level, the value of temperature reads is,
⇒ 10.8 degree cooler
Given that;'
Rob finds that every 2.5 feet below sea level, the value of temperature reads 1.8 degree cooler.
Hence, For 15 feet below the sea level, the value of temperature reads is, x
Thus, We can formulate;
⇒ 2.5 / 1.8 = 15 / x
⇒ 25/18 = 15/x
⇒ x = 15 × 18 / 25
⇒ x = 10.8 degree cooler
Thus, For 15 feet below the sea level, the value of temperature reads is,
⇒ 10.8 degree cooler
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I need help with this problem if do thank you a lot
Answers
Value of x is 2 in the circle .
What in Geometry Is the Definition of a Circle?
A circle is a curved, two-dimensional form that may be created by connecting points in a plane that are spaced the same fixed distance apart from a fixed point in the same plane. The circle's centre is that specific fixed location.
The diameter and radius of a circle are measured from the centre to its circumference and from one point on the circumference to another point that passes through the centre, respectively. In the actual world, a pizza foundation is among the most prevalent instances of a circular.
In circle,
3 * (x + 2) = x * 6
3x + 6 = 6x
6 = 3x
x = 2
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A new car valued at 28000 and depreciate at 9% per year from original price. Find the value of the car 1 year after the purchae
Answers
Answer:
25480
Step-by-step explanation:
Hopefully it's right.
Sector Area & Arc Length What is the area of the shaded sector?
Answers
Answer:
Step-by-step explanation: 70.7
Given:
r=46
angle from arc =88
Formula and Explanation of formula:
You want to find the proportion/precent of the circle you want to find and multiply it by the full length of the circle, which is the circumference.
[tex]L=\frac{Part of circle}{full circle} Circumference\\\\\\L=\frac{Part of circle}{full circle} 2\pi r[/tex]
Plug Given into Formula:
[tex]L=(\frac{88}{360})(2)\pi (46)[/tex] Plug into calculator
L = 70.7
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=46\\ \theta =88 \end{cases}\implies s=\cfrac{(88)\pi (46)}{180}\implies s=\cfrac{1012\pi }{45}\implies s\approx 70.65[/tex]
The volume of a rectangular prism is 60 cubic units. The height of the prism is 5 units. Draw a rectangular prism with these units.
Answers
The rectangular prism with length of the base is 4 units, the width of the base is 3 units, and the height is 5 units is shown below.
Since the volume of the rectangular prism is 60 cubic units and the height is 5 units, we can find the length and width of the base by dividing the volume by the product of the height and base. That is,
Volume = Length * Width * Height
60 = Length * Width * 5
Length * Width = 12
We can choose any two numbers whose product is 12 as the length and width of the base. Let's choose 3 and 4 for simplicity. Then, the rectangular prism would look like as shown in picture where the length of the base is 4 units, the width of the base is 3 units, and the height is 5 units.
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Pls help question is in the image
Answers
Answer:
In this situation, [tex]t[/tex] (time) is the independent variable, and [tex]p[/tex] is the dependent variable, since calculating it relies on [tex]t[/tex]. In a real-world context, [tex]p[/tex] represents the number of hard drives sold in [tex]t[/tex] number of years.
Represent the following sentence as an algebraic expression, wher
number" is the letter x. You do not need to simplify.
The product of 8 and the sum of a number and 5.
F
Answers
Answer: 8 (5+x)
Step-by-step explanation:
The height (in feet) of a rocket from ground level is given by the function f(t) = -16t² + 220t. What is the instantaneous velocity of the rocket 12 seconds after its launch?
Answers
-32t + 220
= -32(12) + 220
-384 + 220 =
-164
first step is to take the derivative. next is to plug in 12 into the function
La suma de tres mineros es 300 el mayor excede al del medio en 50 y al menor en 85 determina los números
Answers
The largest number is 145, the middle number is 95 and the smallest number is 60.
Given that, the sum of three miners is 300, the largest exceeds the middle one by 50 and the smallest by 85.
Let the three numbers be x, y and z.
Here, the largest number is x, middle number is y and smallest number be z.
y=x-50, z=x-85
Here, x+y+z=300
x+x-50+x-85=300
3x-135=300
3x=435
x=145
y=95 and z=60
Therefore, the three number are 145, 95 and 60.
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Francisco had a rectangular piece of wrapping paper that was inches on two sides and 17 inches on the longer sides. Monica has a similar piece of paper with two longer sides that each measure 34 inches. What is the measurement of the two shorter sides in Monica's wrapping paper? A.26 2/3 inches B.27 1/3 inches C.28 1/3 inches D.54 2/3 inches
Answers
The shorter sides of Monica's wrapping paper measure 8 inches. Therefore, the correct option is A. 26 2/3 inches.
What is rectangle?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
We can set up a proportion to solve for the shorter sides of Monica's wrapping paper. Let x be the length of the shorter sides of Monica's paper. Then we have:
x/34 = 2/17
To solve for x, we can cross-multiply:
x = 34 * (2/17) = 4 * 2 = 8
Therefore, the shorter sides of Monica's wrapping paper measure 8 inches.
Alternatively, we can simplify the proportion first by dividing both sides by 2:
x/17 = 1/2
Then, we can solve for x by cross-multiplying:
x = 17 * (1/2) = 8
Either way, the answer is the same. Therefore, the correct option is A. 26 2/3 inches.
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In Park City public schools there are 2 teachers for every 43 students. If there are 645 students
Answers
2 x 645 = 1290/2 = 30
Therefore, the answer is C
find the exact value of sin Q in simplest radical form
Answers
The value of the sin A in simplest radical form is 0.651 units
From the Figure,
We have the following information :
The triangle in the image is Right angle triangle.
The value of side AB is [tex]\sqrt{85}[/tex].
The value of side BC is 6.
The value of side CA is 7.
And we know that :
In the Right angle triangle, One angle is 90 degree.
So, The value of angle ABC is 90 degree.
For solving, we use the sin law:
Sine law-The law of sine can be used to calculate the remaining sides or angle of the triangle when 2 or more sides or angle are known.
[tex]\frac{AB}{SinC} =\frac{BC}{Si nA }[/tex]
Plug all the values in above formula:
[tex]\frac{\sqrt{85} }{Sin 90} =\frac{6}{Sin A}[/tex]
Now, Solving value of Sin A
Sin A = (6 × sin 90)/[tex]\sqrt{85}[/tex]
Sin A = 6 /[tex]\sqrt{85}[/tex]
Sin A = 0.651
Hence, the value of the sin A in simplest radical form is 0.651 units.
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The equation and the table show the cost, y, for different sports programs as function of the number of classes x.
Here’s the answers
You don’t have to answer this is just for anyone who needs it.
Answers
When the number of classes is 1, football is less expensive.
When the number of classes is 2, 3, or 4, basketball is less expensive.
How to evaluate the sport programs function?In order to determine the sport which is less expensive, we would have to calculate the total cost for a basketball program by substituting the number of classes (x) into the function which models it as follows;
y = 9x + 10
When the number of classes x = 1, the total cost is given by;
y = 9(1) + 10
y = $19.
Therefore, a total cost of $19 is greater than $15 for a football program.
When the number of classes x = 2, the total cost is given by;
y = 9(2) + 10
y = $28.
When the number of classes x = 3, the total cost is given by;
y = 9(3) + 10
y = $37.
When the number of classes x = 4, the total cost is given by;
y = 9(4) + 10
y = $46.
Therefore, a total cost of $46 is less than $60 for a football program.
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