Answers
Answer:
D
Step-by-step explanation:
Note that I will be using a, b, and y instead of their Greek counterparts.
First, we know that sin(c+d) = sin(c)cos(d) + cos(d)sin(a) and sin(c-d) = sin(c)cos(d) - cos(d)sin(a). We can apply these here to get
sin(b+y) = sin(b)cos(y) + cos(b)sin(y)
sin(b-y) = sin(b)cos(y) - cos(b)sin(y)
sin(a+y) = sin(a)cos(y) + cos(a)sin(y)
sin(a-y) = sin(a)cos(y) - cos(a)sin(y)
Plugging these into our equation, we get
(sin(b)cos(y) + cos(b)sin(y) - (sin(b)cos(y) - cos(b)sin(y)))
/
(sin(a)cos(y) + cos(a)sin(y)-(sin(a)cos(y) - cos(a)sin(y)))
=
2cos(b)sin(y) / 2cos(a)sin(y)
= cos(b)sin(y)/cos(a)sin(y)
= cos(b)/cos(a)
Next, we can see that a+b = π, so we can subtract b from both sides to get a = π -b. Plugging that in for a in our equation, we get
cos(b) / cos(π-b)
After that, we know that cos(c-d) = cos(c)cos(d) - sin(c)sin(d). Plugging that in here, we get
cos(π-b) = cos(π)cos(b) - sin(π)sin(b)
= -cos(b) + 0
= -cos(b)
Plugging that back into our equation, we get
cos(b) / -cos(b) = -1
Related Questions
The area of a circle is 16π cm2. What is the circle's circumference?
Answers
Answer:
C = 8 pi cm
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
16 pi = pi r^2
Divide each side by pi
16 = r^2
Taking the square root
4 = r
The circumference is
C = 2 * pi *r
C = 2* pi *(4)
C = 8 pi cm
PLZ HELP MEH:(
Mean, Median, and Mode
quenage
Find the mean, median, mode and range for each set of data.
1. 6. 9, 2, 4, 3, 6,5
2. 25, 18, 14, 27, 25, 14, 18, 25, 23
3. 453, 345, 543, 345, 534
4. 13, 6, 7, 13,6
5. 8, 2,9, 4, 6, 8,5
6. 13, 7, 17, 19, 7, 15, 11, 7
7. 1, 15, 9, 12, 18, 9, 5, 14, 7
8. 28, 32, 23, 43, 32, 27, 21, 34
9. 3,9, 4, 3, 9, 4, 2, 3, 8
10. 42, 35, 27, 42, 38, 35, 29, 24
11. 157, 124, 157, 124, 157, 139
Answers
Answer:
to find the mean add all numbers the divide by the ammount of numbers given
Step-by-step explanation:
ex: 1 , 2 , 3
add:
1+2+3=6
divide:
6 / 3 = 2
your mean is 2
all good?
Answer: to find the mean add up all numbers and divide them by the amount of numbers there and to find the median that is the middle number write it on a piece of paper and cross out the beginning and end till you get the to the middle that is your median
Step-by-step explanation:
A 4-pack of greeting cards costs $7.40. What is the unit price?pls answer fast
Answers
Answer:
The unit price of the problem is that one pack of greeting cards costs $1.85
Step-by-step explanation:
In order to find the unit rate, you have to divide the price by the quantity of the product. So, we will divide 7.40 by 4 so we can see the price of one pack.
7.40 ÷ 4 = 1.85
So, one pack of greeting cards costs $1.85 which is also our unit price.
Answer:
1.85
Step-by-step explanation:
First, divided the money ( $7.40 ) by the whole number ( 4 )
Then, you will receive your answer
a box's volume set is 112 cubic inches. it has an open top. what is the length, width, and height?
Answers
hi
it a cube so it's height,length and width are the same.
if volume is 112 so one if this measure is : 112^(1÷3) =4,82
Select all of the numbers that are correctly written in scientific notation. 10.8\times10^{-3}10.8×10 −3 0.54\times10^60.54×10 6 1\times10^{-4}1×10 −4 7.6\times10^{2.5}7.6×10 2.5 9.8\times10^59.8×10 5
Answers
Answer:
1×10⁻⁴ and 9.8×10⁵Step-by-step explanation:
The standard form of writing a scientific notation is expressed as [tex]a.b*10^n[/tex] where a, b and n are integers. Note that a, b and n cannot be a fraction. When writing in scientific notation, the value of 'a' must not be equal to zero and it must not be a 'two digits values' but just 'a digit value'.
Based on the above conclusion, the following numbers are correctly written in scientific notation.
1×10⁻⁴ and 9.8×10⁵
- The expression 10.8×10 −3 is not correctly written because the value of a on comparison is a two digits number i.e 10.
- Also, 0.54×10^6 is not correctly written because a is zero on comparison
- 7.6×10 2.5 is not correctly written because the power is a decimal number i.e 2.5. We must only have an integer as the degree.
the sum of three consecutive numbers is 276. What is the smallest of these intengers?
Answers
Answer:
91
Step-by-step explanation:
Let x be the smallest one:
● x is the first number
● x+1 is the second number
● x+2 is the third number
The sum of these numbers is 276
● x+(x+1)+(x+2) =276
● x+x+1+x+2 = 276
● 3x + 3 = 276
Substract 3 from both sides:
● 3x+3-3 = 276-3
● 3x = 273
Divide both sides by 3
● (3x)/3 = 273/3
● x = 91
So the smallest one is 91
Doubling both the area of the bases and the height of a prism doubles its volume. T/F
Answers
Answer:
True.
Step-by-step explanation:
Answer: False
==========================================================
Explanation:
Let's consider a prism that has dimensions of
L = 3 ft W = 4 ft H = 5 ftand we'll say that the base is a rectangle with length L and width W. The area of the base is L*W = 3*4 = 12 sq ft. The volume of this prism is L*W*H = 3*4*5 = 60 ft^3
If we double the area of the base, then we go from 12 ft^2 to 24 ft^2. If we double the height, then we go from 5 ft to 10 ft.
The new volume of this larger prism is (area of base)*(height) = (24)*(10) = 240 ft^3
The jump from 60 ft^3 to 240 ft^3 is not "times 2". Instead, the multiplier is 240/60 = 4. This example shows that the volume has been quadrupled.
What is the LCD of 1/2 and 3/5
Answers
Answer:
10
Step-by-step explanation:
How you find LCD (lowest common denominator) is that you have to look at the denominator (the bottom number) and try to find the lowest multiple between both of the numbers that is on the bottom (in this case it is 2 and 5). Sometimes you have to multiply both denominators together to get a LCD.
Example of multiplying two denominators together to get an LCD:
1/3 and 1/13 LCD is 39 because you multiply 3 and 13.
1/5 and 1/4 LCD is 20 because you multiply 5 and 4.
Ashish is 175 cm tall his sister Annu is 8% shorter than him what is Annu's height
pls help
Answers
Answer:
8% out of 175 = ( 8 ÷ 100 ) × 175 = 14
175 cm - 14 = 161 cm
...............
A jet ski rental company charges h dollars for the first hour its jet skis are rented and k
dollars per hour for each hour rented after the first. If a jet ski is rented for t total hours,
where t is an integer greater than 2, which of the following represents the total rental cost
of the jet ski?
h+t+k
B
h+ tk
h+k(t-1)
h+k(t + 1)
h+
Answers
Answer:
C. h + k (t - 1)
Step-by-step explanation:
If we use an example, you can plug in the numbers and test out which equation works. Say the first hours costs $10 and each hour after that is an additional $5. If someone rents a jet ski for 4 hours, how much did it cost?
The first hour = $10
The 3 additional hours (totaled) = $15
Cost = $25
So now that we know the cost, we can plug in our numbers to these equations to find which one comes out with $25.
h = 10
k = 5
t = 4
A. 10 + 4 + 5 = 19
B. 10 + (4 · 5) = 10 + 20 = 30
C. 10 + 5 (4 - 1) = 10 + 5 (3) = 10 + 15 = 25
D. 10 + 5 (4 + 1) = 10 + 5 (5) = 10 + 25 = 35
E. 10 + (4/5 - 1) = 10 + (-0.2) = 9.8
C is the only problem that comes out as $25, therefore it must be the correct answer.
6) By which least number should each of the following numbers be divided to make them perfect squares?
a) 3920
Answers
3920|2
1960|2
980|2
490|2
245|5
49|7
7|7
1
[tex]3920=2^4\cdot5\cdot7^2=(2^2)^2\cdot5\cdot7^2[/tex]
It's 5
!!! i only need part c !!! There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborhood B has 45 homes. Each year, 3 new homes are built in Neighborhood B.
Part A: Write functions to represent the number of homes in Neighborhood A and Neighborhood B throughout the years. (4 points)
Part B: How many homes does Neighborhood A have after 5 years? How many does Neighborhood B have after the same number of years? (2 points)
Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically. (4 points)
(10 points)
Answers
HELLLLPPPPP PLZZZZ!!!!
Answers
Answer:
width = 5 ft
Step-by-step explanation:
1.9 times of width = length
1.9*w = 9.5 ft
1.9w = 9.5
Divide both sides by 1.9
w = 9.5/1.9
w = 5 ft
Answer:
1.9w=9.5
w=width
1.9(w)=9.5
1.9(5)=9.5
Width(w)=5
Variance 0.7775
Find the standard deviation (hint: the standard deviation is the square root of the variance)
Answers
Answer:
0.88175960442
Step-by-step explanation:
The square root of 0.7775 is 0.88175960442
The value of standard deviation will be;
⇒ 0.8803
What is mean by square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The value of Variance = 0.7775
Now,
Since, The standard deviation is the square root of the variance.
Hence, We can formulate;
The value of standard deviation = √0.7775
= 0.8803
Thus, The value of standard deviation will be;
⇒ 0.8803
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Quadrilateral ABCD is inscribed in a circle. m∠A is 64°, m∠B is (6x + 4)°, and m∠C is (9x − 1)°. What is m∠D?
Answers
Answer:
m∠D = 97.34°
Step-by-step explanation:
Concept used"
sum of all angles of Quadrilateral is 360 degrees.
If any Quadrilateral is inscribed in circles then sum of opposite angle of that Quadrilateral is 180 degrees
________________________________________________
Given
Quadrilateral ABCD is inscribed in a circle
thus,
pair of opposite angles will be
m∠A and m∠C
m∠B and m∠D
thus,
m∠B + m∠D = 180
Thus,
m∠A + m∠C = 180
64+ (9x - 1) = 180
9x = 180 - 63 + 1 = 118
x = 118/9 = 13.11
thus, value of
m∠B is (6x + 4)°
m∠B = (6*13.11 + 4)° = 82.66°
m∠B + m∠D = 180
82.66 + m∠D = 180
m∠D = 180 - 82.66 = 97.34°
Thus,
m∠D is 97.34°
HELP !!! find the surface area of each figure. Round it to the nearest tenth.
Answers
Answer:
556
Step-by-step explanation:
Surface area=2*(lb+bh+lh)=2*(110+80+88)=556
The product of (4z2 + 7z – 8) and (–z + 3) is –4z3 + z2 + z – 24.
Answers
The product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24
How to find product of expressions(4z² + 7z – 8) and (–z + 3)
= -4z³+ 12z² - 7z² + 21z + 8z - 24
collect like terms= -4z³ + 5z² + 29z - 24
Therefore, the product of (4z² + 7z – 8) and (–z + 3) is -4z³ + 5z² + 29z - 24
Learn more about product:
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Triangle ABC is translated to image A′B′C′. In this translation, A(5, 1) maps to A′(6, –2). The coordinates of B′ are (–1, 0). What are the coordinates of B? B( , )
Answers
Answer:
-2, 3
Step-by-step explanation:
To find the coordinates of B, we need to understand the translation that has taken place. In a translation, each point of a figure is moved the same distance and in the same direction.
In this case, point A(5, 1) has been translated to point A'(6, -2). To find the distance and direction of the translation, we subtract the coordinates of A from the coordinates of A': Translation Vector [tex]= (6 - 5, -2 - 1) = (1, -3)[/tex] The translation vector represents the change in x and y coordinates between the original figure and its translated image.
Since B' has coordinates (-1, 0), we can apply the translation vector to find the coordinates of B as follows: B = B' - Translation Vector B [tex]= (-1, 0) - (1, -3)[/tex] B [tex]= (-1 - 1, 0 - (-3)) B = (-2, 3)[/tex] So, the coordinates of B are (-2, 3).
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Maria sold t-shirts at a festival. She made 6$ for each t-shirt she sold. Her expenses were 30$. If she made a profit of 84, how many t-shirts did she sell?
Answers
84 - $30 = 54
54/9 = $6
I hope I explained it, Goodluck :)
Waldnice!
8. I have a maximum/minimum thermometer in my greenhouse. It records the highest and
lowest temperatures reached since the time I reset it. I reset it on Sunday when the
temperature was 4°C. Overnight the temperature fell by 5°C. Then during Monday it rose by
6°C. before falling by 10°C during the night. On Tuesday it rose by 4°C and fell by 2°C
overnight.
What were the maximum and minimum temperatures recorded when I looked at the
thermometer on Wednesday morning?
Answers
Answer:
The maximum and minimum temperatures recorded by the thermometer when checked by Wednesday morning are 5°C and -5°C
Step-by-step explanation:
The given parameters are;
A maximum and minimum thermometer is used which records maximum and minimum values as follows;
Initial temperature on Sunday at the time of resetting the thermometer = 4°C
Temperature drop overnight = 5°C, new low = 4 - 5 = -1°C,
Temperature rise on Monday = 6°C. New high = -1 + 6 = 5°C
Temperature drop on Monday night = 10°C. New low = 5 - 10 = -5°C
Temperature rise on Tuesday = 4°C = New high = 4 + - 5 = -1°C
Temperature drop on Tuesday night = 2°C. New low = -1 - 2 = -3°C
Therefore, the maximum and minimum temperatures recorded by the thermometer when checked by Wednesday morning are 5°C and -5°C.
Find the mode for the data set 18 24 24 24 25 37 37 46
Answers
Answer:
the mode would be 24
Step-by-step explanation:
it is what numbers appears most often
Find the midpoint of the line segment whose endpoints are (2.6,5.1) and (3,4.7).
1. (0.2, 0.2)
2. (1.45, 4.9)
4. (2.8, 4.9)
Answers
Answer:
Mid point is: (2.8;4.9)
Step-by-step explanation:
To find midpoint of a line segment we can use the general equation:
[tex]Mid=\frac{x_1+x_2}{2} ;\frac{y_1+y_2}{2}[/tex]
Where the point of the line are: (x₁;y₁) and (x₂;y₂).
In the problem, x₁ = 2.6, y₁ = 5.1 and x₂ = 3 and y₂ = 4.7. Replacing in the equation:
[tex]Mid=\frac{2.6+3}{2} ;\frac{5.1+4.7}{2}[/tex]
Mid point is: (2.8;4.9)Answer:
(2.8, 4.9)
Step-by-step explanation:
Please answer answer question
Answers
Answer:
The correct answer is
Step-by-step explanation:
11 square centimeters.
Hope this helps....
Have a nice day!!!!
Marcus played 3 different activities this week after school. The time he spent playing is described below. Swam forof an hour Played soccer for 9/10 2/3 2/4 of an hour Jogged forof an hour Which statement correctly compares the times of 2 of his activities?
Answers
Answer:
A
Step-by-step explanation:
We can find a common denominator for all of these fractions, compute, and then compare the values to find the right answer.
What is the sign of -xy? Will give the brainlest to who ever answers it
Answers
Answer:
positive
Step-by-step explanation:
X is positive since it is to the right of zero
Y is negative since it is to the left of zero
-xy
- ( +) ( -)
negative times positive times negative
negative times negative
positive
Re:A package of 8-count AA batteries costs $6.32. A package of 20-count AA batteries costs $16.00. Which statement about the unit prices is true?
A. The 8-count batteries have a lower rate unit price of $0.79 per battery
B. The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.
C. The 20-count pack of AA batteries has a lower unit price of $0.80 per battery.
D. The 8-count pack of AA batteries has a lower unit price of $0.80 per battery.
Answers
Answer:
b
Step-by-step explanation:
Answer:
B. The 20-count pack of AA batteries has a lower unit price of $0.79 per battery.
Step-by-step explanation:
I just have an educated guess out of the info that you gave me.
Solve for x : 2^(x-5) . 5^(x-4) = 5
Answers
Answer:
x = 5
Step-by-step explanation:
Notice that there is also a base 5 on the right hand side of the equation, therefore, let's move [tex]5^{x-4}[/tex] to the right by dividing both sides by it. and then re-writing the right hand side as 5 to a power:
[tex]2^{x-5}\,*\,5^{x-4}=5\\2^{x-5}=5/5^{x-4}\\2^{x-5}=5\,*\,5^{4-x}\\2^{x-5}=5^{5-x}[/tex]
Now apply log to both sides in order to lower the exponents (where the unknown resides):
[tex](x-5)\,log(2)=(5-x)\,log(5)[/tex]
Notice that when x = 5, this equation is true because it makes it the identity: 0 = 0
So, let's now examine what would be the solution of x is different from 5, and we can divide by (x - 5) both sides of the equation:
[tex]log(2)=\frac{5-x}{x-5} \,log(5)\\log(2)=-1\,\,log(5)\\log(2)=-log(5)[/tex]
which is an absurd because log(2) is [tex]\neq[/tex] from log(5)
Therefore our only solution is x=5
Answer:
if decimal no solution
if multiply x =5
Step-by-step explanation:
If this is a decimal point
2^(x-5) . 5^(x-4) = 5
Rewriting .5 as 2 ^-1
2^(x-5) 2 ^ -1 ^(x-4) = 5
We know that a^ b^c = a^( b*c)
2^(x-5) 2 ^(-1*(x-4)) = 5
2^(x-5) 2 ^(-x+4) = 5
We know a^ b * a^ c = a^ ( b+c)
2^(x-5 +-x+4) = 5
2^(-1) = 5
This is not true so there is no solution
If it is multiply
2^(x-5) * 5 ^(x-4) = 5
Divide each side by 5
2^(x-5) * 5 ^(x-4) * 5^-1 = 5/5
We know that a^ b * a^c = a^ ( b+c)
2^(x-5) * 5 ^(x-4 -1) = 1
2^(x-5) * 5 ^(x-5) = 1
The exponents are the same, so we can multiply the bases
a^b * c*b = (ac) ^b
(2*5) ^ (x-5) = 1
10^ (x-5) = 1
We know that 1 = 10^0
10^ (x-5) = 10 ^0
The bases are the same so the exponents are the same
x-5 = 0
x=5
Find the sum of the geometric sequence. 1, 1/2,1/4,1/8,1/16
Answers
Answer:
31/16
or
1 15/16
Step-by-step explanation:
1/8 = 2/16
1/4 = 4/16
1/2 = 8/16
1 = 16/16
then:
1 + 1/2 + 1/4 + 1/8 + 1/16
= 16/16 + 8/16 + 4/16 + 2/16 + 1/16
=(16+8+4+2+1)/16
= 31/16
31/16 = 16/16 + 15/16 = 1 + 15/16 = 1 15/16
Find the Area of the figure below, composed of a rectangle and one semicircle, with another semicircle removed. Round to the nearest tenths place.
I need help, please
Answers
Answer:
so you multiply the 13 by 12. Then divid 12 by 2 to get 6 as the radius then use a calculator and type in 2(PIE SYMBOL) R. R=radius then whatever number you get cut it in half then subtract it from 13x12.
How many feet did Courtney walk at the park if she loves walked 2.4 miles
Answers
Answer:
12672 feet
Step-by-step explanation:
1 mile=5280 feet
2.4 miles=5280*2.4=12672 feet
Answer:
Awnser: 12,672 feet
Step-by-step explanation:
1 mile is 5280 feet
2 miles is 10560 feet
.4 miles is 2112 feet
10560+2112 = 12,672 feet