[tex]\textit{Sum and Difference Identities} \\\\ sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta) \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(A-B+C)\implies sin[~(\stackrel{Z}{A-B})~+C]\implies sin(Z+C) \\\\\\ sin(Z)cos(C)+cos(Z)sin(C)\implies sin(A-B)cos(C)+cos(A-B)sin(C) \\\\[-0.35em] ~\dotfill\\\\ \textit{and since we know that}\\\\ sin(A-B)\implies sin(A)cos(B)-cos(A)sin(B)[/tex]
[tex]cos(A-B)\implies cos(A)cos(B)+sin(A)sin(B)\\\\ then \\\\[-0.35em] ~\dotfill\\\\\ [sin(A)cos(B)-cos(A)sin(B)]cos(C)+[cos(A)cos(B)+sin(A)sin(B)]sin(C) \\\\\\ ~\hfill \begin{array}{cllll} sin(A)cos(B)cos(C)-cos(A)sin(B)cos(C)\\\\ +\\\\ cos(A)cos(B)sin(C)+sin(A)sin(B)sin(C) \end{array}~\hfill[/tex]
help pls!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
y = -3x - 1
hope this helps!
which of the following would be considered a statistical question
1. who was the highest paid athlete in 2020?
2. how much does a gallon of gasoline cost?
3. how many people voted for president in 2016?
4. what are the different types of maple trees?
Help plez . What is the mean absolute deviation of the data set?
8, 5, 12, 4, 5, 8, 7
1
2
5
7
Answer:
2
Step-by-step explanation:
first, add terms
8 + 5 + 12 + 4 + 5 + 8 + 7 = 49
seven terms, therefore we divide by 7
49/7 = 7
find distance
8-7= 1
7-5= 2
12-7=5
7-4=3
7-5=2
8-7=1
7-7=0
added together you get 14,
14/7 = 2
your answer is 2
hope this helps:)
“Solve the following system of equations using the method of substitution.” Please help!!!
Answer: -17/4
Step-by-step explanation:
Can someone help me please!!!
Answer:
5. is 18 your welcome
Step-by-step explanation:
i need this answer as fast and soon as possible
Each of the digits 2, 3, 4, 5 and 7 must be placed in the circles so that the sum of each straight line is 15.
(Fill in the empty circle spaces)
Answer:
1st horizontal lines is 2,5,8=15
2nd horizontal line 4,5,6
vertical line 5,5,5
Answer:
See below ~
Step-by-step explanation:
there are light-bulbs at the factory
nice. are they filament lightbulbs or fluorecent lightbulbs
Please help me with this really please
Answer:
You need 443.2 square inches of wrapping paper to completely cover the prism.
Step-by-step explanation:
Calculate the area of each side.
Triangles:
Base * Height * 1/2
10 in. * 8.7 in. * 1/2
87 in.^2 * 1/2
43.5 in.^2
There are two sides with the triangle so we multiply the 43.5 in.^2 by two
(43.5 in.^2) * 2
87 in.^2
Side Rectangles:
Length * Width
13 in. * 8.7 in.
113.1 in.^2
There are two sides with this size rectangle so we multiply the 113.1 in.^2 by two
(113.1 in.^2) * 2
226.2 in.^2
Bottom Rectangle
Length * Width
13 in. * 10 in.
130 in.^2
There is only one side with the bottom rectangle.
Add up all the calculate areas.
Triangles + Side Rectangles + Bottom Rectangle
87 in.^2 + 226.2 in.^2 + 130 in.^2
443.2 in.^2
A pool is leaking at a rate of a quarter of a gallon per minute. What is this rate in gallons per hour?
Answer:
15 gallons per hour
Step-by-step explanation:
So, what is given in the equation is that 1/4 of a gallon is leaking per minute. We have to change this to gallons per hour. Set it up like this:
[tex]\frac{\frac{1}{4}gallon }{1 minute} *\frac{60 min}{1 hour}[/tex]
Use a calculator and multiply 1/4 by 60.
After doing this, you should get:
[tex]\frac{15 gallons}{1 hour}[/tex]
Thus, the answer is the pool will leak 15 gallons per hour.
Hope this helps!! Ask questions in comments if needed!
A student would like to estimate the mean length of words in a book report he just finished writing. He selects a random sample of 20 words and determines the mean length to be 4 characters. Later, he discovers how to use a built-in function of his word-processing program that reveals that the mean length of all words in his book report is 4.3 characters. Which of the following describes the number, 4.3?
sample
statistic
population
parameter
Answer:
Parameter
Step-by-step explanation:
A statistic is a piece of data we derive from analyzing the data from a sample, a subset of a larger population. A parameter is derived from analyzing that population. Here, we would call the mean of the sample - 4 - a statistic, and the mean of the population - 4.3 - a parameter.
The turtle’s distance from his starting point is increasing between
seconds.
The turtle’s distance from his starting point is constant between
seconds.
The turtle’s distance from his starting point is decreasing between
seconds.
Answer:
Option A is the correct option
Answer:1) 0-6, 2)6-8, 3)8-12
Step-by-step explanation:
Translate shapes
Draw the image of AABC under a translation by 2 units down.
y
6
5+
3
2
A
A
-7 -6 4 -3 -2
2
1 2 3 4 5 6 7
-24
-3
Answer:
Just think about it.............. 77 + 33 = 100
Step-by-step explanation:
You add
The diameter of a circle is 8 in. Find the circumference \textit{to the nearest tenth}to the nearest tenth.
Answer: C ≈ 25.1
Step-by-step explanation:
The circumference of a circle can be found with the following formula. We will plug in the diameter given, and solve.
C = dπ
C = (8)π
C ≈ 25.1
The question is attached.
Answer:
B
Step-by-step explanation:
1/8 + 1/8 + 1/8 + 2/8 + 5/8 = 10/8 (The total amount of oj in each jug.)
(10/8)/5 = 2/8 (5 for the amount of jugs.)
2/8 = 1/4
Solve for x and find the degree of the other two angles.
m<2 = 9x + 6
Answer:
x = 7 and the degree of other two angles is 69.
Step-by-step explanation:
As we can see it is an isosceles triangle so base angles of an isosceles triangle are equal so
9x + 6 + 9x + 6 + 42 = 180 (being sum of angles of triangle )
18x + 54 = 180
18x = 180 - 54
18x = 126
x = 126/18
x = 7
the degree of the other two angle is
= 9*7 + 6
= 69
Hope it helps :)
The ages of Charlotte and Olivia are in the ratio 6:10. After 10 years, their ratio will become 4:6. Find their ages.
Answer:
Charlotte's age = 30 years
Olivia's age = 50 years
Step-by-step explanation:
Present ages of Charlotte & Olivia = 6:10.
Then, their present ages are:
Charlotte = 6x
Olivia = 10x
Now, in 10 years, their ratio = 4:6
Then,
Ratio of Charlotte's & Olivia's present age + 10 years each = Ratio of their ages in 10 years
[tex]\frac{6x + 10}{10x + 10} = \frac{4}{6} \\6(6x + 10) = 4 (10x + 10) \: \: \: \: [\mathrm{cross\: multiplication}]\\36x + 60 = 40x + 40\\36x - 40x = 40 - 60\\4x = 20\\\boxed{\bf\:x = 5}[/tex]
So,
Charlotte's present age [tex]= 6x = 6(5) = {\boxed{\bf\:30 \:years}[/tex]
Olivia's present age = [tex]10x = 10(5) = \boxed{\bf\:50 \: years}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
1,000 km = 1 mm
True or False
Answer: Heavily false. False by a long shot.
Step-by-step explanation: 1,000 kilometers is equivalent to 1e+9 millimeters. This is nine zeros after 1. So, this can be simplified as 1,000,000,000 milimeters, or rather, 1 billion millimeters. You can calculate this yourself by multiplying 1000 by 1,000,000 (1km = 1,000,000 mm.)
A rectangular prism with a length of 3.8 meters and a width of 1.5 meters has a volume of 16.53 cubic meters.
What is the height of the prism?
2.9 m
6.525 m
11.23 m
21.83 m
How can these models be used to find the sum 1.8 + 1.56?
Enter your answers in the boxes.
The models show a total of 2 wholes,
tenths, and
hundredths. After regrouping 10 tenths into 1 whole, there are
wholes,
tenths, and
hundredths. Therefore, the sum of the numbers is
.
First row. One large square divided into a 10 by 10 grid of 100 small squares. Eight columns, each divided into 10 small squares. Second row. One large square divided into a 10 by 10 grid of 100 small squares. Five columns, each divided into 10 small squares. Six small squares.
Answer:
The sum of 1.8 and 1.56 is 3.36 according to the model
Sum of decimals
Given the expression 1.8 + 1.56
Using the partial sum method
1.8 + 1.56 = (1.0 + 0.8) + (1.0+0.56)
Regroup as whole and decimal number
1.8 + 1.56 = (1.0 + 1.0) + (0.8 +0.56)
1.8 + 1.56 = 2.0 + 1.36
1.8 + 1.56 = 3.36
Hence the sum of 1.8 and 1.56 is 3.36 according to the model
Plot the points: A(4, 5), B(3, 3), C(6.9), D(8, 13), and E(10, 15).
All but one of the points are on the same line. Which one is not?
Answer:
E (10, 15)
Step-by-step explanation:
Plotting the points on a graph : (Check attachment)
On plotting the points, and joining a line that connects all points except one, it becomes evident that the point not on the line is :
E (10, 15)Answer:
E
Step-by-step explanation:
work out value of a
Answer:
a=99
Step-by-step explanation:
First, let's subtract 136 from 180. We get 44, which means that the angle of the other side is 44 degrees.
180-136=44
Next, let's subtract 125 from 180. 180-125 = 55. This means the other angle next to 125 degrees is 55 degrees.
180-125=55
We know that the sum of a triangle's angles is = 180 degrees
We can find the last angle of the triangle by adding 44 & 55, and then subtracting that sum from 180 (the total sum).
44+55=99
180-99=81
For our last and final step, let's subtract 81 from 180 to find the angle NEXT to 81 (a).
180-81=99
a = 99 degrees
Hope this helped :) If you have any questions, don't be afraid to comment!
Answer:
The value of a is 99°check photo for detailed analysisFind the distance between the points L(-7, -6) and M(-2, 6).
Graph the image of rectangle CDEF after a translation 2 units right and 10 units down.
Answer:
Graph these points:
(-6, -6)
(0, -6)
(0, -1)
(-6, -1)
A 12 _ foot ladder is leaning against a house the ladder reaches 7.7 feet up the wall wha is the angle of elevation of the ladder?
Check the picture below.
Make sure your calculator is in Degree mode.
Lisa's test grades are 79, 89 and 90
b. There will be one more test this year. If Lisa wants her test average to at least be 88, what is the lowest grade she could get on her last test.
Answer:
94
Step-by-step explanation:
Equating the mean to the scores :
88 = 79 + 89 + 90 + x / 4352 = 258 + xx = 94So
Let that be n
n+79+89+90/4=88n+258/4=88n+258=352n=94Ajay wraps a gift box in the shape of a triangular pyramid. The figure below shows a
net for the gift box.
8.66 m
10 m
If all the triangles are equilateral, how much wrapping paper
did he use, in square meters?
Ajay wraps a gift box in the shape of a triangular pyramid. The amount
of wrapping paper he uses is 173.2 square inches.
How to calculate the surface area of a triangular pyramid?The formula for calculating the total surface area is expressed as:
Area = 4(area of triangle)
The area of the triangle
A = 0.5(8.66)(10)
A = 43.3 square inches
The total surface area will be
TSA = 4(43.3)
TSA = 173.2 square inches
Hence the amount of wrapping paper Ajay uses is 173.2 square inches
Learn more on the total surface area here:
brainly.com/question/1297098
#SPJ1
can anyone tell me what point I plot these two at pls
Answer:
[tex]x^{2} +y^{2}=25[/tex]
[tex]x^{2} +y^{2}=5[/tex]
Radius: 5
Radius: [tex]\sqrt{5}[/tex]
Step-by-step explanation:
(see images below)
Hope this helped!
~rere
14 boys and 16 girls in class
What is the ratio of girls to the total number of students in class? Write ratio in 3 ways
Answer:
1) 16 : 30
2) 8 : 15
3) [tex]\displaystyle \frac{8}{15}[/tex]
Step-by-step explanation:
Boys = 14
Girls = 16
Total students:
= 14 + 16
= 30
Ratio of Girls to total number of students in class:
= 16 : 30
÷2 ÷2
= 8 : 15
= [tex]\displaystyle \frac{8}{15}[/tex]
[tex]\rule[225]{225}{2}[/tex]
What is “y is __ times x”
Answer:
6
Step-by-step explanation:
Let X and Y be the following sets:
X = {5, 6, 10, 12, 15, 18}
Y = {6, 10, 12, 15)
Which of the following is the set X UY?
Answer:
i think the answer is X, because the elements of both X and Y are in X
