By trigonometric formulas and algebra properties, the equivalence between the trigonometric expression (sin x - cos x)² and the trigonometric expression 1 - 2 · sin x · cos x.
How to prove the equivalence between two trigonometric expressions
In this problem we need to prove if the trigonometric expression (sin x - cos x)² is equivalent to the trigonometric expression 1 - 2 · sin x · cos x, this can be proved by trigonometric formulas and algebra properties. First, write the initial expression:
(sin x - cos x)²
Second, expand the binomial:
sin² x - 2 · sin x · cos x + cos² x
Third, use the fundamental trigonometric expression:
1 - 2 · sin x · cos x
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Kelly earns $96 in 12 hours. At this rate, how many dollars will she earn in 20
hours?
OA. $160
OB. $240
O C. $200
O D. $80
96/12 = x/20
Solve it and get the answer.
Mike had 6 1/4 pounds of potatoes to share with his friends. He gave them 3 4/5 pounds. How many pounds of potatoes does Mike have left?
Answer: 2 9/20
Step-by-step explanation:
First, rewriting our equation with parts separated
=6+14−3−45
Solving the whole number parts
6−3=3
Solving the fraction parts
14−45=?
Find the LCD of 1/4 and 4/5 and rewrite to solve with the equivalent fractions.
LCD = 20
520−1620=−1120
Combining the whole and fraction parts
3−1120=2920
Solution by Formulas
First:
Convert any mixed numbers to fractions.
Then your initial equation becomes:
254−195
Applying the fractions formula for subtraction,
=(25×5)−(19×4)4×5
=125−7620
=4920
Simplifying 49/20, the answer is
=2 9/20
In Silvergrove, the library is due south of the courthouse and due west of the community swimming pool. If the distance between the library and the courthouse is 9 kilometers and the distance between the courthouse and the city pool is 10 kilometers, how far is the library from the community pool? If necessary, round to the nearest tenth.
The distance of the library from the community pool is given as 4.4 km
How to solve for the distanceWe have to solve this problem with the use of the Pythagoras theorem.
The formula is given as
a² = b² + c²
The total distance flown would be represented by a = 10 kilometer
the distance for the courthouse would be given as 9 kilometers
When we put these values in the formula we would have
10² = a² + 9²
100 = a² + 81
a² = 100 - 81
a² = 19
a = √19
a = 4.4 km
Hence the calculated distance is given a 4.4 km from the library to pool.
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An elevator travels310ft in 10 seconds. How far will it travel in 12 seconds
Answer: 372ft
Step-by-step explanation:
310 divided by 10 equals 31.
31 times 12 = 372
And so it is 372 ft
Melissa’s mom embroiders 5 flowers on each side of a handkerchief. There is one flower at each corner, how many flowers are embroidered on the handkerchief altogether? If she gets Rs. 6 for embroidering 2 flowers, how much did she get paid for this handkerchief
Answer:
20 flowers at sides and 4 flowers at the corner then
total flowers are 24
cost of 2 flowers is 6 then of one flower will be 3
total cost of the flowers will be 24×3=72
Step-by-step explanation:
Think About the Process You have 30 quarters. You find 20% more quarters in your room. Then you go shopping and spend 50% of the total number of quarters. Write an expression to represent the total number of quarters you take with you shopping. Calculate, in dollars, the amount of money you have left.
Answer: $4.5 left.
Step-by-step explanation:
You have 30 quarters, and find 20% more. To convert percentages to decimals for calculations, simply move the decimal two spaces to the left.
20% is 20. ---> 2.0 ---> .20
30 * 0.2 = 6. Now add 6 (found) to 30 (original) to get the total.
30+6 = 36 total quarters.
You spend 50% of the quarters, 36 * 0.5 = 18.
This means you have 18 quarters left (or you spent 18).
18 quarters, each quarter is worth 0.25 dollars, so multiply the number left by how much each is worth.
18 * 0.25 = $4.5.
$4.50 is the amount left
What is the midpoint of AB?
Answer:h
Step-by-step explanation:
8+-6=2
SOLVE FOR FF
10f+10=9f
F=
Answer:
-10
Step-by-step explanation:
I would explain it but my keyboard won't let me type certain things.
Please give brainlist T-T
A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y = 4x + 3.5 represents the cost y of bowling x games. Interpret the parameters of the function.
What represents the price per game?
What represents the shoe rental charge?
Answer: the price per game is 4 per game and the shoe rental is the additional fee to bowl
Step-by-step explanation:
Sergio buys 684 red stickers and
729 blue stickers for his 24 classmates
Each classmate receives the same
number of stickers. Sergio gives the
leftover stickers to his younger brother.
How many stickers does Sergio give to
his younger brother?
Hence, Sergio give to his younger brother is [tex]58[/tex].
What is the division?
Division is the opposite of multiplication. If three groups of four make twelve in multiplication, twelve divided into [tex]13[/tex] equal groups give four in each group in division.
Here given that,
Sergio buys [tex]684[/tex] red stickers and [tex]729[/tex] blue stickers for his [tex]24[/tex] classmates.
Each classmate receives the same number of stickers.
Total number of stickers are
[tex]684+729=1413[/tex]
So, the Sergio give to his younger brother is
[tex]\frac{14131}{24}=58[/tex]
Hence, Sergio give to his younger brother is [tex]58[/tex].
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a. How many cubes with an edge length of b. What is the volume, in cubic inches, of inch are needed to build a cube with one cube with an edge length of inch? an edge length of 1 inch?
The number of cubes of edge length 1/3 is 27 and the volume of the cube is 1 cubic inches
How to determine the number of cubesFrom the question, we have the following parameters that can be used in our computation:
Edge length of cube 1 = 1/3 inchEdge length of cube 2 = 1 inchThe volume of a cube is the cube of its edge length
This means that the volumes are
Volume = Edge length³
So, we have
Volume of cube 1 = (1/3 inch)³ = 1/27 cubic inches
Volume of cube 2 = (1 inch)³ = 1 cubic inch
The number of cubes is then calculated as
Number of cubes = Volume of cube 2/Volume of cube 1
This gives
Number of cubes = 1/(1/27)
Number of cubes = 27
The volume of the cubesHere, we have
Edge length of cube = 1 inch
The volume of a cube is the cube of its edge length
This means that the volumes are
Volume = Edge length³
So, we have
Volume of cube = (1 inch)³ = 1 cubic inch
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Complete question
a. How many cubes with an edge length of 1/3 inch are needed to build a cube with an edge length of 1 inch?
b. What is the volume, in cubic inches, an edge length of 1 inch?
Solomon invested money in his bank account. He had a principal, P,
of $100 in his account at the beginning of the period, which
increased at a rate, r, of 0.15 per year. At the end of the period, he
had interest, I, of $135 in his account. Use the simple interest
formula 1 Prt, to solve for the time, t, in months that it took to
earn this amount. (1 point)
h
O 9 months
O 108 months
O 233 months
900 months
The total time required in months is 108 months.
What is simple interest?
Simple interest is defined as the amount of interest paid on a specific principal, an amount at a specific interest rate. It is given by
I = Prt
where, I = simple interest, P = Principal, r = rate of interest, t = time taken
Given, P = $100
I = $135
r = 0.15
t = ?
So, simple interest is given by:
I = Prt
or, 135 = 100*0.15*t
or, 135 = 15*t
or, t = (135/15) = 9 years = 9*12 = 108 months
Hence, the total time required in months is 108 months.
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Answer: 108
Step-by-step explanation:
just took test
Three verticies of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex. (please helpp!!)
Answer:
AE=19
EAD=34
Step-by-step explanation:
Look at the image for step by step help.
-Hope this helped
Length (cm): Length (m)
100: 1
250: 2.5
78.2: .782
123.9: 1.239
y: ? I need to know what goes next to the y
Write an equation for the proportional relationship. Let x represent a length measured in meters and y represent the same length measured in centimeters. I don't know what would be the equation.
The equation for the proportional relationship is x=y×(1/100) where x represents length in meters and y represents same length in centimeters.
What is meant by proportionality?The phrase proportionality refers to any relationship that always has the same ratio. The quantity of apples in a crop, for example, is proportionate to the number of trees in the orchard, with the ratio of proportionality being the average number of apples per tree.
In mathematics, two sequences of numbers, generally experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is known as the coefficient of proportionality or proportionality constant.
Given,
Length(cm): Length(m)
100 : 1
250 : 2.5
78.2 : 782
123.9 : 1.239
The value that goes next to y is,
y: y×(1/100)
Therefore, x=y×(1/100)
The equation for the proportional relationship is x=y×(1/100)
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If 9 cows can fit in a field, how many fields are necessary to make sure 65 cows are all in a field?
Answer:
7.2 field or 7 field
Step-by-step explanation:
9 cows=1 field
65 cows=x field
cross multiply
9x=65×1
x=65÷9
x=7.2/7 field
Scott whose eye level is 1.5m above the ground, stands 30m from a tree. The angle of elevation of a bird at the top of the tree is 36 degrees. How far above the ground is the bird?
A. 21.8 m
B. 23.3 m
C. 41.3 m
Using trigonometric ratio, the distance of the bird is 21.8m
Angle of ElevationThe angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
To solve this problem, we have to use trigonometric ratio of SOHCAHTOA
Let's define the variables given;
Using Tangent of an angle;
tanθ = opposite / adjacent
tan 36 = x / 30
Cross multiply both sides and solve for x
30 tan36 = x
21.8 = x
The distance above the ground from the bird is 21.8 meter.
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Plot four lines to connect the points in adjacent
quadrants. One is done for you.
Line
# 1 y= -2 (x-6)+1
10
# 2?
#3?
#4?
Answer:
[tex]\textsf{Line \#2}: \quad y=x-5[/tex]
[tex]\textsf{Line \#3}: \quad y=\dfrac{1}{4}(x-1)-4[/tex]
[tex]\textsf{Line \#4}: \quad y=-8x-29[/tex]
Step-by-step explanation:
Given points:
(-4, 3)(6, 1)(1, -4)(-3, -5)To find the equations for each of the lines:
Find the slope of the line by substituting two points on the line into the slope formula.Substitute the found slope and one of the points on the line into the point-slope formula and simplify.Line #2Points:
Let (x₁, y₁) = (6, 1)Let (x₂, y₂) = (1, -4)Find the slope:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{1-6}=\dfrac{-5}{-5}=1[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1=1(x-6)[/tex]
[tex]\implies y=(x-6)+1[/tex]
[tex]\implies y=x-5[/tex]
Line #3Points:
Let (x₁, y₁) = (1, -4)Let (x₂, y₂) = (-3, -5)Find the slope:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-5-(-4)}{-3-1}=\dfrac{-1}{-4}=\dfrac{1}{4}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-4)=\dfrac{1}{4}(x-1)[/tex]
[tex]\implies y+4=\dfrac{1}{4}(x-1)[/tex]
[tex]\implies y=\dfrac{1}{4}(x-1)-4[/tex]
Line #4Points:
Let (x₁, y₁) = (-3, -5)Let (x₂, y₂) = (-4, 3)Find the slope:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-(-5)}{-4-(-3)}=\dfrac{8}{-1}=-8[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-5)=-8(x-(-3))[/tex]
[tex]\implies y+5=-8(x+3)[/tex]
[tex]\implies y=-8(x+3)-5[/tex]
[tex]\implies y=-8x-24-5[/tex]
[tex]\implies y=-8x-29[/tex]
Suppose that 16 inches of wire costs 80 cents. At the same rate, how many inches of wire can be bought for 45 cents?
Write an equation for (-5,3) and (0,-7)
The equation of line is y + 2x +7 =0 for the points (-5,3) and (0,-7).
What is equation of line?A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
The many points that collectively make up a line on the coordinate axis are represented as a group of variables (x, y) to create an algebraic equation, also known as an equation of a line.
The given points are (-5, 3) and (0, -7).
To find the equation of line, use formula,
y - y₁ = m(x - x₁) where m = (y₂-y₁)/(x₂-x₁),
y - 3 = (-7 - 3)/(0-(-5)) (x - (-5))
y - 3 = -10 / 5 (x + 5)
y - 3 = -2 (x + 5)
y + 2x +7 =0
The required equation of line is y + 2x +7 =0 .
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Consider the curve given by the equation y² - 6y - 9x² - 144x = 576. It can be shown that dy/dx=
9(x + 8)/ Y-3
Find the x-coordinate of the point where the line tangent to the curve is the x-axis.
The x-coordinate of the point where the line tangent to the curve is the x-axis is; x = -8
How to Interpret the tangent line to a curve?To get he x-coordinate of the point that the line tangent to the curve is the x-axis, what we will do is to equate the numerator of the derivative to zero.
Now, we are given the equation of the curve as;
y² - 6y - 9x² - 144x = 576.
We are told that It can be shown that;
dy/dx = 9(x + 8)/(y - 3)
From our earlier definition, the x-coordinate will be at;
9(x + 8) = 0
divide both sides by 9 to get;
x + 8 = 0
x = -8
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The U.S. Postal Service delivers about 212 billion pieces of mail each year. Of this mail, 4/5 is sent by big commercial users. About how many pieces of mail are sent by big commercial users each year? Hint: billion is part of the label “billion pieces of mail”.
The mail that are sent by big commercial users is 169.60 billion.
How many mails are sent by big commercials users?A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 4/5.
In order to determine the pieces of mail that are sent by big commercial users, multiply the fraction by the total number of mails delivered each year.
The mail that are sent by big commercial users = 4/5 x 212 billion = 169.60 billion
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0 Assignment is past due
5.PS-20
Question Help
Doug dives from a platform that is 7.5 meters above water. His dive takes him 1.5 meters below the surface of the water. How
far does Doug's dive take him?
Doug's dive takes him meters.
Answer:
9 meters
Step-by-step explanation:
|7.5|+|-1.5|=9
(the || on either side of each number shows that it's representing how far the number is from 0, so it's essentially 7.5+1.5)
Lena buys a 32-oz package of cheese. Does she have enough cheese to make 2 batches of mac-and-cheese and 3 pizzas? Explain.
Answer:
how much oz does it take to make mac and cheese and pizza? will edit when get answer
Step-by-step explanation:
Please Help!! It's really simple and I've done half already but I REALLY need help on the other half!!!! My assignment is on the first page and the first half that I've done is on the second page.
The equation of asked line is y = x/3+3
What is equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
The equation of a line passing through two points (x1, y1) and (x2, y2) is
y-y1 = (y2-y1)/(x2-x1)*(x-x1)
The two points are (6, 5) and (3, 1)
Equation =
y-5 = -4/-3*(x-6)
y-5 = 4/3*(x-6)
3y - 15 = x-6
3y = x+9
y = x/3+3
Hence, the required equation is y = x/3+3
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Which of the following items is shaped MOST LIKE the Moon?
O An egg
O Asphere
O A cone
O A circle
Answer:
An egg
Step-by-step explanation:
Hope this helps you
SOLVE FOR N
3/2 -1/2n= 2n+3
N =
Answer: n= -3/5 OR n= -0.6
Step-by-step explanation:
exact form and decimal form
Chindi puts 2 3/5 kg of bird seed in his large feede. This is 1 3/10 times as much bird seed as he puts in his smaller feeder. How much bird seed does Chidi put in his smaller feeder?
A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
The total amount in the smaller feeder is 2 kg.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Chindi puts 2(3/5) kg of bird seed in his large feed.
This is 1(3/10) times as much bird seed as he puts in his smaller feeder.
The total amount is represented by 1.
Now,
1(3/10) = 2(3/5) kg
13/10 = 13/5 kg
Multiply both sides by 10/13
1 = 10/13 x 13/5 kg
1 = 2 kg
This means the total amount of seeds in the smaller feeder is 2 kg.
Thus,
The total amount in the smaller feeder is 2 kg.
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Given f(x) = 2x and g(x) = f(x − 4) + 5, write the new function rule (equation) for function and
describe
The new function rule is g(x) = 2x -3
What is a function?A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
This means that if the object x is in the set of inputs (called the domain) then a function f will map the object x to exactly one object f(x) in the set of possible outputs (called the codomain).
if f(x) = 2x, then f(x-4) = 2(x-4)
g(x) = f(x-4) + 5
substitute f(x-4) into g(x)
g(x) = 2(x-4) + 5
g(x) = 2x -8 + 5
g(x) = 2x - 3
In conclusion, the function rule g(x) is 2x - 3
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Please help with this question
[tex]10 \sqrt{2} [/tex]
Answer:
The answer is approximately equal to 14.14214
Find x when () = 2. Please explain step by step
Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.
Step-by-step explanation: