Answer:
9
Step-by-step explanation:
this is the explanation 6×3=18 18÷2=9
What are the domain and range of the function f(x)= -long(5-x)+b
The domain of the function f(x)= -long(5-x)+b is Dom(f) = [– ∞, 5]., range is all real numbers except for x = 5.
What is function?IF function is the process or state of instruction that text inputs performance is specific task and produce an output functional key components of programming language allowing the quarter to create complex commands with simple instruction for example a function can be used to add two numbers together or to generate a random number function can also be combined to create more complex sequence of instruction.
The range of this function is all real numbers as the long function will never return a negative value. The value of b determines the exact range of the function, as it shifts the graph up or down.
The formula is: f(x) = - log(5 - x) + b.
Limitation for the f domain:
5 – x > 0
x < 5
Hence, f's domain is
Dom(f) = {x ∈ R: x < 5}
Alternatively by notating intervals,
Dom(f) = [– ∞, 5].
Secondly, we wish to demonstrate that there is always an x Dom(f) for any given y R.
y = f(x) (x)
Once we've demonstrated that, we can say that f's operating range is R. (all real numbers).
How to find x in an equation:
[tex]y = f(x)\\y = - log(5 - x) + b\\y - b = - log(5 - x) (5 - x)\\-(y - b) = log(5 - x) (5 - x)\\b - y = log(5 - x) (5 - x)\\5 - x = 10^{(b - y) (b - y)}\\x = 5 - 10^{(b - y) (b - y)}\\[/tex]
Because y is not constrained, the range of f is R. (all real numbers).
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A certain forest covers an area of 2500km Suppose that each year this area decreases by 6.25% What will the area be after 15 years Use the calculator provided and round your answer to the nearest square kilometer.
The area of the forest decreases by 6.25% each year, and after 15 years, the area will be approximately 1089 km.
The area of a forest is a crucial aspect of understanding its size and its impact on the environment.
In this question, we are know that the forest with an initial area of 2500 km, which decreases by 6.25% each year. Our task is to find the area of this forest after 15 years. To do this, we need to perform a calculation that takes into account the decrease in area each year.
Mathematically, we can represent the area of the forest after n years as:
A = 2500 * (1 - 0.0625)ⁿ
Where n is the number of years that have passed. To find the area after 15 years, we can plug in n = 15:
A = 2500 * (1 - 0.0625)¹⁵
Using the calculator provided, we find that the area of the forest after 15 years is approximately 1089.38 km. Rounding this to the nearest square kilometer, we get 1089 km.
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7. The Bidvest Wanderers Cricket Stadium holds approximately 34 000 spectators. A one-day cricket match between England and South Africa is attended by 18 460 people. What percentage of the seats are taken? Give your answer correct to the nearest percent.
8. A bus can seat 60 passengers. It was full and some passengers got off, leaving 0,4 of the seats occupied. How many passengers got off the bus?
9. The three most commonly spoken languages in the world are Mandarin, spoken by approximately 867 200 000 people, English, spoken by approximately 341 000 000 people, and Spanish, spoken by approximately 350 000 000 people.
a) Using your calculator, determine how many more people speak Mandarin than English. Give your answer correct to the nearest million.
b) If the world population is approximately 7 000 000 000 (7 billion), use your calculator to determine what percentage of the entire population speaks Spanish. Give your answer correct to two decimal places.
7. The percentage of the seats taken by 18,460 attendees out of 34,000 capacity spectators of the Bidvest Wanderers Cricket Stadium is 54%.
8. If a bus can seat 60 passengers and some passengers got off, leaving 0.4 of the seats occupied, the number of passengers who got off the bus is 36, representing 60 percent.
9a) The population that speak Mandarin more than English is 526,200,000.
9b) If the world population is approximately 7 000 000 000 (7 billion), the percentage of the entire population that speaks Spanish is 5.00%.
What is the percentage?The percentage represents the ratio of one value compared to another.
The percentage is determined as the quotient from dividing the numerator by the denominator and multiplying by 100.
7) The spectator capacity of the Bidvest Wanderers Cricket Stadium = 34,000
Attendees at a one-day match = 18,460
Percentage of seats taken = 54.3% (18,460/34,000 x 100)
8) Bus passenger capacity = 60
The percentage of seats occupied = 0.4
The number of passengers who got off the bus = 36 (60 x (1 - 0.4)
9) Most Commonly Spoken World Languages:
Mandarin 867 200 000 people
English 341 000 000 people
Spanish 350 000 000 people.
a) The more Mandarin speakers than English = 526,200,000 (867,200,000 - 341,000,000)
b) World Population = 7 billion
Percentage of Spanish speakers to World Population = 5.00% (350,000,000/7,000,000,000 x 100)
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18. The area of a playground is 204y * d ^ 2 The width of the playground is 5 yd longer than its length.
The playground's length and breadth are 12 yards and 17 yards, respectively.
The playground's area is 204 square yards, according to the statistics provided in the inquiry.
204 square yards is the area.
The playground's breadth is 5 yards more than its length.
Let the playground be 'l' yards long.
The playground's width will then be (l + 5) yards.
The formula for the playground area is Length × Width.
A = Length x width
204 = l (l + 5)
204 = + 5l
+ 5l - 204 = 0
+ 17l - 12l - 204 = 0
l (l + 17) -12 (l + 17) = 0
(l + 17) (l - 12) = 0
(l + 17) = 0 or (l - 12) = 0
l = -17 or l = 12
The length value cannot be negative.
As a result, the length is 12 yards.
The breadth is thus equal to l + 5.
Width = 12 + 5
17 yards wide
As a result, the length is 12 yards and the breadth is 17 yards.
Option (b) is the right answer.
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A playground has a surface area of 204 yd2. The playground's breadth is 5 yards greater than its length. Determine the playground's length and breadth.
a.) 17 yards in length, 22 yards in breadth
b.) 12 yard length, 17 yard breadth
c.) 22 yard length, 17 yard breadth
d.) 17 yard length, 12 yard breadth
a parking garage charges $5 for the first hour, $10 for up to two hours, and $12 for the entire day. let be the dollar cost of parking for hours. pictured is a graph of the piecewise function. is a function of ?
The graph of this piecewise function is a step function, with steps at x=1 and x=2, where the value of the function changes.
The cost of parking for hours is a function of the number of hours. It can be modeled by a piecewise function, where the cost depends on the number of hours you park.
Here's the piecewise function for the cost of parking in dollars:
f(x) = {5, if 0 < x <= 1
{10, if 1 < x <= 2
{12, if x > 2
The graph of this piecewise function is a step function, with steps at x = 1 and x = 2, where the value of the function changes. The value of the function is constant in each interval (0, 1), (1, 2), and (2, infinity).
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WILL GIVE BRAIN HELP ASAP
Answer:
[tex]5.98xy-8y[/tex]
Step-by-step explanation:
Distribute the y
[tex]5.98xy-5.81y-2.19y[/tex]
Combine like-terms
[tex]5.98xy-8y[/tex]
How much money is pictured below?
Answer:$1. 45
Step-by-step explanation:
The bill is $1
the quarter is .25
and the nickels together are .20
add everything together its 1.45
First, we need to know the value of each coin. The top coin is a quarter, and its value is $0.25. The four coins below are nickels, and they have a value of $0.05. The dollar bill at the bottom has a value of $1.00.
If we have one quarter, we start with a value of $0.25.
[tex]$0.25[/tex]
Now, we add on the nickels.
[tex]0.25 + 0.05+ 0.05+ 0.05+ 0.05 = 0.45[/tex]
Now we have a total of $0.45.
Adding the dollar would look like this:
[tex]1.00 + 0.45 = 1.45[/tex]
Therefore, the value of all the money in the picture is $1.45.
Ngozi earns $24,000 in salary in the first year she works as an interpreter. Each year, she earns a 3.5% raise.
Answer:
Step-by-step explanation:
S=24000x(1.043)^t
find the slope of line represented by the data below
Answer:
-4
Why? I subtract the numbers. How to do that is by looking at the table. You always use two ordered pairs. Let's choose (-3,12) and (-2,8).
Step 1: Choose two ordered pairs (you can choose any two, it doesn't matter).
Now, subtract the y's together and subtract that x's together. So, what is 12-8? That's obvious, it's 4. Alright, how about -3-(-2)? Well, two negatives make a positive, so the problem is actually -3+2. So, what's that? Correct, -1. And, since slope is y/x, the answer would be -4/1, or -4.
a toddler crawls 2 yards, stopped, then continued to crawl 8 more feet. How many feet did he travel?
The toddler crawled a total of 24 feet (2 yards = 6 feet and 8 more feet).
The question asks how many feet the toddler traveled. To answer this question you need to convert yards to feet then add the measurements together. One yard is equivalent to three feet, so the toddler traveled two yards which is six feet. The toddler then stopped and continued to crawl eight more feet. To figure out the total distance the toddler traveled, you need to add the two measurements together. Six feet plus eight feet is equal to fourteen feet. Therefore, the toddler traveled a total of twenty-four feet.
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how many teeth per inch should a hacksaw blade have to cut off a piece of aluminum from 1'' square bar
It depends on the thickness of the aluminum bar. Generally, a hacksaw blade with 18 teeth per inch is used to cut off aluminum from 1'' square bar.
The number of teeth a hacksaw blade should have to cut off a piece of aluminum from 1'' square bar depends on the thickness of the aluminum bar.
2. Generally, a hacksaw blade with 18 teeth per inch is used to cut off aluminum from 1'' square bar.
For example, if the aluminum bar being cut is thin (1/8'' or less) then a hacksaw blade with 18 teeth per inch should be used. On the other hand, if the aluminum bar is thicker (greater than 1/8''), then a hacksaw blade with fewer teeth per inch should be used. The fewer teeth per inch the hacksaw blade has, the thicker the aluminum bar it can cut through. It is important to choose the correct hacksaw blade for the job in order to ensure a clean and safe cut.
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At lake view middle school, there are 2 homeroom teachers assigned to every 48 students. Is the number of students at this school proportional to the number of teachers? Explain your reasoning
Answer:
Step-by-step explanation:
No, the number of students at the school is not proportional to the number of teachers. In a proportional relationship, two quantities have a constant ratio. However, in this case, the number of teachers is not directly proportional to the number of students because there is a fixed number of teachers regardless of the number of students. Even if the number of students changes, the number of teachers remains the same.
A more appropriate way to describe the relationship between the number of teachers and students at the school is to say that there are 2 teachers for every 48 students, or that the ratio of teachers to students is 2:48, which simplifies to 1:24.
find the distaance between the points (-5,7) and (-5,2)
Answer: The distance between these two points is 5.
Step-by-step explanation:
Yay! Love doing distance formula questions!
Okay, so first off, the distance formula goes as follows:
d = [tex]\sqrt(x^{2} - x^1)^2 + (y^{2}-y^1)^2[/tex]
Basically you just plug in your coordinates to the formula.
Step 1:
[tex]\sqrt(-5 + 5)^{2} + (2-7)^{2}[/tex]
Step 2: Distribute the exponent to both parenthesis to get [tex]\sqrt{25}[/tex].
Step 3: Factor the number, which would result in [tex]\sqrt{5^2}[/tex].
As a result of this, your answer would be 5.
Y’all… I’m so confused and this is due tonight. ITS LIKE 20 questions- please help..
It is formatted a bit weird.
u = the radius (im pretty sure)
area of a circle = pi(u)^2
circumference of a circle is 2pi(u)
22/7 = pi
Area = (22/7)(u)^2
Circumference = 2(22/7)u
In a certain chemical, the ratio of zinc to copper is 4 to 11. A jar of the Chemical contains 495 grams of copper. How many grams of zinc of does it contain
The answer to our inquiry is that 180 grams of zinc contain a particular compound.
How is a ratio calculated?Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were going to compare another data item (A) to this other data point (B).
The zinc to copper ratio in a particular compound is 4: 11.
Copper weighs 495 grammes in the chemical.
How much zinc does it chemically contain in grammes.
Assume that y is the scalar multiple of zinc and copper.
as stated
The proportion of zinc over copper in a certain compound is 4 to 11.
Copper weighs 495 g in the chemical.
Equation is than
11y = 495
11y = 495
y = 495/11
y = 45
Zinc in a particular chemical = 4y
= 4x45
= 180 grams
Therefore 180 grams of zinc contain in a certain chemical .
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The space program has 23 astronauts in outer space and 7 astronauts on Earth. What is the ratio of the number of astronauts on Earth to the total number of astronauts?
The ratio of the number of astronauts on Earth to the total number of astronauts is 7 : 30.
A ratio is a mathematical expression that compares two or more values by dividing the size of one value by the size of another.
Ratios can be expressed in several different forms, including fractions, decimals, or percentages, and can be used to compare quantities, measurements, or other values in a meaningful way.
Ratios provide a way to express the relationship between two or more values in a compact and concise format, and can be used in a variety of fields, including mathematics, science, finance, and engineering.
If the space program has 23 astronauts in outer space and 7 astronauts on Earth, then the ratio of the number of astronauts on Earth to the total number of astronauts is:
7 : (23 + 7) = 7 : 30
You can simplify the ratio to 7/30 or approximately 0.23 or 23%.
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Find the quotient 4^-5/4^-2
The quotient to the expression is 1/64
What are exponents?Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.
Given here: The expression 4⁻⁵ / 4⁻²
When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.
Thus simplifying the expression we get
4⁻⁵ / 4⁻²
4⁻⁵× 4²
4⁻⁵ ⁺ ²
4⁻³
1/64
Thus the quotient is 4⁻³
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Which statement best describes the area of the triangle shown below? A coordinate grid is shown with a triangle.. The base is 4 units, and the height is 4 units. (4 points) a It is one-half the area of a rectangle of length 4 units and width 2 units. b It is one-half the area of a square of side length 4 units. c It is twice the area of a rectangle of length 4 units and width 2 units. d It is twice the area of a square of side length 4 units.
The statement that best describes the area of the triangle is:
It is one-half the area of a square of side length 4 units.
Option B is the correct answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Triangle:
The base is 4 units, and the height is 4 units.
Area of the triangle.
= 1/2 x base x height
= 1/2 x 4 x 4
= 8 units²
Now,
a)
It is one-half the area of a rectangle of length 4 units and width 2 units.
This is not possible since we do not have 2 units.
b)
It is one-half the area of a square of side length 4 units.
Area of a square.
= Side²
= 4²
= 16 units²
So,
1/2x 16 = 8 units²
This is true.
c)
It is twice the area of a rectangle of length 4 units and width 2 units.
This is not possible since we do not have 2 units.
d)
It is twice the area of a square of the side length of 4 units.
This is not possible.
Thus,
It is one-half the area of a square of side length 4 units.
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Unit 5: systems of equations and inequalities Homework 3: Solving systems by elimination (All Things Algebra®, LLC)
Answer:
(x, y) = (-3, -5)
Step-by-step explanation:
You want to solve the given system of equations by elimination.
2x -3y = 9-5x -3y = 30EliminationTo eliminate a variable from the equations, we need to add them in such a way that the coefficients for one of the variables have a total of zero.
Here, we observe that the y-coefficients are the same, so subtracting one equation from the other will cancel the y-terms. We want the result of that subtraction to give an equation with x having a positive coefficient, so we elect to subtract the second equation from the first:
(2x -3y) -(-5x -3y) = (9) -(30)
7x = -21 . . . . . simplify (y-terms are gone, x-term has positive coefficient)
x = -3 . . . . . . . divide by 7
SubstitutionThe value of y can be found from either equation. We choose to use the first one:
2x -3y = 9
2(-3) -3y = 9 . . . . . . substitute -3 for x in the first equation
-15 = 3y . . . . . . add 3y-9
-5 = y . . . . . . . divide by 3
The solution is (x, y) = (-3, -5).
18. The area of a playground is 204y * d ^ 2 The width of the playground is 5 yd longer than its length.
The length and the width of the playground 12 yards and 17 yards respectively.
As per the data given in the question the area of the playground is 204 square yards.
Area = 204 square yards.
The width of the playground is 5 yards longer than its length.
Let the length of the playground be 'l' yards.
Then the width of the playground will be (l + 5) yards.
The formula for the area of the playground is Length × Width.
A = Length × Width
204 = l (l + 5)
204 = [tex]l^{2}[/tex] + 5l
[tex]l^{2}[/tex] + 5l - 204 = 0
[tex]l^{2}[/tex] + 17l - 12l - 204 = 0
l (l + 17) -12 (l + 17) = 0
(l + 17) (l - 12) = 0
(l + 17) = 0 or (l - 12) = 0
l = -17 or l = 12
Length cannot be the negative value.
So the value of the length is 12 yards.
Then width = l + 5
Width = 12 + 5
Width = 17 yards
Therefore length is 12 yards and width is 17 yards.
Option (b) is correct.
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The area of a playground is 204 yd2. The width of the playground is 5 yd longer than its length. Find the length and width of the playground.
a.) length 17 yd, width 22 yd
b.) length 12 yd, width 17 yd
c.) length 22 yd, width 17 yd
d.) length 17 yd, width 12 yd
When data are positively skewed, the mean will usually be:
a. greater than the median
b. smaller than the median
c. equal to the median
d. positive
When data are positively skewed, the mean will be greater than the median.
This is because the mean will be pulled in the direction of the higher values in the data set, while the median will ignore the higher values and be more affected by the lower values in the data set.
Positively skewed data is characterized by a long tail on the right side of the distribution graph. This means that the data set contains more values that are higher than the mean and median. As a result, the mean will be a higher value than the median, as the mean will be pulled in the direction of the higher values. The median, however, will remain unaffected by the higher values and will be more affected by the values at the lower end of the distribution.
the complete question is :
When data are positively skewed, the mean will usually be:
a. greater than the median
b. smaller than the median
c. equal to the median
d. positive or negative depending on the data set
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David is writing an explicit function for the arithmetic sequence: 10, 13, 16, 19, 10,13,16,19,…10,, 13,, 16, , 19, , He comes up with s(n)=7+3ns(n)=7+3ns, left parenthesis, n, right parenthesis, equals, 7, plus, 3, n. What domain should David use for sss so it generates the sequence?
Answer:
n ∈ ℕ . . . (Natural numbers)
Step-by-step explanation:
You want the domain of the relation s(n) = 7+3n so that it defines the sequence 10, 13, 16, ....
DomainThe domain of a function is the set of "input" values for which the function is defined. Here, the function is intended for use with values of n that are Natural numbers:
domain = ℕ
__
Additional comment
In general, the domain of any function that defines a sequence will be Natural numbers. That is, values of n will be 1, 2, 3, ....
Occasionally, the sequence represents a relation that is of interest for values of n other than positive integer values. In such a case, the domain may be Whole numbers, or Real numbers.
the missing measure for angle B is ___
the missing measure for angle C is ___
i found the missing measures for B and C by ….
justification: i know that the angle measures for B and C are accurate because…….
Answer:
Missing measure for angle B = 74°
Missing measure for angle C = 74°
Step-by-step explanation:
Side AB = Side AC
∴∠B° = ∠C°
Two sides out of three of this triangle are equal to each other, therefore this is an isosceles triangle
Let x° = ∠B° = ∠C°
Sum of interior angles of a triangle = 180°
∴32° + x° + x° = 180°
= 32° + 2x° = 180°
= 2x° = 180° - 32°
= 2x° = 148°
= x° = [tex]\frac{148}{2}[/tex]
= x° = 74°
∴∠B° = ∠C° = 74°
amy has three times as many star wars toys as carly. total they have 340 star wars toys. how many star wars toys does amy have?
The number of star wars that Amy has is 255 and Carly has is 85
Linear equation:
The linear equation is a combination of algebraic terms that are used to find unknown quantities in a word problem. To solve the given problem represent the unknown value with a variable and form a linear equation according to the given condition. Now solve the equation for the value of the variable.
Here we have
Amy has three times as many star wars toys as Carly.
Let Amy have 'x' star wars and Carly have 'y' star wars
From the given data, x = 3y
It is also given that both have 340-star wars toys in total
=> y + 3y = 340
=> 4y = 340
=> y = 85
Hence, the number of star wars that Carly has = 85
Number of star wars that Amy has = 3(85) = 255
Therefore,
The number of star wars that Amy has is 255 and Carly has is 85
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a box contains 4 red balls, 4 blue balls and 4 white balls. i extract 6 balls at once. what are the number of arrangements of 6 balls with 2 red balls and 2 blue balls ?
The number of arrangements of 6 balls with 2 red balls and 2 blue balls, we need to consider the number of ways to choose 2 red balls from the 4 available red balls and the number of ways to choose 2 blue balls from the 4 available blue balls.
These are both combinations, and we can use the formula for combinations to calculate them:
C(n, k) = n! / (k! (n-k)!).
For the red balls, C(4, 2) = 4! / (2! (4-2)!) = 6.
For the blue balls, C(4, 2) = 4! / (2! (4-2)!) = 6.
The total number of arrangements of 6 balls with 2 red balls and 2 blue balls is the product of the number of arrangements for each type of ball:
C(4, 2) * C(4, 2) = 6 * 6 = 36
So, there are 36 arrangements of 6 balls with 2 red balls and 2 blue balls.
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A teacher received the following answer to a quiz question in which the student was asked to simplify the expression in Step 1:
Step 1: −3(x − 14y) + 6(−3x − 5y)
Step 2: −3x + 42y − 18x − 30y
Step 3: −3x + 18x + 42y − 30y
Step 4: (−3x + 18x) + (42y − 30y)
Step 5: 15x + 12y
Part A: Identify the step where the student made a mistake and explain the specific error that was made. Support your answer using the correct vocabulary. (6 points)
Part B: How would you correct the mistake? Show all your work. (6 points)
Answer:The student made a mistake and explain the specific error that was made. Support your answer using the correct vocabulary. The mistake has been done in Step 2.
PART A: There is a mistake in Step 2, Distributive Property has been employed incorrectly.
7 has to multiply by both the terms inside the bracket, but it has been multiplied with the first term only.
7(-2 x-8 y)=-14 x-56 y and 7(-2 x-8 y) -14 x-8 y
Hence, -5(x-16 y)+7(-2 x-8 y)=-5 x+80 y-14 x-56 y
PART B :
The given equation is
-5(x-16 y)+7(-2 x-8 y)
Applying distributive property to the above equation that states A(B+C)=AB+AC, we get :
-5 x+80 y-14 x-56 y
Now, Writing the terms with the same variable together, we get
(-5 x-14 x)+(80 y-56 y)
Proceeding with solving terms inside the brackets according to BODMAS, we get,
-19 x+24 y
Hence , −5(x − 16y) + 7(−2x − 8y) = -19x +24y
help me on this question please
Answer: rectangle
Step-by-step explanation: because i have eyes
The sine of an angle in a right triangle is 4. 5
Which of these could be the measures of the sides of the triangle?
A) 4 cm, 5 cm and 9 cm
B) 4 cm, 5 cm and √41 cm
C) 6 cm, 8 cm and 10 cm
D) 8 cm, 10 cm and 4√41 cm
The correct answer for the measures of the sides of the triangle is (D) 8 cm, 10 cm, and 4√41 cm.
What is sine of an angle?The sine of an angle is a mathematical function that describes the relationship between the lengths of the sides of a right triangle and the angles within that triangle. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Let's call the side opposite the angle with sine 4.5 "a", and the side adjacent to that angle "b". Using the definition of sine, we can write the following equation:
sin(θ) = a/c
where c is the length of the hypotenuse. We can substitute 4.5 for the sine:
4.5 = a/c
Cross multiplying, we get:
4.5c = a
So, given the length of c, we can find a.
The only option that gives a positive value for c is (D), with c = √41 cm. In this case, a = 4.5 * √41 = 4√41 cm, which matches the value in the answer choices.
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Espan
The lunch special at Teresa's Restaurant is a sandwich, a drink and a dessert. There are 2 sandwiches, 2 drinks, and 3 desserts to choose from. How many lunch
specials are possible?
XS ?
The quantity of lunch specials conceivable is 2 sandwiches * 2 beverages * 3 treats = 12.
The lunch exceptional at Teresa's Café incorporates a sandwich, a beverage, and a sweet. There are 2 choices for sandwiches, 2 choices for beverages, and 3 choices for treats. To decide the quantity of conceivable lunch specials, we want to track down the quantity of blends of these things. The recipe for mixes is n! /(r! * (n - r)!). Nonetheless, since every thing is chosen just a single time, we can basically duplicate the quantity of choices for every thing. For this situation, there are 2 choices for sandwiches, 2 choices for beverages, and 3 choices for pastries, so 2 * 2 * 3 = 12 potential lunch specials.
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Solve the circled questions.
Due to length restrictions, we kindly invite to read the explanation below for further details on equivalence of trigonometric expressions.
How to prove a trigonometric equivalence
In this problem we find five case of trigonometry expressions whose equivalence must be proved by means of algebra properties and trigonometric formulas. Now we proceed to show the solution for each case:
Case 3:
tan θ · cos θ
(sin θ / cos θ) · cos θ
sin θ
Case 5:
(1 - cos θ) · (1 + cos θ)
1 - cos² θ
sin² θ
Case 6:
(1 + sin θ) · (1 - sin θ)
1 - sin² θ
cos² θ
Case 7:
(sec θ + tan θ) · (sec θ - tan θ)
sec² θ - tan² θ
1
Case 10:
(tan θ + cot θ) / tan θ
1 + cot θ / tan θ
1 + cot² θ
csc² θ
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