Answers
Given:
We are required to prove:
\(\frac{\sec\text{ }\theta\text{ }}{\tan\text{ }\theta\text{ + cot}\theta}\text{ = sin}\theta\)From the left-hand side:
\(\begin{gathered} =\frac{\sec\text{ }\theta\text{ }}{\tan\text{ }\theta\text{ + cot}\theta}\text{ } \\ =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{\sin\theta}{\cos\theta}\text{ + }\frac{\cos \theta}{\sin \theta}} \\ =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{\sin ^2\theta+cos^2\theta}{\sin \theta\cos \theta}} \\ \end{gathered}\)From standard trigonometric identity, we have:
\(\sin ^2\theta+cos^2\theta\text{ = 1}\)Substituting we have:
\(\begin{gathered} =\text{ }\frac{\frac{1}{\cos\theta}}{\frac{1}{\sin \theta\cos \theta}} \\ =\text{ }\frac{\sin \theta\cos \theta}{\cos \theta} \\ =\text{ sin }\theta\text{ (Right-hand side)} \end{gathered}\)Related Questions
Joshua ate 2/6 of his sandwich in the afternoon and 2/6 more for a snack later that day. How much of Joshua’s sandwich is left?
Answers
Answer:
1/3 left
Step-by-step explanation:
The total sandwich is 1 or in fraction form 6/6
He ate 2/6
6/6 -2/6 = 4/6
Then he ate 2/6 more
4/6 -2/6 = 2/6
He has 2/6 left
Simplifying
2/6 =1/3
the least common multiple of the two numbers is 40 the ratio of the greater number is the to the lessor number is 5, 4
Answers
if 40 is the least frequent multiple of two whole numbers. The higher number to lesser number ratio is 4:5. The two digits after that are 8 and 10.
What is Least Common Multiple (LCM)?Least Common Multiple is the meaning of the abbreviation LCM.
The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.
It can also be computed using two or more numbers.
Finding the LCM of a given collection of numbers can be done in a variety of ways.
Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.
In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple.
The smallest number among all numbers is called the least common multiple of two or more numbers.
According to our question-
The number LCM is equal to 40.
4 × 5 × x = 40
20 × x = 40
20x=40
x=2
The larger number is equal to 4 x=4(2)=8.
The smaller value is =5x=5(2)=10.
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Complete question-
The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 4:5. What are the two numbers?
Solve the equation 2/3x - 1/5x = x - 1
Answers
Answer:
To solve the equation:
2/3x - 1/5x = x - 1
First, we need to find a common denominator for 2/3 and 1/5, which is 15. So we can rewrite the equation as:
(10/15)x - (3/15)x = 15/15 x - 1
Simplifying the left side:
(7/15)x = 15/15 x - 1
Multiplying both sides by 15:
7x = 15x - 15
Subtracting 7x from both sides:
-8x = -15
Dividing both sides by -8:
x = 15/8 or 1.875
Therefore, the solution to the equation is x = 1.875.
If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation. Otherwise, use the values Σx = 2769 and Σx2 = 132,179 to compute the sample mean and sample standard deviation. (Round s to four decimal places.)
Answers
By using a statistical calculator, the actual sample mean and sample standard deviation are:
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
How to calculate the sample mean for the set of data?In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:
Mean = ∑x/(n - 1)
∑x represents the sum of all data values.(n - 1) represents the number of data contained in a sample.In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:
Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)
x represents the observed values of a sample.\(\bar{x}\) is the mean value of the observations.N represents the total number of of observations.By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Mr. smith planted some new trees at his farm. He measured each tree. The height of each tree is shown in the line plot.
Answers
Answer:
one tree is 3 feet tall
most of the trees are less than 5 feet tall
Step-by-step explanation:
A 3-gallon container of disinfectant costs $36.24. What is the price per quart?
Answers
Answer:
10.74666666666667 per quart
Step-by-step explanation3 divided 36.24
289x63 what dies this =?
Answers
18,207.
pls mark brainliest
Answer:
18,207
Step-by-step explanation:
289 times 63 equals 18,207
Hope that helps ;)
If m < ACD = 100 , then m < ACE = ?
Answers
If m ∠ACD = 100°, then m ∠ACE = 80°, as ∠ACD and ∠ACE are supplementary angles.
Supplementary angles are the angles whose sum is equal to 180°. The angles formed when one straight line intersects the other, on the point of intersection on the same side of any line are always supplementary.
In the given question, AB and DE are two straight lines intersecting at point C. ∠ACD and ∠ACE lie on the same side of the line DE, thus they are supplementary angles.
Therefore, m ∠ACD + m ∠ACE = 180°.
But we know that m ∠ACD = 100°. So,
m ∠ACD + m ∠ACE = 180°,
or, 100° + m ∠ACE = 180°,
or, m ∠ACE = 180° - 100° = 80°.
Therefore, if m ∠ACD = 100°, then m ∠ACE = 80°, as ∠ACD and ∠ACE are supplementary angles.
For the complete question, check attachment 1.
For reference to the solution, check attachment 2.
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What is the inverse operation of subtract 6?
O A. multiply by 6
O B. add 6
O C. subtract 6
O D. divide by 6
Answers
This Venn diagram shows sports played by 10 students.
Karl
Jada
Gabby
PLAYS
BASKETBALL
O A=0.50
OB. 0.29
OC. =0.40
D.
=0.20
Fran
Juan
lan
Ella
Let event A = The student plays basketball.
Let event B = The student plays soccer.
What is P(AB)?
PLAYS
SOCCER
Mickey
Mai
Marcus
Answers
The conditional probability for this problem is given as follows:
C. P(A|B) = 2/5 = 0.4 = 40%.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
For this problem, we have that 5 students play soccer, and of those, 2 play basketball, hence the conditional probability is given as follows:
C. P(A|B) = 2/5 = 0.4 = 40%.
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g is a trigonometric function of the form � ( � ) = � cos ( � � + � ) + � g(x)=acos(bx+c)+dg, left parenthesis, x, right parenthesis, equals, a, cosine, left parenthesis, b, x, plus, c, right parenthesis, plus, d. Below is the graph of � ( � ) g(x)g, left parenthesis, x, right parenthesis. The function has a maximum point at ( 3.5 , − 4 ) (3.5,−4)left parenthesis, 3, point, 5, comma, minus, 4, right parenthesis and a minimum point at ( − 1 , − 5 ) (−1,−5)left parenthesis, minus, 1, comma, minus, 5, right parenthesis. Find a formula for � ( � ) g(x)g, left parenthesis, x, right parenthesis. Give an exact expression. � ( � ) = g(x)=g, left parenthesis, x, right parenthesis, equals A graph of a trigonometric wave on an x y coordinate plane. The x axis scales by two and the y axis scales by one. There is a point on the graph at the minimum at (negative one, negative five) and a point on the maximum next to the mentioned point at (three and one half, negative four).
Answers
The exact expression for g(x) is 2.25cos((2π/4.5)×(x-3.5)) - 4.
Describe Function?A function can be represented using a formula or an equation, and it can be graphed on a coordinate plane. The input values are typically represented on the x-axis and the output values on the y-axis.
From the given information, we know that the function g(x) has a maximum point at (3.5, -4) and a minimum point at (-1, -5).
The general form of a cosine function is f(x) = A×cos(Bx + C) + D, where A is the amplitude, B is the period, C is the phase shift, and D is the vertical shift.
Since the function has a maximum point at (3.5, -4), we know that the graph has been shifted to the left by 3.5 units. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) + D.
Similarly, since the function has a minimum point at (-1, -5), we know that the graph has been shifted upwards by 1 unit. Therefore, we can write the function as g(x) = A×cos(B(x - 3.5)) - 4.
To determine A and B, we can use the fact that the period of the function is 4.5 units (the distance between the maximum and minimum points). Therefore, we have B = 2*pi/4.5.
To determine A, we can use the fact that the amplitude is half the distance between the maximum and minimum points, which is 0.5*(5-(-4)) = 4.5. Therefore, we have A = 4.5/2 = 2.25.
Substituting these values into the equation for g(x), we have:
g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4
Therefore, the exact expression for g(x) is:
g(x) = 2.25cos((2π/4.5)×(x-3.5)) - 4.
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Identify the quadrant or axis that the following point lies on. If the point lies on an axis, specify which part (positive or negative) of which axis (x ory).
(-2,-5)
Answers
Answer:
Quadrant 3! Hope this helps!
Step-by-step explanation:
The x and y are both negative. Meaning that they will lie on quadrant 3 which both axis in this quadrant are negative.
In 1990, a magazine collected data and published an article evaluating freezers. It listed 45 models, giving the brand, cost (dollars), size (cu ft), type, the ratin
(good, excellent, etc.), and repair history for that brand (percentage requiring repairs over the past 5 years).
Identify the 5 W's.
Who:
What:
When:
Where:
How:
Why:
Answers
Complete question is;
In 1990, a magazine collected data and published an article evaluating dryers. It listed 45 models, giving the brand, cost (dollars), size (cu ft), type, estimated annual energy cost (dollars), an overall rating (good, excellent, etc.), and repair history for that brand (percentage requiring repairs over the past 5 years).
The W's are Who, What, When, Where, Why, and hoW.
1) Identify the Who. Choose the correct answer below.
A. 45 models of dryers
B. Dryers
C. Brands of dryers
D. Size of dryers dryers
2) Identify the What. Choose the correct answer below.
A. Brand, type, overall rating
B. Brand, cost, size, type, estimated annual energy cost, overall rating, repair history
C. Cost, size, estimated annual energy cost, repair history
D. Brand, cost, size, type
3) Identify the When. Select the correct choice below and, if necessary, fill in any answer boxes within your choice.
A. The data were recorded in 1990.
B. The information is not provided.
4) Identify the Where. Choose the correct answer below.
A. The 45 models of dryers
B. The information is not provided.
C. The population of dryers
5) Identify the Why. Choose the correct answer below.
A. To provide information to the magazine's readers
B. To write an article about dryers
C. To compare the size of the dryers
D. To collect information about dryers
6) Identify the hoW. Choose the correct answer below.
A. The different dryers belonged to the magazine's employees.
B. The dryers were chosen at random.
C. The information is not provided.
7) Identify each variable as either categorical or quantitative.
Brand
▼
Categorical
Quantitative
Estimated annual energy cost
▼
Quantitative
Categorical
Cost
▼
Categorical
Quantitative
Overall rating
▼
Categorical
Quantitative
Size
▼
Quantitative
Categorical
Repair history
▼
Quantitative
Categorical
Type
▼
Categorical
Quantitative
8) For each quantitative variable, determine the units in which it was measured.
Cost
▼
Dollars
Not specified
Pounds
Estimated annual energy cost
▼
Dollars
Pounds
Not specified
Size
▼
Cubic inches
Cubic feet
Feet
Inches
Not specified
Repair history
▼
Years
Percentages
Not Specified
Answer:
All answered below.
Step-by-step explanation:
1) Option A: 45 models of dryers
2) Option B: Brand, cost, size, type, estimated annual energy cost, overall rating, repair history
3) Option A: The data were recorded in 1990.
4) Option B: The information is not provided.
5) Option A: To provide information to the magazine's readers
6) Option C. The information is not provided.
7) - Brand variable is Categorical
- Estimated annual energy cost variable is Quantitative
- Cost variable is Quantitative
- Overall rating variable is Categorical
- Size variable is Quantitative
- Repair history variable is Quantitative
- Type variable is Categorical
8) - cost is in dollars)
- estimated annual energy cost is in dollars
- size is in cu. ft
- repair history is in percentages
help please? trying to catch up on math
Answers
do B as it goes up 2 then 3 then it repeated the
(b) the sequence is not arithmatic
This is an urgent matter! Please help!
Answers
Answer:
the answer is c a increasing line
PLEASE ANSWER BOTH QUESTIONS WILL MARK BRAINLIEST
Answers
Answer:
2.24
Step-by-step explanation:
the answer is 2.24
6 second answer is six
Answer:
According to me i think this would be the answer
4. $2.24
5. 6
For each sequence, find the first 4 terms and the 10th term.
a) n2+ 3
...
b) 2n2
...
Answers
Answer:
a) n2+ 3
So, first term is (1)²+3=4
Second term is (2)²+3=7
Third term is (3)²+3=12
Fouth term is (4)²+4=20
b) 2n2
So, first term is (1)²+2=3
Second term is (2)²+2=6
Third term is (3)²+2=11
Fouth term is (4)²+2=18
Answer:
( a )
First 4 terms are 4,7,12,19 and the 10th term is 103.
( b )
First 4 terms are 2,8,18,32 and the 10th term is 200.
Step-by-step explanation:
We are given both general term of sequence:
\( \displaystyle \large{ (a) \: \: \: {n}^{2} + 3} \\ \displaystyle \large{ (b) \: \: \: 2{n}^{2}}\)
Let's get to the first sequence.
( a )
We are given:-
\( \displaystyle \large{ {n}^{2} + 3} \)
To find first 4 terms, substitute n = 1,2,3,4 in.
Therefore:-
\( \displaystyle \large{ {1}^{2} + 3 = 4} \\ \displaystyle \large{ {2}^{2} + 3 = 4 + 3 = 7} \\ \displaystyle \large{ {3}^{2} + 3 = 9 + 3 = 12} \\ \displaystyle \large{ {4}^{2} + 3 = 16 + 3 = 19} \)
Therefore, first 4 terms are 4,7,12,19.
Next, to find the 10th term, just substitute n = 10.
\( \displaystyle \large{ {10}^{2} + 3 = 100 + 3 = 103} \)
And we're done for part a!
( b )
We are given:-
\( \displaystyle \large{ 2{n}^{2}}\)
Do the same, substitute n = 1,2,3,4 in.
\( \displaystyle \large{ 2({1})^{2} = 2} \\ \displaystyle \large{ 2({2})^{2} = 2(4) = 8} \\ \displaystyle \large{ 2({3})^{2} = 2(9) = 18} \\ \displaystyle \large{ 2({4})^{2} = 2(16) = 32}\)
Therefore, first 4 terms are 2,8,18,32.
Next, find the 10th term, substitute n = 10 in.
\( \displaystyle \large{ 2{(10)}^{2} = 2(100) = 200} \)
Thus, the 10th term is 200.
Elan surveyed a random sample of 65 students at his high school. He asked them which subject is their first class on Mondays. There are 894
students in his school.
First Class Percent of Students
English
17%
Math
28%
History
40%
Science
15%
Choose two inferences that can be made from the results.
A. Approximately 17% of all students in the city have English first on Mondays.
B. Approximately 28% of the students at Elan's school have Math first on Mondays.
O c. Approximately 40% of the students at Elan's school do not have History first on Mondays.
D. Approximately 85% of the students at Elan's school do not have Science first on Mondays.
Answers
Answer:
b and d
Step-by-step explanation:
Answer:
B and D
Step-by-step explanation:
I have done the MAPS Testing
1 · 3.2 = d
i need the answer now
Answers
Answer:
d = 3.2
Step-by-step explanation:
1 * 3.2 = 3.2
Hence,
d = 3.2
Find the coefficients of the polynomial with a leading coefficient of: one, and roots: zero, nine, and nine.
x^3+__x^2 +81x+__
Answers
\(zeros \begin{cases} x=0\implies &x=0\\ x=9\implies &x-9=0\\ x=9\implies &x-9=0 \end{cases}\qquad \implies a(x)(x-9)(x-9)=\stackrel{y}{0} \\\\\\ \stackrel{\textit{with a coefficient of 1}}{1(x)(x-9)(x-9)=y}\implies x(x-9)^2=y\implies x(x^2-18x+81)=y \\\\\\ ~\hfill {\Large \begin{array}{llll} x^3-18x^2+81x=y \end{array}}~\hfill\)
If every 1 in 20 plants will not bear fruit. If 200 plants are planted, how many will produce fruit?
Answers
Answer:
Step-by-step explanation:
If 1 /20 will not bear fruit then
19/20. Will bear fruit
use ratio method
19/20 = x/200
find x by finding an equivalent fraction
x = 190
190 plants will produce fruit
What is the area of the triangle?
Answers
Answer:
10
Step-by-step explanation:
1/2×(-2-(-7))×(6-(-4))
Which expression is equal to 2
-
6?
Answers
Answer:
-4
Step-by-step explanation:
-4 will equal the expression 2 - 6.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
In other meaning, subtraction is a mathematical operation such that two values are going to subtract and give a resultant value.
The group's total number of items decreases or becomes lower when we subtract from it.
Given the expression,
⇒ 2 - 6
⇒ -4
Hence "-4 will equal the expression 2 - 6".
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sharmila recived 81 texts in 9 minutes
Answers
Answer:
Step-by-step explanation:
81 texts in 9 hours
So you do 81 divided by 9
Which givrs you 9 text an hour
6)
Evaluate the expression.
2(4 + 3)
A)
1
B)
2
C)
4
D)
14
Answers
Answer: It's 14
Step-by-step explanation:
Okay, so we need to follow PEMDAS, or Parenthesis, Exponents, Multiplication and Division, Addition and Subtraction. First we solve what's in the parenthesis. 4 plus 3 is 7. There are no exponents, but there IS multiplication. Whenever you see a number next to an expression inside parenthesis, it always means multiply. In this case we're multiplying 4 plus 3, which is 7, by 2. So 7 times 2 is 14.
Please help just need to finish this class and I graduate thanos in advance
Answers
definition of a tangent?
Answers
Answer:
A tangent is a line that touches the curve or a circle at a point..
Subtract 4x + 6 from 7 + 2x?
Answers
Answer:
1-2x
Step-by-step explanation:
\((7+2x)-(4x+6)=7+2x-4x-6=1-2x\)
Aladder that has a length of 13 m leans against a wall with the base of the ladder 5 m away from the bottom of the wall
Answers
Answer:
3.3m
Step-by-step explanation:
A rectangle with a perimeter of 40 inches has a width that is 3 times the length. What is the length And the width
Answers
The Length is 5 inches and the Breadth is 15 inches
What is Perimeter?
A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter.
Solution:
Perimeter of Rectangle = 2*(Length + Breadth)
According to the question
Breadth = 3*Length
Perimeter = 40
40 = 2*(Length + 3*Length)
20 = 4*Length
Length = 5 inch
Breadth = 15 inch
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