If sinθ⋅cosθ = 1/2, then the value of sinθ + cosθ = √2
We know that the trigonometric sine function is nothinng but the ratio of the length of the opposite side of angle to that of the hypotenuse in a right triangle.
And cosine function (cos function) is the ratio of the length of the adjacent side of angle to that of the hypotenuse.
Given that sinθ⋅cosθ = 1/2
2(sinθ⋅cosθ) = 1 .........(1)
We know that trigonometric identity,
sin(2θ) = 2 sinθ cosθ
so equation (1) becomes,
sin(2θ) = 1
We know that sin(π/2) = 1
Comparing with equation sin(2θ) = 1 we get,
2θ = π/2
θ = π/4
Using trigonometric table,
sin(π/4) = 1/√2
and cos(π/4) = 1/√2
The value of sinθ+cosθ would be,
sin(π/4) + cos(π/4)
= (1/√2) + (1/√2)
= 2/√2
= √2
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The complete question is:
If sinθ⋅cosθ=1/2 find the value of sinθ+cosθ
16. 2m² +13m +20
factor each trinomial
So, (2m + 4)(m + 5) is the factored form of 2m² +13m +20.
Define Factorial.The factorial of a non-negative integer n, represented by n! is the product of all positive integers less than or equal to n. It is the mathematical operation that is applied to a non-negative integer.It is also used in many areas of mathematics, including calculus and number theory, as well as in many areas of science, including physics, chemistry, and computer science.
What is variables and constants ?A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.
To factor a trinomial of the form "ax² + bx + c," we can use the following steps:
First, we need to determine two numbers that multiply to give us "c" and add to give us "b." In this case, the two numbers are 4 and 5 because 4 x 5 = 20 and 4 + 5 = 9, which is equal to "13m".
Next, we can factor the trinomial into the form (ax + b)(cx + d) by grouping the middle term and the constant term together.
So, the factored form of the trinomial is (2m + 4)(m + 5)
So, (2m + 4)(m + 5) is the factored form of 2m² +13m +20.
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EMERGENCY NEED HELP PLEASE HELP THE QUESTION IS ATTACHED TO THE QUESTION THING PLEASE HELP!!!
The required graph of the system of linear equations has been attached below.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The system of linear equations is given in the question, as follows:
2x + y = 8 .....(i)
-x + 2y = 6 .....(ii)
To graph the equations using the slope and y-intercept,
1) To determine the slope m and the y-intercept, write the equation in the form y = mx + b. (0, b).
Plot the y-intercept next.
3) Depending on whether the slope is positive or negative, go up, down, or left or right from the y-intercept.
Thus, the required graph of the system of linear equations.
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Select the correct answer.
Use the quadratic formula to solve the equation below.
x ( x + 16) = -64
Answer:
x = -8 (10
Step-by-step explanation:
x (x + 16) = -64
-8(10 + 16) = -64
-80 + 16 = -64
-64 = -64
In a random sample of 70 people, it was found that 44 of them were fans of the New York Yankees. What is the margin of error for the true proportion of all individuals who are fans of the New York Yankees? A. 0.0088 B. 0.058 C. 0.063 D. 0.116 E. 0.173
The margin of error for the true proportion of all individuals who are fans of the New York Yankees is 0.058.
The Correct option is (B).
How to find the margin of error?The formula to calculate the margin of error for the true proportion is;
M = √[p(1 - p)/n]
Given:
n= 40
p = 44/70
Now, The general formula for the margin of error would be:
z x √[p (1-p) ÷ n]
where:
z = values for selected confidence level
p = sample proportion
n = sample size
Since the confidence level is not given,
√[p (1-p) ÷ n]
=√[44/70 (1 - (44/70) ÷ 70]
=√[0.6286 (0.3714)] ÷ 70
=√0.2335 ÷ 70
= √0.0033357
= 0.05775 or 0.058
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An isosceles trapezoid has a perimeter of 38 ft and a leg measuring 8 ft. A similar trapezoid has a leg measuring 3ft. Find its perimeter.
The perimeter of a trapezoid is 28ft.
An isosceles trapezoid is a trapezoid whose non-parallel sides (the legs) are equal in length.
The perimeter of an isosceles trapezoid (P) = a + b+ 2c
where a is the top, b is the bottom, and c is the leg of the trapezoid
According to the question,
perimeter = 38ft
leg of an isosceles trapezoid = 8ft
38 = a +b +2 × 8
⇒ 38 = a+b +16
⇒a +b = 38 -16
⇒a +b = 22
Another similar trapezoid has a leg measuring 3ft.
Perimeter of this trapezoid is =( 22 + 2× 3) ft
= (22 +6)ft
= 28 ft
So, the perimeter of a trapezoid is 28ft.
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A machine makes 12 articles in half an hour.
How many articles will it make in 6 hours?
Answer:
144
I wish you luck in your assignments.
Answer: 144 articles
Step-by-step explanation:
If it makes 12 in half-hour, then 24 in an hour because 12*2 is 24.
then 24*6=144.
How do you identify the solutions in solving linear inequalities in two variables *?
To identify the solutions in solving linear inequalities in two variables, you can first graph the equation on a coordinate plane. Then, you can use the boundary line to identify which regions of the plane satisfy the inequality.
Any points in the shaded regions will be solutions to the inequality. Additionally, you can use the boundary line to identify the points that are not solutions by finding the points that lie on the boundary line.
Example:
x + 2y ≥ 4
The graph of this inequality is a line with a slope of -2/1 and a y-intercept of 4/2. The line will be shaded on the side of the line containing the greater values, which in this case is the side containing the origin.
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(01.03 MC)
The Kelly school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table below, where Min represents the fewest days attended and Max represents the most days attended for a single student:
School
Min
Max
Range
Mean
Median
IQR
σ
High School M
128
180
52
141
160
55.5
41.5
High School N
131
180
49
159
154
48.5
36.5
High School P
140
180
40
153
165
32.5
31.5
Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. (5 points)
Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically. (5 points) (10 points)
Answer:
a: School W is has the most consistent attendance
b: School W has the highest average attendance
Step-by-step explanation:
For a:
The most consistent school will be the school whose data has the smallest variance. *Consistent doesn't mean the best, it's just the least differing among it's own data. The variance tells us how spread out the data is, so the school with the smallest variance is the most consistent.
See photo 1 for the calculations of the variances of each school...
For b:
Take the mean for each school. Whichever has a higher value is the school with the highest average.
See photo 1 for the calculations if the means for each school. (the mean is used to calculate variance, so we will do this part first)
Someone please answer... In 2010, the population of a city was 59,000. From 2010 to 2015, the population grew by 7.3%. From 2015 to 2020, it fell by 5.3%. To the nearest whole number, by what percent did the city grow from 2010 to 2020?
Radicals help please
Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.
Describe fraction.Components of fractions are the numbers in the numerator and denominator (and ratios). The denominator, which is the smallest number, represents the greatest possible number of parts that can be put together to create a whole. You can tell how many parts you have by looking at the numerator, which is the greatest number. It might not be the whole thing! If the denominator is 0, that is bad. Division by zero is prohibited. If the denominator is a 1, our fraction is actually an integer.
Here,
we can rationalize a radical-containing fraction's denominator by doing the following:
Step 1: In order to eliminate the radical from the denominator, multiply the numerator and denominator by a radical.
Verify in step two that all radicals have been streamlined.
Step three is to simplify the fraction, if necessary.
Therefore, we can rationalize the denominator of a fraction containing a radical by taking the methods outlined above.
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solve the inequality and explain how
thank you :)
Answer:
the answer is A
[tex]x + 7 > 3[/tex]
a) which group has lower mode.
b) what is this mode?
The easiest way to determine the mode of any data set, is to figure out which number appears most frequently, or most common.
You can take all of the numbers and count how many times each number appears. The number that appears the most is called the mode.
In the first pie chart (Group A), we can see that the orange piece is the biggest, therefore the most common. The orange piece has equal value to 4.
In the next group (Group B), we can determine the mode by looking at the highest bar, which would be 5.
4 is less than 5, which means that the answer to this question would be Group A.
Even more geometry stuff pls help
Answer:
[tex]z=\frac{25}{3}[/tex]
Step-by-step explanation:
Using the Pythagorean theorem, the length of the altitude to the hypotenuse is [tex]\sqrt{5^2-3^2}=4[/tex].
Using the geometric mean theorem,
[tex]4^2=3(z-3) \\ \\ 16=3z-9 \\ \\ 25=3z \\ \\ z=\frac{25}{3}[/tex]
What is the degree of 2 polynomial?
A polynomial with a degree of two is referred to as a quadratic polynomial.
What is a quadratic polynomial?When the highest power of a variable term in a polynomial expression equals 2, the term is considered a quadratic polynomial. The exponent of a polynomial is all that is considered when determining its degree. It does not account for the power of a coefficient or constant term.
When a quadratic polynomial is equated to 0, it generates a quadratic equation or a quadratic function. The solutions to a quadratic equation are known as its roots or zeros.
A quadratic polynomial is a second-degree polynomial with the highest degree term having the value 2 as its coefficient. A quadratic equation is written in its general form as ax² + bx + c = 0.
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A circle is the set of all points that are the same distance from one given point. Find an example that contradicts this definition. How would you change the definition to make it more accurate?
An example that contradicts this definition would be an ellipse that set all points such that the sum of the distances between the point and two other fixed points (called foci) is constant.
What is the equation of a circle?The equation of a circle with center (h,k) and radius r is :
r² = (x−h)² + (y−k)²
A circle is defined as the set of all points that are the same distance from one given point, called the center of the circle. An example that contradicts this definition would be an ellipse, which is defined as the set of all points such that the sum of the distances between the point and two other fixed points (called foci) is constant.
An ellipse is not a circle since all points of an ellipse are not equidistant to the center point
To make the definition more accurate, it could be modified to say "A circle is defined as the set of all points that are a fixed distance from one given point, called the center of the circle." or "A circle is defined as the set of all points such that the distance between the point and the center is constant"
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distance of -6,8 and 1,7
Answer:
d ≈ 7.07 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 6, 8 ) and (x₂, y₂ ) = (1, 7 )
d = [tex]\sqrt{((1-(-6))^2+(7-8)^2}[/tex]
= [tex]\sqrt{(1+6)^2+(-1)^2}[/tex]
= [tex]\sqrt{7^2+1}[/tex]
= [tex]\sqrt{49+1}[/tex]
= [tex]\sqrt{50}[/tex]
≈ 7.07 units ( to 2 decimal places )
Write the following using index notation:
2 x 2 x 2
b) 3x3
3 x 3
c)
6 x 6 x 6 x 8 x 8 x 8
d)
3 * 4 * 3 x 4 * 3
Index notations are as follows:
a) 2³
b) 3²
c) 6³ * 8³
d) 3³ * 4²
What are Exponents?A number's exponent demonstrates how many times we are multiplying a given number by itself. 3^4, for instance, indicates that we are multiplying 3 by four. 3*3*3*3 is its expanded form. The power of a number is another name for an exponent. A whole number, fraction, negative number, or decimal are all acceptable.
Let's break down the given index notation one by one:
a) 2 is taken 3 times = 2³
Similarly,
b) 3²
c) 6³ * 8³
d) 3³ * 4²
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A mum of 5 children has truncated her children’s heights in metres to 2 decimal places, and written them down in the table on the left.
a) Write down the intervals within which each child’s actual height lies.
b) Write down the minimum and maximum height difference between the tallest and shortest child.
Answer:
d
Step-by-step explanation:
Why is 3 a polynomial?
A variable has a degree of zero and no exponent. Each constant polynomial has a degree of zero.
A polynomial is what?A polynomial only uses addition, subtraction, multiplication, and non-negative integer exponentiation of the variables as its operations. In mathematics, the term "indeterminate" is frequently used to describe variables. A polynomial is an equation that combines variables, constants, and exponents while using addition, subtraction, multiplication, and division of numbers (No division operation by a variable).
A variable has no exponent, the degree is 0. The degree of each constant polynomial is zero .
Since 3 can be expressed as [tex]3 X 0[/tex] and is a constant polynomial, it has a degree of [tex]0[/tex].
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Jessica and Josh are selling entertainment books to raise money for the art room after school one book sells for $18 Jessica receive the prize for selling the most books in the school Jessica sold 13 times more books than Josh together they sold 280 books how many did each of them sell
Based on the question above, Jessica sold 260 books and Josh sold 20 books.
What is the math equation about?Let x be the number of books Josh sold
We know that:
Jessica sold 13x books
Together they sold 280 books
So we can set up an equation:
x + 13x = 280
14x = 280
x = 20
Josh sold 20 books
Jessica sold 13 * 20 = 260 books
Therefore Jessica = 260 books sold and Josh = 20 books sold.
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HELPPPPPP PLEASEeeeeeeeeeeeeee
it is this answer x≥
3
8
I don't know the step by step solution
Please help! Determine the coordinates of the transformation and plot the image for Rx Axis of the triangle ABC
Answer:
Step-by-step explanation:HI
You got answer already?
Just , look down as in rectangle A" (-6,1)
B"(-1,-3)
C"(-4, 4)
And you have wrong coordinates for C (-4,-4)
All 210 students in a school went roller skating, to a water park, or both. The number of students who went only to the water park is four times the number of students who went only roller skating. The number of students who went only to the water park is two times the number of students who did both. How many students did both?
60 students out of 210 in a school went both roller skating and water park.
What is algebraic equation ?
The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
Have given ,
Total students = 210
Let x = The number of students who went only to the roller skating
and y = The number of students who went to the water park and roller skating
x + 4x + y = 210 ⇒ 5x + y = 210 ......(i)
x + y + 2y = 210 ⇒ x + 3y = 210 ⇒ x = 210 - 3y
Put the value of x in equation no. (i),
5(210 - 3y) + y = 210 ⇒ 1050 - 14y = 210 ⇒ 14y = 1050 - 210
14y = 840 ⇒ y = 60
Hence , 60 students out of 210 in a school went both roller skating and water park.
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How do you solve a 30 60 90 right?
Remembering the ratio of 1: 3: 2 and understanding that the smallest side length is always opposite the shortest angle (30°) and the longest side length is always opposing the greatest angle (90°) can help you recall the 30-60-90 triangle principles.
A 30-60-90 triangle can have three sides, and if you only know one, you can use shortcuts to discover the other two. The three scenarios you encounter when performing these computations are as follows:
You are aware of the short leg (the side across from the 30-degree angle). To determine the hypotenuse, multiply the length by two. The long leg may be calculated by multiplying the short side by the square root of 3.You are aware of the hypotenuse. To get the short side, divide the hypotenuse by two. To determine the long leg, multiply this response by the square root of 3.You are aware of the long leg (the side across from the 60-degree angle). To determine the short side, divide this side by the square root of 3. To determine the hypotenuse, multiply that amount by two.To know more about the 30-60-90 triangle on brainly : brainly.com/question/11751274
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whats an=19-7(n-) in function form
The given expression is the explicit equation for arithmetic progression whose first term is 19 and the common difference is -7.
What is arithmetic progression?Arithmetic progression is the series of numbers that have common differences between adjacent values.
here,
Given expression,
an=19-7(n-1)
The above-given expression is an explicit formula for the arithmetic progression,
Comparing the given expression with general expression an = a + d[n-1]
From the above comparison, we
first term,a = 19 and
the common difference, d = -7
Thus, the given expression is the explicit equation for arithmetic progression whose first term is 19 and the common difference is -7.
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How do you calculate undefined FG?
To calculate undefined FG, subtract the original gravity (OG) from the final gravity (FG) of the beer. This will give you the amount of sugar that has been fermented and, therefore, the amount of alcohol produced. The formula is:
Undefined FG = OG – FG
In order to calculate the undefined FG of a beer, the original gravity (OG) and the final gravity (FG) of the beer must first be determined. The OG is a measure of the sugar content of the wort before fermentation, while the FG is a measure of the sugar content of the beer after fermentation. To calculate the undefined FG, the OG is then subtracted from the FG. This calculation provides the amount of sugar that has been fermented by the yeast, and therefore the amount of alcohol produced. This calculation is important for brewers, as it provides a quick and easy way to determine the ABV of a beer. In addition, the undefined FG can be used as a measure of the fermentation efficiency of the yeast, as a higher undefined FG indicates that more sugar has been fermented than a lower undefined FG. Understanding the undefined FG of a beer can help brewers make informed decisions about their brewing process and the quality of their beers.
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Bautista is planning a vacation to Los Angeles. He already has $42.50 and saves $25.50 each week. If the trip will cost a total of $654.5, how many weeks will it take for him to save for the trip?
Answer:
24 WEEKS
BECAUSE IF U MULTIPLY 24X25.50 U WILL GET 612 ADD 42.50 AND U WILL GET 654.50
A bottle of water is 2/3 full. You drink 1/2 of the water. find the portion of the bottle of water that you drink.
Jorge’s family is taking a car trip to see his grandmother. The family plans to spend 3 days on the road. The distance is 687 miles. About how far must they drive each day?
The areas of the squares adjacent to two sides of a right triangle are 29.2529.2529, point, 25 units^2 2 squared and 131313 units^2 2 squared. 13\text{ units}^213 units 2 29.25\text{ units}^229.25 units 2 xx Find the length, xxx, of the third side of the triangle.
Using the Pythagoras Theorem the third side c of the right-angled triangle is obtained as 6.5 units.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The data given is -
Assume a, b and c are sides of right-angled triangle.
Then, two adjacent sides of right-angled triangle are -
a^2=29.25 squared units
b^2=13 squared units
The unknown side c is taken to be x.
Find the length of c using Pythagoras Theorem -
c^2=a^2+b^2
where, c is the hypotenuse, a is the perpendicular and b is the base.
Plugging the values in the equation -
x^2=29.25+13
x=√(29.25+13)
x=√42.25
x=6.5
Therefore, the third side measures x=6.5 units.
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