[tex]\displaystyle\\Answer:\theta=\frac{\pi }{2}+\pi n.[/tex]
Step-by-step explanation:
[tex]\displaystyle\\7*cosec^2\theta-9*cot^2\theta=7\\7-7*cosec^2\theta+9*cot^2\theta=0\\7-\frac{7}{sin^2\theta}+9*\frac{cos^2\theta}{sin^2\theta} } =0\\\frac{7*sin^2\theta-7+9*cos^2\theta}{sin^2\theta} =0\\\frac{-7*(1-sin^2\theta)+9*cos^2\theta}{sin^2\theta} =0\\\frac{-7*cos^2\theta+9*cos^2\theta}{sin^2\theta} =0\\\frac{2*cos^2\theta}{sin^2\theta}=0\\[/tex]
[tex]2*cot^2\theta=0\\Divide\ the\ right\ and\ initial\ parts\ by\ 2:\\cot^2\theta=0\\cot\theta=0\\\theta=\frac{\pi }{2}+\pi n\ \ \ (n=0,\ 1,\ 2,\ 3\ ...).[/tex]
PLEASE HELP ITS MATH PLEASE
Answer:
y=[4]x + [12]
Step-by-step explanation:
Remember that parallel lines have identical slopes; and to make a line which passes through a point we will use point-slope form.
Familiarize yourself with point-slope form:
[tex]y-y1=m(x-x1)[/tex]
If the line is parallel to [tex]y=4x+11[/tex] the slope must be 4.
[tex]y-y1=4(x-x1)[/tex]
And we know the point it must pass through is (-2,4), so we can fill those values in too.
[tex]y-4=4(x+2)[/tex]
Now all we have to do is solve for y:
[tex]y-4=4(x+2)\\y-4=4x+8\\y=4x+12[/tex]
Answer:
[tex]y = 4x + 12[/tex]
Step-by-step explanation:
The solution is in the attached image
Mrs. kelley asked her students to plot the number of books they read over the summer. a dot blot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots. using the dot plot, what was the total number of students that plotted the number of books they read? 3 6 17 18
The total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.
Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots indicates the numerical value of each variable, it is comparable to a bar graph or a simple histogram. Small amounts of data are shown using dot plots.
In the question, we are informed that Mrs. Kelley asked her students to plot the number of books they read over the summer. a dot plot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots.
We are asked to find the total number of students that plotted the number of books they read using the dot plot.
The dot plot is attached to the solution.
The total number of students = The total number of dots = 1 + 3 + 6 + 2 + 3 + 1 + 2 + 0 = 18.
Thus, the total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.
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the length of a new rectangular playing field is 3 yards longer than quadruple the width. if the perimeter of the rectangular playing field is 586 yards, what are its dimensions?
Answer:
length = 235 yd
width = 58 yd
Step-by-step explanation:
Let the width be W.
L = 4W + 3
perimeter = 2(L + W)
perimeter = 2(4W + 3 + W)
perimeter = 2(5W + 3) = 10W + 6
We are told the perimeter = 586 yd
10W + 6 = 586
10W = 580
W = 58
L = 4W + 3 = 4(58) + 3 = 232 + 3 = 235
length = 235 yd
width = 58 yd
3x 5y = 78 2x - y = 0 the point of intersection of the lines has an x-coordinate of _____. 78 6 -6
The supplied lines' point of intersection has the x coordinate is 6.
What is coordinate geometry?A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more numbers, or coordinates.
The x coordinate of the location where the ensuing lines intersect must be chosen.
3x + 5y = 78 ...........................(1)
2x - y = 0 ...............................(2)
The given system of equations must be solved in order to determine the x coordinate of the site of intersection.
Equation (ii) provides us with
2x = y
y = 2x ........................(3)
Equation I yields the result when the value of y from equation (iii) is substituted.
3x + 5(2x) = 78
3x + 10x = 78
13x = 78
x = 78/13
x = 6.
As a result, the supplied lines' point of intersection has the x coordinate 6.
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I understand that the question you are looking is :
3x 5y = 78 2x - y = 0 the point of intersection of the lines has an x-coordinate of _____.
A. 7
B.8
C. 6
D. -6
The population of a country was increased in the past 4 years. The annual presentage increases are 20%,25%,30%,10% respectively.What the overall percentage increase in these 4years?
The answer is 114.5%.
Let the original population be denoted by x.
Now, let's go through the percentage increase per year.
Year 1
x (1 + 20%)x (1.2)1.2xYear 2
1.2x (1 + 25%)1.2x (1.25)1.5xYear 3
1.5x (1 + 30%)1.5x (1.3)1.95xYear 4
1.95x (1 + 10%)1.95x (1.1)2.145xOverall increase : 214.5% - 100% = 114.5%
Hence, the overall percentage increase in these 4 years is 114.5%.
How many solutions does the equation a+b+c+d+e+f=2006. They are positive integers. Your FINAL answer should be in the form x!/x!•x!, where x is a placeholder
The number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16
How to determine the number of solutions?The equation is given as:
a+b+c+d+e+f = 2006
In the above equation, we have:
Result = 2006
Variables = 6
This means that
n = 2006
r = 6
The number of solutions is then calculated as:
(n + r - 1)Cr
This gives
(2006 + 6 - 1)C6
Evaluate the sum and difference
2011C6
Apply the combination formula:
2011C6 = 2011!/((2011-6)! * 6!)
Evaluate the difference
2011C6 = 2011!/(2005! * 6!)
Expand the expression
2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006 * 2005!/(2005! * 6!)
Cancel out the common factors
2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/6!
Expand the denominator
2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/720
Evaluate the quotient
2011C6 = 9.12 * 10^16
Hence, the number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16
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Answer:
210 = 6!/1!•1!•1!•1!•1!•1!
Step-by-step explanation:
We can use the stars and bars method to solve this problem. Imagine we have 2006 stars and we want to distribute them among 6 bins (a, b, c, d, e, and f). We can represent the stars as follows:
... * (a stars)
| * * * ... * (b stars)
| | * * * ... * (c stars)
| | | * * * ... * (d stars)
| | | | * * * ... * (e stars)
| | | | | * * * ... * (f stars)
The bars divide the stars into 6 bins, and the number of stars in each bin represents the value of the corresponding variable (a, b, c, d, e, or f).
To ensure that each variable is a positive integer, we can add 1 to each variable and distribute the remaining stars. For example, if we add 1 to a, b, c, d, e, and f, the equation becomes:
(a+1) + (b+1) + (c+1) + (d+1) + (e+1) + (f+1) = 2012
Now we have 6 stars and 5 bars, and we can use the stars and bars formula to find the number of solutions:
Number of solutions = (6+5-1) choose (5-1) = 10 choose 4 = 210
Therefore, the equation a+b+c+d+e+f=2006 has 210 positive integer solutions.
Expressing the answer in the form x!/x!•x!, we have:
210 = 6!/1!•1!•1!•1!•1!•1!
The stars and bars formula:The stars and bars formula is a combinatorial formula that allows us to count the number of ways to distribute identical objects into distinct groups.
Suppose we have n identical objects and k distinct groups. We can represent the objects as stars and the groups as bars. For example, if we have 7 objects and 3 groups, we can represent them as:
| | |
The bars divide the 7 stars into 3 groups, and the number of stars in each group represents the number of objects in that group.
The stars and bars formula tells us that the number of ways to distribute n identical objects into k distinct groups is:
(n+k-1) choose (k-1)
where "choose" is the binomial coefficient. This formula can be derived using a technique called "balls in urns" or by using generating functions.
In the example above, we have n = 7 objects and k = 3 groups, so the number of ways to distribute the objects is:
(7+3-1) choose (3-1) = 9 choose 2 = 36/2 = 18
Therefore, there are 18 ways to distribute 7 identical objects into 3 distinct groups.
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I don't get the minutes part
Alex travels 46
miles per hour for
3.2 hours. How far
has he gone?
Answer: 147.2 miles
Step-by-step explanation:
We can answer this by knowing the formula [tex]speed=\frac{distance}{time}[/tex]. Here, the speed is 46 miles/hour and the time is 3.2 hours. Let's put these values into the formula and solve for distance.
[tex]46=\frac{distance}{3.2}\\46*3.2=\frac{distance}{3.2}*3.2\\d=147.2[/tex]
Alex traveled 147.2 miles.
Match the key features of functions terms to their corresponding definitions.
The key features of the above given functions are correctly matched to their corresponding definition.
Definition of termsNegative sections of the graph: They are the parts where the graph is below the x-axis. That is option C.End behaviour: This is what happens to the graph on the far left or far right. That is option E.Positive sections of the graph: This is the parts where the graph is above the x-axis. That is option D.Intercepts: This is the points where the graph crosses an axis. That is option BRelative extrema: This is the points of relative minimum or maximum in a graph. That is option A.Learn more about graphs here:
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Gareth pays $ 60 for 9 m of climbing rope. how much will sophie pay for 15 m at the same store? $
Sophie will pay money equivalent to $ 100 for 15 m at the same store.
The term "money" in mathematics refers to a form of payment, such as bills, coins, and demand deposits, that is used to purchase goods and services. Money is used to pay for the worth or price of an item or service.
A country's monetary system is referred to as its currency.
In the case of Gareth,
Money paid for 9 m of climbing = $ 60
Money paid per m of climbing = $ 60/9
Thus, money paid by Sophie for 15 m of climbing = 15 * 60/9
= $ 100
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How many solutions, in positive integers less than 10, does the equation x + y + z = 20
have?
[tex]\huge \mathbb{ \underline{EXPLANATION:}}[/tex]
Given:▪ [tex] \bold{\: x + y + z = 20}[/tex]
[tex]\\[/tex]
◆ As we have a [tex]\small\bold{sum \: of \: three \: integers}[/tex] equal to 20 and less than 10, we know the integers have to be between 2 and 9 (1 and 0 don't apply because the sum wouldn't be equal to 20 between three integers.
[tex]\large\tt{Note:}[/tex]
The first value would be X value, second Y value and third Z value.
[tex]\huge \mathbb{ \underline{ANSWER:}}[/tex]
[tex] \large\boxed{ \sf 36 \: solution}[/tex]
PLLLLEASE ASAP GUYS PLEASEE OMG
Answer:
27/30
Step-by-step explanation:
9/10 x3 to both sides = 27/30
Answer:
[tex]\dfrac{27}{30}[/tex]
Explanation:
In a normal fraction such as [tex]\frac{a}{b}[/tex], a is the numerator and b is the denominator.
Here the given fraction is [tex]\frac{9}{10}[/tex], to rewrite the fraction with a denominator of 30. Multiply both the numerator and denominator by 3.
[tex]\rightarrow \dfrac{9}{10}[/tex]
[tex]\rightarrow \dfrac{9\:\times\:3}{10 \:\times \: 3}[/tex]
[tex]\rightarrow \dfrac{27}{30}[/tex]
Both the fractions are equivalent to each other.
Given u=(-12,-5) and v=(3,9) what is proj v u?
[tex]\frac{(-12)(3)+(-5)(9)}{3^2 + 9^2} \langle 3, 9 \rangle \\ \\ =-\frac{9}{10} \langle 3, 9 \rangle \\ \\ =\langle -\frac{27}{10}, -\frac{81}{10} \rangle[/tex]
So, the correct answer is Option 1.
Find the area of the irregular figure.
6 in.
13 in.
12 in.
5 in.
4 in.
4 in.
A = [? ]in.² please explain why or how you got the answer for future questions I only have so many points
Answer:
153 in²
Step-by-step explanation:
Area of irregular figure[tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]
[tex]\sf \boxed{\text{\bf Area of square = side *side}}[/tex]
Figure I:
length = 12 in
width = 6 in
Area of figure I = 12 * 6
= 72 in²
Figure II:
length = 13 in
width = 5 in
Area of figure II = 13 * 5
= 65 in²
Figure III:
side = 4 in
Area of figure III = 4 * 4
= 16 in²
Area of irregular shape = 72 + 65 + 16
= 153 in²
Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) sin theta = 1/2 Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.) cos theta = -1
The solution of the given equation is :
cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ
cosθ = -1 when θ = π + 2kπ
Since cos2θ + sin2θ = 1, sin2θ = 1 - cos2θ
So, the given equation is equivalent to 2(1 - cos2θ) - cosθ = 1
-2cos2θ - cosθ + 1 = 0
2cos2θ + cosθ - 1 = 0 (multiplying the entire equation by -1)
(2cosθ - 1)(cosθ + 1) = 0 (taking common)
cosθ = 1/2 or cosθ = -1 (on equating it to zero)
cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ
cosθ = -1 when θ = π + 2kπ
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Which of the graphs below represents the equation 8x-y=-4?
Answer:
Graph X
Step-by-step explanation:
First, convert the equation into slope-intercept form. The first step is the bring the x to the right side by subtracting 8x from both sides: -y=-8x-4. Now multiply both sides by -1: y=8x+4. Now, if you know about the slope-intercept form, you'll know that 4 is the y-intercept and that [tex]\frac{8}{1}[/tex] is the slope. 8 is the rise and 1 is the run, so the answer is graph X.
Select the correct answer.
What is the approximate measure of exterior angle B in the polygon?
Answer:
C
Step-by-step explanation:
the sum of the exterior angles of a polygon = 360°
sum the 4 exterior angles and equate to 360
8x + 9x + 5 + 5x + 4 + 9x + 3 = 360 , that is
31x + 12 = 360 ( subtract 12 from both sides )
31x = 148 ( divide both sides by 31 )
x ≈ 11.23 ( to 2 dec. places )
then exterior angle at B is
9x + 3 = 9(11.23) + 3 ≈ 104° → C
The approximate measure of exterior angle B in the polygon is 104° option (C) is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
A polygon is given in the picture with angle measures.
As we know,
The sum of the exterior angles of a polygon = 360°
8x + 9x + 5 + 5x + 4 + 9x + 3 = 360
31x + 12 = 360
31x = 148
x ≈ 11.23
= 9x + 3 = 9(11.23) + 3
≈ 104°
Thus, the approximate measure of exterior angle B in the polygon is 104° option (C) is correct.
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Please help me if you can
The time, t in seconds that it takes a car to travel a quarter-mile when starting from a full stop can be estimated by using the formula:
[tex]t=5.825\sqrt[3]{w/p}[/tex]
Where w = weight of the car
p = power delivered by the engine in horsepower (hp)
If the quarter-mile time for a 3,590-pound car is 13.4 s, how much power does its engine deliver? Round to the nearest pound.
Two students solved this problem. Natasha’s answer was 295 hp and Daniel’s was 679 hp. Why was Daniel wrong? Show each step that led Daniel to the wrong answer
Step-by-step explanation:
Plug in known values
[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]
Divide both sides by 5.825
[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]
Cube both sides
[tex]12.1738 = \frac{3590}{P}[/tex]
Multiply both sides by P
[tex]12.1738P = 3590[/tex]
Divide both sides by 12.1738
[tex]P = 294.895[/tex]
Round to nearest hp
[tex]P = 295[/tex]
So if you look at the radical, it's possible for it to be mistake for a square root, and not a cube root. This was Daniels mistake, so his steps were
[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]
Divide both sides by 5.825
[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]
Square both sides
[tex]5.29197 = \frac{3590}{P}[/tex]
Multiply both sides by P
[tex]5.29197P = 3590[/tex]
Divide both sides by 5.29197
[tex]p\approx 678.385[/tex]
He also probably rounded during his steps, which would explain how he got 679 instead of 678 when rounding in the final, but either way his answer is completely off, and this is due to him mistakenly thinking the cube root was a square root.
Find the surface area of the composite figure.
8 cm
6 cm
7 cm
8 cm
SA =
6 cm
[?] cm²
9 cm
6 cm
Answer:
382 cm²
Step-by-step explanation:
Front face + Back face:
A = 2(a + b)h/2
A = 2(14 cm + 8 cm)(7 cm)/2
A = 154 cm²
Left face:
A = 7 cm × 6 cm = 42 cm²
Right face:
A = 9 cm × 6 cm = 54 cm²
Bottom face:
A = 14 cm × 6 cm = 84 cm²
Top face:
A = 6 cm × 8 cm = 48 cm²
Total surface area =
= (154 + 42 + 54 + 84 + 40) cm²
= 382 cm²
Write an algebraic expression to match the graph
please help!
the graphed equation is:
y = -|x| + 1
How to find the algebraic expression that matches the graph?On the graph, we can see an absolute value equation, which opens downwards, and passes through the points (1, 0) and (0,1).
The general absolute value equation is:
y = a*|x - b| + c
Because the vertex is at the point (0, 1), we know that:
b = 0, c = 1
Replacing that we get:
y = a*|x| + 1
Now, this must be zero when we evaluate in x = 1, then:
0 = a*|1| + 1
a = -1
Then the graphed equation is:
y = -|x| + 1
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please answer these questions
Answer:12
Step-by-step explanation:
Answer:
8. -3, 16
9. -3, 4.5
Step-by-step explanation:
See attached worksheet.
The chart below shows conversion between kilometers and miles.
Conversion Chart
Kilometer
Miles
2
1.2
7
4.2
20
?
30
18
What is the missing value in the table?
Answer:Answer:
12 (D)
Step-by-step explanation:
The first one is 2:1.2 so i did x10 on it to get 20:12.
Step-by-step explanation:Oh and hey if it's right u have to make me brainliest i need award
Write 304.9% as a decimal.
Answer:
3.049
Step-by-step explanation:
Move the decimal place in 304.9% to the left two places in order to convert from a percentage to a decimal. 3.049 is the answer.
Brainliest, please :) Hope this helps!
How to Simplify using suitable property: (-3/7) * 6/5 + (3/2) - (6/5) * 1/14
I will mark the first answerer as brainliest
The value of the given expression is 9/10. The properties of real numbers, such as commutative and distributive are used for solving this expression.
What are the required properties for solving an expression?The properties are:
Associative property: (a + b) + c = a + (b + c) Commutative property: a + b = b + c or a × b = b × aDistributive property: a × (b + c) = a × b + b × cCalculation:The given expression is
(-3/7) × 6/5 + (3/2) - (6/5) × 1/14
applying commutative law (a + b = b + c)
⇒ (-3/7) × 6/5 - (6/5) × 1/14 + (3/2)
again applying commutative law (a × b = b × a)
⇒ (-3/7) × 6/5 - 1/14 × (6/5)+ (3/2)
applying distributive law (a × (b + c) = a × b + b × c) in reverse order
⇒ (-3/7 - 1/14) × (6/5)+ (3/2)
⇒ (-7/14) × (6/5)+ (3/2)
⇒ (-1/2) × (6/5)+ (3/2)
⇒ (-6/10) + (3/2)
⇒ (-6 + 15)/10
⇒ 9/10
Thus, the required value is 9/10 and the suitable properties are commutative and distributive.
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The number 20 is multiplied either by 4 or by 5, then the product is increased either by 3 or by 5, and then the sum is divided either by 6 or by 7. What is the final quotient, if it is a natural number?
50 POINTS !! Charlotte has a map of the village. The scale on the map is such that 1cm represents 25m.
a) On the map, the church is 7cm from the village store. What is the real distance from the church to the village store?
b) Charlotte calculates her car is parked approximately half a kilometer from the church. On the map, how many cm would represent this distance?
Answer:
a) 175 m
b) 20 cm
Explanation:
scaled size → actual size
1 cm represents 25 m
a)
In the scaled size on the map, the distance from church to village is 7 cm.
Then actual size,
1 cm → 25 m
7 cm → (25 × 7) m
7 cm → 175 m
b)
half a kilometer = 0.5 km = 500 m
Then scaled size,
25 meter → 1 cm
500 meter → 500/25 cm = 20 cm
Simplify the expression 120x^3/18xy
Solve this:
NO INCORRECT or report
Answer:
D
Step-by-step explanation:
Let x be the first batch
let y be the second batch
y=2x
His brothers each received 9 rolls from the second batch i.e. 9×4=36
So
2x= 36+ (10÷6)x
2x - (10÷6)x = 36
12x-10x = 216
x=108
and y= 2 × 108= 216
30 POINTSS ABD BRAINLIEST !! Let p be a prime number. Circle one expression below which could also be a prime number.
2p 7p p - 4 p squared
Give a reason for your answer above
Answer:
p - 4
Step-by-step explanation:
Prime number is a number that only has 2 factors, 1 and the number itself. Therefore, multiplying p by 2 or 7 means giving the number more than 2 factors, which would make the number no longer prime. Squaring the prime number itself does the same.
Let p = 7.
2p = 2*7 = 14 14 = 1*2*7*14
7p = 7*7 = 49 49 = 1*7*49
p - 4 = 7 - 4 = 3 3 = 1*3
p^2 = 7^2 = 49 49 = 1*7*49
Use the given data set to complete parts (a) through (c) below. (Use α=0.05.)
1. The value of the linear correlation coefficient r is given as 0.8159. The correct option is a. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables
2. The scatterplot reveals a distinct pattern that is not a straight-line pattern.
What is the linear correlation coefficient?This is the data that we get when we try to get the existing relationship that is in existence between the variables that are used in a regression equation.
The value of r was calculated using a statistical tool online. The graph showed us it was not a straight line. The value of the r = 0.8159
The results of the test is in the attachment
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