The values of angles for the intervals given are obtained as 135°, 405° and -135° respectively.
What are trigonometric ratios?The trigonometric ratios are defined for a right angled triangle.
The example of these ratios are sin, cos, tan, cosec, sec and cot.
The trigonometric ratios are useful in determining the heights and distances of the large objects.
The given trigonometric equation is sin(θ) = √2/2.
It can be written as,
sin(θ) = √2/2
⇒ sin(θ) = 1/√2
⇒ θ = 45°
(a) The value of the angle in interval 90° < θ < 270° is given as,
⇒ 180°- θ = 180° - 45° = 135°
(b) The value of the angle in interval 270° < θ < 450° is given as,
⇒ 360°+ θ = 360°+ 45° = 405°
(c) The value of the angle in interval -270° < θ < -90° is given as,
⇒ -180° + θ = -180° + 45° = -135°
Hence, the required values of angles for the given interval are 135°, 405° and -135° respectively.
To know more about trigonometric ratio click on,
https://brainly.com/question/25122825
#SPJ1
Which is 4logx-2log(x-3) written as a single logarithm
The correct single logarithm expression will be;
⇒ log x⁴ / (x - 3)²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 4 log x - 2 log (x - 3)
Now,
Since, The expression is,
⇒ 4 log x - 2 log (x - 3)
Simplify by the properties of logarithmic as;
⇒ log x⁴ - log (x - 3)²
⇒ log x⁴ / (x - 3)²
Thus, The value of single logarithm is,
⇒ log x⁴ / (x - 3)²
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ1
Slope of 3y-9x=9
Slope of x+3y=-6
Answer:
Slope of 3y-9x=9 is 3
Slope of x+3y=-6 is -1/3
Step-by-step explanation:
First, convert each of the two equations into the form y = mx + c.
Next, to determine the slope of the graph, find the value of m (m represents the gradient of the graphs)
Equation 3y - 9x = 9:
Rewrite equation: 3y = 9x + 9
y = 3x + 3
m = 3
gradient/slope = 3
Equation x + 3y = -6:
Rewrite equation: 3y = - x - 6
y = -1/3x - 2
m = -1/3
gradient/slope = -1/3
FOr every 5 coins Carmen gets she gives frankle 2 if Carmen has 9 how many dose frankle have
Answer:2
Step-by-step explanation:
She has 2
9 - 5 = 4
no more to give so only 2
Two roses cost $3.50. How many roses can you
buy for $21?
Answer:
6 roses
Step-by-step explanation:
divide 21 and 3.50 hope this helps:)
Answer:6
Step-by-step explanation:
21 Divided by 3.5 = 6
what is 860x67 divided by 65
Answer:
886.461538462
Step-by-step explanation:
What is the perimeter of a rectangle with a length of 8 1/6 feet and a width of 6 2/3 feet
Answer:
29 2/3 ft
Step-by-step explanation:
The perimeter is found using the formula
P = 2 ( l+w)
where l is the length and w is the width
P = 2(8 1/6 + 6 2/3)
Getting a common denominator
P = 2 ( 8 1/6 + 6 4/6)
= 2 ( 14 5/6)
= 28 10/6
Changing the improper fraction to a mixed number
= 28 + 1 4/6
Simplifying
= 29 2/3 ft
Dishwasher detergent is sold in individual packs. It is sold in 20-, 60-, and 90-pack containers.
a. Which container do you think has the lowest unit rate of dollars per pack? Why?
b. The 20-pack container sells for $5.49. What is the unit rate in dollars per pack? Round your answer to the nearest cent.
c. The 60-pack container sells for $10.97. What is the unit rate in dollars per pack? Round your answer to the nearest cent.
d. The 90-pack container sells for $18.95. What is the unit rate in dollars per pack? Round your answer to the nearest cent.
e. Which container has the lowest unit rate> how does this compare with your answer in part (a)?
Answer:
b) 0.27
c) 0.18
d) 0.21
e) c has the lowest rate per container
is the point (2,-1) is true for the system? 3x - y =7 2x+3y=1
Answer:
yes it is true
Step-by-step explanation:
3(2)-(-1)=7 2(2)+3(-1)=1
The figures below are similar to each other. Find the scale factor of the smaller figure to the larger figure.
(Given that the triangles are oriented in the same direction)
35
5:2
2:5
20:7
7:20
40
25
14
16
The scale factor of the smaller figure to the larger figure is 5:2
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Given that two triangles are similar.
The side lengths of the triangle must be proportional.
Let us consider first triangle as ABC, where AB is 35, BC is 40 and AC is 25.
and triangle DEF as DE is 14 and EF is 16.
Now AB/DE=BC/EF
35/14=40/16
5/2=5/2
Hence, the scale factor of the smaller figure to the larger figure is 5:2
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ1
5. When there is a snow day at Russel's school, one person will contact 4 people and each of
people will contact 4 other people, and so on. How many people will be contacted in the fifth
round?
The number of people who will be contacted in the fifth round is 4^5, or 1024.
What is arithmetic calculation?
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. The basic operations of math are addition, subtraction, multiplication, and division. These operations are denoted by the given symbols.
If one person contacts four people in the first round, and each of those people contacts four more people in the second round,
then the total number of people contacted in the second round is 4 * 4 = 16.
In the third round, each of those 16 people would contact 4 more people each, for a total of 16 * 4 = 64 people contacted.
In the fourth round, each of those 64 people would contact 4 more people each, for a total of 64 * 4 = 256 people contacted.
In the fifth round, each of those 256 people would contact 4 more people each, for a total of 256 * 4 = 1024 people contacted.
Hence, The number of people who will be contacted in the fifth round is 4^5, or 1024.
To learn more about arithmetic calculation visit,
https://brainly.com/question/13181427
#SPJ1
You and your friends want to go on a canoe trip. River Run Canoes Charges an initial fee of $10 plus $10 per hour. The cost for Clear Water Canoes is represented by the graph. ( Graph has a y intercept of 16, and goes right 2, so its starting at 16/2 )
The graph of the amount of money that River Run Canoes have a y intercept of 10 and slope of 10.
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
The standard form of a linear equation is:
Ax + By = C
Where A, B and C are constants.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the initial value (y intercept).
Let y represent the total amount of money that River Run Canoes Charges for a trip lasting x hours.
River Run Canoes Charges an initial fee of $10 plus $10 per hour, hence:
y = 10x + 10
The graph of the amount of money that River Run Canoes have a y intercept of 10 and slope of 10.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
HELPPPPPPP im to lazy
Answer: help is on the way
Step-by-step explanation:
The plane x + y + z = 1 cuts the cylinder x2 + y2 = 1 in an ellipse. We want to find the points on the ellipse that lie closest to the origin. Using Lagrange Multiplier method, set up a system of equations for such points. Need not solve it. Hint: Let (x, y, z) be the point on the ellipse. Then the goal is to minimize f(x, y, z) = x2 + y2 + z2 (= square of the distance from the origin), under a constraint. Write the constraint function clearly,
The points on the ellipse that lie closest to the origin is (0, 1, 0).
f(x)=x²+y²+z²
h(x)=x²+y²=1
g(x)=x+y+z=1
⟨2x,2y,2z⟩=λ⟨2x,2y,0⟩+μ⟨1,1,1⟩
This results in the equations:
2x = 2xλ +μ
2y = 2yλ + μ
2z = μ
By taking λ = 1
2x = 2x + μ
μ = 0 so z = 0
x + y = 1
y=1 and x=0
The Lagrange multiplier method in mathematics is a technique for locating the local maxima and minima of a function subject to equality restrictions (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). [1] It bears the name Joseph-Louis Lagrange after the mathematician.
The fundamental concept is to transform a limited problem into a format that still allows the derivative test of an unconstrained problem to be used. The Lagrangian function is a reformulation of the original issue that results from the relationship between the gradient of the function and gradients of the constraints.
To learn about Lagrange :
https://brainly.com/question/17227640
#SPJ4
Describe and correct the error writing 39 over 40 as a percent.
Answer:
Multiply instead of divide
Step-by-step explanation
39/40=0.975 (Correct)
0.975x100=97.5%
If it were me I would just move the decimal point in 0.975 right twice, but since they're asking for a formula you would multiply instead of divide.
Hope this helps :)
Based on the data in the box plots, what is the best evidence to show which class has had greater success on field day over the last 10 years? mrs. cai’s class was more successful because her interquartile range was less spread out. mrs. cai’s class was more successful because she had the greater total spread. mr. roland’s class was more successful because his class always won at least one event. mr. roland’s class was more successful because his class’s lower quartile was the same as mrs. cai’s class’s upper quartile.
The best evidence to show which class has had greater success on field day over the last 10 years based on the data in the box plots would be Mrs. cai's class was more successful because her interquartile range was less spread out.
To determine this
The interquartile range (IQR) is a measure of the spread of the middle 50% of the data. A smaller IQR indicates that the data is more concentrated or less spread out, while a larger IQR indicates that the data is more spread out. If Mrs Cai's class has a smaller IQR, it suggests that the scores for that class are more consistent and less variable compared to the scores for Mr Roland's class. This could be a good indication that Mrs Cai's class has had greater success on field day over the last 10 years.
To learn more about the interquartile range (IQR), visit:
brainly.com/question/15616988
#SPJ4
How many solutions does the equation y = -2x2 - 7x + 5 have?
The number of solutions which the equation y = -2x² -7x + 5 has as required in the task content is; 2.
What is the number of solutions for the given equation?As evident in the task content; the number of solutions which the given equation has is to be determined.
Since the given equation; y = -2x² -7x + 5 is a quadratic equation.
It follows that the number of solutions which the equation has is two.
PS; Quadratic equations are polynomials with degree 2 and hence, have two solutions.
Read more on quadratic equations;
https://brainly.com/question/24546586
#SPJ1
hurry please and thank you #2
When the rate of change of AB is -1/5, and line CD is 5 then line AD will be -1
What is linear function ?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the change of the output values to the input values, otherwise known as the rate of change.
In the figure, the rate of change is given to be -1/5 and by definition rate of change which is the slope has the formula
m = change of the output values / change in the input values
m = AC / CD
-1/5 = AC / 5
hence AC = -1
Learn more about slope of linear functions at:
https://brainly.com/question/20277632
#SPJ1
The robot factory can produce robots of all different
sizes.
The shade of green you chose is made by mixing two
paint colors (as shown in the table below).
Complete the table to color several robots.
Cups of Green Paint
4
H
Cups of White Paint
3
For 10 cups of Purple Paint there are 7.5 cups of White paint.
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
The cups of purple paint is proportional to cups of white paint.
Then, the ratio is
Purple / White = 4/3
So, when Purple paint is 10 then the white paint will be
= 10 x 3/4
= 30/4
= 7.5
Learn more about Ratio here:
https://brainly.com/question/29774220
#SPJ1
Write the equations below in slope-intercept form,
x + 3y = 12
Answer: x-3y=-12
Step-by-step
The slope-intercept form is
y
=
m
x
+
b
, where
m
is the slope and
b
is the y-intercept.
y
=
m
x
+
b
Click on the graph until the graph that best represents the given statement appears.
Height Above Ground
Time
The graph consists of the relationship between the height of the object and time.
What is the graph?The graph is a demonstration of curves that gives the relationship between the coordinate axes x and y-axis.
here,
In the figure,
The graph shows the relationship between the height of the object dependent on time. Where the vertical axis represents the height of the object, and the horizontal axis represents the time.
Thus, the graph shows the relationship between the height of the object and time.
Learn more about graphs here:
brainly.com/question/16608196
#SPJ1
How much would you need to invest at 8.75% interest rate compounded daily for 50 years to have $1,000,000 at the end of that time period?
Answer:
You would need to invest $12594.78-------------------------
Given:
Interest rate r = 8.75% or 0.0875,Time t = 50 years,Compound number n = 365,Future amount A = $1000000Find the invested amount P using compound interest equation:
[tex]A=P(1+r/n)^{nt}[/tex]Substitute to get:
[tex]1000000=P(1+0.0875/365)^{365*50}[/tex][tex]1000000=P(79.398)[/tex][tex]P=1000000/79.398[/tex][tex]P=12594.78[/tex]car rental agency has two locations in a city. The boxplots below summarize the miles driven for one day of single day car rentals at each location Location A DO Location B 0 100 300 400 200 Miles Driven Based on the boxplota, which statement provides the best comparison of the two locations?A. The number of single day rentals is greater for location A than for location B. The number of single day rentals in less for location A then for location . C Compared with location A, the miles driven for location display more variability and the median is greater D. Compared with location A, the miles driven for location display lese variability, and the median in greater E. Compared with location A, the miles driven for location display less variability, and the median is about the name
Among the given statements, the following statement "Compared with location A, the miles were driven for location B display more variability and the median is greater" provides the best comparison of the two locations.
Hence, option (C) is the correct choice.
For finding the interquartile range for location, first, find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1.
The interquartile range for location B is Q3 - Q1 = almost 140 - 40 = 100, while it is Q3 - Q1 = nearly 60 - 40 = 20 for location A.
Therefore, the miles travelled for position B are more variable than they are for place A.
Greater than Location A's almost 50 medians is Location B's nearly 80 median.
Therefore, location B's median miles driven is higher than it is for location A.
For more questions on interquartile range
https://brainly.com/question/4102829
#SPJ4
a section of lawn that is 25.5 feet by 75.0 feet needs fertilizer. the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn. if each box costs $1.65, how much will it cost to fertilize the lawn?
it cost 5 pound then = 1912.5*5= 9562.5 when the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn. if each box costs $1.65
a section of lawn that is 25.5 feet by 75.0 feet needs fertilizer.
the fertilizer is sold in 5.00 pound boxes and 1.00 pound of fertilizer is needed for 10.0 square yards of lawn.
if each box costs $1.65, how much will it cost to fertilize the lawn?
We would solve this question by cross multiplication.
If a sound of fertilizer covers 45 square feet of lawn and the lawn is 8666.7 square feet
To get fertilizer quantity we have
1 pound = 45 square
Unknown = 8666.7 square feet
8666.7/45
= 192.59 when approximated we get 193.
Therefore she has to buy 193 pounds of fertilizer
total become 25.5*75=1912.5
it cost 5 pound then = 1912.5*5= 9562.5
learn more about of fertilizer here
https://brainly.com/question/17297470
#SPJ4
Which equation has no solution 4 x 3 2x 6 x 2 5 2 3 2x x 3 x 1?
The equation given in B which is "5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )" has no solution.
In order to determine which equation has no solution we need to solve the equation to check to see if after solving they give the left-hand side (LHS) and right-hand side (RHS) equal.
If both LHS and RHS are equal, it means the equation has a solution; but if LHS and RHS are not equal, it means that the equation has no solution.
So first solve the equation given in A:
4 ( x + 3 ) + 2x = 6 ( x + 2 )
4 x + 12 + 2 x = 6x + 12
6 x + 12 = 6 x + 12
LHS is equal to RHS so this equation has the solution.
So now solve the equation given in B:
5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )
5 + 6 + 4 x = x + 3 x + 3
11 + 4 x = 4 x + 3
or
(4 x + 11) = (4 x + 3)
LHS is not 'equal' to RHS so this equation has no solution.
"
Complete question is
Which equation has no solution
A: 4 ( x + 3 ) + 2x = 6 ( x + 2 )
B: 5 + 2 ( 3 + 2x ) = x + 3 ( x + 1 )
"
You can learn more about equation with no solution at
https://brainly.com/question/1792644
#SPJ4
You start at (4, -4). You move left 9 units and down 1 unit. Where do you end?
4
Submit
W
N
H
-5 -4 -3 -2 -10
-1
-2
i
1 2
3
4 5
Answer: (-5, -5)
Step-by-step explanation:
Left and right is 'x'
Up and down is 'y'
Looking on a standard graph, left and down are negative, right and up is positive.
left 9 is -9, down 1 is -1
Jason made a model stop sign for his model train
set. An actual stop sign measures 12 inches on
each side. Jason's model stop sign measures
1 inch on each side.
What is the scale of the model sign to the actual
sign?
On solving the provided proportionality question we got that, U = 7.72, is rounded off nearest to tenth digit.
What is proportionality?When two quantities or variables are linearly related in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable decreases in proportion to the other when it falls to 1/100th of its previous value.We must determine the ratio of the two quantities for each value supplied in order to determine if two quantities are proportionate. The proportionate link between them is evident if their proportions are equal. Their connection is not proportionate if all the ratios are out of balance.
Here,
U/5 = 17/11
U = 17/11 X 5
U = 7.72
To know more about proportionality visit:
brainly.com/question/8598338
#SPJ1
How do you find the value of z?
If you are trying to find the value of a particular variable, z, you will need to first look at the equation or expression in which it is used. Once you have identified the equation or expression, you need to solve for z by substituting the known values and manipulating the equation until you arrive at the solution.
1. Identify the equation or expression in which the variable, z, is used.
2. Substitute the known values into the equation and manipulate the equation until you arrive at the solution for z.
3. Solve for z by applying the appropriate operations and rules of algebra.
4. Check your answer to make sure it is correct.
If you are trying to find the value of a particular variable, z, you will need to first look at the equation or expression in which it is used. Once you have identified the equation or expression, you need to solve for z by substituting the known values and manipulating the equation until you arrive at the solution.
Learn more about equation here
https://brainly.com/question/29657992
#SPJ4
What is the y intercept for the 1st graph.
Answer: 2
Step-by-step explanation:
Whatever point the line crosses when crossing the Y axis is the y-intercept.
In this graph it is crossing over 2
let f(x) = 1 2x . compute lim h→0 f(5 + h) − f(5) h .
The value of f(5 + h) - f(5)h when h =0 is 60.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(x) = 12x
Now,
f(5 + h) = 12 (5 + h) = 60 + 12h
f(5) = 12 x 5 = 60
Now,
f(5 + h) - f(5)h
= 60 + 12h - 60h
h = 0
= 60 + 0 - 0
= 60
Thus,
The value of the limit is 60.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
How do you write fractions in Python?
The fraction module in Python can be used to create fractions such as 3/4. This module can be imported and then the Fraction class can be used to create the fraction object. The fraction object can then be printed to display the fraction.
1. Import the fraction module: from fractions import Fraction
2. Create the fraction object: f = Fraction(3, 4)
3. Print the fraction: print(f)
4. The output will be: 3/4
The fraction module in Python is used to create and manipulate fractions. This module can be imported using the following command: from fractions import Fraction. Once imported, the Fraction class can be used to create the fraction object. The Fraction class takes two parameters which represent the numerator and denominator of the fraction. The fraction object can then be printed to display the fraction. For example, to create a fraction of 3/4, the following code can be used: f = Fraction(3, 4). This will create a fraction object which can then be printed with the print() function to display 3/4. The fraction module in Python is a great way to work with fractions in a programmatic way.
Learn more about fraction here
https://brainly.com/question/10354322
#SPJ4
