Drawing an altitude and computing the side lengths of the resulting half triangle for an equilateral and isosceles triangle, would give the trigonometric functions for multiples of 30 and 45 respectively.
What is the significance of 30°-60°-90° and 45°-45°-90° right triangles?In a 30°-60°-90° right triangle, the longer leg is [tex]\sqrt{3}[/tex] times longer than the shorter leg, and the hypotenuse is twice as long. In a 45°-45°-90° right triangle, sides opposite to the equal angles (45°) are equal and the hypotenuse is [tex]\sqrt{2}[/tex] times the other sides.
To find the trigonometric functions of multiples of 30°, first consider a equilateral triangle of, say, side-length 2. Draw an altitude for the triangle. Each of the half triangle are 30°-60°-90° right triangle. Clearly the base will be divided into 2 equal parts of length 1 each. Now using Pythagorean Theorem on one of the 30°-60°-90° right triangle, trigonometric functions for multiples of 30° could be obtained.
Draw x and y axis. Now take a length of , say , 2 in the x-axis and using a compass pointed at origin and mark the point on y axis with a length 2. Now join these points on x and y axis. A 45°-45°-90° isosceles right triangle with side-length 2 is obtained. Now using Pythagorean Theorem, trigonometric functions for multiples of 45° could be obtained.
To learn more about greatest right angled triangles visit the below link,
https://brainly.com/question/14729820
#SPJ4
Selected values of the continuous function f are shown in the table below. Determine the validity of the following statement:
f(x)=0 has at least two solutionsin the interval {2,9}
True
False
could be true or false
Function may return true or false.
What does "continuous function" mean?A continuous function is one in which a continuous variation of the input (i.e., a change without a jump) results in a continuous modification of the function's value. This indicates that there aren't any discontinuities, or sudden changes in value.
Here, the function f(x) is continuous.
It follows that if x = 2 then f(x) = 3,
if x = 5 then f(x) = -9,
if x = 7 then f(x) = -15,
if x = 9 then f(x) = -13.
There are at least two solutions in the interval {2,9} for the graph of the function cross x axis f(x) = 0, hence it is not provided.
Therefore, it may be true or false.
To know more about continuous function click the link:
brainly.ph/question/16769929
#SPJ1
For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean and compare the result to the expected percentage of a normal distribution.
{8, 12, 27, 32, 45, 57, 61, 73, 82, 94}
A. 40%; This percentage is lower than expected in a normal distribution.
B. 50%; This percentage is lower than expected in a normal distribution.
C. 60%; This percentage is lower than expected in a normal distribution.
D. 70%; This percentage is close to the expected percentage in a normal distribution
In a normal distribution, a minimum percentage of 68% is anticipated, while an expected percentage of 60% is lower at 60%.
What is standard Deviation ?The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is.
According to the given information
8, 12, 27, 32, 45, 57, 61, 73, 82, 94 data points are provided.
Their average mean is 49.1.
The computed standard deviation is 29.31988.
The lower and upper limits are provided by the following when one standard deviation from the mean is taken into account.
= [ 49.1 - 29.31988, 49.1 + 29.31988 }
= [ 19.78012 , 78.41988 ]
We can observe that only six points—27, 32, 45, 57, 61 and 73—or 60% of the total—remain within one standard deviation of the mean.
In a normal distribution, a minimum percentage of 68% is anticipated, while an expected percentage of 60% is lower at 60%.
To know more about Standard Deviation
https://brainly.com/question/17484299
#SPJ4
Answer: C 60%; This percentage is lower than expected in a normal distribution.
just type 2 for the answer
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Alavaro selects a colored marble at random from a bag, records the color, and replaces the marble in the bag. After 20 trials, the experimental probability of selecting a pink
marble is selecting a yellow marble is, and selecting an orange marble is. On the 21st trial, Alavaro selects a blue marble. What is the experimental probability of
selecting a pink marble after 21 trials?
Answer:
0.325
Step-by-step explanation:
Cecil started from Point A and moved according to the expression 10 + (−5) + 19 + 6 + (−19) + 5 + (−10). What one additional step
does Cecel need in order to return to the starting point?
The number of steps in order to return to the starting point will be negative 16.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
Cecil started from Point A and moved according to the expression 10 + (−5) + 19 + 6 + (−19) + 5 + (−10).
Let 'x' be the number of steps in order to return to the starting point. Then the equation is given as,
x + 10 + (−5) + 19 + 6 + (−19) + 5 + (−10) = 0
Simplify the equation, then the equation is given as,
x + 10 − 5 + 19 + 6 − 19 + 5 − 10 = 0
x + 40 − 24 = 0
x + 16 = 0
x = − 16
The number of steps in order to return to the starting point will be negative 16.
More about the number line link is given below.
https://brainly.com/question/13189025
#SPJ1
guys pls help!! i really need help on these two questions
In order to prove the opposite sides are congruent, the two diagonals of parallelogram ABCD needed.
The given quadrilateral WXYZ is a parallelogram.
What is a parallelogram?A parallelogram is a quadrilateral with opposite sides parallel.
The quadrilateral ABCD have congruent opposite sides only when the diagonals are bisect.
Given that the diagonals of quadrilateral WXYZ intersect at point R.
Since the R is the midpoint.
The opposite sides are equal and opposite angles are equal.
Hence we can say that the given quadrilateral WXYZ is a parallelogram.
Similarly, in order to prove the opposite sides of the parallelogram ABCD is congruent, both diagonal required.
To learn more about parallelogram, use the link given below:
https://brainly.com/question/29147156
#SPJ1
A small coffee shop sells a variety of different pastries and treats. The banana bread is sold
by the loaf, and each loaf is sold for the same price. The cookies are sold by the dozen, and
each dozen is sold for the same price.
On Friday, the bakery collected $260 from selling 40 loaves of bread and 35 dozen cookies.
On Saturday, the bakery collected $360 from selling 64 loaves of bread and 42 dozen
cookies.
At what price does the bakery sell each item for?
Using system of linear equations, the price of bread is $3 and cookies is $4
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
Let;
x = bread y = cookiesWe can write a system of linear equation with this;
40x + 35y = 260 ....eq(i)
64x + 42y = 360 ...eq(ii)
Solving equation (i) and (ii)
The value of x is 3 and y is 4
This shows that the price of bread is $3 and cookies is $4
Learn more on system of linear equation here;
https://brainly.com/question/13729904
#SPJ1
the teacher decides to let your class get in groups of four to complete the homework. if you are like most people, your effort on this group task will be
The effort required to complete this group task will be less than the effort required to complete the task as individual homework.
In social psychology, social influence is a topic of study. Social compliance, persuasion methods, brainwashing, and social obedience are a few examples of issues studied in this field.
Several phenomena show how having others around affects performance, one of which is social loafing.
When someone works less hard on a task when doing it in a group, this unique phenomena happens.
Your class is divided into groups of four and given the assignment by the teacher. This group assignment will require less effort from you than completing it as individual homework would have required. This exemplifies the social loafing principle.
To know more about social loafing here
https://brainly.com/question/29750055
#SPJ4
what percent of twenty is 11
Answer:
55%
Step-by-step explanation:
first, you set up the problem as two fractions: 11 is to 20 as x is to 100. you cross multiply the 11 and 100, then divide that by 20 which gives you 55, which you divide by 100 for the percentage answer.
Darren ha a piece of wood that i 7 in by 8 in. Explain how he could divide thi large rectangle into two maller rectangle
On solving the provided question, we got that - he could divide the large rectangle into two smaller rectangle by cutting into 7 inches by 4 inches each.
What is rectangle?The opposite sides of a rectangle are equal and parallel, making it a form of quadrilateral. Four of its sides are equal to 90 degrees, making it a four-sided polygon. Two-dimensional shapes include rectangles.
We know that Darren has a wood piece that measures 7 inches by 8 inches. We are expected to explain how he managed to separate these two enormous rectangles into smaller ones.
Let's imagine that a huge rectangle has a width of 8 inches and a length of 7 inches.
Darren needs to cut two rectangles that are each 4 inches wide and 7 inches long to divide a giant rectangle into two smaller rectangles.
In order to make two smaller rectangles that are each 7 inches long and 4 inches broad, Darren can cut a larger rectangle.
To know more about rectangle visit:
https://brainly.com/question/15019502
#SPJ4
Dear Everyone, Please solve thid problem
1+1+1-1=
Answer:
2
Step-by-step explanation:
Pretty sure u know how to do this but
You have 1 dot and you add another dot which gives you 2 dots. And then you add another dot which gives you 3 dots. And then your mean friend takes away one of yours dots, which gives you 2 dots left.
THE SOULITIONS TO the inequality y>-3x+2 are shaded in the graph. Which point is a solution?
A. (0,2)
B. (2,0)
C. (1,-2)
D.(-2,1)
Point (2,0) is the solution for the inequality y > -3x +2
What is the solution of inequality?Here we have,
y > -3x +2
The shaded area above the dotted line is the solution.
We are aware that
If a point is a solution to an inequality, then its coordinates must satisfy the inequality.
We will investigate all cases to find a solution to the problem.
A) Point (0,2)
Here,
x = 0
y = 2
Verify the inequality by changing the values of x and y.
2 > -3 x 0 + 2
2 > 2
It is not correct.
Therefore the point is not to solve the inequality.
B) Point (2,0)
Here
x = 2
y = 0
Verify the inequality by changing the values of x and y.
0 > -3 x 2 + 2
0 > -4
This is correct
Therefore the point is to solve the inequality.
Therefore point B is the solution.
To learn more about inequalities refer to :
brainly.com/question/25275758
#SPJ1
PLEASE HELP ASAP!!!!!!!!
Answer:
The lie is #3.
Step-by-step explanation:
1 divided by 7^-3 is not equal to 7^-3. 7^-3/1 is equal to 7^-3 though.
How do I do y=mx+b in these type of questions
1. y<-3/4x+2
2. y≤5
3. x+y>6
With linear inequalities in two variables, you still have y=mx+b and it still tells you the same thing.
The inequality portion adds two additional layers on top of the y=mx+b line.
If the inequality is > or <, then you draw the line as a dashed line.
If the inequality is ≥ or ≤, then you draw the line as a solid line.
The difference is that points on the > or < line do NOT make the inquality true, while points on the ≥ or ≤ line do.
The other piece is that all the points on one side of the line will also make the inequality true.
If you have "y>mx+b" or "y≥mx+b", then you shade above the line.
If you have "y<mx+b" or "y≤mx+b", then you shade below the line.
So there are three parts:
1. Where is the line?
2. Is the line solid or dashed?
3. Do you shade above or below the line?
The three graphs are attached.
What is 6/2(19x6+17)
What are the coordinates of the point on the directed line segment from (1, 5) to
(6, 10) that partitions the segment into a ratio of 3 to 2?
(4,6) are the coordinates of the point on the directed line segment from (1,5) to(6, 10) that partitions the segment into a ratio of 3 to 2.
Define mid point theorem,According to the midpoint theorem, the line segment drawn from the intersection of two triangle sides is parallel to and equal to half of the third side. To determine precise information about the lengths of triangle sides, one uses the Midpoint Theorem. According to the Midpoint Theorem, the segment connecting two triangle sides at their midpoints is parallel to the third side and is half its length.
Given
Points (1,5) (6.10)
Ratio 3 :2
Using mid point theorem,
( (mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n) )
3(6) + 2 (1)/ 3+2, 3(10) + 2(5)/ 2+3
18 + 2/5 , 20 + 10/5
20/5 , 30/5
4, 6
(4,6) are the coordinates of the point on the directed line segment from (1,5) to(6, 10) that partitions the segment into a ratio of 3 to 2.
To learn more about mid point theorem, visit:
https://brainly.com/question/19505549
#SPJ1
Hello please solve this with steps
The dimensions of the rectangular prism are:
Length = 4 meters.
Width = 2 meters.
Height = 2 meters.
What are the dimensions of the storage space?A rectangular prism of width W, height H, and length L has a volume given by the formula:V = W*H*L
Here we know that: the height and the width are both 2 meters less than the depth, then:W = L - 2H = L - 2 and the volume is 16 cubic meters
Replacing that in the volume equation we will get:16 = L*(L - 2)*(L - 2)It is ratter easy to notice that if we take L = 4, we will get:16 = 4*(4 - 2)*(4 - 2) 16 = 4*(2)*(2)16 = 4*416 = 16 So L = 4 is a solution, then:
W = L - 2W
= 4 - 2 = 2
And also the height is:H = 4 - 2 = 2
These are the dimensions.
Learn more about volume:
https://brainly.com/question/1972490
#SPJ1
In it's first four games, a netball team scores an average of 31 points per game. After the fifth game, the average for the first five games is 30. How many points did the team score in the fifth game?
The netball team scored 26 points in their fifth game.
What is the arithmetic mean or average?Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.
Let x be the no. of points the netball team scores in the fifth game.
∴ (31 + 31 + 31 + 31 + x)/5 = 30.
(124 + x)/5 = 30.
124 + x = 150.
x = 26.
So, They scored 26 points in their fifth game.
learn more about averages here :
https://brainly.com/question/29550341
#SPJ1
Write an equation in slope-intercept form of the line that is perpendicular to the one given and passes through the given point. (4,8); y=-2x - 4
An equation in slope-intercept form of the line perpendicular to y = 2x-4
is y =(-1/2)x+10.
What are lines and their slopes?We are aware that there are many types of equations for lines, with the
general type being Ax+ By + C = 0, and the slope-intercept form equation
being y = mx + b.
m is the slope, and b is the y-intercept.
The y-intercept is the point (0,b) where the line intersects the y-axis when
x = 0, and the slope is the rate of change of the y-axis relative to the x-axis.
We are aware that the slopes of perpendicular lines are oppositely negative.
The slope of the given line, y = 2x-4, is 2.
Consequently, the given line will pass through point with a slope of (-1/2). (4,8).
∴8= (-1/2)(4)+b
8= -2+b
b = 10.
∴ y =(-1/2)x+10 is our required line.
To know more about lines and slopes here :
https://brainly.com/question/14511992
#SPJ1
If 5 bunnies can eat all the crops in a garden in 8 hours, how long would it take for 8 bunnies to eat the same amount of crops? Please help!
Answer:
5 hours
Step-by-step explanation:
40=8x
x=5
The number of hours taken for 8 bunnies to eat the same amount of crops will be 5 hours.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If 5 bunnies can eat all the crops in a garden in 8 hours. The relation between work and time will be inverse. Then the product of the number of bunnies and the number of hours remains constant.
Let 'x' be the number of hours. Then the equation is given as,
8 × x = 5 × 8
Simplify the equation, then we have
8 × x = 5 × 8
8x = 40
x = 40 / 8
x = 5 hours
The number of hours taken for 8 bunnies to eat the same amount of crops will be 5 hours.
More about the ratio and the proportion link is given below.
https://brainly.com/question/14335762
#SPJ2
Point A has coordinates
(-4, -2). Point B has
coordinates (6, 3). Find the coordinates of
point P on directed line segment AB that
partitions AB so that AP: AB is 3:5.
i have no clue how to do this please help me out :))
Answer:
∆QRS / ∆XZY = 1/2
Step-by-step explanation:
You want the similarity ratio of ∆QRS to ∆XZY. Side lengths are marked in the diagram.
The similarity ratio will be the ratio of two corresponding side lengths.
Corresponding sidesYou can find corresponding sides several ways:
Use the similarity statement to identify corresponding vertices. A side will be defined by 2 of them. Use vertex identifiers that are in the same positions in both triangle names: QR : XZ (first two vertices listed), for example.Use the markings in the figure to identify corresponding sides. Corresponding sides will have the same angle marks at either end. For example, the side marked 1 in ∆QRS has 1-arc and 3-arc angle markings at its ends. The side marked 2 in ∆XZY also has 1-arc and 3-arc angle markings at either end. It will be the corresponding side.Use side lengths. When both triangles have their side lengths sorted into increasing order, the corresponding numbers are corresponding sides. The side lengths in ∆QRS are {1, 2, 2}. In ∆XZY, they are {2, 4, 4}.The ratios of corresponding sides are 1:2, 2:4, and 2:4. The 2:4 ratios reduce to 1:2, which is the answer you're looking for. Written as a fraction, the ratio is ...
1/2 . . . . ratio of ∆QRS to ∆XZY
I just need to know how to get to 55 pls
Answer/Step-by-step explanation:
Okay, so this question really is a nightmare, because this image is just not possible. Like, literally, Z is or is not the center, you do or do not have enough info. Its a bad question. This is not your fault. If you don't care why its a bad question scroll down to "How could someone get 55°"
If Z is the center, BZ and CZ are radii and equal. Angle CBZ is 60° because
AngleABC + Angle CBZ = 180°
120° + CBZ = 180°
CBZ = 60°
That means AngleC is also 60°. And then, since 180° in a triangle, AngleCZB also must be 60°.
This makes AngleCZD 120°.
But if Z is the center and ArcCD is 115°, then AngleCZD should be 115°.
Contradiction! Angle CZD can't be both 120° and 115° something is wrong here. See image.
How could someone get 55°? Well, it is also not correct but... If ArcCD is 115° then AngleCZD is 115° (if Z is the center) So AngleCZB is 180°-115°, which is 65°.
AngleCBZ is 60°
60° + 65° + C = 180°
125 + C = 180
C = 55°
what is the probability that a randomly selected person will have a birthday in august? assume that this person was not born in a leap year. express your answer as a simplified fraction or a decimal rounded to four decimal places.
the probability of a randomly selected person having a birthday in August is 1/12 or 0.0833 rounded to four decimal places.
The probability of a randomly selected person having a birthday in August is 1/12. There are 12 months in a year and August is one of them. Therefore, The probability of a randomly selected person having a birthday in August is 1/12 because there are 12 months in a year and August is one of them. Each month has an equal chance of being chosen since they all have the same number of days. This probability remains the same regardless of whether or not it is a leap year. Therefore, the probability of a randomly selected person having a birthday in August is 1/12 or 0.0833 rounded to four decimal places.The probability of a randomly selected person having a birthday in August is calculated by dividing the number of days in August (31) by the total number of days in a year (365). This works out to be 1/12 or 0.0833 rounded to four decimal places.
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
What is the simplified form of the expression the quantity x squared plus 10x plus 21 end quantity divided by 4 times the quantity x plus 3 end quantity?
the quantity x minus 7 end quantity divided by 4 the quantity x plus 7 end quantity divided by 4 the quantity x plus 7 end quantity divided by quantity x plus 3 end quantity the quantity x minus 7 end quantity divided by quantity x plus 3 end quantity
Answer:
[tex]\frac{x+7}{4}[/tex]
(B) is your answer :)
Step-by-step explanation:
do you need me to work it out?
Answer:
b
Step-by-step explanation: took the test
During a class trip to an apple orchard, a group of
students picked 2436 apples. They packed them into
6 boxes to take to the local food bank. If each box
held the same number of apples, how many apples
were in each box?
2) 46
3) 460
4) 406
5) 14,616
The answer is 406 apples.
2436 apples divided by 6 boxes gives you the number of apples in each box.
50 points!! (Factoring Algebraic Expressions MC)
Rewrite 1/14 x^3y +8/14xy^2 using common factor
1/7xy(2x^2 + 8y)
1/7x^2y(2x+8y)
1/14xy(x^2+ 8y)
1/14 x^3y^2(y+8)
Answer:
7
x
y
out of
−
7
x
y
(
2
x
2
y
−
3
x
)
−
7
x
y
(
−
2
)
.
−
7
x
y
(
2
x
2
y
−
3
x
−
2
)
Step-by-step explanation:
PLEASE HELP
Fill in the blanks below with the correct units.
Answer:
a) Liters.
b) Kilograms.
c) Kilometers.
Step-by-step explanation:
I'm not completely sure about C). But after some researching and calculating these answers seem the most correct. But I'm pretty sure A) and B) are right.
Is 3 : 9 and 6 : 36 equivalent ratios?
Answer: False
Step-by-step explanation: they are not the same because if you times 3:9 ratio times 2 then it makes it 6 and 18 and does not make 6 : 36
Your welcome - your friend green
There are 28 right-handed students in a class of 3 1. What is the probability that a student
chosen at random will be left-handed?
31/28
28/31
3/28
3/31
Answer:
3/31
Step-by-step explanation:
31 - 28 = 3 left handed students
31 total students
probability that a student chosen at random will be left-handed is 3/31