1. The degree form of 4π/9 is approximately 228.6°.
2. A positive coterminal angle to -123° that is between 500° and 750° is 677°. A negative coterminal angle to -123° that is between -300° and -500° is -243°.
3. The terminal side of 215° lies in the second quadrant.
4. The radius of the circle is approximately 15.7.
1. The degree form of 4π/9 is approximately 228.6°. To express an angle in degrees, we multiply its radian measure by 180°/π.
2. A positive coterminal angle to -123° that is between 500° and 750° is 677°. A negative coterminal angle to -123° that is between -300° and -500° is -243°. To find a coterminal angle, we can add or subtract 360° as many times as necessary to bring the angle into the desired range.
3.
In the standard position, an angle is measured counterclockwise from the positive x-axis. The positive x-axis corresponds to the 0° angle, the positive y-axis corresponds to the 90° angle, the negative x-axis corresponds to the 180° angle, and the negative y-axis corresponds to the 270° angle. Angles in the first quadrant are between 0° and 90°, angles in the second quadrant are between 90° and 180°, angles in the third quadrant are between 180° and 270°, and angles in the fourth quadrant are between 270° and 360°.
So, the terminal side of 215° lies in the second quadrant.
4.
We can set up the equation l = Cθ/2π and solve for r.
Substituting the given values, we have 56π = (2πr)(120°/180°), which simplifies to r = 56π/(2π) = 28.
Dividing this value by 2, we get the radius of the circle as approximately 15.7.
Learn more about the quadrant of the graph here:
brainly.com/question/7196312
#SPJ1
9. Marcus vegetable is drawing a plan for his garden. He graphs one corner at (-7.2, 2). He reflects (-7.2, 2) across the x-axis. Then Marcus reflects the new points across the y-axis. What shape is the vegetable garden?
Answer: To reflect a point across the x-axis, you need to change the sign of the y-coordinate. Therefore, the point (-7.2, 2) reflected across the x-axis becomes (-7.2, -2).
To reflect a point across the y-axis, you need to change the sign of the x-coordinate. Therefore, the point (-7.2, -2) reflected across the y-axis becomes (7.2, -2).
The resulting shape is a rectangle with one corner at (-7.2, 2) and the opposite corner at (7.2, -2).
Step-by-step explanation:
Helpp!! I’m stuck on this!!
y is inversely proportional to x
when y = 7, x = 9
a) work out an equation connecting y and x
b) work out the value of y when x = 21
The equation connecting y and x is y = 63/x and the value of y when x =21 is 3
a) work out an equation connecting y and xFrom the question, we have the following parameters that can be used in our computation:
Variation = inverse variation
y = 7, x = 9
An inverse variation is represented as
k = xy
Where k is the constant of proportion
Substitute the known values in the above equation, so, we have the following representation
k = 7 * 9
Evaluate
k = 63
So, we have the following representation
xy = 63
Make y the subject
y = 63/x
b) work out the value of y when x = 21Substitute the known values in the above equation, so, we have the following representation
y = 63/21
Evaluate
y = 3
Hence, the solution is 3
Read more about inverse variation at
https://brainly.com/question/11177292
#SPJ1
Which statement could most likely be a description of the org
expression 12 - 3x ?
a. The amount of money, in dollars, Eloise is left with, if she had
$12 and with that, she bought x + 3 flowers.
b. The amount of money, in dollars, Eloise is left with, if she had
$12 and with that, she bought 3x flowers.
c. The amount of money, in dollars, Eloise is left with, if she had
$3 and with that, she bought 12 flowers at $x each.
The amount of money, in dollars, Eloise is left with, if she had
$12 and with that, she bought x flowers at $3 each
Need help ASAP!! Plssss
Answer: b that is too easy
Step-by-step explanation:
Does the table below represent a proportional relationship?
A. Yes, because all the ratios of y to x are equal to 2.
B. Yes, because all the ratios of y to x are equal to 3.
C. No, because all the ratios of y to x are not equal.
D. No, because all the numbers are positive.
The table represents a proportional relationship because all the ratios of y to x are equal to 3. (option B)
What is a proportional relationship?Two variables exhibit a proportional relationship if the constant of proportionality remains constant for all the given values in the table.
The equation that is used to represent a proportional relationship is:
y = kx
Where:
k = constant of proportionality
Value of k when x is 1:
3 = k
Value of k when x is 2:
6 = 2k
k = 6 / 2
k = 3
Value of k when x is 3:
9 = 3k
k = 9 / 3
k = 3
Value of k when x is 4:
12 = 4k
k = 12 / 4
k = 3
To learn more about proportional relationships, please check: https://brainly.com/question/20048815
#SPJ1
So i am trying to help out my son with his homework and i do not remember this at all if anyone could help me it would greatly be appreciated
Answer:51x900/100
Step-by-step explanation:
So you’ll do 51 x 900
And then at the denominator when there is no number it is automatically 1 so the denominator will be 100.
Complete the proof of ∆JKL ≅ ∆LMN, by providing the reason for each of the statements below. Reasons MAY be used more than once. NOT ALL reasons will be used.
1. JK ∥ LM, KL ∥ MN (Given)
2. ∠KJL ≅ ∠MLN; ∠KLJ ≅ ∠MNL
a. Reflexive Property
b. Alternate Interior Angles
c. Corresponding Angles
d. ASA
e. AAS
3. JK ≅ LM (Given)
4. ∆JKL ≅ ∆LMN
a. Reflexive Property
b. Alternate Interior Angles
c. Corresponding Angles
d. ASA
e. AAS
Answer:
See belowStep-by-step explanation:
1. JK ∥ LM, KL ∥ MN Given
2. ∠KJL ≅ ∠MLN; ∠KLJ ≅ ∠MNL c. Corresponding Angles
3. JK ≅ LM Given
4. ∆JKL ≅ ∆LMN e. AAS
n x (5 + 3) = (6 x 5) + (6 x 3) write the missing number.
Answer:
6 is the missing number
Step-by-step explanation:
Solve what is inside of the parenthesis, then evaluate.
N x (8) = (30) + (18)
8N = 48
Solve for N.
N = 48/8
N = 6
Write and solve a system of equations for each of the following problems. You must write two questions for each problem, thank you
1. Ella is a landscape photographer. She sells small prints for $50 each, and large prints for $75
each. One weekend she sold a total of 52 prints for a total of $2975. How many of each size print did
Ella sell?
2. At a hot air balloon festival, Georges's balloon is at an altitude of 40 meters and rises at a rate of
10 meters per minute. William's balloon is at an altitude of 165 meters and descends at a rate of 15
meters per minute. In how many minutes will both balloons be at the same altitude? What is that
altitude?
The system of equations that satisfy the given problems is x + y = 52 and 50x + 75y = 2975, and the value of x = 15 and y= 37.
What is system of equations?A system of linear equations consists of two or more equations and looks for common answers.
1. Let us suppose small prints = x
Large prints = y
Total prints sold can be written as follows:
x + y = 52
The total cost of the prints can be written as follows:
50x + 75y = 2975
The system of equations is:
x + y = 52 . . . equation 1
50x + 75y = 2975 . . .equation 2
Using equation 1 we have:
x = 52 - y
Substituting the value of x in equation 2 we have:
50(52 - y) + 75y = 2975
2600 - 50y + 75y = 2975
25y = 2975 - 2600
25y = 375
y = 15
Now, substituting the value of y in equation 1 we have:
x + 15 = 52
x = 52 - 15
x = 37
Hence, the solution of the system of equations is y = 15 and x = 37.
2. Let us suppose the altitude = x.
The rising balloon can be thus written as:
40 +10x
The descending balloon can be written as:
165 - 15x
Solving the system of equations by substituting the value of x we get x= 5.
Hence, the altitude at which both the balloons are at the same height is 5m.
Learn more about system of equations here:
https://brainly.com/question/12895249
#SPJ1
4. ABCD below is a rectangle. BE=6x+2 and ED=4x+6. Find the length of AC.
Answer:
28 units
Step-by-step explanation:
ABCD is a rectangle. AC and BD are diagonals intersecting at point E.
Diagonals of a rectangle bisect each other.
[tex] \therefore BE = ED[/tex]
[tex] \therefore 6x + 2 = 4x + 6[/tex]
[tex] \therefore 6x - 4x= 6-2[/tex]
[tex] \therefore 2x= 4[/tex]
[tex] \therefore x= \frac{4}{2} [/tex]
[tex] \therefore x= 2 [/tex]
[tex] \therefore 6x + 2= 6*2+2= 12+2= 14 [/tex]
[tex] \therefore BE= 14\: units [/tex]
[tex] \because BD = 2BE[/tex]
[tex] \therefore BD = 2(14)= 28\: units [/tex]
[tex] \because AC = BD[/tex] (diagonals of a are equal in measure)
[tex] \therefore AC = 28\: units [/tex]
Convert the following component vectors to a linear combination:
< 20 , 14 , -23 >
The component vectors to a linear combination is given by the equation
A = 20 i^ + 14 j^ - 23 k^
What is the product of vectors?The dot product, or inner product, of two vectors, is the sum of the products of corresponding components. Equivalently, it is the product of their magnitudes, times the cosine of the angle between them . The dot product , also known as the inner product, of u and v to be the number u ⋅ v given by
u ⋅ v = u₁v₁ + u₂v₂ + u₃v₃
An equivalent definition, typically used in physics, is
u ⋅ v = ∣u∣ ∣v∣ cos θ,
where θ is the angle between u and v
Two nonzero vectors are perpendicular, or orthogonal, if and only if their dot product is equal to zero
Given data ,
Let the component vectors be represented as A
The value of A is
< 20 , 14 , -23 > be equation (1)
On simplifying the equation to the linear combination , we get
< 20 , 14 , -23 > = 20 i^ + 14 j^ - 23 k^
So , the linear combination of the vectors is given by the equation ,
A = 20 i^ + 14 j^ - 23 k^
Hence , the equation is 20 i^ + 14 j^ - 23 k^
To learn more about vectors click :
https://brainly.com/question/11044032
#SPJ1
If BD = 8x - 27 and EC = 2x + 33, find BD.
The surface area of a rectangular prism is 400m ^ 2 . What will be the new surface area if all of the dimensions are doubled ?
What is 6,789,694,976 x 9,452,569,132
*Can not use calculator
The product of the given numbers can be represented in a scientific notation form as = 6418 × 10^19 (approximately)
What is multiplication?Multiplication can be defined as the repeated addition of a given value with the purpose of arriving to an expected value.
The multiplication of two given numbers is the same thing as the products of the given number and it's represented by the sign (X)
The product of 6,789,694,976 x 9,452,569,132 = 6418 × 10^19
Learn more about multiplication here:
https://brainly.com/question/28768606
#SPJ1
I really need help on this question offering 10 points if anybody could help me with this with proof I'd be very thankful
Answer:
n=15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
First off we divide both sides by [tex]\frac{1}{5}[/tex] and get:
[tex]\frac{1}{5}[/tex]n÷ [tex]\frac{1}{5}[/tex]=3÷ [tex]\frac{1}{5}[/tex]
n=3×5
n=15
A 1050-kg car travels on the freeway at a speed of 33 m/s. What is the cars kinetic energy ?
9514 1404 393
Answer:
571,725 J
Step-by-step explanation:
KE = 1/2mv²
KE = 1/2(1050 kg)(33 m/s)² = 571,725 J
Every time an insect jump forward the distance covered is half of previous jump. if the insect initially jumped 8.4cm calculate to the nearest two decimal places distance of sixth jump
The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.
What is a geometric sequence?Let a₁ be the first term and r be the common ratio.
Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
Every time an insect jump forward, the distance covered is half of the previous jump. If the insect initially jumped 8.4 cm.
The equation is given as,
aₙ = 8.4 · (1/2)ⁿ⁻¹
The distance that he jumped in the sixth jump will be given as,
a₆ = 8.4 · (1/2)⁶⁻¹
a₆ = 8.4 / 64
a₆ = 0.13125
a₆ ≈ 0.13
The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.
More about the geometric sequence link is given below.
https://brainly.com/question/11266123
#SPJ1
The box plots show the target heart rates of men 20-40 years old and men 50-70 years old.
Target Heart Rates of Men
20-40 years old
50-70 years old
Which statement is best supported by the information in the box plots?
A )
The range of the data for men 20-40 years old is less than the range of the data for men
50-70 years old.
B )
The median of the data for men 20-40 years old is less than the median of the data for
men 50-70 years old.
C )
The minimum target heart rate for men 20-40 years old is less than the minimum target
heart rate for men 50-70 years old.
D )
The interquartile range of the data for men 20-40 years old is greater than the
interquartile range of the data for men 50-70 years old.
Answer:
anong ka pong grade?
Step-by-step explanation:
matanong ko Lang!
Please help, no links
Answer:
m<1=90°
m<2=38°
hope this helps
Several minutes later, Raul decides to measure the water temperature again. He finds that the temperature changed by -0.6°F. What is the temperature of the water now? Show your work.
The current temperature of the water is given as follows:
71.7 ºF.
How to obtain the current temperature of the water?The defining statement from the problem is given as follows:
He finds that the temperature changed by -0.6°F.
The change by the negative amount of -0.6ºF means that the current temperature of the water is obtained subtracting the previous temperature of the water by 0.6 ºF.
The previous temperature of the water is given as follows:
72.3°F.
Hence the current temperature of the water is obtained subtracting 72.3ºF and 0.6ºF, as follows:
72.3 - 0.6 = 71.7 ºF.
Missing InformationThe previous temperature of the water is given as follows:
72.3°F.
More can be learned about the subtraction between two amounts at https://brainly.com/question/17301989
#SPJ1
Explain step by step please thank you!
The ratio of teachers to students in a school district is 2 to 47. The number of teachers in the district is 130, how many students are there?
Answer:
Number of students in district = 3,055 students
Step-by-step explanation:
Given:
Ratio [Teachers to students] = 2 : 47
Total number of teachers in district = 130
Find:
Number of students in district
Computation:
Number of students in district = Total number of teachers in district[47/2]
Number of students in district = 130[47/2]
Number of students in district = 65[47]
Number of students in district = 3,055 students
Sixteen high school students completed a math exam, but only 12 students received a passing grade. Which expression represents the ratio of passing grades to failing grades?
Answer:
4:3 that's the answer
for the question
Answer:
4:3 is the correct answer
Step-by-step explanation:
The total students that took the exam is 16 but the students that passed are only 12 the ratio that represent it is remember ratio means division so is 16/12 which one / 4 will give you for over 3 as a correct answer
points A and B are shown on a coordinate plane
point A is at (-8, 6) point B is at (-2, -2)
What is the length of AB and the coordinates of its midpoint?
AB= __ units
the midpoint of AB is (_,_)
The length of AB would be = 10 units and the midpoint of segment AB would be (-5, 2).
What are the distance formula and midpoint of a segment?
The distance formula is a mathematical formula that can be used to determine the distance between two points in a coordinate plane. The distance between two points (x1, y1) and (x2, y2) is given by the formula:
[tex]d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
The midpoint of a segment is a point that is exactly in the middle of a line segment. Given the endpoints of the line segment, (x1, y1) and (x2, y2) the coordinates of the midpoint, (x, y) can be calculated using the following formulas:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
The given points are (-8, 6) and (-2, -2).
Given two points A(x1, y1) = (-8, 6) and B(x2, y2) = (-2, -2), we can use the distance formula to find the length of the line segment AB. The distance formula is:
[tex]d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\\\d= \sqrt{((-2) - (-8))^2 + ((-2) - (6))^2}\\\\d=\sqrt{36 + 64}\\\\d=\sqrt{100}\\\\d=10[/tex]
The length of AB would be 10.
To find the coordinates of the midpoint of AB, we can use the midpoint formula:
x = (x1 + x2) / 2
y = (y1 + y2) / 2
Plugging in the values for A and B, we get:
x = (-8 + (-2)) / 2 = -5
y = (6 + (-2)) / 2 = 2
The coordinates of the midpoint of AB are (-5, 2).
Hence, the length of AB would be = 10 units and the midpoint of segment AB would be (-5, 2).
To learn more about the distance formula and midpoint of a segment, visit:
https://brainly.com/question/28778717
#SPJ1
Convert 13
12
from radians to
degrees.
Answer:
195°
Step-by-step explanation:
Fill in the missing part of the proportion.
GH
C. CD
B. HI
A. GF
Step-by-step explanation:
the answer is GH, the can be the only answer
How many cubed with side lengths 1/2 cm does it take to fill the prisim?
IF ITS CORRECT ILL GIVE BRAINLEIST
Draw a line plot to represent the data
Answer:
Make sure you include the words ^-^
Step-by-step explanation:
Christopher measured a line to be 12.2 inches long. If the actual length of the line is 12.1 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
If Christopher measured a line to be 12.2 inches long. If the actual length of the line is 12.1 inches, the percent error of the measurement, to the nearest tenth of a percent is: 0.83%.
How to find the percent error?Using this formula to find the percent error
Percent error = Measurement - Actual length / Actual length
Let plug in the formula
Percent error = 12.2 - 12.1 / 12.1
Percent error = 0.1 /12.1
Percent error = 0.0083 or 0.83%
Therefore we can conclude that the percent error is 0.83%.
Learn more about percent error here:https://brainly.com/question/1600371
#SPJ1
Estimate the answer by rounding the divisor to the nearest whole number.
196,900÷4.084
Answer:
48,213
Step-by-step explanation:
The full answer is 48,212.5367, but because there is a 5 in the tenths place you round the whole number up
9514 1404 393
Answer:
49,000
Step-by-step explanation:
The divisor is 4.084. When it is rounded to the nearest whole number, it is 4.
Then the division problem becomes ...
196,900/4 ≈ 49,000 . . . . . . showing just 2 significant digits for the estimate
__
The point of an estimate is to obtain an approximate answer that is within a few percent of the actual answer. Here, rounding 4.084 to 4.000 gives an error on the order of .084/4 ≈ 2.1%. Because we're using a smaller divisor, the value we obtain for our estimate will be too large by about that amount.
Often, an estimate that has 1 or 2 significant digits is "close enough" for the purpose. Because a change in our estimated value of 1 in the least significant digit is a change of about 2%, we judge this estimate to be "close enough", given the rounding we did to start. Keeping 3 significant digits in our estimate would claim an accuracy that it does not have.