By using a protractor or visual estimation, we can estimate the measure of angle ABC to the nearest degree.
To answer your question, let's first start with defining what an angle is. An angle is formed by two rays or line segments that share a common endpoint, called the vertex. The measure of an angle is usually given in degrees and is determined by how much the two rays are turned away from each other.
Now, let's look at the specific angle you asked about, angle ABC. Without a diagram or any additional information about the position of point B and C, it is impossible to determine the measure of angle ABC. However, we can make some general assumptions based on the fact that angle measures range from 0 to 360 degrees.
Assuming that angle ABC is a standard angle and not a reflex angle (i.e. it measures less than 180 degrees), we can estimate the measure of angle ABC to the nearest degree by using a protractor or by visual estimation. A protractor is a tool used to measure angles in degrees, and can be found at most office supply stores or online.
If we don't have access to a protractor, we can still estimate the measure of angle ABC by comparing it to other angles we know the measure of. For example, if angle ABC looks to be about halfway between a right angle (90 degrees) and a straight angle (180 degrees), we can estimate that angle ABC measures around 135 degrees.
In summary, without additional information about the specific position of points B and C, we cannot determine the exact measure of angle ABC. However, by using a protractor or visual estimation, we can estimate the measure of angle ABC to the nearest degree.
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))
Which operation should be completed first to find the value of the expression
below?
6-3
12+ 30 (6-3) + 1
12+ 30
306
3+1
Don
Answer:
(6-3)
Step-by-step explanation:
6x^2-12x-18 factor the polynomial
Answer:
6x² - 12x - 18
the factors are -18 and 6
6x² - 18x + 6x - 18
6x(x - 3) + 6 (x - 3)
(6x + 6) or (x - 3)
the factors are:
(6x + 6) or (x - 3)
Question 1 (Multiple Choice Worth 2 points)
(Multiplying Linear Expressions MC)
Simplify ---
O
45
m²
8.
45
8
45
2
m²-m
35
2
-m² + m
35
8
45
2
·m² + m
35
Answer:
[tex] - \frac{2}{5} m( - \frac{4}{9} m - \frac{1}{7} ) = [/tex]
[tex] \frac{8}{45} {m}^{2} + \frac{2}{35} [/tex]
simplify completely
sin(90°-x)co(180°-X)+tanX×cos(-x)sin180°+x)
Therefore , the solution of the given problem of trigonometry comes out to be -1 is the simplified formula.
What is a trigonometry?Some claim that the fusion of various fields contributed to the development of astrophysics. With the aid of precise mathematical methods, many metric issues can be resolved or the output of a computation can be determined. The scientific investigation of all six fundamental geometric calculations is known as trigonometry. They are known by a number of names and abbreviations, such as sine, variance, angle, and others. (csc).
Here,
Let's first use trigonometric identities to separately simplify each term:
=> cos(x - 90°) equals sin(x)
=> cos(x - 180°) = -cos(x)
=> tan(x) = cos(x) / sin(x)(x)
=> x(cos(-)) = x(x)
=> (180° + x) sin = -sin(x)
When we replace the equation with these simplifications, we get:
=> cos(x) * sin(180° plus x) * cos(x) * (-cos(x)) + (sin(x) / cos(x))
=> sin(180° plus x) * sin(-cos2(x))
=> -cos²(x) - sin(x)*sin(180° + x) (using the equation sin(x)*sin(x)) = -sin^2(x))
Using the identity sin2(x) +cos2(x) = 1, we get = -1.
Consequently, -1 is the simplified formula.
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Draw the image of triangle△ABC under a dilation whose center is C and scale factor is 2
The original triangle ABC is down below.
PLEASE HELP
The resulting triangle would have twice the area and all sides would be twice as long as the original triangle, but the angles would remain the same.
What is triangle?A triangle is a geometric shape that consists of three straight line segments or sides that are connected at three points called vertices. Triangles are two-dimensional and are the simplest polygon that can exist in Euclidean space. Triangles can be classified according to the size and shape of their sides and angles. Triangles are used in many different areas of mathematics, science, and engineering. They are also common in everyday life, for example in construction, architecture, and design.
Here,
To dilate a triangle with a center point C and a scale factor of 2, you would first draw a ray from C through each vertex of the triangle. Then, you would measure the distance from C to each vertex of the original triangle and multiply it by the scale factor (2 in this case) to find the distance from C to each corresponding vertex of the dilated triangle. Finally, you would draw lines connecting the dilated vertices to form the dilated triangle.
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PLEASE HELP WILL MARK BRAINLIEST
20 points
write an explicit formula for each sequence
1,4,7,10….
SHOW WORK PLS
Answer:
aₙ = 3n - 2
Step-by-step explanation:
The given sequence is an arithmetic sequence with the first term a₁ = 1 and the common difference d = 3.
The explicit formula for an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
where aₙ represents the nth term in the sequence.
Substituting the values we have:
aₙ = 1 + (n - 1)3
Simplifying the equation we get:
aₙ = 3n - 2
Therefore, the explicit formula for the given sequence 1, 4, 7, 10, ... is aₙ = 3n - 2.
Can 2x divided by 3y be simplified
Answer:
No, you cannot simplify it.
Step-by-step explanation:
Because 2 and 3 are one of the lowest numbers that cannot be simplified.
Write an expression that can be a rule for the number sequence below.
6, 9, 12, 15, 18, … (PLS ANSWER FAST!!)
3n, where n is equal to 2, 3, 4, 5, 6
3 + n, where n is equal to 2, 3, 4, 5
6n, where n is equal to 0, 1, 2, 3, 4
6 + n, where n is equal to 1, 2, 3, 4
The arithmetic sequence expression for the given sequence 6, 9, 12, 15, 18....... would be aₙ = 6+(n-1)3.
What is an arithmetic sequence?A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor.
The common difference of that mathematical progression is the constant difference.
'n' denotes the term's position in the supplied arithmetic sequence in the formula for obtaining the general term: a = a1 + (n - 1) d. For instance, a2 denotes the second phrase in the sequence.
So, the given sequence is:
6, 9, 12, 15, 18
Common difference (d) is: 9 - 6 = 3
Then, the sequence expression would be:
aₙ = 6+(n-1)3
Therefore, the arithmetic sequence expression for the given sequence 6, 9, 12, 15, 18....... would be aₙ = 6+(n-1)3.
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The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17
The IQR is the best measure of variability for this data set, and its value is 4.
What is median?
Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.
The correct answer is:
The IQR is the best measure of variability, and it equals 4.
The box plot shows the median (represented by the line in the box), the interquartile range (IQR) (represented by the length of the box), and the range (represented by the lines outside the box).
The IQR is the range between the first quartile (Q1) and the third quartile (Q3) of the data set, which contains the middle 50% of the data. In this case, the box extends from 17 to 21, indicating that Q1 is 17 and Q3 is 21. Therefore, the IQR is the difference between Q3 and Q1, which is 21-17=4.
The range is the difference between the maximum and minimum values in the data set, which is 27-10=17. However, the range can be affected by outliers and is not as robust as the IQR.
Therefore, the IQR is the best measure of variability for this data set, and its value is 4.
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suppose that 5% of teachers at a university attended a conference. if 4000 teachers are enrolled at the university, about how many teachers attended the conference?
Answer: 200 teachers attended the conference
Step-by-step explanation:
To answer this question, we will find 5% of 4,000. A percent divided by 100 becomes a decimal, and "of" means multiplication in mathematics.
5% / 100 = 0.05
4,000 * 0.05 = 200 teachers attended the conference
The answer is 200
If 5% of teachers at a university attended a conference and 4000 teachers are enrolled at the university, about 200 teachers attended the conference. What is the problem asking for? The problem is asking us to calculate how many teachers attended a conference given that 5% of the total number of teachers at a university attended the conference and that the university has 4000 teachers .What is the formula for percentage? The formula for percentage is given by:(Part/Whole)*100Let T be the total number of teachers at the university, and let x be the number of teachers that attended the conference. We know that 5% of teachers at a university attended a conference, therefore:(5/100)*T = x,. Given that there are 4000 teachers in the university, we can substitute this value into the equation: (5/100)*4000 = x. Simplifying the equation, we get: x = 0.05 * 4000x = 200.
Therefore, about 200 teachers attended the conference.
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Very confused on this question, unsure of the answer
Answer:
a = 9 , b = 5 , c = 25
Step-by-step explanation:
using the Cosine rule in the triangle
a² = b² + c² - 2bc cosA
where a is the side opposite ∠ A and b, c the sides adjacent to ∠ A
here
a = y , b = x + 5 , c = 3x and A = Θ , then
y² = (x + 5)² + (3x)² - [ 2(x + 5) × 3x × cosΘ ]
y² = x² + 10x + 25 + 9x² - [ 6x(x + 5) × [tex]\frac{1}{6}[/tex] ]
y² = 10x² + 10x + 25 - x(x + 5)
y² = 10x² + 10x + 25 - x² - 5x
y² = 9x² + 5x + 25 ← in the form y² = ax² + bx + c
with a = 9 , b = 5 , c = 25
Problem 5.2 A cone has volume V, radius r, and a height of 12 cm. Another cone has the same height and 3 times the radius of the original cone. Write an expression for its volume. | Submit
Answer: The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
For the original cone with radius r and height 12 cm, we have:
V = (1/3)πr^2h
V = (1/3)πr^2(12)
V = 4πr^2
For the second cone with 3 times the radius of the original cone and the same height of 12 cm, we have:
V' = (1/3)π(3r)^2h
V' = (1/3)π9r^2(12)
V' = 36πr^2
Therefore, the expression for the volume of the second cone is 36πr^2.
Step-by-step explanation:
dustin has 3 cups of buttermilk.does he have enough to make four batches of muffins.explain(he needs 3/4 cup butter milk to make 1 batch)
Answer:
Step-by-step explanation:
The math used shows how much cups it would take to make 4 batches, 3 cups. Therefor yes, he does have exactly enough to make 4 batches of muffins.
Three numbers whose sum is 26 are in GP.If 5,9 and 5 are added to them respectively, then the three numbers are in AP. Find the numbers.
The three numbers are:
(-1 + √(97))/2, (-1 ± √(97))/2, (-1 ± 7√(97))/2
What is an arithmatic progression?
An arithmetic progression is a sequence of numbers in which each term after the first is obtained by adding a fixed constant to the preceding term. The fixed constant is called the common difference, denoted by d.
Let the three numbers in the GP be a/r, a, and ar, where a is the middle term.
Then we have:
a/r + a + ar = 26 (sum of GP)
(a/r + 5) + (a + 9) + (ar + 5) = 3(a + 4) (sum of AP)
Simplifying the second equation, we get:
a(r - 1) = 3
Substituting this into the first equation, we get:
a/r + a + ar = 26
1/r + 1 + r = 26/a
r^2 + r - 26/a = 0
Solving for r using the quadratic formula, we get:
r = (-1 ± √(1 + 104/a))/2
Since r > 0 (because the terms are in GP), we take the positive root:
r = (-1 + √(1 + 104/a))/2
Substituting this into the equation a(r - 1) = 3, we get:
a(-1 + √(1 + 104/a))/2 - a = 3
-a + a √(1 + 104/a) - 2 = 0
a √(1 + 104/a) = -a + 2
a² (1 + 104/a) = a² - 4a + 4
104a = 4a² - 4a + 4
a² - a + 1 = 26
(a - 1/2)² + 3/4 = 26
(a - 1/2)² = 97/4
a - 1/2 = ±√(97)/2
a = (1 ± √(97))/2
Since the terms are in GP, we can use the value of a to find the other two terms:
a/r = (1 ± √(97))/(2(-1 + √(1 + 104/a))/2) = (-1 ± √(97))/2
ar = (1 ± √(97))/(2(-1 - √(1 + 104/a))/2) = (-1 ± 7√(97))/2
Therefore, the three numbers are:
(-1 + √(97))/2, (-1 ± √(97))/2, (-1 ± 7√(97))/2
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the edges of a cube increase at a rate of 2 centimeters per second. how fast is the volume changing when the length of each cube edge is 50 centimeters ?
The required volume of the cube is increasing at a rate of 15,000 cubic centimeters per second when the length of each edge is 50 centimeters and the edges are increasing at a rate of 2 centimeters per second.
Let us consider V be the volume of the cube,
And s be the length of one edge of the cube.
Volume of a cube is equal to,
V = s^3
To find how fast the volume is changing with respect to time,
Use the chain rule of differentiation,
dV/dt = dV/ds × ds/dt
where dV/dt is the rate of change of volume with respect to time,
dV/ds is the rate of change of volume with respect to the length of one edge of the cube,
And ds/dt is the rate of change of the length of one edge of the cube with respect to time.
ds/dt = 2 cm/s,
find dV/dt when s = 50 cm.
First, find dV/ds,
dV/ds = 3s^2
Then, we can plug in s = 50 cm,
dV/ds = 3(50)^2
= 7500 cm^2
Finally, we can plug in the values we have to find dV/dt,
dV/dt = (dV/ds) × (ds/dt)
= 7500 cm^2/s × 2 cm/s
= 15,000 cm^3/s
Therefore, the volume of the cube is increasing at a rate of 15,000 cubic centimeters per second .
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please help with this question?!!
Answer: SHawn
Step-by-step explanation:
The weight of a puppy is modeled by 2x - y=-2, where x represents the puppy's age in
weeks and y represents its weight in pounds. Which graph models the puppy's growth?
Answer:
Graph H
Step-by-step explanation:
intercept (0,2)
students arrive at the administrative services office at an average of one every 14 minutes, and their requests take, on average, 8 minutes to be processed. the service counter is staffed by only one clerk, judy gumshoes, who works eight hours per day. assume poisson arrivals and exponential service times. a. what is the utilization rate? b. the average number of students in line. c. the average time of waiting in line.
A. The Utilization rate is 0.5714 or 57.14%, B. The average number of students in line is 0.9 students and C. The average time of waiting in line was 4.57 minutes.
The utilization rate refers to the proportion of time Judy Gumshoes spends processing student requests.
To calculate this rate, divide the average service time by the average time between arrivals. In this case, the average service time is 8 minutes, and students arrive every 14 minutes on average.
a) Utilization rate: 8 minutes / 14 minutes = 0.5714 or 57.14%
b) To determine the average number of students in line,
we can use the formula L = λW, where L represents the average number of students in the system, λ is the arrival rate (1 student per 14 minutes), and W is the average time a student spends in the system (waiting and being served). Since we know the utilization rate,
we can calculate the average waiting time (Wq) using the formula,
Wq = (U^2) / (1 - U), where U is the utilization rate.
In this case, Wq = (0.5714^2) / (1 - 0.5714) = 0.3265 or 32.65% of 14 minutes = 4.57 minutes.
W = Wq + service time
= 4.57 minutes + 8 minutes
= 12.57 minutes.
Finally, L = λW = (1 student / 14 minutes) * 12.57 minutes
= 0.9 students.
c) The average time of waiting in line is the same as the average waiting time in the system (Wq), which we calculated as 4.57 minutes.
In summary, the utilization rate of the service counter is 57.14%, the average number of students in line is 0.9, and the average waiting time in line is 4.57 minutes.
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HELPPPPP DUE SOON!!!!
The distance between the points H (-9, 1), and K (-1, 8) in the coordinate plane, obtained using the distance formula is; Distance: 10.63
What is the distance formula?The distance formula is a formula that is used to find the distance between two points on the coordinate plane.
The specified points are; H = (-9, 1), and K = (-1, 8)
The distance formula can be used to calculate the distance between the points as follows;
The distance formula is; d = √((x₂ - x₁)² + (y₂ - y₁)²)
Where; (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
When, (x₁, y₁) = (-9, 1), and (x₂, y₂) = (-1, 8), we get;
d = √((-1 - (-9))² + (8 - 1)²) = √(8² + 7²) =
√(8² + 7²) = √(64 + 49) = √(113) ≈ 10.63 (rounded to the nearest hundredth)
The distance between the points is about 10.63 units
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Are these right? If not, can you tell the right answers so I can change them please?
Answer:
O=0
T=-5
c = 0
R = -2
6 = 8
2 = 8
11=-3
Step-by-step explanation: Sorry for the late answer It took me a bit to solve all the problems but I hope this helps you!!
One card each is drawn from four different standard decks of cards. Find the total number of outcomes
Since there are 52 cards in a standard deck, there are 52 possible outcomes for the first draw from the first deck. Similarly, there are 52 possible outcomes for the first draw from the second, third, and fourth decks. Therefore, the total number of outcomes for the first draw is 52 + 52 + 52 + 52 = 208.
For the second draw, there are only 51 possible outcomes for each deck, since one card has already been drawn. Therefore, the total number of outcomes for the second draw is 51 + 51 + 51 + 51 = 204.
For the third draw, there are only 50 possible outcomes for each deck, since two cards have already been drawn. Therefore, the total number of outcomes for the third draw is 50 + 50 + 50 + 50 = 200.
For the fourth draw, there are only 49 possible outcomes for each deck, since three cards have already been drawn. Therefore, the total number of outcomes for the fourth draw is 49 + 49 + 49 + 49 = 196.
The total number of outcomes for drawing one card each from four different standard decks of cards is the product of the outcomes for each draw: 208 x 204 x 200 x 196 = 338,401,792.
44% of c is 72. find the value of c
Answer: 163.6363...
Step-by-step explanation:
44% of c is 72, so then [tex]0.44*c=72\\[/tex].
Divide both sides by 0.44 to solve for c, and you get c=163.6363...
Tip: if you are ever trying to figure out what a number is a percentage of, like in this problem, just divide the number by the percent in decimal form.
help with this problem
Answer:
PQ = 165.60m
Step-by-step explanation:
Since triangles are similar
PQ/70 + 210 = 124.2/210
PQ = 124.2 (70 + 210)/210 = 165.60m
The standard form of a circle is (x-5)^2+(y-5)^2=16. Convert the standard form into general form.
Therefore, the general form of the circle is:
[tex]x^2 + y^2 - 10x-10y+34=0[/tex].
What is circle?A circle is a geometric shape that is defined as the set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). The distance from the center to any point on the circle is always the same. Circles are often represented using the symbol "O" or "⚪" and are important in mathematics, geometry, and physics. They have many properties, such as circumference (the distance around the circle), area (the space inside the circle), and diameter (the distance across the circle through the center). Circles are used in various fields, including architecture, engineering, and art.
To convert the standard form of a circle to the general form, we expand and simplify the equation as follows:
[tex](x - 5)^2 + (y - 5)^2 = 16[/tex]
[tex]x^2 - 10x + 25 + y^2 - 10y + 25 = 16[/tex] (using the identity [tex](a - b)^2 = a^2 - 2ab + b^2)[/tex]
[tex]x^2 + y^2 - 10x-10y+34=0[/tex]
Therefore, the general form of the circle is:
[tex]x^2 + y^2 - 10x-10y+34=0[/tex]
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when a study sample shows representativeness, what can be concluded about the study? group of answer choices the study results show evidence of sampling bias the study used strict inclusion and exclusion criteria to limit the sample size the study is most likely not generalizable because the sample was obtained using specific inclusion criteria. the study is most likely generalizable, with results that can be applied to the target population
When a study sample is representative of the target population, it allows for the results to be generalizable, meaning they can be applied to the broader population.
This is an important aspect of research, as it ensures the study's findings are relevant and useful beyond the specific sample studied.
When a study sample shows representativeness, it means that the sample accurately reflects the characteristics of the target population.
In this case, the study is most likely generalizable, with results that can be applied to the target population.
To achieve representativeness, researchers often use random sampling techniques, which help minimize the potential for sampling bias.
Sampling bias occurs when certain groups within the target population are over- or under-represented in the sample, which can lead to inaccurate conclusions.
In contrast, if a study used strict inclusion and exclusion criteria to limit the sample size or relied on specific inclusion criteria, it could result in a sample that is not representative of the target population.
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Review the information on FICO score calculations to answer the question:
Category Percentage
Payment History 35%
Amount Owed 30%
Length of Credit History 15%
New Credit and Inquiries 10%
Credit Mix 10%
A borrower has a credit score of 725. How many points come from amount owed and length of credit history?
290
322.65
363
326.25
From the given percentage values, 326.25 points come from amount owed and length of credit history.
What is percentage?
Percentage is a method of representing a value as a fraction of 100. This is frequently used to make comparisons, demonstrate ratios, or determine a fraction of a whole.
The borrower's credit score is 725, and we need to find out how many points come from amount owed and length of credit history.
From the information given, we know that these two categories make up a total of 45% of the score calculation (30% for amount owed and 15% for length of credit history).
We can set up a proportion:
(30% + 15%) / 100% = x / 725
Simplifying the left side:
45% / 100% = 0.45
0.45 = x / 725
Multiplying both sides by 725:
x = 0.45 * 725
x = 326.25
Therefore, 326.25 points come from amount owed and length of credit history.
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Hey, we're doing IXLs in pre-alg rn
After solving the given equation 1/4b - 2 = -1/2b + 4, the resultant value of b is 8/3 respectively.
What are equations?An equation is a mathematical expression with two equal sides and an equal sign.
4 + 6 = 10 is an illustration of an equation.
On the left side of the equal sign, you can see 4 + 6, and on the right, you can see 10.
A formula exists in every equation.
Some equations do not have formulae.
Equations are designed to be solved for a variable.
We look over formulas.
So, we have the equation:
1/4b - 2 = -1/2b + 4
Now, solve the equation for b as follows:
1/4b - 2 = -1/2b + 4
1/4b = -1/2b + 6
1/4b + 2/1b = 6
1+8/4b = 6
9/4b = 6
b = 6 * 4/9
b = 2 * 4/3
b = 8/3
Therefore, after solving the given equation 1/4b - 2 = -1/2b + 4, the resultant value of b is 8/3 respectively.
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Solve for z in the proportion.
60
90
Z =
22
Z + 17
Submit
The equation is not a proportion, and the value of z in the equation is 17
Calculating the value of z in the equationGiven that
2Z = Z + 17
To solve for z in the proportion:
2z = z + 17
We can start by simplifying the equation by subtracting z from both sides:
2z - z = 17
Simplifying further, we get:
z = 17
Therefore, the solution to the proportion is z = 17.
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if the average (arithmetic mean) of n consecutive odd integers is 10, what is the least of the integers? the range of the n integers is 14. the greatest of the n integers is 17.
The least of the integers in arithmetic mean of n consecutive odd integers is 3.
The formula to calculate average or arithmetic mean of evenly distributed set is -
Average = sum of first and last term/2
Keep the values in formula to find the least integer. Since these are consecutively arranged, the first number will be the least number.
10 = first number + 17/2
First number + 17 = 10×2
Performing multiplication on Right Hand Side
First number + 17 = 20
First number = 20 - 17
Performing subtraction
First number = 3
Hence, the least integer is 3.
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given the circle below with chords NO and PQ find the length of NR round to the nearest tenth if necessary
the length of NR is approximately 22.8, rounded to the nearest tenth.
To find the length of NR, we need to first identify any relationships between the chords and the arcs they intercept in the circle. From the diagram, we can see that chord PQ intersects arc ONR and chord NO intersects arc PQN.
There are two main properties we can use to solve this problem: the chord-chord power theorem and the angle-arc theorem. The chord-chord power theorem states that if two chords intersect in a circle, the product of the lengths of their segments is equal. That is:
(PQ)(QR) = (NO)(NR)
We know that PQ = 48 and NO = 21, so we can plug those values into the equation and solve for NR:
(48)(QR) = (21)(NR)
QR = (21NR)/48
To find QR, we can use the angle-arc theorem. This theorem states that the measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the arcs they intercept. That is:
∠QNR = (arc PN + arc OQ)/2
We know that arc PN is equal to arc PQ (since they are intercepting the same arc), and we know that arc OQ is equal to the entire circumference of the circle minus arc PQ. The circumference of a circle is given by 2πr, where r is the radius. We don't know the radius of the circle, but we can find it using the Pythagorean theorem. We know that NO and PQ are both chords, so they must intersect at the center of the circle. Therefore, the line segment connecting the center of the circle to the midpoint of chord NO is a perpendicular bisector of NO. This gives us a right triangle with legs of 10.5 and 24 (half of 21 and half of 48). Using the Pythagorean theorem, we can find that the radius of the circle is approximately 26.2.
Now we can plug in our values for arc PN and arc OQ:
∠QNR = (arc PQ + (2πr - arc PQ))/2
∠QNR = πr
We know that QR is the side opposite the angle ∠QNR in right triangle QNR. Therefore, we can use the sine function to find QR:
sin(∠QNR) = QR/r
sin(πr) = QR/26.2
QR = 26.2sin(πr)
Now we can substitute this value for QR into our equation from the chord-chord power theorem:
(48)(26.2sin(πr)) = (21)(NR)
NR ≈ 22.8
Therefore, the length of NR is approximately 22.8, rounded to the nearest tenth.
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