For the given figure, where m and nare relatively prime positive integers. The value of m+n is 32.
Explain Law of Cosines.The law of cosines, also known as the law of cosines, relates all three sides of a triangle to one angle of the triangle. Most useful for searching for missing information in triangles. For example, if you know all three sides of a triangle, you can use the law of cosines to find the measure of the angle. Similarly, if you know two sides and the angle between them, you can find the length of the third side by the law of cosines.
Let X be the intersection of the circles with centers B and E, and Y be the intersection of the circles with centers C and E.
Since the radius of B is 3, AX = 4.
Assume AE = p.
Then EX and EY are radii of circle E and have length 4 + p.
AC = 8, and ∠CAE = 60° because we are given that triangle T is equilateral.
Using the Law of Cosines on Δ CAE, we obtain
(6+p)² =p² + 64 - 2(8)(p) cos 60
The 2 and the cos 60 terms cancel out:
p² + 12p + 36 = p² + 64 - 8p
12p+ 36 = 64 - 8p
p = 28/20
= 7/5
The radius of circle E is 4 + (7/5)
= 27/5,
So, the answer is 27 + 5 = 32
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Jaidyn’s family drinks a total of 10 gallons of milk every 5 weeks . How many gallons of milk does the family drink per week? How many weeks does it take the family to consume one gallon of milk?
Answer:
2 gallons of milk per week
0.35 weeks(3.5 days) to consume 1 gallon
Step-by-step explanation:
Jaidyn's family drinks 10 gallons of milk every 5 weeks, which is a ratio of
10:5
To find how many gallons of milk they drink per week, you'd have to divide 10/5
10 ÷ 5 = 2
Considering that 1 week is 7 days, it would take them 0.35 weeks to consume 1 gallon of milk, which is the same as 3 and a half days.
There are 200 students, where 86 of them were in the athletics team. Therefore, ___% of the students were in the athletics team.
Answer:
43%
Step-by-step explanation:
calculate percentage as
( number of students in athletics team ÷ total students ) × 100%
= ( 86 ÷ 200) × 100%
= 0.43 × 100%
= 43%
Convert the number into standard form, please!
Convert from number format to standard form as a decimal multiplied by a power of 10.
What is standard form?Standard form is a way of writing a number so it is easier to read. It is often used for very large or very small numbers. Standard form is like scientific notation and is typically used in science and engineering.A number is written in standard form when it is represented as a decimal number times a power of 10.As an example, consider the speed of light which travels at about 671,000,000 miles per hour. Written in standard form this number is equivalent to 6.71 x 108.step 1
convert 1.5806*10rais to 4
Convert to decimal notation
1.5806*10^4
The exponent is 4, making it 10 to the power of 4. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 4 time(s)
1.5806 ->15806
step 2
final result
15806
Simplify the expression
1.581*10^4
Simplify exponents and square roots
1.581*10^4
10 ^4 = 10 × 10 × 10 × 10 = 10,000
1.581*10000
Perform any multiplication or division, from left to right:
1.581*10000
15806
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help me this is a little confusing for me and i need to be done with it by tomorrow
Answer:
p(r(-3)) = 114
Step-by-step explanation:
I assume you want help with just #4:
[tex]r(x)=5r+2\\r(-3)=5(-3)+2=-15+2=-13\\\\p(x)=x^2+4x-3\\p(r(-3))=p(-13)=(-13)^2+4(-13)-3=169-52-3=117-3=114[/tex]
A line passes through the points (–6,5) and (8,–2). What is its equation in point-slope form?
Answer:
y - (-2 ) = 1\2 ( x- 8)
Step-by-step explanation:
The point slope form equation is y-y₁=m(x-x₁)
( -6 , 5 ) ( 8 , -2 )
( x , y ) (x1 , y1 )
Firstly we need to find the slope
y1 - y -2 - 5
we can find the slope by this equation : ------------- = --------------
x1 - x 8 - (-6)
The slope is 1\2
If 70% of the members remembered the password but 21 members forgot, then how many members were there in all?
Please show work if you can
Thxs
Answer:
70 members
Step-by-step explanation:
Let's call the number of total members x. We know that 30% or [tex]\frac{3}{10}[/tex] of the members forgot, so our equation looks like this:
[tex]\frac{3}{10}x = 21[/tex]
Then, we will multiply both sides by 10 to get rid of the fraction:
3x = 210
Finally, we will divide both sides by 3 to find out our variable, x:
x = 70
So, there are 70 members in total.
Hope this helped!
How many ways are there to arrange $6$ beads of distinct colors in a $2 \times 3$ grid if reflections and rotations are considered the same
There are 90 ways to arrange 6 beads of distinct colors in a 2*3 grid if reflections and rotations are considered the same.
In order to reach this result, we may use Burnside's Lemma, which states that the average number of arrangements of a symmetric object's symmetric parts, is taken throughout the set of all possible symmetry operations of the object.
You may fix one element and position the rest around it because of the rotation. You now have a total of 90 configurations available.
Thus, If reflections and rotations are treated equally, there are 90 ways to arrange 6 beads of different colors on a 2*3 grid.
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solve by completing the square
-x^2=5x-14
Answer:
Roots: -7, 2
Step-by-step explanation:
-x² = 5x - 14
-x² -5x +14 = 0
x² + 5x - 14 = 0
(x + 7)(x -2) = 0
x = -7 or x = 2
Four students are in the final rounds of a chess tournament. Based on their chess rankings, Gloria is twice as likely as Devon to win. Devon is twice as likely as Janet to win. Janet is just as likely as Harry to win. Create a table of fractional probabilities of winning for the four-person sample space.
need pointz
Step-by-step explanation:
179÷[618- (241-)]÷12 =
I don't know what I'm doing pls help this urgent
Answer: 215
Step-by-step explanation:
Whats the answer to the equation
(-7.14) + (-5.2)
The answer to the addition equation (-7.14) + (-5.2) = -12.34
What is addition?Addition is a mathematical operation in which two numbers are combined together using the addition symbol, +.
What is the answer to the given equation?Since we have the equation (-7.14) + (-5.2), we desire to add both numbers together. We proceed to add the two numbers as follows.
(-7.14) + (-5.2) = -7.14 - 5.2
= -12. 34
So, we see that the answer to the addition equation (-7.14) + (-5.2) = -12.34
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49x+ 0.10= 117.90
I need help please
Subtract 0.1 from both sides49x+ 0.10= 117.90
49x+0.1-0.1=117.9-0.1
x=2.404
What is meant by variables?A quantity that may assume any one of a set of values. : a symbol representing a variable. : something that is variable. : a factor in a scientific experiment that may be subject to change.A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data item. Age, sex, business income and expenses, country of birth, capital expenditure, class grades, eye colour and vehicle type are examples of variables.A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common generic symbols used for variables49 x+0.1=117.9Move 0.1 to the right side49 x=117.8Divide both sides by 4949 x/49=117.8/49Simplifyx=2.40408To learn more about variables refers to:
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Write 5 2/3+2 1/5 as a mixed number
Answer: 7 13/15
Step-by-step explanation:
First of, you have to get your common denominator, as it's impossible without one.
The closest common denominator is 15, and it will ask you for a simplified version.
Multiply the 2/3 in 5 2/3 by 5 on both sides to get 5 10/15
Multiply the 1/5 in 2 1/5 by 3 on both sides to get 2 3/15
Then add up your sum.
5 10/15+2 3/15=7 13/15
Answer:
7 13/15
Step-by-step explanation:
5 2/3+2 1/5
We need to get a common denominator for the fraction
3*5 = 15
2/3 *5/5 = 10/15
1/5 * 3/3 = 3/15
5 10/15 + 2 3/15 = 7 13/15
45 POINTS -Find the perpendicular line. Don’t explain
By analytical geometry, the line y = - 2 · x - 1 represents a line perpendicular to the line shown in the picture. (Correct choice: C)
How to find the equation of a line perpendicular to another line
According to analytical geometry, lines are described by polynomials of the form:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variable.y - Dependent variable.And the equation of the perpendicular line pass through a point of original line and is related to the slope of the line by following relationship:
m · m' = - 1
Where:
m - Slope of original line.m' - Slope of perpendicular line.First, determine the slope and intercept of the original line:
(x, y) = (0, 1)
1 = m · 0 + b
b = 1
(x, y) = (2, 0)
0 = m · 2 + b
2 · m + b = 0
m = - b / 2
m = - 1 / 2
Second, calculate the slope of the perpendicular line:
m' = 1 / (- 1 / 2)
m' = - 2
Third, we conclude by discarding options that the equation of the perpendicular line is y = - 2 · x - 1.
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If 2 of the 1000 test subjects are randomly selected find the probability that they both had false positive results. Is it unlikely to randomly select 2 subjects and get 2 results that are both false positive results
Using the concept of conditional probability and the conditions provided, The answer is [tex]\frac {p^2}{2pq}[/tex] .
What do you mean by probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probabilities can be calculated using the ratio of the number of favorable outcomes to the total number of possible outcomes. It helps us to understand the uncertainty of events.
What do you mean by false positive results?A false positive result is when a test indicates that a particular condition or attribute is present, when in reality it is not. For example, in medical testing, a false positive result would occur when a test for a disease returns a positive result but the person being tested does not actually have the disease. False positives can have serious consequences, as they can lead to unnecessary treatments, further testing, and anxiety for the person being tested.
p=probability of occurrence
q=1-p
P(false positive for both subjects | false positive for one subject) = P(false positive for both subjects and false positive for one subject) / P(false positive for one subject)
P(false positive for both subjects | false positive for one subject) = p^2 / (2pq)
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What is the height formula of isosceles triangle?
The formula for finding the height of an isosceles triangle is h = (2*A)/b, where h is the height, A is the area of the triangle, and b is the base of the triangle.
The formula for finding the height of an isosceles triangle is h = (2*A)/b, where h is the height, A is the area of the triangle, and b is the base of the triangle. To use this formula, the area of the triangle must first be calculated. To do this, multiply the base of the triangle by its altitude, or the perpendicular distance from the base to the vertex opposite it. Once the area is known, the height of the triangle can be calculated by multiplying the area by two and dividing it by the base. This will give the height of the triangle. For example, if a triangle has a base of 5 and an area of 10, then the height of the triangle is (2*10)/5, or 4.
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What is logically equivalent example?
Two statements are logically equivalent if they have the same truth value in all possible circumstances, meaning that they are either both true or both false in any given context.
For example, the statement "All dogs are mammals" is logically equivalent to the statement "All non-mammals are not dogs." Although the statements use different words and phrasing, they convey the same information and are both true.
Another example would be the statement "x>2" is logically equivalent to the statement "x>=3" because they both would have the same solutions.
Logical equivalence is important in logical reasoning, proof and in computer science where it is used to determine if two statements are logically equivalent which leads to simplify the boolean expressions.
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I need to know how to solve e,d,f im so confused it’s about angles in a circle
When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.
what is circle ?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetric about the center at every angle. Every pair of points in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally symmetric about the center at every angle.
given
in 6th figure
61° + 52° + x = 180° ( sum of exterior angle )
113° + x = 180°
x = 67°
y = 67°
When two inner angles are stated as 61° and 52° in the sixth figure, x and y are both set to 67°.
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Type the correct answer in each box. Use numerals instead of words. Find the missing side and angle measures in triangle ABC. Round your answers to the nearest tenth. Scalene triangle ABC with side AC labeled 23 and side BC labeled 15. Angle A measures 40 degrees. The measure of angle B is approximately . The measure of angle C is approximately . The length of side AB is approximately
The measures of the angles of the triangles are
The measure of ∠B = 80.3°
The measure of ∠C = 59.7°
The length of side AB = 20.2 units
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of side AC = 23
The measure of side BC = 15
The measure of ∠A = 40°
From the law of sines , we get
( sin A ) / a = ( sin B ) / b = ( sin C ) / c
Substitute the value of A and a in the equation , we get
sin ( 40 )° / 15 = sin B / 23
On simplifying the equation , we get
sin B = ( 23/15 ) x sin ( 40 )°
Now , m∠B = 80.27°
So , the measure of angle ∠B = 80.3°
And ,
The interior angles of a triangle is 180°
So , The measure of angle ∠C = 180° - ( 80.3° + 40° )
On simplifying the equation , we get
The measure of angle ∠C = 59.7°
Now ,
From the law of cosines , c² = a² + b² - 2ab ( cos C )
Substitute the value of a , b and cos C in the equation , we get
c² = 15² + 23² - 2 ( 15 ) ( 23 ) cos ( 59.7 )°
On simplifying the equation , we get
c² = 225 + 529 - 348.12363
c² = 405.87
Taking square roots on both sides of the equation , we get
c = 20.156
c = 20.2 units
Therefore, the measure of side AB = 20.2 units
Hence , the measures angles of triangle is solved
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Given that there are 3 feet or 36 inches in 1 yard, which of the following amounts is greater than 6 feet? Select all that apply. Video A) 2 yards, 3 inches B) 5 feet, 8 inches C) 96 inches D) 3 yards, 2 feet E) 1 yard, 2 feet
Answer: its D
Step-by-step explanation: 3 yard is bigger then 6 feet because 3 yards equals 9 feet hope this helps
How do you match a logarithmic function with its graph?
Matching a logarithmic function with its graph can be done by understanding the key characteristics of logarithmic functions and how they are represented on a graph.
A logarithmic function is of the form y = log base b (x), where b is the base of the logarithm (usually 10 or e).
The graph of a logarithmic function is a reflection of the exponential function of the same base b, across the line y=x.
Here are some key characteristics of logarithmic functions and their corresponding graphs:
1) Asymptote: The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.
2) Domain: The domain of a logarithmic function is x>0, since the logarithm of a negative number is undefined.
3)Range: The range of a logarithmic function is all real numbers
4) Increasing or decreasing: A logarithmic function is increasing over its domain
5) Shape: The graph of a logarithmic function is concave down.
6) x-intercept: The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.
By keeping these characteristics in mind, you can match a logarithmic function with its graph by observing the shape, asymptote, domain and range of the graph.
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URGENT!!!
Which of the following points best represents the location of -1 5/8 on the number line?
A
B
C
D
Answer:
A
Step-by-step explanation:
[tex]-2<-1 \frac{5}{8}<-1[/tex], and A is the only point between -2 and -1.
Answer: i believe your answer would be C.
Step-by-step explanation: it is located where -1 is and is on the 5th line. between -1 and the letter C there are 8 lines. So answer would be letter C. sorry if that’s wrong.
Question 3: Use the graph to fill in the blank with the correct number. f(3) =
10A
5
•
0
5
•
-5.
-10%
Your answer
Answer:
f(3) = 2
Step-by-step explanation:
See the attached graph. f(3) = ____ is asking us to find the value of the function, f, at the point x = 3. At x = 3, the value of y is 2.
Find the measure of the two marked angles NEED HELP ASP!!!!!
The measure of the two marked angles are as follows:
60°60°How to find angles when parallel lines are cut by a transversal?When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate exterior angle, alternate interior angles, linear angles, vertically opposite angles, same side interior angles etc.
According to the diagram the parallel lines are cut by the transversal and formed the angles.
Hence, the angles are alternate exterior angles.
Alternate exterior angles are congruent. Hence, the angles are as follows:
10x - 20 = 7x + 4
10x - 7x = 4 + 20
3x = 24
x = 24 / 3
x = 8
Therefore, the angles are as follows:
10x - 20 = 10(8) - 20 = 80 - 20 = 60 degrees
7x + 4 = 7(8) + 4 = 56 + 4 = 60 degrees.
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(03.05 MC) The table below shows the wavelength of four electromagnetic waves in meters (m). Electromagnetic Wave A C D Wavelength 3.0 x 10²m 4.0 x 10-6 1.2 x 10-¹2 m 2.0 x 10 m de According to the table, which electromagnetic wave has the least amount of energy?
According to the table the wavelength that has the least amount of electromagnetic energy is B having a wavelength of 4.0 x 10⁻⁶ m
What is electromagnetic energy?Radiant energy that moves in waves at the speed of light is called electromagnetic energy. It can also be referred to as radiant energy, electromagnetic radiation, electromagnetic waves, light, or the movement of radiation.
Wavelength is the separation between identical points (adjacent crests) in successive cycles of a waveform signal traveling through space or over a wire.
This length is often stated in meters when using wireless technology (m),
The relationship between a electromagnetic energy and wavelength is in inverse relation. This means that the least wavelength will result to greatest electromagnetic energy
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complete question
(03.05 MC) The table below shows the wavelength of four electromagnetic waves in meters (m).
Electromagnetic Wave Wavelength
A 3.0 x 10² m
B 4.0 x 10^-6 m
C 1.2 x 10-¹2 m
D 2.0 x 10 m
According to the table, which electromagnetic wave has the least amount of energy?
Your grandmother has given you some money, and now you plan to save what she has given you along with a certain amount of money each week. After 17 weeks, you have $570, and after 29 weeks, you have $822. a) Find an equation (in slope-intercept form) of the amount of money saved after × weeks.
An equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.
What is the slope intercept form?The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.
The standard form of the slope intercept form is y=mx+c.
Given that, after 17 weeks, you have $570, and after 29 weeks, you have $822.
Here, (17, 570) and (29, 822)
Substitute (x₁, y₁)=(17, 570) and (x₂, y₂)=(29, 822) in m=(y₂-y₁)/(x₂-x₁)
= (822-570)/(29-17)
= 252/12
= 21
Substitute, m=21 and (x, y)=(17, 570) in y=mx+c, we get
570=21×17+c
570=357+c
c=213
Substitute, m=21 and c=213 in y=mx+c, we get
y=21x+213
Therefore, an equation in slope-intercept form of the amount of money saved after x weeks is y=21x+213.
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Please help me with my hw
Answer:
9m^8 n^2
Step-by-step explanation:
Open up the parenthesis and simplify to find your answer.
The difference between the two groups compared will have more significance as the p-value becomes __________. The difference between the two groups compared will have more significance as the t-value becomes __________.
The significance of the difference between the two groups under comparison will increase as the p-value decreases. The significance of the difference between the two groups under comparison will increase as the t-value rises.
If there is a significant difference between two groups, what does that mean?A difference that is "statistically significant" does not necessarily have to be "large, important, or significant in terms of the utility of the finding"; it simply means that there is statistical evidence that there is a difference.
When the p-value exceeds the significance level, what does that mean?In general, when the null hypothesis H0 is true, our sample results could have happened by random chance alone when the p-value is "high" (i.e. greater than or equal to the significance level).
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Which line L has a slope of zero?
Answer:
D
Step-by-step explanation:
GradientA Gradient is also called a slope of a line, which represents how steep a line is.
Formula of slope: Vertical difference ÷ Horizontal difference
For a slope to be zero, the line must be horizontal.
SolutionBased on the question given, we can deduce that D is a horizontal line and therefore the slope is zero.
Determine two numbers that have a
square root between 326 and 327, are
divisible by 100, and are a multiple of 6.
It divides by three. According to the law of divisibility for three, a number is fully divisible by three if its digit sum is likewise divisible by three.
What is divisibility test?The divisibility rule is a clear and useful method for determining if an integer is divisible by a given set of divisors without actually doing division, sometimes simply looking at the integer's digits. The divisibility test allows you to rapidly determine if a given integer can be divided by a specified divisor without actually doing the division process. The quotient must be an integer and the remainder must be zero when dividing two numbers precisely.
here
add all the numbers,
326 = 3+2+6 = 11
so it is not divisible by 3
327 = 3+ 2 + 7 = 12
so it is divisible by 3
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