2016n 2 (mod 217) in this situation because 2016n 1 (mod 31) indicates that 2016n Following the resolution of the question
what is the cube's root?The cube root of a number is a value that, when multiplied by itself three times, returns the original value.
Let r1, r2, and r3 be the three integer roots of x3 + x + 4 (2 2016n) = 0.
According to Vieta's formulae, we have:
r1 + r2 + r3 = 0 r1r2 + r1r3 + r2r3 = r1r2r3 = r1r2r3 = 2 2016n - 4
Because r1, r2, and r3 are integers, their product r1r2r3 is an integer as well. As a result, 2 2016n - 4 must be an integer. That is, 2016n must be an integer plus 2/2n.
Because 2016 is divisible by 25, we may write 2016n as (25)n = 2(5n). As a result, 2/2n can be condensed to 2(1-n).
Thus, 2016n = k + 2(1-n), where k is an integer. That is, 2016n is congruent to 2(1-n) modulo 1.
We see that 2 is a primitive root modulo 31, which indicates that every integer close to 31 may be written as a power of 2 modulo 31. Specifically, 230 1 (mod 31), so 215 1 (mod 31).
We have 2016 0 (mod 2), 9 (mod 31), and 6 (mod 7), since 2016 = 25 32 7. As a result, 2016n = 0 (mod 2), 1 (mod 31), and 1 (mod 7).
We analyse three possible scenarios:
Case 1 consists of 2016n 0 (mod 2) and 2016n 1 (mod 7).
2016n 1 (mod 31) in this situation because 2016n 1 (mod 7) indicates that 2016n 1, 9, 15, or 23 (mod 31) and 2016n is even. As a result, 2016n 1 (mod 31) and 2016n 1 (mod 7).
2016n 1 (mod 217) is the sole possibility.
Case number two: 2016n 1 (mod 31) and 2016n 1 (mod 7).
2016n 1 (mod 217) because 2016n 1 (mod 31) indicates that 2016n 1, 15, or 16 (mod 217), and 2016n 1 (mod 7). As a result, the sole option is 2016n 1 (mod 217).
Cases 3 and 4: 2016n 1 (mod 31) and 2016n 2 (mod 7).
2016n 2 (mod 217) in this situation because 2016n 1 (mod 31) indicates that 2016n.
to know more about root of cube here -https://brainly.com/question/12726345
#SPJ1
The possible values of α are:
-2(504ⁿ - 1) - 2n², where n ≥ 0 is an integer (Case 1)
-2(504ⁿ - 1) - 2
what is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
Let the three integer roots of the given cubic equation be denoted by p, q and r, so we have:
x³ + αx + 4 - (2 × 2016ⁿ) = (x - p)(x - q)(x - r)
Expanding the right-hand side and equating coefficients with the left-hand side, we get:
p + q + r = 0
pq + qr + rp = α
pqr = 2 × 2016ⁿ - 4 = 4(504ⁿ - 1)
Since p, q, and r are integers, their sum is also an integer, which means that they must have the same parity (i.e., they are either all even or all odd). Moreover, since their product is even, at least one of them must be even. Therefore, we have two cases to consider:
Case 1: p, q, and r are all even
In this case, we can write p = 2m, q = 2n, and r = 2k, where m, n, and k are integers. Substituting these into the equations above, we get:
m + n + k = 0
4mn + 4nk + 4km = α/2
8mnk = 4(504ⁿ - 1)
Since m + n + k = 0, we have k = -(m + n). Substituting this into the second equation, we get:
-4mn - 4nm - 4n² = α/2
-8mn - 8n² = α
Substituting the expression for 8mnk from the third equation, we get:
-2(504ⁿ - 1) - 2n² = α
Therefore, in this case, α is of the form -2(504ⁿ - 1) - 2n², where n ≥ 0 is an integer.
Case 2: p, q, and r are all odd
In this case, we can write p = 2m + 1, q = 2n + 1, and r = 2k + 1, where m, n, and k are integers. Substituting these into the equations above, we get:
m + n + k = -1
4mn + 4nk + 4km = α
8mnk + 2(m + n + k) = 4(504ⁿ - 1)
Since m + n + k = -1, we have k = -(m + n + 1). Substituting this into the second equation, we get:
-4mn - 4nm - 4n² - 4m - 4n - 4 = α/2
-8mn - 8n² - 8m - 8n - 8 = α
Substituting the expression for 8mnk from the third equation, we get:
-2(504ⁿ - 1) - 2n² - 2(m + n + 1) = α
Therefore, in this case, α is of the form -2(504ⁿ - 1) - 2n² - 2(m + n + 1), where m, n, and k are integers such that m + n + k = -1.
In summary, the possible values of α are:
-2(504ⁿ - 1) - 2n², where n ≥ 0 is an integer (Case 1)
-2(504ⁿ - 1) - 2
To learn more about algebra from the given link:
https://brainly.com/question/24875240
#SPJ1
Need help will give brainliest and 5 stars! :)
Answer: 7
Step-by-step explanation:
If a surgery has a 92% change of being successful, what is the probability that a surgeon does 8 surgeries out of which 5 are successful?
According to probability, the answer to the question is that an average surgeon performs 8 operations, of which 5 are successful. 18.9%.
What is Binomial probability?In a fixed number of independent trials, each of which can only have one of two outcomes—success or failure—the number of successes is expressed as a probability distribution known as a binomial probability. Additionally, it is presummated that each trial has an equivalent chance of success.
The binomial probability formula can be used to determine the likelihood that a surgeon will perform 5 successful operations out of 8 given that each operation has a 92% chance of being successful.
You may find the binomial probability formula by using:
[tex]P(X = k) = C(n, k)*p^k*(1 - p)^{(n - k)}[/tex]
Where:
P(X = k) is the likelihood that, out of n surgeries, exactly k will be successful.
The binomial coefficient, C(n, k), is defined as the number of ways to select k successful operations among n surgeries C(n, k) = n! / (k! * (n - k)!), where ! denotes factorial.
p is the likelihood that a single surgery will succeed (92% in this case, or 0.92).
The number of successful operations that interests us is k.
The total number of operations is n, which in this case is 8.
By entering the values, we can determine the probability using the formula below:
P(X = 5) = C(8, 5) * 0.92⁵ * (1 - 0.92)⁽⁸⁻⁵⁾
C(8, 5) = 8! / (5! * (8 - 5)!) = 56
0.92⁵ = 0.659
(1 - 0.92)³ = 0.512
P(X = 5) = 56 * 0.512 * 0.659 = 18.89 or 18.9%
Given a 92% success rate for each surgery, the likelihood that a surgeon will perform 5 successful operations out of 8 is roughly 18.9%.
To know more about Binomial probability, visit:
brainly.com/question/30764478
#SPJ1
Find the direction of this
vector:
174 M
88.4 m
Remember, angles are measured from
the +x-axis.
direction (deg)
The direction of the vector is 27 degrees
How to find the vectorThe vector is the hypotenuse and the angle showing magnitude and direction.
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem.
hypotenuse^2 = opposite^2 + adjacent^2
hypotenuse^2 = 88.4^2 + 174^2
hypotenuse ≈ 195.17 m
Therefore, the magnitude of the vector (hypotenuse of the right triangle) is approximately 194.8 m.
The direction
We can use the trigonometric function of tangent to find the angle between the opposite and adjacent sides of a right triangle.
tan(θ) = opposite/adjacent
We are given
the opposite side as 88.4 m and the adjacent side as 174 mso we can use these values to find the angle θ:
tan(θ) = 88.4/174
θ = arc tan (88.4/174)
θ ≈ 26.93 degrees
Therefore, the angle between the opposite and adjacent sides of the right triangle is approximately 27 degrees.
Learn more about vectors at
https://brainly.com/question/25705666
#SPJ1
Data is given to represent the number of each of the types of clubs three different schools in your area offer. Academic Clubs Service Clubs Sporting Clubs Eastern High School 6 3 10 Central High School 8 9 9 West-Side High School 4 7 12 Which of the following matrices can be used to accurately represent the data? (2 points) matrix with row 1 showing 6 and 3 and 10, row 2 showing 8 and 9 and 9, row 3 showing 4 and 7 and 12 matrix with row 1 showing 6 and 3 and 10, row 2 showing 8 and 9 and 12, row 3 showing 4 and 7 and 9
Answer:
The matrix with row 1 showing 6 and 3 and 10, row 2 showing 8 and 9 and 9, row 3 showing 4 and 7 and 12 can be used to accurately represent the data.
The following matrix that can be used to accurately represent the data is the matrix:
[tex]\left[\begin{array}{ccc}6&3&10\\8&9&9\\4&7&12\end{array}\right][/tex]
What is the matrix?A matrix is a collection of numbers, encompassed by brackets.
The numbers are known as matrix elements or entries. The components are organized in rows (horizontal) or columns (vertical), which determine the matrix's size (dimension or order).
As per the question, the entry in row i and column j represents the number of type j clubs offered by school i.
The matrix that can be used to accurately represent the data is the matrix:
[tex]\left[\begin{array}{ccc}6&3&10\\8&9&9\\4&7&12\end{array}\right][/tex]
This is because the rows represent the three different schools, and the columns represent the number of each of the types of clubs they offer.
The given data matches the entries in this matrix, so it can be used to accurately represent the data.
To learn more about the matrix click here:
https://brainly.com/question/28180105
#SPJ2
Rewrite 5^/4. /2 as a single radical
O 10^/2^9
O10^/20^9
O9^/2^10
The expression can be rewriten as a single radical as:
[tex]\sqrt[5]{4} *\sqrt{2} = \sqrt[10]{2^9}[/tex]
How to rewrite the expression as a single radical?We want to rewrite the expression below as a single radical:
[tex]\sqrt[5]{4} *\sqrt{2}[/tex]
First remember that 4 = 2², then we can replace that to get:
[tex]\sqrt[5]{4} *\sqrt{2} = \sqrt[5]{2^2} *\sqrt{2}[/tex]
Converthing the roots to exponents we will get.
[tex]\sqrt[5]{2^2} *\sqrt{2} = 2^{2/5}*2^{1/2}[/tex]
Now the exponents are just added:
[tex]2^{2/5}*2^{1/2} = 2^{2/5 + 1/2} = 2^{4/10 + 5/10} = 2^{9/10} = \sqrt[10]{2^9}[/tex]
That is the correct option.
Learn more about roots at:
https://brainly.com/question/428672
#SPJ1
Simplify remove all perfect squares from inside the square root assume b is positive
Answer:
Step-by-step explanation:
You take items out of a square root if you have a pair of numbers or if you know the square root.
[tex]\sqrt{48b^{7} }[/tex]=[tex]\sqrt{4*4*3*bbbbbbb}[/tex]
So I know the [tex]\sqrt{4}[/tex]=2 so i can take both out so outside the root will be 2*2 and inside the root will be 3
Now for the b's for every pair there are, you can take that out. There are 3 pairs of b's so b³ is outside and one b is left inside.
Answer:
4b³[tex]\sqrt{3b}[/tex]
8TH GRADE MATH: what is the distance from the store to the park? ‼️PLS ANSWER ASAP i’ll give any amount of points❕
Answer:
Step-by-step explanation:
assuming that every square is 1 unit, the distance from the store to home should be 5 units, I hope this helped
f(x)=-1/2x+3. G is a quadratic function with the following properties: g has lesser y-intercept than f; the maximum value of g and y-intercept are not equal; first g increases and the it decreases. Graph function g
The equation is [tex]g(x) = -\frac{1}{16} (x - 1)^2 + 2[/tex] Graphing this equation below, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).
Define the term graph?To demonstrate the connection between the two variables, a line or curve is drawn between the plotted points.
To graph function g, we need to find its equation that satisfies the given properties. We know that the y-intercept of g is less than that of f, so we can choose it to be 1. Also, the parabola of g opens downwards and its vertex is between the two x-intercepts, which are at x = -2 and x = 4. We can use these points to find the equation of the parabola in the standard form: g(x) = a(x - h)² + k. Using the fact that g(0) = 1 and the x-intercepts, we can solve for a, h, and k. The resulting equation is:
[tex]g(x) = -\frac{1}{16} (x - 1)^2 + 2[/tex]
Graphing this equation, we get a parabola that opens downwards and intersects the x-axis at x = -2 and x = 4, with a vertex at (1, 2).
To know more about graph, visit:
https://brainly.com/question/11803331
#SPJ1
1. The ratio of faculty members to students at a college is 1:18. If there are 16000 students, how many faculty members are there? Round to the nearest whole number
Therefore, there are approximately 889 faculty members at the college.
What is ratio?Ratio is a mathematical concept that expresses the relationship between two or more quantities or values. It is a way to compare the size of two numbers, by dividing one number by the other. The result of this division is a numerical expression of the relative size of the two numbers.
Ratios are often expressed as a fraction or a colon (:) between the two numbers. For example, if there are 4 red balls and 6 blue balls in a bag, the ratio of red balls to blue balls can be expressed as 4/6 or 4:6. This means that for every 4 red balls in the bag, there are 6 blue balls.
Ratios are commonly used in various fields, such as finance, statistics, and science, to compare different values and make meaningful interpretations.
To solve this problem, we need to use the ratio between faculty members and students, which is given as 1:18. This means that for every one faculty member, there are 18 students.
If there are 16000 students in the college, we can find the number of faculty members by dividing the number of students by the ratio of students to faculty members:
Number of faculty members = 16000 / 18
This gives us 888.888, but since we are asked to round to the nearest whole number, we should round up to 889. Therefore, there are approximately 889 faculty members at the college.
To know more about number visit:
https://brainly.com/question/17429689
#SPJ1
For the winter clothing drive, Jada's class collected 7 2/3 pounds of clothing. Wesley's class collected 1 5/6 times as much clothing as Jada's class. How many pounds of clothing did Wesley's class collect?
Write your answer as a fraction or as a whole or mixed number.
Wesley's class collected 253/18 pounds of clothing, which can also be written as 14 1/18 pounds (rounded to the nearest hundredth).
What is a whole number example?Whole numbers include natural numbers that begin from 1 onwards. Let us look at some examples of whole numbers. The set of whole numbers is denoted by the alphabet 'W'. W = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,.…}
Jada's class collected 7 2/3 kilograms of clothes. Wesley's class collected 15/6 times as many clothes as Jada's class, which means they collected:
1 5/6 x (7 2/3) pounds of fabric
To multiply fractions, you can first convert the mixed numbers to improper fractions, then multiply the numerators and denominators separately and simplify if possible.
Convert mixed numbers to improper fractions:
7 2/3 = (37 + 2)/3 = 23/3
1 5/6 = (61 + 5)/6 = 11/6
Multiply Fractions:
(11/6) * (23/3) = (1123)/(63) = 253/18
Therefore, Wesley's class collected 253/18 pounds of clothing, which can also be written as 14 1/18 pounds (rounded to the nearest hundredth).
Learn more about Natural number here
https://brainly.com/question/17429689
#SPJ1
find the product
-5(-8)
Answer:
40
Step-by-step explanation:
In order to find your answer, you would need to multiply -5, by -8 which equals 40.
:)
-5(-8) = 40
Because both the 5 and 8 being multiplied are negative, the commutative multiplication property states that the product should be positive. Since 5*8=40, -5*-8=40
A bus traveled on a level road for 4 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 4 hours. Find the average speed on the level road if the entire trip was 400 miles.
Answer:
Let's call the speed of the bus on the winding road "s". Then we know that the bus traveled at a speed of "s + 20" on the level road. We also know that the time spent on the winding road was 4 hours, so the distance traveled on the winding road is:
distance = speed × time = s × 4
Similarly, the distance traveled on the level road is:
distance = speed × time = (s + 20) × 4
Since the entire trip was 400 miles, we can write:
4s + 4(s + 20) = 400
Simplifying this equation, we get:
8s + 80 = 400
8s = 320
s = 40
Therefore, the speed of the bus on the winding road was 40 mph, and the speed on the level road was 40 + 20 = 60 mph.
To check that this solution is correct, we can calculate the distance traveled on each road:
distance on winding road = 40 × 4 = 160 miles
distance on level road = 60 × 4 = 240 miles
The total distance traveled is indeed 160 + 240 = 400 miles, so our solution is correct.
Therefore, the average speed on the level road was 60 miles per hour.
I need help with this problem
Answer:
its 32 square units
Step-by-step explanation:
The Shape is a rectangle. Area of a rectangle is Length x Width
8 x 4 = 32
Answer:
32 Square units
Step-by-step explanation:
You can see that there are 8 spaces of width by using the graph. And 4 spaces of height. So, assuming each space is 1 Square unit. All you have to do is 8×4 which is 32.
How can you write 10/3 as a division expression and as a mixed number?
Show your work!
Answer:
[tex] \frac{10}{3} = 10 \div 3 = 3 \frac{1}{3} [/tex]
Answer: Mixed Number Form: 3[tex]\frac{1}{3}[/tex]
Decimal Form: 3.3 repeating
can i have brainliest please i need it
Question 2 (Essay Worth 10 points)
(02.02, 02.05 MC)
The linear function f(x) = 0.5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents
the average test score in your science class, where x is the number of the test taken.
g(x)
81
83
Part A: Determine the test average for your math class after completing test 2. (2 points)
Part B: Determine the test average for your science class after completing test 2. (2 points)
Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 polnts)
The science class had a higher average of 85 compared to te math's average of 81
Maths class
The function si given as
f(x) = 0.5x + 80
After completing test 2, we have
f(2) = 0.5 * 2 + 80
f(2) = 81
Science class
The function si given as
The table
The equation of the table is
g(x) = 2x + 81
After completing test 2, we have
g(2) = 2(2) + 81
g(2) = 85
This means that the science class had a higher average
Read more about linear function at
https://brainly.com/question/30318449
#SPJ1
help! offering 20 points!!!
What unit of measurement would you use to weigh an elephant? A Ounce B Ton C Millimeter D Pound
Answer:
B
Step-by-step explanation:
The unit of measurement that would typically be used to weigh an elephant is the ton. Elephants are very large animals, and they can weigh several tons, depending on their species and size. While other units of measurement like pounds, kilograms, or ounces could also be used to measure the weight of an elephant, the ton is the most appropriate unit for such a large animal.
Evaluate and simplify the expression
when X = 3 and y = 5.
2y + 3(x - y) + x2 = [?]
Answer:
Step-by-step explanation:
substitute:
2(5) + 3(3-5) + 3² Do PEMDAS order (parenthesis, exponent, mult/div, add/sub
2(5) + 3(-2) +3²
2(5) + 3(-2) + 9
10 + 3(-2) +9
10-6+9
4+9
13
The function f(x) = 12x - 4.8x^2 models the height of a beach ball x seconds after it is tossed.
Find the average rate of change over the interval 0 < x < 2.
_____ feet per second
The average rate of change of a beach ball thrown according to the function[tex]f(x) = 12x - 4.8x^2[/tex] over the interval 0 < x < 2 is -9.6 feet per second.
To find the average rate of change, we need to find the height of the ball at x = 0 and x = 2, and then find the change in height over the time interval.
At x = 0, the height of the ball is:
[tex]f(0) = 12(0) - 4.8(0)^2 = 0[/tex]
At x = 2, the height of the ball is:
[tex]f(2) = 12(2) - 4.8(2)^2 = -19.2[/tex]
The change in height over the time interval 0 < x < 2 is:
-19.2 - 0 = -19.2
Therefore, -19.2/2 = -9.6 feet per second is the average rate of change over the range 0 x 2.
The average change throughout the range of 0 x 2 is therefore -9.6 feet per second.
For another problem involving an average rate of change, you can check brainly.com/question/14481908
#SPJ1
How was pre-image ABC transformed to create image A′B′C′ ?
Responses
reflection over BC⎯
90° clockwise rotation around point C
translation up
translation down
The answer of the given question based on the image transformation is , (a) reflection over line BC⎯.
What is Reflection?Reflection is a transformation in which a figure or an object is flipped across a line or a plane. The line or plane across which figure is flipped is called line or plane of reflection. In two-dimensional geometry, a reflection can be thought of as a "flip" of the figure over the line of reflection. Any point on the figure that lies on the line of reflection will remain fixed, while all other points will be reflected across the line.
The pre-image ABC was transformed to create image A′B′C′ through a reflection over line BC⎯.
To visualize this transformation, imagine folding the original figure over line BC⎯, so that point A maps to point A′, point B maps to point B′, and point C maps to point C′. The resulting image is the reflection of the original figure over line BC⎯.
The other options listed (90° clockwise rotation around point C, translation up, and translation down) would create different images, but not the image A′B′C′ shown in the diagram.
To know more about Line of reflection visit:
https://brainly.com/question/31019596
#SPJ1
Which description compares the domains of Function A and Function B correctly? Function A: f(x)=logx Function B: A square root function graphed on a grid in Quadrant One, with the x and y axis beginning at negative ten and increasing in increments of two until reaching ten. The function, labeled g of x, contains a filled in point at begin ordered pair one comma zero end ordered pair and passes through begin ordered pair eight comma two end ordered pair as a smooth curve while extending to infinity. Responses The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1. The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1. The domain of both functions is the set of real numbers greater than or equal to 1. The domain of both functions is the set of real numbers greater than or equal to 1. The domain of Function A is the set of real numbers greater than or equal to 1. The domain of Function B is the set of real numbers greater than 1. The domain of Function A is the set of real numbers greater than or equal to 1. The domain of Function B is the set of real numbers greater than 1. The domain of both functions is the set of real numbers.
The domain of function A and function B are compared by the statement of Option A: The domain of Function A is the set of real numbers greater than 0. The domain of Function B is the set of real numbers greater than or equal to 1.
What is a function?
A function is a fundamental concept in mathematics that relates a set of inputs (also known as the domain) to a corresponding set of outputs (sometimes referred to as the codomain). For each input, there exists exactly one output, and the output can be linked to its corresponding input in a unique manner.
The domain of a function refers to the set of all possible input values for which the function can produce an output.
In Function A, the domain consists of all real numbers greater than 0, since it is a logarithmic function that can take any positive number as an input.
In contrast, the domain of Function B includes all real numbers greater than or equal to 1, since it is a square root function that begins at (1,0) and continues to infinity.
This means that any number greater than or equal to 1 can be used as an input to produce a corresponding output.
It is essential to define the domain of a function accurately to ensure that the function is well-defined and to avoid potential errors or ambiguities in mathematical computations.
Therefore, the correct statement is A.
To learn more about function from the given link
https://brainly.com/question/2284360
#SPJ1
3 The headmaster at a private school wants to
update the student dress code. He wishes to
survey a select group of parents of the students
enrolled at the school to determine their
opinion on the addition of a blazer to the school
uniform. Which method can be used to ensure
an unbiased sample is obtained for the survey?
A All parents attending the next PTO meeting
are surveyed.
B Every fifth person on a list of parent
volunteers is surveyed.
C All parents waiting in the pick-up line after
school are surveyed.
D All parents of students whose birthdays are
on even numbered days are surveyed.
(I will give brainliest if you proof your answer)
The best method to ensure an unbiased sample is to randomly select parents from the entire population of parents with enrolled students at the school.
To ensure an unbiased sample for the survey, the method used should not favor any particular group or exclude any group from the population.
Option A: Surveying all parents attending the next PTO meeting would not be an unbiased sample as not all parents attend PTO meetings.
Option B: Surveying every fifth person on a list of parent volunteers would also not be an unbiased sample as it may exclude parents who are not on the list.
Option C: Surveying all parents waiting in the pick-up line after school may not be an unbiased sample as it may exclude parents who do not pick up their children from school.
Option D: Surveying all parents of students whose birthdays are on even-numbered days may not be an unbiased sample as it excludes parents whose children's birthdays are on odd-numbered days.
Therefore, the best method to ensure an unbiased sample is to randomly select parents from the entire population of parents with enrolled students at the school.
To know more about random sampling visit:
brainly.com/question/30759604
#SPJ1
whats angle A pls help
Answer :
Angle A = 19.6°
Step-by-step explanation :
According to the question It is given that,
Angle A = x
Angle B = 5x
Angle C = 4x - 16
We will apply angle sum property in the question.
Angle sum property states that sum of all the angles of triangle is 180°
[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180
[tex]\: :\implies [/tex] x + 5x + 4x - 16 = 180
[tex]\: :\implies [/tex] 10x - 16 = 180
[tex]\: :\implies [/tex] 10x = 180 + 16
[tex]\: :\implies [/tex] 10x = 196
[tex]\: :\implies [/tex] x = 196/10
[tex]\: :\implies [/tex] x = 19.6
Hence,
Angle A = x
[tex]\: :\implies [/tex] 19.6 °
Angle B = 5x5 × 19.6
[tex]\: :\implies [/tex] 98
Angle c = 4x - 16
[tex]\: :\implies [/tex] 4 × 19.6 - 16
[tex]\: :\implies [/tex] 78.4 - 16
[tex]\: :\implies [/tex] 62. 4
We must also check our answer.
Sum of all angles = 180°
[tex]\: :\implies [/tex] ∠A + ∠B + ∠ C = 180
[tex]\: :\implies [/tex] 19.6 + 98 + 62.4 = 180
[tex]\: :\implies [/tex] 117.6 + 62.4 = 180
[tex]\: :\implies [/tex] 180 = 180
Hence, Verified.
Therefore, The Measure of Angle A is 19.6°
Answer:
angle A = 19.6°
Explanation:
angle ABC + angle ACB + angle BAC = 180°
5x + (4x - 16)° + x = 180°
Simplifying:
5x + x + (4x + -16) = 180
Reorder the terms:
5x + x + (-16 + 4x) = 180
Remove parenthesis around (-16 + 4x)
5x + x + -16 + 4x = 180
Reorder the terms:
-16 + 5x + x + 4x = 180
Combine like terms: 5x + x = 6x
-16 + 6x + 4x = 180
Combine like terms: 6x + 4x = 10x
-16 + 10x = 180
Solving
-16 + 10x = 180
Solving for variable 'x'.
Add '16' to each side of the equation
-16 + 16 + 10x = 180 + 16
Combine like terms: -16 + 16 = 0
0 + 10x = 180 + 16
10x = 180 + 16
Combine like terms: 180 + 16 = 196
10x = 196
Divide each side by '10'
x = 19.6
The measure of angle A is 19.6°
What is the slope of the line?
Answer:
It could be 0, is the question multiple choice?
a horizontal line always has a slope of 0, now, for the sake of a silly proof, let's do some rigamarole to get it.
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{7}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-3)}}} \implies \cfrac{0}{7 +3} \implies \cfrac{ 0 }{ 10 } \implies \stackrel{ }{\text{\LARGE 0}}[/tex]
Michael invested $380 into an account that earns 8% interest, compounded continuously. How much will be in the account after eight years round to the nearest cent.
Answer:
Step-by-step explanation:
The formula for continuous compound interest is:
A = P(1 + r/100)^t
where A is the amount after t years, P is the principal, r is the annual interest rate as a decimal, and t is the time in years.
In this case, we have P = $380, r = 0.08 (8%), and t = 8 years. Plugging in these values, we get:
A = 380 x (1+8/100)^8
A= 380 x (1+0.08)^8
A=380 x (1.08)^8
A= 380 x 1.8509..
A= $703.35
Therefore, the amount in the account after eight years, rounded to the nearest cent, is $703.35.
Find a degree 3 polynomial with real coefficients having zeros x = 3 and x = 1 − 2 i and a lead coefficient of 1. Write in expanded form.
Step-by-step explanation:
(x-3)(x-1 +2i)(x-1-2i) The imaginary roots always come in pairs : 1+- 2i
Which of these expressions is equivalent to log (46)?
OA. log (6) log (4)
OB. log (6) - log (4)
OC. 6. log (4)
OD. log (6) + log (4)
Answer: the answer is B
Step-by-step explanation:
Three-year-old boys in the United States have a mean height of 38 inches and a standard deviation of 2 inches, and 10-year-old girls have a mean height of 54.5 inches and a standard deviation of 2.5 inches.
Mrs. Davis has two children: a 3-year-old boy 43 inches tall and a 10-year-old girl 57 inches tall.
Which of Mrs. Davis' children is more unusually tall for his
or her age and gender? Explain, showing any calculations you perform.
The 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.
To solve this problemA z-score calculates how many standard deviations an observation is from the mean. An observation is said to be above the mean if the z-score is positive, while it is said to be below the mean if the z-score is negative.
For the 3-year-old boy, the z-score is:
z = (43 - 38) / 2 = 2.5
The z-score for the 10-year-old girl is:
z = (57 - 54.5) / 2.5 = 1
The 3-year-old boy has a higher z-score than the 10-year-old girl, indicating that he is more unusually tall for his age and gender. This is due to his height, which is higher than the average for his age group 38 inches .
Therefore, the 3-year-old boy is more unusually tall for his age and gender than the 10-year-old girl.
Learn more about standard deviations here : brainly.com/question/28225633
#SPJ1
(CLASSKICK) 7k+8=71 and -9=3-y.
show the answer and steps.
Answer:
k = 9 y = -6Step-by-step explanation:
7k+8=71
7k=71-8
7k=63
k=63/7
k=9
-9=3-y
-9+3=y
-6=y
y=-6
IF MY ANSWER IS HELPFUL THEN PLEASE RATE IT, LIKE IT, FOLLOW ME AND GIVE ME A BRAINLEST...PLEASE.
THANK YOU...!
Salut! Comment allez-vous? Comment s'est passée ta journée?
What is the angle SWY
The angle SWY is 59°.
What is points of tangency?
Points of tangency is a point When a line is tangent to a circle.
It intersects the circle at exactly one point.
This point is always perpendicular to the radius of the circle which passes through it which means that the tangent line and the radius form a right angle.
The measure of an arc is equal to the measure of the central angle which delete it. This means that if you know the measure of an arc.
We can find the measure of the central angle that subtends it.
If we assume that point Y is on the tangent line and is between point W and point S, then angle SWY is an inscribed angle that intercepts arc WS. In a circle, the measure of an inscribed angle that intercepts an arc is half the measure of the arc.
So, if the measure of arc WS is 118 degrees, then the measure of angle SWY is half of 118 degrees, which is 59 degrees.
Learn more about point of tangency here,
https://brainly.com/question/30427524
#SPJ1
