This is the vector equation equivalent to A = [2 7 -5 -1 2 -6 4 8], x = [2 -3], and b = [17 7 -22 16].
What is matrix equation ?Simultaneous equations can be presented and solved more simply using matrix algebra, a type of mathematical notation. It can be used to generate a mathematical model of the structure and to provide a clear statement of a structural issue.
The vector equation is as follows
r = a(l – t)+ b t
where,
t is some parameter and
for points between A and B then 0≤t ≤ 1.
According to question:
The matrix equation [2 7 -5 -1 2 -6 4 8][2 -3] = [17 7 -22 16] can be written as a vector equation using the definition of the product of a matrix and a vector.
Let's call the matrix [2 7 -5 -1 2 -6 4 8] as matrix A and the vector [2 -3] as vector x. The product of matrix A and vector x is a new vector, which we'll call vector b.
The equation [2 7 -5 -1 2 -6 4 8][2 -3] = [17 7 -22 16] can be written as:
A * x = b
where,
A = [2 7 -5 -1 2 -6 4 8], x = [2 -3], and b = [17 7 -22 16].
This is the vector equation equivalent of the matrix equation, which represents the same linear relationship between the matrix, the vector, and the result vector.
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Exponential Functions
The percent decrease of the exponential function is 22%
What is the percent decrease of the given function?Suppose we have an initial value A and we increase/decrease it by a percentage X, the new value will be:
A' = A*(1 ± X/100%)
Where the sign depends if it is an increase or decrease.
And if we apply that t times, then we have the exponential function:
A'(t) = A*(1 ± X/100%)^t
If we want to solvethe percentage, then we need to solve:
0.78 = 1 ± X/100%
Obviously we need to take the negative sign:
0.78 = 1 - X/100%
X = 100%*(1 - 0.78) = 22%
Thet is the percent decrease.
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How find all zeros calculator works?
Answer:
In general, given the function, f(x), its zeros can be found by setting the function to zero. The values of x that represent the set equation are the zeroes of the function. To find the zeros of a function, find the values of x where f(x) = 0.
Step-by-step explanation:
i have 3 more after this one
Answer:
2399.03
Step-by-step explanation:
2000*(1+2.3%)^8 =2399.03
Answer: 2399.0
Step-by-step explanation: because you would multiply 2000 by 1+2.3% ^8 and get your answer 2399.0 and if you round it to be the nearest hundredth you will get 2399.03
Two friends shop for fresh fruit. Jackson buys a watermelon for $8.25 and 5 pounds of cherries. Tim buys a pineapple for $2.15 and 4 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries. Write and simplify an expression to represent how much more Jackson spent.
please its to tonight at 11:59pm
Answer:
Step-by-step explanation:
Jackson -
8.25 + 5p
Tim -
2.15 + 4p
8.25 - 2.15 = 6.1
5p - 4p = 1p or p
simplified expression
6.1 + p is how much more Jackson spent
(I’m sorry if it’s wrong not 100 percent sure)
The table shows a proportional relationship.
Workout (hours) 1 2 3
Calories Burned 190 380 570
Create a description in words for the table.
The number of calories burned is dependent on the number of hours working out. For every 190-hour workout, there is 1 calorie burned, and for every 380-hour workout, there are 2 calories burned.
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 190 calories burned, and for a two-hour workout, there are 380 calories burned.
The number of hours working out is dependent on the number of calories burned. For every 190-hour workout, there is 1 calorie burned, and for every 380-hour workout, there are 2 calories burned.
The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 190 calories burned, and for a two-hour workout, there
The description of the proportional relationship on the table is given as follows:
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 190 calories burned, and for a two-hour workout, there are 380 calories burned.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
The variables for this problem are given as follows:
Input: number of hours.Output: number of calories burned.Hence the constant is given as follows:
k = 570/3 = 380/2 = 190/1 = 190 calories burned per hour.
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Pete i 15 and amy i 14 year old. Find out the maximum number of day that pete i older than amy
The maximum number of day is- 30472249.
Find out the maximum number of day that Pete i older than amy?Simply by subtracting the birth date from the current date. This conventional age formula can also be used in Excel. The first part of the formula (TODAY()-B2) returns the difference between the current date and date of birth is days, and then you divide that number by 365 to get the numbers of years.
Healthspan: years lived in good health. Chronological age: the number of years you have been alive. Biological age: how old your cells appear to be based on their current condition.
Age after n years = X + n.
Age n years ago = X – n.
n times the present age = nX.
If ages in the numerical are mentioned in the ratio A:B, then A:B will be AX and BX.
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A computer and monitor sold for $510. The computer costs $310 more than the monitorHow much did each item cost?
Answer:
computer sold for $410
Monitor sold for $100
Step-by-step explanation:
The computer cost = x
the monitor = x-310
2x-310=510
x=410
So computer sold for $410
Monitor sold for $100
Answer: The monitor sold for 200.
Step-by-step explanation:
If you have a total of $510, and one item costs $310, subtract $310 from $510 and you get $200.
Example: $510 - $310 = $200
the owner of a natural foods store made 20 lb of a dried fruit and granola blend that is 50% dried fruit by mixing a dried fruit and granola blend that is 20% dried fruit with a blend that is 60% dried fruit. how many pounds of each type were used to get the desired blend?
Answer:
see below
Step-by-step explanation:
20 lb of a dried fruit and granola blend 50% dried fruit
mixing 20% dried fruit x lbs
60% dried fruit y lbs
x+y=20 so x=20-y
0.2x+0.6y =0.5*20 =10
0.2(20-y) +0.6y=10
4 -0.2y+0.6y =10
0.4y =6
y=15
x=5
If you live in a town with a current population of 5,000 people and this population is increasing at a rate of 3.4% every 5 years, how many people will live in the town after 15 years?
Mr. Hunt gave out award ribbons to everyone who made honor roll. An image of the award ribbon is shown on the plane below. The award ribbon was pink and had an image of the school's logo
covering part of the ribbon. In the diagram, each grid square measures 1 inch by 1 inch.
The total area of the ribbon is equals to 46 sq. inches with a 4 square inches of school logo in between.
What is a Quardilateral ?The four-sided polygonal shape known as a quadrilateral has four edges and four corners. The Latin words quadri, a variation of four, and latus, meaning "side," were used to create the term.
Its sides are AB, BC, CD, and DA.There are four of them: Indicators A, B, C, and DThe angles are ABC, BCD, CDA, and DAB.Angles A and B are near one other.The polar opposite angles are A and C.They are the opposing parties, AB and CD.The neighboring sides are ABC.A 4-sided planar figure is called a quadrilateral. The following are some crucial characteristics of quadrilaterals:There are 4 vertices, 4 angles, and 4 sides in every quadrilateral.Its inner angles add up to 360 degrees.In American and Canadian English, a quadrilateral having at least one set of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides.
The total area of the ribbon = area of the top square + area of the bottom trapizium
Area of the square = 4*4 = 16 sq. inches
Area of the trapizium = (1/2)*(sum of parallel sides)*height = (1/2)*(4+8)*5 = 30 sq. inches.
The total area of the ribbon is equal to 30 + 16 = 46 sq. inches with a 4 square inches of school logo in between.
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Assume that T is a linear transformation. Find the standard matrix of T. T: R2-R2 first reflects points through the line x2 = xy and then reflects points through the vertical x2-axis. A= (Type an integer or simplified fraction for each matrix element.)
T is a linear transformation. the standard matrix of T. T: R2-R2 first reflects points through the line x2 = xy and then reflects points through the vertical x2-axis. A= (Type an integer or simplified fraction for each matrix element.) is: [[0, - 1], [1, 0]]
What is linear transformation in matrix?Only if g(x) is a certain kind of function known as a linear transformation can we. If each term of each component of the function g(x) is a number multiplied by one of the variables, the function g(x) is a linear transformation.
We are looking for a 2 × 2 matrix that reflects points through the horizontal axis and then reflects points through the line x₂ = x₁.
First the points need to be reflected through the horizontal 1-axis. This then means that the x₁ -coordinate remains unaffected and the x₂ coordinate changes sign:
R₁= [[1, 0], [0, - 1]]
Note: if you multiply this matrix by the vector (x₁, x₂)/T to the right, then you obtain the vector (x₁, - x₂)/t
Next the points need to be reflected through the line x₂ = x₁.
The x₁-coordinate and x₂ -coordinate then interchange.
R₂ = [[0, 1], [1, 0]]
Note: if you multiply this matrix by the vector (x₁, x₂)^T to the right, then
you obtain the vector (x₂, x₁)ⁿ
The combination of the reflections is then the product of the reflection matrices, with the first reflection matrix to the right.
T = R₂ × R₁ = [[0, 1], [1, 0]] × [[1, 0], [0, - 1]] = [[0, - 1], [1, 0]]
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Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes to be equal to if she rolls the two number cubes times?
LOADING... Click the icon to view the possible sums.
Question content area bottom
Part 1
The sum should be equal to 9 about ___ enter your response here the time(s).
The sum of the two cubes to be equal to 5 if she rolls the two number cubes 180 times will be 25.
What is the expected value?In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
The total number of events is 36. And the favorable event is 5. Then the probability is given as,
p = 5 / 36
Then the expected value is given as,
E(x) = 180 (5/36)
E(x) = 900 / 36
E(x) = 25
The sum of the two cubes to be equal to 5 if she rolls the two number cubes 180 times will be 25.
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The complete question is attached below.
ways to measure error haven't been discussed in class yet, but accuracy is an easy one to understand--it is simply the percent of labels that were correctly predicted (either true or false). write a function to calculate accuracy using the actual and predicted labels. using the function, calculate the accuracy of this k-nearest neighbors model on the data.
A new data point is classified using the K-NN algorithm based on similarity after all the existing data has been stored.
Define the K-NN algorithm?The k-nearest neighbours algorithm, sometimes referred to as KNN or k-NN, is a supervised learning classifier that employs proximity to produce classifications or predictions about the grouping of a single data point.The K-NN algorithm saves all the information that is available and categorises new input based on similarity.k-nearest neighbours (kNN) classifier is supervised machine learning algorithm that is non-parametric. It is distance-based and categorises things according to the classes of their close neighbours. Although it can be used for regression issues as well, kNN is most frequently utilised for classification tasks.Non-parametric denotes the absence of parameter adjustment throughout the model's training phase. K is a hyperparameter even if it can be viewed as an algorithm parameter in some ways.Here I attached the answers
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What is the simplest form of the radical expression √ 2 √ 5 √ 2 − √ 5?
The radical expression is written as 38 in its simplest form.
Explain about the expression?A mathematical expression shows the value of something by combining numbers, variables, and operators. A mathematical statement known as an equation involves setting two expressions equal to one another.
Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
1 + 7n - 5 will therefore equal:
= 1 + 7n - 5
= 1 + 7(6) - 5
= 1 + 42 - 5
= 38
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lil help please thanks, I think I like math
The factored form of the equation is g(x) = -(x + 2)(x − 4)..
What is Factored form?A quadratic expression that is written as the product of a constant times two linear factors is said to be in factored form.
Given:
As, the equation of the function in factored form,
g(x) = a(x − [tex]r_1[/tex])(x − [tex]r_2[/tex]),
The function has x-intercepts of -2 and 4.
So (x + 2 )and (x − 4) are factors of the equation.
Now, the value of y changes for 1 unit to the right of the vertex.
The y-value goes down 1 unit for a point 1 unit to the right of the vertex, so a = -1.
So, the equation of this quadratic function is
g(x) = -(x + 2)(x − 4).
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How do you convert grams to mole?
The grams can be converted to moles and vice versa, the conversion factor used is molar mass.
What is the equation to convert grams to moles?In chemistry, the SI unit of substance amount is the mole. The mole is a unit of measurement for the quantity or amount of a substance. We know that one mole of any element contains 6.0221023 atoms, also known as the Avogadro number.The following equation will convert the mass of any substance into moles:W/M = n
where,
n = number of moles
W = mass given
M stands for molar mass.
We can convert the mass of any object to moles and moles to mass using the formula that is shown above.As a result, the conversion factor used for this is molar mass (M).To learn more about grams refer to :
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csc²x-cscx+2/CSCX-1
So csc²x-cscx over CSCX-1
Or
csc²x-cscx divided by CSCX-1
(This isn't multiple equations it's just one but I wanted to clarify everything is divided by CSCX-1)
I have to simplify completely using trig identifies to make it one value
Example:(1/sin) csc so answer is csc because it's one value you so I have to simplify everything all to one value (I hope I'm explaining this right also explain it like you would to a 5yro because I can't do this)
I attached a picture hope this helps
The simplification of csc²x-cscx+2/CSCX-1 = 1/sin²(x) - sin(x) / (sin²(x)-1)
How did we arrive at the value?First, let's recall the definition of cosecant (csc): it's the reciprocal of sine, so csc(x) = 1/sin(x).
Next, we can simplify the equation by substituting the definition of cosecant into the equation:
csc²x-cscx / CSCX-1 = (1/sin(x))² - (1/sin(x)) / (1/(sin(x))-1)
Next, we can simplify the numerator and denominator using algebraic identities:
(1/sin(x))² = 1/sin²(x)
(1/sin(x)) / (1/(sin(x))-1) = sin(x) / (sin²(x)-1)
So, the equation becomes:
1/sin²(x) - sin(x) / (sin²(x)-1)
And this is the simplified form of the equation.
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If you flip a fair coin 10 times what is the probability of getting all tails?
If you flip a fair coin 10 times , then the probability of getting all tails is 1/1024 .
The outcomes in flipping a coin is = {H , T} ;
probability of getting a tail is = 1/2 ;
the number of times the coin is flipped is = 10 times .
The probability of getting a sequence of 10 independent events, each with a probability of 1/2 of occurring. The overall probability is found by multiplying the probability of each event:
⇒ (1/2) × (1/2) × (1/2) × ... × (1/2) = (1/2)¹⁰ = 1/1024 .
Therefore , the probability of getting "all tails" in 10 coin flips of a fair coin is 1/1024 , which means that if we flip the coin 10 times repeatedly, we would expect to get all tails only once in approximately 1024 trials .
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Circle F is centered at the origin. Is point (7, -7) on the circle? Circle on grid No because the distance from the origin to point (7, -7) is greater than the radius of the circle. Yes because the distance from the origin to point (7, -7) is equal to the radius of the circle. No because the distance from the origin to point (7, -7) is less than the radius of the circle. Yes because the distance from the origin to point (7, -7) is greater than the radius of the circle.
Answer:
Yes because the distance of (7,-7) from origin is equal to the radius of the circle.
Step-by-step explanation:
India's Population at the end of the year 2019 was 1.37 billion. The country's growth in
population can be modeled by the function G(x) = 1.37(1.003), where x is the number of
years since 2019.
What is the country's annual growth factor?
Find the constant percent rate of change and interpret in the context.
The formula (y2y1)/(x2x1) (y 2y1)/(x 2x1) can be used to determine the constant rate of change.
What is constant rate?When the ratio of the output to the input remains constant at every given point along the function, the rate of change is said to be constant. The slope exist as a another name for the constant rate of change. The rate of change for linear functions will be constant. One quantity changes in respect to another when something changes at a consistent rate. For instance, a pigeon may go 25 miles in every half-hour of flight. This constant rate can be expressed as a ratio. The equation y = mx + b, where m and b are constants, can be used to express a linear function, which has a constant rate of change.To learn more about constant rate, refer to:
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Is the estimated intercept Bo meaningful in this case? O A. Yes. B. No.
Yes the estimated intercept B meaningful in this case
The estimated intercept, also known as the constant, is the point at which the regression line intersects the y-axis.
In this case, the meaning of the estimated intercept Bo is crucial in understanding the results of the regression analysis.
The intercept represents the expected value of the dependent variable when all independent variables are equal to zero.
In conclusion, the estimated intercept can be a meaningful and valuable tool in regression analysis, but it is important to consider the context of the data and the relationships between the variables before interpreting the results.
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There are 30 tudent in cla 8B. 3 tudent tudy both German and French. 12 tudent tudy only German. 15 tudent tudy only French
Answer:
Step-by-step explanation:
1. Total number of students in class 8B: 30
2. Number of students studying both German and French: 3
3. Number of students studying only German: 12
4. Number of students studying only French: 15
ch the fraction with the equivalent percentage. There will be 2 percentages that will not be used.
Prompt 15/16
31.25%
Prompt 23/12
Prompt 312/40
Prompt 41/8
The percentage 31.25% has no equivalent fraction or decimal
How to determine the equivalent percentageFrom the question, we have the following parametes that can be used in our computation:
Percentage = 31.25%
Convert the percentage to decimal
So, we have
Decimal = 0.3125
When the fractions are evaluated, we have
15/16 = 0.9375
23/12 = 1.9167
312/40 = 7.8
41/8 = 5.125
See that none of these values can be evaluated to 0.3125
Hnce, the percentage has no equivalent expression in the options
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Complete the table for different values of x in the polynomial expression -7x^2 +32x+240. Then, determine the optimal price that the taco truck should sell its tacs for. Assume whole dollar amounts for the tacos
If the taco truck were to sell its tacos for $1, it would earn a profit of $267. However, if they were to sell their tacos for $-1, they would incur a loss of $202.
[tex]x | -7x^2 + 32x + 240[/tex]
[tex]-1 | -7(-1)^2 + 32(-1) + 240 = 6 + 32 - 240 = -202[/tex]
[tex]0 | -7(0)^2 + 32(0) + 240 = 240[/tex]
[tex]1 | -7(1)^2 + 32(1) + 240 = -5 + 32 + 240 = 267[/tex]
The optimal price that the taco truck should sell its tacos for is $0. This is because when x is equal to 0, the value of the polynomial expression is at its highest point. This means that the taco truck will earn the most profit when they sell their tacos for $0.
However, it is important to note that this is not a realistic scenario and the taco truck would need to sell its tacos for a positive whole dollar amount.
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Kelly rolls two number cubes 50 times. After each roll, she records whether the number on
each cube is even (E) or odd (O). Her results are shown in the graph. Based on Kelly's results,
which is the most reasonable prediction for the number of times two odd numbers will occur
when two number cubes are rolled 2,000 times?
The most reasonable prediction for the number of times two odd numbers will occur when two number cubes are rolled 2,000 times is 480.
Option D is the correct answer.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Number of times the dice were rolled = 50
The number of times two odd numbers occur = 12
The percentage of two odd numbers occurs.
= 12/50 x 100
= 12 x 2
= 24%
Now,
Number of times the dice were rolled = 2000
The most reasonable prediction for the number of times two odd numbers will occur.
= 24% of 2000
= 24/100 x 2000
= 24 x 20
= 480
Thus,
The most reasonable prediction for the number of times two odd numbers will occur is 480.
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a histogram of sample means converges to a normal distribution as the sample size increases.. T/F
Yes, this is true. This phenomenon is known as the Central Limit Theorem and it states that, as the sample size increases, the distribution of the sample mean converges to a normal distribution.
Yes, this is true. According to the Central Limit Theorem, as the sample size increases, the distribution of the sample mean converges to a normal distribution. This means that, when the sample size is large enough, the histogram of sample means will appear to be close to a normal distribution. This is because the mean of a large enough sample size will be close to the population mean, regardless of the shape of the original population distribution.
The Central Limit Theorem also states that the larger the sample size, the more closely the sample distribution will resemble a normal distribution. This is why, when the sample size is large enough, a histogram of sample means will appear to be a normal distribution.
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Manoj and shira asked to find an explicit formula for the sequence -9, -27, -81, -243.
manoj said the formula is h(n) = -9*3^n, and
shira The formula is h(n) =-3*3^n. Which one of them is right?
A. Only manoj
B. Only shira
C. Both manoj and shira
D. Neither manoj nor shira
Option (A) Only Manoj is the correct answer. the correct formula for the sequence -9, -27, -81, -243 is [tex]h(n) = -9 * 3^n[/tex], as proposed by Manoj.
The formula for a sequence represents a pattern in the terms of the sequence. By finding an explicit formula for a sequence, we can generate any term of the sequence without having to list out all of the terms.
In this case, the sequence -9, -27, -81, -243 follows a pattern where each term is obtained by multiplying the previous term by 3. This can be represented by the formula [tex]h(n) = -9 * 3^n[/tex], where n is the index of the term in the sequence and [tex]3^n[/tex] represents 3 raised to the power of n.
In contrast, Shira's formula [tex]h(n) = -3 * 3^n[/tex] results in a different sequence, -3, -9, -27, -81, which does not match the given sequence.
Therefore, the correct formula for the sequence -9, -27, -81, -243 is[tex]h(n) = -9 * 3^n[/tex], as proposed by Manoj.
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So variables x and y are proportional. Use the values to find the constant of proportionality then write an equation that relates x and y when y equals 20 and x equals 12
The constant of proportionality is 5/3.
and, the equation is y= 5/3x.
What is Proportionality Constant?The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional. When y and x are two values that are directly proportional to one another, the proportionality constant k is defined as k=y/x.
Given:
y=20 and x= 12
As, from equation of proportionality we have
y=kx
20=k(12)
k= 20/12
k = 5/3
So, Based on the above calculations, the equation that relates x and y is:
y= (5/3)x
y =1.667 x
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PLEASE HELP!!! 20 POINTS UP FOR GRABS!!!
The size of the angle x is 33.7 degrees.
What are Trigonometric Functions?Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.
Given is a right angled triangle, whose one of the angle is 90°.
Definition of the sine trigonometric function in a right angled triangle is,
sin θ = Opposite side / Hypotenuse
Here, hypotenuse = 18 cm
Opposite side to angle x = 10 cm
sin x = 10 / 18
sin x = 0.556
x = sin⁻¹ (0.556)
x = 0.589 radians ≈ 33.7 degrees
Hence the measure of the angle x is 33.7 degrees.
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Li and Amber are writing number patterns. Both patterns start at 2. Li uses the rule "Add 1, then multiply by 3." Amber uses the pattern "Add 2, then multiply by 2." Write the first five ordered pairs with an x-coordinate representing the number Li's pattern and the y-coordinate representing the corresponding numbers in Amber's pattern.
Based on the information provided the coordinates would be
What is Li's sequence?To know her sequence, let's apply the rule given"Add 1, then multiply by 3"
2 + 1 = 3 x 3 = 9
3+1 = 4 x 3 =12
4 +1 = 5 x 3 =14
5 + 1 = 6x3 = 18
What is Amber's sequence?Let's apply the rule given "Add 2, then multiply by 2"
2+ 2 = 4x2= 8
3+2= 5x2= 10
3+3= 6x 2= 12
4+3=7x 12 = 14
Based on this, the coordinates are (2,2), (9,8), (12,10), (14,12), (18,14).
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