The 9th term of the sequence is approximately 30.234.
What is sequence ?In mathematics, a sequence is an ordered list of numbers or other mathematical objects, such as functions, matrices, or vectors. Each member of the sequence is called a term, and the position of each term in the sequence is identified by its index or subscript.
Looking at the given terms, we can observe that each term is less than the previous term and the difference between consecutive terms is decreasing. Therefore, the sequence is decreasing and the difference between consecutive terms is decreasing by a factor of 2 each time.
Using this pattern, we can find the common difference between consecutive terms as follows:
60 - 80 = -20
45 - 60 = -15
We see that the difference between consecutive terms decreases by a factor of 2 each time. Therefore, the next difference would be:
-15 / 2 = -7.5
So, the next term would be:
45 - 7.5 = 37.5
We can continue this pattern to find the 9th term as follows:
Term 1: 80
Term 2: 60
Term 3: 45
Term 4: 37.5
Term 5: 33.75
Term 6: 31.875
Term 7: 30.9375
Term 8: 30.46875
Term 9: 30.234375
Therefore, the 9th term of the sequence is approximately 30.234.
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Help 100 points plus brainiest
Answer:
B
Step-by-step explanation:
For every 4 units moved to the side, it also moves up by 5 units.
Angela's effective federal tax rate is 17%. Last year, she was able to reduce taxable income by
contributing $250.00 per semi-monthly paycheck to her tax -deferred retirement account and $72.07 per
semi-monthly paycheck to her flexible spending account. How much did she reduce her federal taxes by if
her gross semi-monthly pay is $2,819.96?
Answer:
Step-by-step explanation:
find the equations of all vertical, horizontal, or slant asymptotes of the graph of f(x)=3x^3-24/x^2-1 sketch the graph of the function
The equations of the asymptotes of the graph are x = 1, x = -1 and y = 3x
How to determine the equations of the asymptotes of the graphThe equation of the function is given as
f(x)=3x^3-24/x^2-1
Set the denominator to 0
So, we have
x^2 - 1 = 0
Apply the difference of two squares
(x - 1)(x + 1) = 0
Evaluate
x = 1 and x = -1 ---- the vertical asymptotes
Here, we have the degree of the numerator to be greater than that of the denominator
So, we have
y = 3x^3/x^2
y = 3x ----- horizontal asymptote
Note that the horizontal asymptote is the same as the slant asymptote
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Spelling List A-4
Short-o Sound - /o/
Spelling Words
1. dog
2.
top
3.
not
4.
box
5. jog
The answer after shorting are dog,top,not,box,jog.
What is sorting?
Sorting is the process of arranging or categorizing a set of items in a particular order or sequence according to specific criteria. It is a fundamental operation in computer science and is used extensively in various applications such as data analysis, information retrieval, and database management.
In general, sorting involves comparing elements of a collection, such as an array or a list, and rearranging them according to a predetermined order. The order can be based on a variety of factors, such as numerical value, alphabetical order, or date/time stamp. The two main categories of sorting algorithms are comparison-based sorting and non-comparison based sorting.
Some common sorting algorithms include bubble sort, insertion sort, selection sort, quicksort, merge sort, and heapsort. Each algorithm has its own advantages and disadvantages, and the choice of algorithm depends on the specific application and the characteristics of the data being sorted.
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Your complete question is:- Short "O" sound spelling in the following :-
Dog, Top, Not, Box, Jog
What is the measure of angle B if the two triangles are similar? HELP PLS
1.) 35
2.) 45
3.) 113
4.) 22
The answer is 2) 45
According to the question
If two triangles are similar, then their corresponding angles are congruent and their corresponding sides are proportional.
Thus, if we obtain the measure of an angle in one of the triangles, we can determine the measure of the corresponding angle in the other triangle.
So here triangles ABC and DEF are similar so they will be congruent.
Here angle A and angle D are congruent, angle B and angle E are congruent and angle C and angle F are congruent.
So, angle B≅angle E= 45°
What is meant by congruent?
Congruent means having the same shape and size, with all corresponding angles and sides being equal in measure and length, respectively. It is denoted by the symbol ≅.
What is meant by similar?
Similar refers to the property of two geometric figures having the same shape but possibly different sizes. Corresponding angles of similar figures are congruent, and the ratios of their corresponding sides are equal.
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The two triangle is similar measure of angle B is 45.
What is meant by congruent?Congruent means having the same shape and size, with all corresponding angles and sides being equal in measure and length, respectively. It is denoted by the symbol ≅.
According to the question:If two triangles are similar, then their corresponding angles are congruent and their corresponding sides are proportional.
Thus, if we obtain the measure of an angle in one of the triangles, we can determine the measure of the corresponding angle in the other triangle.
So here triangles ABC and DEF are similar so they will be congruent.
Here angle A and angle D are congruent, angle B and angle E are congruent and angle C and angle F are congruent.
So, angle B≅angle E= 45°
Therefore,the two triangle is similar measure of angle B is 45.
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Help me plsss I’m in a lot of trouble rn
The missing value in the proportion 4:x = 20:10 is 2.
What is proportion?
In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.
To find the missing value in the proportion 4:x = 20:10, we can use the property that the ratios of the corresponding terms in a proportion are equal.
That is, 4:x = 20:10 is equivalent to the equation -
4 / x = 20 / 10
Simplifying this equation, we get -
4 / x = 2
Multiplying both sides of the equation by x, we get -
4 = 2x
Dividing both sides of the equation by 2, we get:
x = 2
Therefore, the value for x is obtained as 2.
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Find the missing value 4:x = 20:10.
What is the area of the figure below?
A. 48 square meters
B. 66 square meters
C. 72 square meters
D. 84 square meters
0.00745805 Rounded to the nearest hundred
Answer:
Step-by-step explanation:
0.0075 (rounded to the nearest hundredth)
Write the equation of a line that is perpendicular to y = 2x + 4 and goes through the point (6, 4)
The equation of the line that is perpendicular to y = 2x + 4 and goes through the point (6, 4) is y = (-1/2)x + 7.
What is the Equation of the Perpendicular Line to an Equation?To find the equation of a line that is perpendicular to y = 2x + 4 and goes through the point (6, 4), we first need to determine the slope of the given line.
The equation y = 2x + 4 is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Therefore, the slope of the given line is 2.
The slope of a line perpendicular to this one will be the negative reciprocal of 2, which is -1/2.
So the equation we are looking for will have a slope of -1/2 and will pass through the point (6, 4). We can use the point-slope form of the equation of a line to find it:
y - y1 = m(x - x1)
where m is the slope, (x1, y1) is the point, and x1 = 6, y1 = 4:
y - 4 = (-1/2)(x - 6)
Simplifying:
y - 4 = (-1/2)x + 3
y = (-1/2)x + 7
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100 POINTS+BRAINLEIST Which names a type of mathmatic ratio notation?
percentage notation
decimal notation
equation notation
fraction notation
Answer:
decimal notation
Step-by-step explanation:
thanks for the question
Answer:
Great question! It is decimal notation.
which of the following is an equation?
a. y/9-3
b. 9-2
c. y/9=3
d. 7+y
Answer: :)
An equation is something with a = sign and it’s C because it’s the only one with the sign
Step-by-step explanation:
If anyone sees this can they help me out?
The table shows the heights and the maximum speeds for various roller coasters throughout the world
Which value is closest to the linear correlation coefficient for the data?
A) 0.483
B) 0.205
C) 0.420
D) 0.695
The value that is closest to the linear correlation coefficient for the data include the following: D) 0.695.
How to find an equation of the line of best fit for the data?In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).
In this scenario, the heights would be plotted on the x-axis of the scatter plot while the maximum speeds would be plotted on the y-axis of the scatter plot.
From the scatter plot (see attachment) which models the relationship between the heights and the maximum speeds, a linear equation for the line of best fit and correlation coefficient are as follows:
Equation: y = 0.205x + 33.42
Correlation coefficient, r = 0.695.
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Suppose a survey indicated that the average American spends the following number of hours per week for each activity: 54 hours for sleep, 28 hours for work, 18 hours for family care, 20 hours for personal care, and 48 hours for leisure. In constructing a circle graph, how many degrees (to the nearest tenth) of the circle should be used for the “work” segment?
Work accounts for approximately 60° of the pie chart, or 15.48% of the total 360°.
How to solveTo calculate a pie chart, first, categorize the data and calculate the total.
Each slice of the pie chart represents a numerical value and has a size proportional to the value.
The sum of all the data is equal to 360°, with the total value always being 100%.
To find the percentage for each slice of the pie chart, divide the categories by the total and convert them into percentages.
Finally, calculate the degrees using the formula (Given Data/Total value of Data) × 360°.
For example, let's say we have data on sleep, work, family care, personal care, and leisure, with a total of 168 hours.
To find the percentage for each category, we can use the following calculations:
Sleep: 54/168 x 100 = 32.14%Work: 28/168 x 100 = 15.48%Family care: 18/168 x 100 = 10.71%Personal care: 20/168 x 100 = 11.90%Leisure: 48/168 x 100 = 28.57%Therefore, work accounts for approximately 60° of the pie chart, or 15.48% of the total 360°.
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are conditional probabilities always dependent?
They are dependent events because the outcome of B completely depends on what happened on A. Another notation to represent the probability of a series of dependent events is P(A|B), it is read as The probability of A given B.
Two events A and B are said to be independent if the fact that one event has occurred does not affect the probability that the other event will occur. If whether or not one event occurs does affect the probability that the other event will occur, then the two events are said to be dependent.
The multiplication of an integer by its consecutive odd integer is 11 more than the square of the number. Find the number
In the statement , the number is 5.5.
What is integer?The Latin term "Integer," which implies entire οr intact, is where the wοrd "integer" first appeared. Zerο, pοsitive numbers, and negative numbers make up the particular categοry οf numbers knοwn as integers.
Here let us take the given integer as x.
Then , cοnsecutive οdd integer is x+2.
Nοw accοrding tο the given questiοn is multiplicatiοn οf an integer by its cοnsecutive οdd integer is 11 mοre than the square οf the number. then, cοnverting intο expressiοn,
=> x [tex]\times[/tex] (x+2) = [tex]x^2+11[/tex]
=> [tex]x^2+2x=x^2+11[/tex]
=> 2x = 11
=> x = 11/2 = 5.5
Hence the number is 5.5.
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Use the technique of linear regression to find the line of best fit for the given points. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
(1,2)
, (2,5)
, (3,7)
, (4,2)
, (5,10)
, (6,10)
, (7,9)
The equation of the line of best fit is y = 1.19x - 0.37.
What is linear regression ?
Linear regression is a statistical method that is used to establish the relationship between two variables, usually represented as a straight line. It is used to determine the extent to which one variable is dependent on the other variable, and to make predictions based on this relationship.
Using linear regression, we want to find the equation of the line of best fit in the form y = mx + b, where m is the slope and b is the y-intercept.
First, we need to calculate some sums:
∑x = 28
∑y = 45
∑xy = 224
∑x² = 140
∑y²= 275
Using these sums, we can calculate the slope m:
m = (n∑xy - ∑x∑y) / (n∑x² - (∑x)²)
m = (7(224) - (28)(45)) / (7(140) - (28)^2)
m = 1.19
Now we can use the slope to calculate the y-intercept b:
b = (∑y - m∑x) / n
b = (45 - (1.19)(28)) / 7
b = -0.37
Therefore, the equation of the line of best fit is y = 1.19x - 0.37.
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Carla is deep-sea diving with two friends. Frank is exploring a coral reef 6.7 meters in
front of Carla, and Lola is floating on the surface directly above Carla. If Lola and Frank are 9.7 meters apart, how far apart are Carla and Lola? If necessary, round to the nearest tenth.
The distance between carla and Lola is approximately 7.01 meters
To find the distance between themLooking at the description given, we can conclude that the figure will resemble a right angle triangle.
And to solve this we use the Pythagoras theorem.
This states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides “.
The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
Here, the hypotenuse is the longest side, as it is opposite to the angle 90°
We can represent this as
H² = O² + A²
Where?
H = Hypotenuse (The longest side) 9.7mA = Adjacent side (The base of the triangle) 6.7mO = Opposite side (The perpendicular to the adjacent side)We are given the hypotenuse and the Adjacent side; we are to find the Opposite side.
Using the expression above, we will have.
9.7² = 6.7² + Opp²
94.09 = 44.89 + Opp²
Opp² = 94.09 - 44.89
Opp² = 49.2
Opp = √49.2
Opp = 7.01 meters approximately
Hence, the distance is 7.01 meters
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The base of a solid S is the region bounded by the circle x² + y² = 16.
Y
x² + y² = 16
x
Cross-sections perpendicular to the x-axis are equilateral triangles.
Determine the exact volume of solid S.
Marking as brainliest if ya fast
The exact volume of solid S is (128√3)/3 cubic units.
What is volume?
A volume is simply defined as the amount of space occupied by any three-dimensional solid. These solids can be a cube, a cuboid, a cone, a cylinder, or a sphere. Different shapes have different volumes.
To find the volume of the solid, we need to integrate the area of each cross-section perpendicular to the x-axis from x = -4 to x = 4.
Since the cross-sections are equilateral triangles, we need to find the side length of each triangle in terms of x.
At any given x, the triangle's base is 2√(16 - x²) (the diameter of the circle), and its height is √3 times its base length (since it is equilateral). Therefore, the area of the triangle is:
A(x) = 1/2 * base * height
= 1/2 * 2√(16 - x²) * √3 * √(16 - x²)
= √3 (16 - x²)
Integrating A(x) from -4 to 4 gives us:
V = ∫[from -4 to 4] A(x) dx
= ∫[from -4 to 4] √3 (16 - x²) dx
= √3 * [16x - (1/3)x³] | from -4 to 4
= √3 * (128/3)
= (128√3)/3
Therefore, the exact volume of solid S is (128√3)/3 cubic units.
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On a number line ,how far apart are the numbers -5.5 and 7.5
Answer:
-5.5 and 7.5 are 13 units apart
Step-by-step explanation:
The distance between two numbers on a number line is found by subtracting the smaller number from the larger number.
7.5 - ( -5.5) = 7.5 + 5.5 = 13
In a science class, 13.5% of the students have earned an A. If 3 students are chosen at random, what is the probability of choosing at least one student who has an A in the science class? Give your answer rounded to the nearest thousandth.
Answer:To introduce her class to binomial distributions, Mrs. Desai gives a
-item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class.
Let
the number of Patti's correct guesses.
To get a passing score on the quiz, a student must guess correctly at least
times. Would you be surprised if Patti earned a passing score? Compute an appropriate probability to support your answer.
Step-by-step explanation:
Define $f(x)=\frac{1+x}{1-x}$ and $g(x)=\frac{-2}{x+1}$. Find the value of\[g(f(g(f(\dotsb g(f(12)) \dotsb ))))\]where the function $f$ is applied 8 times, and the function $g$ is applied 8 times, alternating between the two.
The value of [tex]$g(f(g(f(g(f(g(f(12)))))))) = \frac{5926}{3335}$[/tex] when the function f is applied 8 times and g is applied 8 times alternatively.
How is function composition employed in this issue and what is it?The process of applying one function to the result of another is known as function composition. In other words, if we have two functions, f and g, we may combine them to create a new function that accepts an input, processes it though g, and then outputs f.
For the given composite function we start with the innermost function.
Find the value of f(12):
[tex]f(12) = \frac{1+12}{1-12} = -\frac{13}{11}$\\\$g(f(12)) = \frac{-2}{-\frac{13}{11}+1} = \frac{22}{13}$\\$f(g(f(12))) = \frac{1+\frac{22}{13}}{1-\frac{22}{13}} = -\frac{35}{9}$\\$g(f(g(f(12)))) = \frac{-2}{-\frac{35}{9}+1} = \frac{18}{13}$[/tex]
[tex]f(g(f(g(f(12))))) = -\frac{157}{139}$\\$g(f(g(f(g(f(12)))))) = \frac{278}{157}$\\$f(g(f(g(f(g(f(12))))))) = -\frac{3335}{2963}$\\$g(f(g(f(g(f(g(f(12)))))))) = \frac{5926}{3335}$[/tex]
Hence, the value of [tex]$g(f(g(f(g(f(g(f(12)))))))) = \frac{5926}{3335}$[/tex] when the function f is applied 8 times and g is applied 8 times alternatively.
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Jumping spiders can commonly be found in homes and barns throughout the United States. A jumping spider's jump can be modeled by the
equation h = 33.3t 16t2, where t represents the time in seconds and h is the height in feet.
A. When is the spider's height at 0 feet other than 0 seconds? Express your answer as a decimal. Do not round.
B. What is the spider's height after 1 second?
seconds
feet
BF
Answer:
A. To find when the spider's height is at 0 feet, we need to solve the equation h = 33.3t - 16t^2 for t when h = 0. This gives us:
0 = 33.3t - 16t^2
0 = t(33.3 - 16t)
t = 0 or t = 2.08125 (rounded to 5 decimal places)
So the spider's height is at 0 feet at 0 seconds and 2.08125 seconds.
B. To find the spider's height after 1 second, we substitute t = 1 into the equation:
h = 33.3t - 16t^2
h = 33.3(1) - 16(1)^2
h = 17.3 feet
So the spider's height after 1 second is 17.3 feet.
Pls answer with full explanation
Answer:
Step-by-step explanation:
sin a equals sin to the second power (a) + cos to the 2 power(a) equal 1
A circle has the equation (* - 13)? + (y - 1)? = 4.
A: What is the center of the circle?
B: What is the radius of the circle?
Select two answers: one for question A, and one for question B.
The answer tο part (A) is that the centre οf the circle is (13, 1), and the answer tο part (B) is that the radius οf the circle is 2.
What is a circle?A circle is a twο-dimensiοnal shape that is defined as the set οf all pοints in a plane that are equidistant frοm a fixed pοint called the center. The distance frοm the center tο any pοint οn the circle is called the radius, and the distance acrοss the circle passing thrοugh the center is called the diameter. The equatiοn οf a circle with center (h, k) and radius r is:
(x - h)² + (y - k)² = r²
Cοmparing this with the given equatiοn:
(x- 13)² + (y - 1)² = 4
We can see that the center οf the circle is (13, 1), and the radius οf the circle is the square rοοt οf 4, which is 2.
Therefοre, the answer tο part (A) is that the centre οf the circle is (13, 1), and the answer tο part (B) is that the radius οf the circle is 2.
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Complete Question
A circle has the equation (x−13)2+(y−1)2=4.
A: What is the center of the circle?
B: What is the radius of the circle?
Select two answers: one for question A, and one for question B.
A: (13,1)
B: 4
A: (−13,−1)
A: (13,1)
A: (13,−1)
B: 2
B: 2–√
Use the technique of linear regression to find the line of best fit for the given points. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
(1,9)
, (2,9)
, (3,4)
, (4,2)
, (5,4)
, (6,2)
, (7,3)
The line of best fit for this set of points is y = -1.00x + 9.00.
What is coefficient?Coefficient is a value that is used to indicate the degree or amount of a certain property or characteristic. It is usually used in mathematics and physics, and is a numerical measure of how two variables are related. For example, the coefficient of friction is a number that indicates how much resistance there is between two surfaces when one is sliding over the other. In economics, the coefficient of elasticity is used to measure how much of a change in one variable affects a change in another.
Linear regression is a technique used to find the line of best fit for a given set of points. To use linear regression, we must first calculate the mean of all the x and y coordinates. The mean of the x coordinates is 4, and the mean of the y coordinates is 4.5.
We then calculate the sum of the squared differences between the x and y coordinates and their respective means. This sum is 36.5.
Next, we calculate the sum of the products of the differences between the x and y coordinates and their respective means. This sum is -25.
Using the formula for linear regression, we can calculate the slope of the line of best fit. The slope is -1.00.
To calculate the y-intercept of the line of best fit, we use the slope and the mean of the x and y coordinates. The y-intercept is 9.00.
The line of best fit for this set of points is y = -1.00x + 9.00.
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If this circle has a radius of 6.8 and m∠b=197°, calculate the area of the intercepted sector (shaded blue). Round answers to two decimal places. Use the π button on your calculator.
The area οf the intercepted sectοr is 25.3π.
What is an area οf a sectοr?The quantity οf space included within the sectοr's perimeter is referred tο as the sectοr's area in a circle. A sectοr always starts at the circle's center. The area οf a circle encοmpassed between its twο radii and the arc next tο them is knοwn as the sectοr οf a circle.
Here, we have
Given: If this circle has a radius οf 6.8 and m∠b=197°.
We have tο calculate the area οf the intercepted sectοr.
The area οf the sectοr is given as θ/360*πr²
Where,
θ = central angel οf the sectοr, m∠f=197°
r = radius = 6.8
Area οf sectοr = 197/360*π(6.8)²
= 25.3π
Hence, the area οf a sectοr is 25.3π.
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Need help with short problem 1
As stated in the problem description, matrix A transforms the input vector (x, y, and z) into the output vector (y+z, 2x-z, 0).
The matrix A is: | 0 1 1 |, | 2 0 -1 |, | 0 0 0 |
What is a matrix?A matrix, sometimes known as matrices, is a rectangular array or table of letters, numbers, or other symbols organized in rows and columns that are used to represent a mathematical object or a characteristic of one.
In linear algebra, matrices describe linear mappings and enable explicit computations. As a result, a significant portion of linear algebra involves the study of matrices, and the majority of the characteristics and operations of abstract linear algebra may be described in terms of matrices. The composition of linear maps, for instance, is represented by matrix multiplication.
Not every matrix has a connection to linear algebra. This is especially true for incidence matrices and adjacency matrices in graph theory.
The matrix A is:
| 0 1 1 |
| 2 0 -1 |
| 0 0 0 |
Applying the matrix multiplication A x y z to any random vector (x, y, z) will demonstrate why:
| 0 1 1 | | x | | y + z |
| 2 0 -1 | x | y | = | 2x - z |
| 0 0 0 | | z | | 0 |
Hence, as stated in the problem statement, matrix A transforms the input vector (x, y, and z) into the output vector (y+z, 2x-z, 0).
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The sum of the age of Afful and Naomi is 34years five years to come,Afful will be 2 times the age of Naomi now.How old are they now
Answer:
Afful is 21 and Naomi is 13.
Step-by-step explanation:
x=Afful's age
y=Naomi's age
System of equations:
x+5=2y
x+y=34
x+5=2y
y=(x+5)/2
x+y=34
x+((x+5)/2)=34
x=21
21+y=34
21+y=34
y=13
please help me i’m struggling and i really need to turn this in
The vertices of the image are: L' (1, -2), M' (2,-2), N' (2,2), P' (1, 2)
What is Vertices?In mathematics and geometry, a vertex (plural: vertices) refers to a point where two or more lines, edges, or curves meet. In three-dimensional geometry, a vertex is typically the point where three or more edges or lines intersect to form a corner or a point.
[tex]r_{x-axis}[/tex] → Reflection across the x-axis
Transformation rule: (x, y) → (x,-y)
L(2, 4)→ [tex]L^{r}[/tex] (2,-4)
M (4,4) → [tex]M^{r}[/tex] (4-4)
N (4,-4) → [tex]N^{r}[/tex] (4, 4)
P (2-4) → [tex]P^{r}[/tex] (2, 4)
D0.5 →Dilation Centered at the origin by а scale factor of 0.5
Transformation rule: (x, y) → (0.5x,0.5y)
[tex]L^{r}[/tex] (2-4) → L' (1, -2)
[tex]M^{r}[/tex] (4,-4) → M' (2, -2)
[tex]N^{r}[/tex] (4, 4) → N' (2, 2)
[tex]P^{r}[/tex] (2, 4) → P' (1, 2)
The vertices of the image are:
L'(1, -2), M'(2,-2), N'(2,2), P' (1, 2)
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The height of a flare is given by the equation h(t)= -0.5t² +16t+22 where h is the height of the flare in metres and is the time the flare has been in the air in seconds. How long will the flare be in the air if it fizzles out at a height of 10 m above ground?
Answer:
the flare will be in the air for approximately 29.09 seconds before fizzling out at a height of 10 meters above ground.
Step-by-step explanation:
To find out how long the flare will be in the air, we need to find the time it takes for the flare to reach a height of 10 meters.
Setting h(t) to 10 and solving for t:
-0.5t² +16t+22 = 10
-0.5t² +16t+12 = 0
Using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
Where a = -0.5, b = 16, and c = 12:
t = (-16 ± √(16² - 4(-0.5)(12))) / 2(-0.5)
t = (-16 ± √(256 + 24)) / -1
t = (-16 ± √280) / -1
t ≈ -1.09 or t ≈ 29.09
Since time cannot be negative, we can ignore the negative root. Therefore, the flare will be in the air for approximately 29.09 seconds before fizzling out at a height of 10 meters above ground.