100 Points! Geometry question. Photo attached. Find x in the right triangle. Please show as much work as possible. Thank you!
Answers
Answer:
x = 12
Step-by-step explanation:
sin45 = x/17 (sin = opposite/hypotenuse)
x = (sin45)(17) = 12.02 ≈ 12
Related Questions
I am having a hard time figuring out the domain and range
Answers
Answer:
domain= [-5,5]
range= [-3,3]
Step-by-step explanation:
the domain is with the x axis you have to look for the farthest x axis which would be - 5 in this case and the closest axis which is 5 so the x can be anywhere between - 5 and 5
then for the range is with the y axis you would look for the farthest y axis which is - 3 and the closes which is 3 so the y can be anywhere in between - 3 and 3
For Exercises 24-29, find each value.
24. Sin x
25 cos x
26 tan x
27. Sin y
28. Cos y
29. Tan y
Answers
All the values of expressions are,
24. Sin x = 1/√17
25 cos x = 4/√17
26 tan x = 1/4
27. Sin y = 4/√17
28. Cos y = 1/√17
29. Tan y = 4
We have to given that,
A right triangle is shown in figure.
Now, We can simplify all the values,
24. Sin x = Opposite / Hypotenuse
sin x = 2 / 2√17
sin x = 1/√17
25) cos x = Base / Hypotenuse
cos x = 8 / 2√17
cos x = 4/√17
26) tan x = Opposite / Base
tan x = 2 / 8
tan x = 1/4
27. Sin y = Opposite / Hypotenuse
sin y = 8 / 2√17
sin y = 4/√17
28. Cos y = Base / Hypotenuse
cos y = 2 / 2√17
cos y = 1/√17
29. Tan y = Opposite / Base
tan y = 8 / 2
tan y = 4
Thus, All the values of expressions are,
24. Sin x = 1/√17
25. cos x = 4/√17
26. tan x = 1/4
27. Sin y = 4/√17
28. Cos y = 1/√17
29. Tan y = 4
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What is the value of x?.
4
B
24
Q
R
15
40
C
X
1 2
Answers
The value of x would be,
⇒ x = 15
We have to given that;
A figure with QC is parallel to BR
Now, We can formulate that,
Triangle BDR and triangle CDQ are similar.
Hence, By using proportionality we get;
⇒ BD / DR = QD / CD
Substitute all the values we get;
⇒ (24 + 40) / (15 + x) = 40 / x
Solve for x,
⇒ 64 / (15 + x) = 40 / x
⇒ 64x = 40 (15 + x)
⇒ 8x = 5 (15 + x)
⇒ 8x = 45 + 5x
⇒ 8x - 5x = 45
⇒ 3x = 45
⇒ x = 15
Thus, The value of x would be,
⇒ x = 15
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Fill in the y-intercept to complete the function equation.
Answers
Answer:
y=3x+5
Step-by-step explanation:
you do 4 times 3 then subtract that from 17
geometry worksheet find the measure of the arc or angle indicated
Answers
The value of the measure of the arc or angle indicated are,
⇒ m ∠DCE = 54°
⇒ m ∠MON = 53°
Now, We can simplify as,
4) As shown in figure,
m arc DE = 360° - (121° + 131°)
m arc DE = 360° - 252°
m arc DE = 108°
So, We get;
⇒ m ∠DCE = m DE / 2
⇒ m ∠DCE = 108 / 2
⇒ m ∠DCE = 54°
4) As shown in figure,
m arc MN = 360° - (109° + 145°)
m arc MN = 360° - 254°
m arc MN = 106°
So, We get;
⇒ m ∠MON = m MN / 2
⇒ m ∠MON = 106 / 2
⇒ m ∠MON = 53°
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pedro walks at a rate of 4 miles per hour and runs at a rate of 8 miles per hour. Each Week, his exercise program requires him to cover a total fist of 20 miles with some combination of walking and/or running.
A. write an equation that represents the different amounts of time pedro can walk, x, and run, y, each week.
B. graph the equation
C. what is the y- intercept? what does this tell you?
Answers
The equation showing the problem is: 4x + 8y = 20
The graph is attached and the y intercept is (0, 2.5)
How to model the equationAssuming that:
Time spent walking x hoursTime spent running y hoursSince Pedro walks at a rate of 4 miles per hour, the distance he covers by walking would be
4x milesAlso Pedro runs at a rate of 8 miles per hour, the distance he covers by running would be
8y milesAccording to the given information, the total distance Pedro covers each week is 20 miles. Therefore, we can write the equation:
4x + 8y = 20
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For what value of x is the rational expression below undefined?
x-3
3+x
A. 3
OB. -1
O C. 0
OD. -3
Answers
Answer:
x= -3
Step-by-step explanation:
x-3
-----------
x+3
This expression is undefined when the denominator is zero.
x+3 =0
x= -3
100 Points! Geometry question. Photo attached. Use the Pythagorean Theorem to find x. Please show as much work as possible. Thank you!
Answers
The value of x is,
⇒ x = 21.65
We have to given that,
A right triangle is shown in image.
Since, The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Hence, We get;
⇒ 25² = 12.5² + x²
⇒ 625 = 156.25 + x²
⇒ x² = 625 - 156.25
⇒ x² = 468.75
⇒ x = 21.65
Thus, The value of x is,
⇒ x = 21.65
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Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 35 students, she finds 4 who eat cauliflower. Obtain and interpret a 99% confidence interval for the proportion of students who eat cauliflower on Jane's campus using Agresti and Coull's method. Click the icon to view Agresti and Coull's method. Construct and interpret the 99% confidence interval. Select the correct choice below and fill in the answer boxes within your choice. (Round to three decimal places as needed.) A. There is a 99% chance that the proportion of students who eat cauliflower on Jane's campus is between Jane's and OB. One is 99% confident that the proportion of students who eat cauliflower on Jane's campus is between OC. There is a 99% chance that the proportion of students who eat cauliflower in Jane's sample is between OD. The proportion of students who eat cauliflower on Jane's campus is between and 99% of the time. and and
Answers
Based on the information, A. There is a 99% chance that the proportion of students who eat cauliflower on Jane's campus is between 5.03% and 17.83%.
How to calculate the valueCalculate the sample proportion:
= x / n = 4 / 35
= 0.1143
Calculate the Agresti and Coull's adjustment factor:
zα/2 = z(1 - α/2) = z(1 - 0.99/2)
= 2.576
Calculate the margin of error:
= 2.576 √(0.1143(1 - 0.1143) / 35)
= 0.064
Calculate the confidence interval:
= 0.1143 ± 0.064
= (0.0503, 0.1783)
We are 99% confident that the true proportion of students who eat cauliflower on Jane's campus is between 5.03% and 17.83%.
In other words, if we were to repeat this study many times, we would expect to obtain a confidence interval that includes the true proportion of students who eat cauliflower on Jane's campus 99% of the time.
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Using a calculator or statistical software, find the linear regression line for the data in the table below.
Using the regression with the values rounded to the nearest hundredth, find the value of y at x=7. Round your answer to the nearest hundredth if necessary.
x y
0 2.83
1 3.33
2 6.99
3 8.01
4 7.62
5 7.66
Answers
Rounded to the nearest hundredth, the value of y at [tex]x = 7[/tex] is approximately [tex]12.78[/tex], according to the concept of linear regression line.
To find the linear regression line for the given data, we can use statistical software or a calculator. The equation of the linear regression line is of the form [tex]y = mx + b[/tex], where m represents the slope and b represents the y-intercept.
Using the provided data, the linear regression line equation is:
[tex]\[ y = 1.3642x + 3.2324 \][/tex]
To find the value of [tex]y[/tex] at [tex]x = 7[/tex], we substitute [tex]x = 7[/tex] into the equation:
[tex]\[ y = 1.3642(7) + 3.2324 \][/tex]
Simplifying the equation, we get:
[tex]\[ y = 9.5494 + 3.2324 \]\[ y = 12.7818 \][/tex]
In conclusion, the linear regression analysis allows us to determine the relationship between the variables x and y in the given data set. By finding the equation of the linear regression line, we can estimate the value of y for any given x. In this case, the linear regression line equation is [tex]y = 1.3642x + 3.2324[/tex]. By substituting [tex]x = 7[/tex] into the equation, we find that the estimated value of y is approximately [tex]12.78[/tex]. This analysis provides a useful tool for predicting and understanding the relationship between variables, allowing us to make informed decisions and interpretations based on the data.
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In the figure below, S is the center of the circle. Suppose that JK = 20, LM = 3x + 2, SN = 12, and SP = 12. Find the
following.
Answers
The values are x = 2 and NS = 3.5.
Given is a circle with center S, we need to find the missing measure,
K = 16, MP = 8, LP = 2x+4, and PS = 3.5, we need to find the measures of x and NS.
We know that the perpendicular drawn from the center of a circle bisect the chords into two halves,
And the perpendiculars are congruent.
Therefore,
MP = PL
2x+4 = 8
x+2 = 4
x = 2
Also,
NS = PS
So, NS = 3.5
Hence the values are x = 2 and NS = 3.5.
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Solve the compound inequality.
2y+3≥-9 or -3y<-15
Write the solution in interval notation.
Answers
To solve the compound inequality 2y + 3 ≥ -9 or -3y < -15, we'll solve each inequality separately and then combine the solutions.
First, let's solve the first inequality: 2y + 3 ≥ -9.
Subtract 3 from both sides:
2y ≥ -12
Divide both sides by 2 (note that dividing by a positive number does not change the inequality direction):
y ≥ -6
Next, let's solve the second inequality: -3y < -15.
Divide both sides by -3 (remember to reverse the inequality direction when dividing by a negative number):
y > 5
Now, let's combine the solutions. We have y ≥ -6 or y > 5.
In interval notation, we can express the solution as (-∞, -6] ∪ (5, ∞). This means that the solution includes all real numbers less than or equal to -6, as well as all real numbers greater than 5.
Taylor recorded Weekly grocery expense for the past 16 weeks and determine the mean weekly expense was $83.20 later she discovers that one week expense of $90 was incorrectly recorded at $38. What is the mean
Answers
The mean weekly expense, after correcting the incorrectly recorded week, is $81.25.
How to solveGiven that Taylor recorded the past 16 weeks' expenses, excluding the incorrect recording of $90 as $38, we have 15 correct expense values.
Sum of correct expenses = $83.20 * 15 = $1248
Now we need to include the corrected expense of $90 instead of $38.
New sum of expenses = $1248 - $38 (incorrectly recorded) + $90 (corrected) = $1300
Finally, we calculate the mean by dividing the new sum by the total number of weeks, which is 16.
Mean weekly expense = $1300 / 16 = $81.25
Therefore, the mean weekly expense, after correcting the incorrect recording, is $81.25.
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Which of the following answers to the question below is correct (multiple answers can be chosen)?
Question: Let s(t) be the position of a moving particle at time t. Choose ALL that represent the average speed of the particle over the time interval [0,4]?
1. s(4)/4
2. s(4)-s(0)/4
3. The slope of the secant line from (0, s(0)) to (4, s(4))
4. The slope of the tangent line at (0, s(0))
Answers
Answer:
The average speed of a particle over a time interval is defined as the total distance traveled divided by the time elapsed. In this case, the average speed of the particle over the time interval [0,4] is represented by options 2 and 3. Option 2 represents the change in position over the time interval [0,4] divided by the time elapsed. Option 3 represents the slope of the secant line connecting the points (0,s(0)) and (4,s(4)), which is equivalent to the average rate of change of position over the time interval [0,4].
the correct answers are, 2 and 3
(02.02 MC)
If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A′′′ lie?
Trapezoid formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at 0, 1.
(1, −1)
(−4, 1)
(1, 1)
(−4, −1)
Answers
The location of point A''' after the three transformations would be (-4, 1).
To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.
When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.
So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).
When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).
When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).
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Jesse took a survey of her classmates on how many pairs of shoes they owned.
Which frequency distribution matches the data
{3,8,5,6,4,3,7,8,9,5,5,6,4,12,14,10,8}
Answers
The frequency distribution that matches the data {3,8,5,6,4,3,7,8,9,5,5,6,4,12,14,10,8} is C.
Number
of Shoes Frequency
3-5 7
6-8 6
9-11 2
12-14 2
What is a frequency distribution?A frequency distribution is a frequency table or chart that visually displays the actual number of observations in each range or class or the percentage of the observations.
In this frequency distribution, the group 3-5 has the highest frequency of 7 followed by 6-8 with 6 frequencies.
3,8,5,6,4,3,7,8,9,5,5,6,4,12,14,10,8
Number
of Shoes Frequency
3-5 IIIIIII 7
6-8 IIIIII 6
9-11 II 2
12-14 II 2
Total 17
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Please help (easy economics question)!!!
Answers
The dollar value of total revenue at each price is $[tex]0[/tex], $[tex]10[/tex], $[tex]12[/tex], $[tex]12[/tex], $[tex]10[/tex], and $[tex]6[/tex]. Total revenue will be the greatest at a price of $[tex]4[/tex], with [tex]3[/tex] units sold.
To find the dollar value of total revenue at each price, we can multiply the price by the corresponding quantity in the demand schedule:
Price: $[tex]6[/tex]
Quantity: [tex]0[/tex]
Total Revenue: $[tex]6 \times 0[/tex] = $[tex]0[/tex]
Price: $[tex]5[/tex]
Quantity: [tex]2[/tex]
Total Revenue: $[tex]5 \times 2[/tex] = $[tex]10[/tex]
Price: $[tex]4[/tex]
Quantity: [tex]3[/tex]
Total Revenue: $[tex]4 \times 3[/tex] = $[tex]12[/tex]
Price: $[tex]3[/tex]
Quantity: [tex]4[/tex]
Total Revenue: $[tex]3 \times 4[/tex] = $[tex]12[/tex]
Price: $[tex]2[/tex]
Quantity: [tex]5[/tex]
Total Revenue: $[tex]2 \times 5[/tex] = $[tex]10[/tex]
Price: $[tex]1[/tex]
Quantity: [tex]6[/tex]
Total Revenue: $[tex]1 \times 6[/tex] = $[tex]6[/tex]
To determine at which price the total revenue will be the greatest, we observe that the highest total revenue occurs at the price with the highest quantity sold. In this case, the price with the highest quantity is $[tex]3[/tex], and the corresponding quantity sold is [tex]4[/tex] units.
Therefore, at a price of $[tex]3[/tex], the total revenue will be the greatest, with [tex]4[/tex] units sold.
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Which expression is equivalent to -32^3/5
Answers
The expression which is equivalent to -32^3/5 is -32768 / 125.
We are given that;
Expression=-32^3/5
Now,
To find an equivalent expression for -32^3/5 is to use the property of exponents that says [tex](a/b)^n = a^n / b^n.[/tex] Applying this property, we get:
-32^3/5 = (-32)^3 / 5^3
Now we can simplify the numerator and denominator by cubing them:
-32^3/5 = -32768 / 125
This is an equivalent expression for -32^3/5. There may be other ways to find equivalent expressions, such as factoring or using common denominators.
Therefore, by the expression the answer will be -32768 / 125.
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What additional information is needed to prove the triangles are congruent by the SAS Postulate?
Answers
An additional information that is needed to prove the triangles are congruent by the SAS Postulate is: D. ∠BAC ≅ ∠DAC.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar.
Based on the side, angle, side (SAS) similarity theorem, we can logically deduce that ∆BAC is congruent to ∆DAC when the angles A (∠A) are congruent by the reflexive property.
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when an exponent of the power is an even number and the base is a negative number the value is always
Answers
Answer:
When an exponent of the power is an even number and the base is a negative number, the value is always positive.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The length of the radius of the circle of equation (x + 3)² + (y - 7)² = 289 is given as follows:
b) 17.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by the equation presented as follows:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The equation for the circle in this problem is given as follows:
(x + 3)² + (y - 7)² = 289.
Hence the center and the radius are obtained as follows:
Center (-3, 7).Radius of r = 17, as 17² = 289.Hence option B is the correct option for this problem.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
The equation of the circle is (x - 2)² + (y - 3)² = 36
Determining the equation of the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
Where, we have
Center = (a, b) = (2, 3)
Radius, r = 6 units
The equation of the circle is represented as
(x - a)² + (y - b)² = r²
So, we have
(x - 2)² + (y - 3)² = 6²
Evaluate
(x - 2)² + (y - 3)² = 36
Hence, the equation is (x - 2)² + (y - 3)² = 36
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find the surface area
Answers
The Surface area of Triangular Prism is 132 cm².
We have have the dimension of prism as
Sides = 3 cm, 4 cm, 5 cm
and, l = 10 cm
and, b= 4 cm
Now, Surface area of Triangular Prism as
= (sum of sides) l + bh
= (3 + 4 + 5)10 + 4 x 3
= 12 x 10 + 12
= 120 + 12
= 132 cm²
Thus, the Surface area of Triangular Prism is 132 cm².
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which table does not show y as a function of x?
Answers
Answer:
I am confident the answer is H.
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
A. mBC = 71
B. mAB = 142
C. AD = 30
D. BD = 30
E. YD = 16
F. DC = 18
Step-by-step explanation:
A. mBC = mAC = 71
B. mAB = mBC + mAC = 71 + 71 = 142
C. AD = AB/2 = 60/2 = 30
D. BD = AD = 30
E. YA^2 = YD^2 + AD^2
YD^2 = YA^2 - AD^2 = 34^2 - 30^2 = 1156 - 900 = 256
YD = √256 = 16
F. DC + YD = YC
DC = YC - YD = 34 - 16 = 18
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Applying the angle of intersecting secants theorem, the measure of arc LN in the circle is: 56°.
How to Find the Arc Measure Using the Angle of Intersecting Secants Theorem?Given the circle in the image above where the two secants intersect outside the circle, the angle of intersecting secants theorem states that:
external angle formed = 1/2 * (the measure of arc KP - the measure of arc LN)
Plug in the values:
20 = 1/2 * (96 - m(LN))
2 * 20 = 96 - m(LN)
40 = 96 - m(LN)
m(LN) = 96 - 40
m(LN) = 56°
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Descrive in words the rule that is used to determine the term value from its position in the sequence
Answers
The rule used to determine the term value from its position in the sequence is often referred to as the "nth term" rule.
What is the nth-term rule?The nth-term rule involves identifying a pattern or relationship between the position (n) of a term in the sequence and the value of that term.
By analyzing the pattern, such as the common difference or common ratio, the nth-term rule allows us to express the value of any term in the sequence based on its position.
This rule provides a formula or equation that relates the position of a term to its corresponding value in the sequence.
Mathematically, the rule is:
T(n) = a + (n - 1) * d
where:
T(n) represents the value of the term at position n.a represents the first term in the sequence.n represents the position or index of the term in the sequence.d represents the common difference (for arithmetic sequences) or the common ratio (for geometric sequences) between consecutive terms.More on sequence and series can be found here: https://brainly.com/question/15583579
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Given the number pattern:
20; 18: 14; 8;
a) Determine the nth term of this number pattern.
b) Determine the value of T12 in this number pattern.
c) Which term in this number pattern will have a value of - 36?
A quadratic number pattern has a second term equal to 1, a third term equal to -6 and a fifth term equal to - 14.
a) Calculate the second difference of this quadratic number pattern.
b) Hence, or otherwise, calculate the first term of this number pattern.
Answers
Answer:
[tex]\textsf{a)} \quad T_n=-n^2+n+20[/tex]
[tex]\textsf{b)} \quad T_{12}=-112[/tex]
[tex]\textsf{c)} \quad \sf 8th\;term[/tex]
a) Second difference is 2.
b) First term is 10.
Step-by-step explanation:
The given number pattern is:
20, 18, 14, 8, ...To determine the type of sequence, begin by calculating the first differences between consecutive terms:
[tex]20 \underset{-2}{\longrightarrow} 18 \underset{-4}{\longrightarrow} 14 \underset{-6}{\longrightarrow}8[/tex]
As the first differences are not the same, we need to calculate the second differences (the differences between the first differences):
[tex]-2 \underset{-2}{\longrightarrow} -4 \underset{-2}{\longrightarrow} -6[/tex]
As the second differences are the same, the sequence is quadratic and will contain an n² term.
The coefficient of the n² term is half of the second difference.
As the second difference is -2, the coefficient of the n² term is -1.
Now we need to compare -n² with the given sequence (where n is the position of the term in the sequence).
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}\sf operation&+21&+22&+23&+24\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}[/tex]
We can see that the algebraic operation that takes -n² to the terms of the sequence is to add (n + 20).
[tex]\begin{array}{|c|c|c|c|c|}\cline{1-5}n&1&2&3&4\\\cline{1-5}-n^2&-1&-4&-9&-16\\\cline{1-5}+n&0&-2&-6&-12\\\cline{1-5}+20&20&18&14&8\\\cline{1-5}\sf sequence&20&18&14&8\\\cline{1-5}\end{array}[/tex]
Therefore, the expression to find the the nth term of the given quadratic sequence is:
[tex]\boxed{T_n=-n^2+n+20}[/tex]
To find the value of T₁₂, substitute n = 12 into the nth term equation:
[tex]\begin{aligned}T_{12}&=-(12)^2+(12)+20\\&=-144+12+20\\&=-132+20\\&=-112\end{aligned}[/tex]
Therefore, the 12th term of the number pattern is -112.
To find the position of the term that has a value of -36, substitute Tₙ = -36 into the nth term equation and solve for n:
[tex]\begin{aligned}T_n&=-36\\-n^2+n+20&=-36\\-n^2+n+56&=0\\n^2-n-56&=0\\n^2-8n+7n-56&=0\\n(n-8)+7(n-8)&=0\\(n+7)(n-8)&=0\\\\\implies n&=-7\\\implies n&=8\end{aligned}[/tex]
As the position of the term cannot be negative, the term that has a value of -36 is the 8th term.
[tex]\hrulefill[/tex]
Given terms of a quadratic number pattern:
T₂ = 1T₃ = -6T₅ = -14We know the first differences are negative, since the difference between the second and third terms is -7. Label the unknown differences as -a, -b and -c:
[tex]T_1 \underset{-a}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-b}{\longrightarrow}T_4 \underset{-c}{\longrightarrow} -14[/tex]
From this we can create three equations:
[tex]T_1-a=1[/tex]
[tex]-6-b=T_4[/tex]
[tex]T_4-c=-14[/tex]
The second differences are the same in a quadratic sequence. Let the second difference be x. (As we don't know the sign of the second difference, keep it as positive for now).
[tex]-a \underset{+x}{\longrightarrow} -7\underset{+x}{\longrightarrow} -b \underset{+x}{\longrightarrow}-c[/tex]
From this we can create three equations:
[tex]-a+x=-7[/tex]
[tex]-7+x=-b[/tex]
[tex]-b+x=-c[/tex]
Substitute the equation for -b into the equation for -c to create an equation for -c in terms of x:
[tex]-c=(-7+x)+x[/tex]
[tex]-c=2x-7[/tex]
Substitute the equations for -b and -c (in terms of x) into the second two equations created from the first differences to create two equations for T₄ in terms of x:
[tex]\begin{aligned}-6-b&=T_4\\-6-7+x&=T_4\\T_4&=x-13\end{aligned}[/tex]
[tex]\begin{aligned}T_4-c&=-14\\T_4+2x-7&=-14\\T_4&=-2x-7\\\end{aligned}[/tex]
Solve for x by equating the two equations for T₄:
[tex]\begin{aligned}T_4&=T_4\\x-13&=-2x-7\\3x&=6\\x&=2\end{aligned}[/tex]
Therefore, the second difference is 2.
Substitute the found value of x into the equations for -a, -b and -c to find the first differences:
[tex]-a+2=-7 \implies -a=-9[/tex]
[tex]-7+2=-b \implies -b=-5[/tex]
[tex]-5+2=-c \implies -c=-3[/tex]
Therefore, the first differences are:
[tex]T_1 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}T_4 \underset{-3}{\longrightarrow} -14[/tex]
Finally, calculate the first term:
[tex]\begin{aligned}T_1-9&=1\\T_1&=1+9\\T_1&=10\end{aligned}[/tex]
Therefore, the first term in the number pattern is 10.
[tex]10 \underset{-9}{\longrightarrow} 1 \underset{-7}{\longrightarrow} -6 \underset{-5}{\longrightarrow}-11 \underset{-3}{\longrightarrow} -14[/tex]
Note: The equation for the nth term is:
[tex]\boxed{T_n=n^2-12n+21}[/tex]
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
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Answer:
Step-by-step explanation:
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What is the meaning of "The set of all functions from X to Y"?
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"The set of all functions from X to Y" refers to the collection of all possible functions that can be defined from a set X to a set Y. This set is denoted as Y^X or X→Y.
Each element of the set Y^X is a function that maps each element of set X to a unique element of set Y. The notation for such a function f is f: X → Y.
Given,
f is a function from X to Y .
Note:
The cardinality (size) of the set Y^X is given by |Y^X| = |Y|^|X|. In other words, if the set X has m elements and the set Y has n elements, then the set of all functions from X to Y has n^m elements.
It is often used to describe the space of all possible solutions to a given problem or equation.
To know more about sets,
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