The first five terms of the sequence with the given nth term are 1, 3/2, 3/2, 9/8, 27/40.
In this question,
The nth term of the sequence is [tex]a_n=\frac{3^{(n-1)} }{n!}[/tex]
Now substitute the values of n = 1,2,3,4,5
For n = 1,
⇒ [tex]a_1=\frac{3^{(1-1)} }{1!}[/tex]
⇒ [tex]a_1=\frac{3^{0} }{1}[/tex]
⇒ a₁ = 1
For n = 2,
⇒ [tex]a_2=\frac{3^{(2-1)} }{2!}[/tex]
⇒ [tex]a_2=\frac{3^{(1)} }{(1)(2)}[/tex]
⇒ [tex]a_2=\frac{3}{2}[/tex]
For n = 3,
⇒ [tex]a_3=\frac{3^{(3-1)} }{3!}[/tex]
⇒ [tex]a_3=\frac{3^{(2)} }{(1)(2)(3)}[/tex]
⇒ [tex]a_3=\frac{9}{6}[/tex]
⇒ [tex]a_3=\frac{3}{2}[/tex]
For n = 4,
⇒ [tex]a_4=\frac{3^{(4-1)} }{4!}[/tex]
⇒ [tex]a_4=\frac{3^{(3)} }{(1)(2)(3)(4)}[/tex]
⇒ [tex]a_4=\frac{27}{24}[/tex]
⇒ [tex]a_4=\frac{9}{8}[/tex]
For n = 5,
⇒ [tex]a_5=\frac{3^{(5-1)} }{5!}[/tex]
⇒ [tex]a_5=\frac{3^{(4)} }{(1)(2)(3)(4)(5)}[/tex]
⇒ [tex]a_5=\frac{81}{120}[/tex]
⇒ [tex]a_5=\frac{27}{40}[/tex]
Hence we can conclude that the first five terms of the sequence with the given nth term are 1, 3/2, 3/2, 9/8, 27/40.
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Charlie is watching hot air balloons. balloon a has risen at a 50° angle. balloon b has risen at a 78° angle. if the distance from balloon a to the ground is 1,000 feet, how far is balloon b from balloon a? round your answer to the nearest whole number.
The distance from Balloon A to Balloon B, d ≈ 1,052 feet
What is distance ?
Distance is defined to be the magnitude or size of displacement between two positions. Note that the distance between two positions is not the same as the distance traveled between them. Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector.The given parameters are;
The angle at which Balloon A rises, x° = 50° above horizontal
The angle at which Balloon B rises, y° = 78° above horizontal
The (vertical) distance of Balloon A to the ground, h = 1,000 ft.
The required parameter;
The distance from Balloon A to Balloon B, d
We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule
Let,
The height of the balloon strings are equal
The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.
The distance of the Balloon A from Charlie, l₁, is given as follows;
l₁ × sin(x°) = h₁
∴ l₁ = h₁/(sin(x°))
Which gives;
l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.
l₁ ≈ 1,305.41 ft.
For Balloon B, we get;
h₁ = h₂ = 1,000 ft.
∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.
l₂ ≈ 1,022.34 ft
The angle between the balloon strings, θ = 180° - (x° + y°)
∴ θ = 180° - (50° + 78°) = 52°
The angle between the balloon strings, θ = 52°
By cosine rule, we have;
d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))
∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet
Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet
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Which of the following scatter plots does not have a zero correlation?
Given u=2i-9j and v=-5i+7j, what is u•v?
The value of the vector will be -53. The correct option is C.
What are vectors?In mathematics and physics, the term "vector" is used informally to describe certain quantities that cannot be described by a single number or by a set of vector space elements.
The dot product, also known as the scalar product, is an algebraic operation that takes two sequences of integers of equal length and outputs a single number.
The given vectors are u=2i-9j and v=-5i+7j, the dot product of the vectors will be calculated as below:-
u.v = ( 2i-9j ).( -5i+7j)
u.v = -10i² + 17 (i.j) -45(i.j) -63j²
Substitute i² = 1, j² = 1 and (i.j) = 0 in the above equation.
u.v = -10 + 63
u.v = 53
Therefore, the value of the vector will be -53. The correct option is C.
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for f(x)=7x and g(x)=x+1, find the following functions. a.(fog)(x); b.(gof)(x); c.(fog)(4); d.(gof)(4)
Answer:
[tex]a.(fog)(x) = 7x + 7 \\ b.(gof)(x) = 7x + 1 \\ c.(fog)(4) = 35 \\ d.(gof)(4) = 29[/tex]
Step-by-step explanation:
Greetings !
a. (fog)(x)= f[g(x)] = 7(x+1)
(fog)(x)= 7x+7b. (gof)(x) = g[f(x)] =7x+1
c. (fog)(4)=7(4)+7=28+7=35
d. (gof)(4)= 7(4)+1=28+1=29
(fog)(x)
f(g(x))f(x+1)7x+7(gof)(x)
g(f(x))g(7x)7x+1(fog)(4)
7(4)+735(gof)(4)
7(4)+129find the perimeter of parallelogram PORS when side PQ=12cm and QR =7cm (with solution)
The answer is 38cm.
The formula used is perimeter of rectangle so in this case it will be 2(PQ+QR).
So,
=2×(12+7)
=2×19
=38cm
The variable used to predict another variable in a regression analysis (usually x) is called the?
The variable used to predict another variable in a regression analysis (usually x) is called the independent variable.
The regression analysis is used to determine the effect on the dependent variable with every one unit change in the independent variable.
The dependent variable is also known as response.
and the independent variable is also known as predictor.
In case of simple linear regression there is only one independent variable and in cases of multiple linear regression there are more than one independent variables.
The general form of simple linear regression is:
[tex]y=mx+c[/tex]
The general form of multiple linear regression is:
[tex]y=c+m_1x_1+m_2x_2+...+m_nx_n[/tex]
The dependent variable are usually denoted by the letter "y" and the independent variables are usually denoted by the letter "x".
Therefore, the variable used to predict another variable in a regression analysis (usually x) is called the independent variable.
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A school dance committee has 14 volunteers. Each dance requires 3 volunteers at the door, 5 volunteers on the floor, and 6 floaters. If two of the volunteers, Christine and Samuel, cannot work together since they are new, in in how many ways can the volunteers be assigned?
There are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned from 14 volunteers.
Given that a school dance committee has 14 volunteers and each dance requires 3 volunteers at the door, 5 volunteers on the floor and 6 on floaters.
We are required to find the number of ways in which the volunteers can be assigned.
Combinations means finding the ways in which the things can be choosed to make a new thing or to do something else.
n[tex]C_{r}[/tex]=n!/r!(n-r)!
Number of ways in which the volunteers can be assigned is equal to the following:
Since 2 have not been assigned so left over volunteers are 14-2=12 volunteers.
Number of ways =14[tex]C_{12}[/tex]
=14!/12!(14-12)!
=14!/12!*2!
=14*13/2*1
=91 ways
Hence there are 91 such ways in whih the volunteers can be assigned if two of them cannot be assigned.
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Kamden is a mind-reading alien. He had each friend draw and look at a card, then he guessed whether the card had a star on it.
The two-way frequency table below shows data on guess and true status of the cards the friends drew.
Complete the following two-way table of column relative frequencies.
The completed table will have values filled into it accordingly from left to right and the downwards.
What values are required to complete the table?The concept of relative frequencies involves expressing the frequency of occurrence of events as a fraction of a whole frequency.
Hence, it follows that the blank space on the top-leftmost corner of the table can be filled with the value; 4/5 = 0.8.
For the top-rightmost blank space in the table, the required value is; 2/754 = 0.0027.
For the bottom-leftmost blank space, the required value to fill the table is; 1/5 = 0.2.
For the bottom-rightmost blank space, the required value is; 752/754 = 0.9973.
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Estimate each of these square roots.
a) √80
b) √27
c) √110
d) √0.03
e) √0.12
Answer:
a) √80 ≈ 9
b) √27 ≈ 5
c) √110 ≈ 10
d) √0.03 ≈ 0.2
e) √0.12 ≈ 0.3
Step-by-step explanation:
a) √8080 is close to 81
Therefore, √80 can be estimated as √81
√81 = 9
[tex]\Large\boxed{\sqrt{80}\approx9 }[/tex]
b) √2727 is close to 25
Therefore, √27 can be estimated as √25
√25 = 5
[tex]\Large\boxed{\sqrt{27}\approx5 }[/tex]
c) √110110 is close to 100
Therefore, √110 can be estimated as √100
√100 = 10
[tex]\Large\boxed{\sqrt{110}\approx10 }[/tex]
d) √0.030.03 is close to 0.04
Therefore, √0.03 can be estimated as √0.04
√0.04 = 0.2
[tex]\Large\boxed{\sqrt{0.03}\approx0.2 }[/tex]
e) √0.120.12 is close to 0.09
Therefore, √0.12 can be estimated as √0.09
√0.09 = 0.3
[tex]\Large\boxed{\sqrt{0.12}\approx0.3 }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
What is the solution to the inequality 3x - 12| ≥ 6?
0-6
02
Ox<-6 or x> 18
Ox≤2 or x ≥6
========================================
Work Shown:
|3x-12| ≥ 6
3x-12 ≥ 6 or 3x-12 ≤ -6 ..... see note below
3x ≥ 6+12 or 3x ≤ -6+12
3x ≥ 18 or 3x ≤ -6+12
3x ≥ 18 or 3x ≤ 6
x ≥ 18/3 or x ≤ 6/3
x ≥ 6 or x ≤ 2
x ≤ 2 or x ≥ 6
----
Note: if |A| ≥ B, then A ≥ B or A ≤ -B where B is some positive number.
Example: |x| ≥ 5 means either x ≥ 5 or x ≤ - 5
guys pls make it fast [tex]3^{3x-2\\} =\sqrt[3]{9}[/tex]
What is the tenth term in the sequence 9, 13, 17, 21, 25…?
Step-by-step explanation:
its 29 9x4=29 9+4=13 13+4=17
I’m stuck on this problem
The value of the f(-8) from the given f(x) is 1/53.
According to the statement
we have given that the value of f(x) and with the value of this we hav eto find the value of f(-8).
So, For this purpose,
The given value of f(x) :
The function f(x) is
f(x) = 1 / x^2 -11
Now we find the value of the f(-8) then
For this put Put x is -8 in the f(x) then the equation become
f(x) = 1 / x^2 -11
f(-8) = 1 / (-8)^2 -11
f(-8) = 1 / 64 -11
f(-8) = 1 / 53.
here the value becomes 1/53.
So, The value of the f(-8) from the given f(x) is 1/53.
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What is the 7th term of an AP: 50+45+40
Answer:
20
Step-by-step explanation:
using the arithmetic progress formula
tn=a+(n-1)d
from the series given above a which is your first term is 50
the d which is the common difference.. you minus the first term from the second term which is 45-50=-5
so the 7th term which our n=7
we have:
t7=50+(7-1)(-5)
t7=50+(6)(-5)
t7=50-30
t7=20
Answer:
a₇ = 20
Step-by-step explanation:
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 50 and d = 45 - 50 = - 5 , then
a₇ = 50 + (6 × - 5) = 50 + (- 30) = 50 - 30 = 20
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary Minimum: Lower quartile: Median: Upper quartile: Maximum: Interquartile range:
The five number summary can be calculated as follows:
lower quartile(Q₁) = 54 + 56 / 2 = 55
Median = 63.5
Upper quartile(Q₃) = 74
Maximum = 80
Interquartile range = Q₃ - Q₁ = 74 - 55 = 19
How to find the five number summary ?The five number summary can be found as follows;
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
minimum = 48
lower quartile(Q₁) = 54 + 56 / 2 = 55
The median is the middle number when the data is arranged in ascending or descending order.
Median = 63 + 64 / 2 = 127 / 2 = 63.5
Upper quartile(Q₃)= 74 + 74 / 2 = 148 / 2 = 74
Maximum = 80
Interquartile range = Q₃ - Q₁ = 74 - 55 = 19
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PLS HELP LOTs OF POINTS!!!!What is the difference of….
[tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex] is the difference.
What is an expression?
⇒ An expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)
Calculation :
⇒ [tex]\frac{3x^{2} }{(x^{2} -7x+10)}- \frac{5x} {x-2}[/tex]
⇒ [tex]\frac{3x^{2} }{(x-2)(x-5)}- \frac{5x} {x-2}[/tex]
⇒1/(x-2) [(3x²-5x{x-5})/(x-5)]
⇒1/(x-2) [(3x²-5x²+25x)/(x-5)]
⇒1/(x-2) [ (-2x²+25x)/(x-5)]
⇒[tex]\frac{-2x^{2} +25x }{(x-2)(x-5)}[/tex]
at x=2 and x=5 the denominator becomes zero If the denominator of a fraction is zero, the expression is not a legal fraction because its overall value is undefined.
⇒ [tex]\frac{-2x^{2} +25 }{(x-2) (x-5)} ,x\neq 2,x\neq 5[/tex] is the difference
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Which option is the fraction 28/31 closest to? 0, 1/2 or 1?
Answer:
1 is the closest to 28/31
Step-by-step explanation:
0 is technically 28 spaces away and 1/2 is around 13 spaces away but 1 is only 3. :)
Two students compared the scores on their math tests. Their results on 9 tests are shown in the box plots below.
Which statements are true?
Ben has the smaller range of test scores.
The lower quartile and upper quartile of Nadia’s data are both higher than the lower quartile and upper quartile of Ben’s data.
The median of Nadia’s data is equal to the median of Ben’s data.
Nadia had the highest score on a test.
Ben’s lowest score was equal to Nadia’s lowest score.
The statements which are true regarding the students whose results on 9 tests are as shown are; The median of Nadia's data is equal to the median of Ben's data.
Nadia had the highest score on a test.
Which statements are true regarding the scores on the tests?According to the task content, it follows that the results of the students in discuss are indicated by means of a box plot as in the attached image.
Consequently, it follows from observation that the median of Nadia and Ben as indicated in the attached box plot is 92 in both cases as indicated by the vertical line in both boxes.
Additionally, the highest score by Nadia is 100 while that for Ben is; 99.
Hence, Nadia had the highest score on a test.
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Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles
The height of the triangle is 11.3 in. The correct option is C. 11.3 in
Calculating height of triangleFrom the question, we are to determine the height of the given triangle
The height of the given triangle is x in.
Now, we will determine the value of x
In the diagram, we can observe that the height divides the triangle into two equal halves
Thus,
By the Pythagorean theorem, we can write that
12² = x² + 4²
144 = x² + 16
144 - 16 = x²
∴ x² = 144 - 16
x² = 128
x = √128
x = 11.3
Hence, the height of the triangle is 11.3 in. The correct option is C. 11.3 in
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45.255=
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Ahmed made a fruit smoothie in his blender, shown below. He gave 320 milliliters of the smoothie to his brother. How much smoothie is left for Ahmed to drink?
625 ml is the amount of smoothie is left for Ahmed to drink.
According to the statement
we have given that the
Ahmed made a 625 ml fruit smoothie in his blender and out of this he gave
320 milliliters of the smoothie to his brother and we have to find that the
How much smoothie is left for Ahmed.
So, For this purpose,
The total smoothie = 625 ml
Smoothie he gave to his brother = 320 ml
Now, we have to find the Amount of smoothie left for ahmed.
So, Smoothie left for ahmed = 625 ml - 320 ml
Smoothie left for ahmed = 305 ml
So, 625 ml is the amount of smoothie is left for Ahmed to drink.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Ahmed made a fruit smoothie in his blender, shown below. He gave 320 milliliters of the smoothie to his brother. How much smoothie is left for Ahmed to drink? check the image below.
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Can someone help me with this? I cannot figure it out
Answer:
Step-by-step explanation:
To graph by hand I would first convert both equations into y=mx+b.
We start with:
[tex]\left \{ {{2x-2y=4} \atop {x+2y=8}} \right.[/tex]
Solve for y for 2x-2y=4
[tex]2x+2y=4\\2y=4-2x\\y=2-x[/tex]
Solve for y for x+2y=8
[tex]x+2y=8\\2y=8-x\\y=4-\frac{x}{2}[/tex]
Giving the new but equal system of equations:
[tex]\left \{ {{y=2x-x} \atop {y=4-\frac{x}{2} }} \right.[/tex]
From this point on you can graph the two functions to find where the two lines intersect, thats your solution.
I've gone ahead and graphed it on desmos for you
Find the surface area of the figure.
2 m
2 m
11 m
11 m
2 m
5 m
5 m
SA = [? ]m²
Answer:
174m²
Step-by-step explanation:
SA = 2(wl + hl + hw)
= 2(5m x 11m + 2m x 11m + 2m x 5m)
= 2(55m² + 22m² + 10m²)
= 2 x 87m²
=174m²//
Please help me solve!
Answer:
Step-by-step explanation:
Comment
There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2
The graph shows that there is a peak at x = 2. That is where the maximum volume is,
Answer
x = 2
3² +4² = 5²,
6² + 8² = 10² and
9² + 12² = 15²
Can you prove,using algebraic method,that this relationship will be true for any multiple of the triple,
3, 4, 5?
Prove that the statement
5² +12² =13² will hold true for any multiple of this triple.
Answer:
They are all true
Step-by-step explanation:
1. 3² +4² = 5²
3x3 + 4x4 = 5x5
9 + 16 = 25
25 = 25
-----------------------
2. 6² + 8² = 10²
36 + 64 = 100
100 = 100
------------------
3. 9² + 12² = 15²
81 + 144 = 225
225 = 225
-------------------
4. 5² +12² =13²
25 + 144 = 169
169 =169
-------------------
Solve:
4(2 + a) = 24
A =
Answer:
a=4Step-by-step explanation:
Simplify both sides of the equation:
4 (2 + a) = 24
( 4 )( 2 ) + ( 4 )( a ) = 24 (Distribute)
8 + 4a = 24
4a + 8 = 24
subtract 8 from both sides:
4a + 8 − 8 = 24 − 8
4a = 16
Divide both sides by 4:
4 a/4 = 16/4
a = 4
Multiple bracket out first:
4 x 2 =8
4 x a = 4a
8 +4a = 24
-8
4a. = 16
÷4
a = 4
Hope this helps!
If you have 66 data observations in a sample, how many classes (bins) does the sturges' rule recommend for you to construct a frequency distribution?
According to Sturge's rule, number of classes or bins recommended to construct a frequency distribution is k ≈ 7
Sturge's Rule: There are no hard and fast guidelines for the size of a class interval or bin when building a frequency distribution table. However, Sturge's rule offers advice on how many intervals one can make if one is genuinely unable to choose a class width. Sturge's rule advises that the class interval number be for a set of n observations.
Given,
n = 66
We know that,
According to Sturge's rule, the optimal number of class intervals can be determined by using the equation:
[tex]k=1+log_{2} n[/tex]
Here, n is equal to 66 and by substituting the value to the equation we get:
[tex]k=1+log_{2} (66)[/tex]
k = 7.0444
k ≈ 7
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The temperature during a day can be modeled by a sinusoid. Answer the following question given that the low temperature of 7 degrees occurs at 5 AM and the high temperature for the day is 45 degrees.
Find the temperature, to the nearest degree, at 9 AM.
The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)
What is the temperature of a place at a given time?
Sinusoids are expressions with trascendent functions, to be more specfic, trigonometric functions, whose form is described below:
T(t) = A · sin (2π · t / T + C) + B (1)
Where:
A - Temperature amplitude, in degrees.B - Middle temperature, in degrees.T - Period, in hours.C - Angular phase, in radians.The temperature amplitude and the middle temperature can be found by the following expressions:
A = (t' - t'') / 2 (2)
B = (t' + t'') / 2 (3)
Where t' and t'' are maximum and minimum temperatures, in degrees.
Then, we proceed to find each constant of the sinusoidal model:
A = (45 - 7) / 2
A = 38 / 2
A = 19
B = (45 + 7) / 2
B = 52 / 2
B = 26
We assume a period of 24 hours (T = 24).
If we know that t = 0, T = 24, A = 19, B = 26, T(t) = 7, then the angular phase is:
7 = 19 · sin [(π / 12) · 0 + C] + 26
- 19 = 19 · sin C
sin C = - 1
C = π
T(t) = 19 · sin (π · t / 12 + π) + 26
Then, the temperature at 9 AM is: (t = 4)
T(4) = 19 · sin (π · 4 / 12 + π) + 26
T(4) ≈ 9.545
The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)
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The half life of a substance is defined as the time required for the substance to decrease by half. If the weight of a substance begins at 128 grams, and the half life is 7 years, what will be the weight of the substance after 28 years?
the weight of the substance after 28 years is 8 grams.
How to determine the amountWe have that the half life of a substance is defined as the time required for the substance to decrease by half
The formula for calculating the half - life of a material is given as;
[tex]N(t) = N0 (\frac{1}{2} )^\frac{t}{t^\frac{1}{2} }[/tex]
Where
N(t) is final amountNo is the initial amount = 128 gramst1/2 is the half life = 7 yearst is the time elapsed = 28 yearsSubstitute into the formula
N(t) = 128 × (0. 5) ^28/ 7
N (t) = 128 × ( 0. 5) ^ 4
N(t) = 128 × 0. 0625
N(t) = 8 grams
Thus, the weight of the substance after 28 years is 8 grams.
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what is the measure of an angle if it is 660 less than 6 times its own supplement
Answer:
60
Step-by-step explanation:
Since this angle is unknown, let's just represent it with the variable "x". So the supplement angle of "x" is essentially, the value of the angle that we need to add to "x" to get 180. In other words let's just say that the supplement angle is "y". This means that: [tex]x+y=180[/tex]. If we subtract x from both sides we can represent "y" or the supplement angle as: [tex](180-x)[/tex].
Since it's 660 less than 6 times it's own supplement let's first multiply the supplement by 6
[tex]6(180-x) = 1,080-6x[/tex]
Now let's subtract 660 from it, since it's 660 less
[tex](1,080 - 6x) - (660) = 420 - 6x[/tex]
This value should be equal to the angle, which is represented as "x". So let's set it equal to x
[tex]420-6x=x[/tex]
Add 6x to both sides
[tex]420=7x[/tex]
Divide both sides by 7
[tex]60 = x[/tex]
Choose the division problem represented by this model.
Answer:
The answer is C
Step-by-step explanation:
