Use the origin as the center of dilation and the given scale factor to find the coordinates of the vertices of the image of the polygon.
K = 1/3
Answers
The coordinates of the points after dilation is D'(-5/3,1), E'(1,-2/3), F'(5/3,-1), and C'(-1,-4/3)
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size.
Given that the scale factor is 1/3. The coordinates of the points after dilation is,
D(-5,3) = D'(-5/3,1)
E(3,-2) = E'(1,-2/3)
F(5,-3) = F'(5/3,-1)
C(-3,-4) = C'(-1,-4/3)
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Related Questions
f(x) =(x - 5)/3 find the inverse function of this
Answers
The inverse function of f(x) = (x - 5)/3 is f^-1(x) = 3x + 5.
What is inverse function? How to calculate it? In mathematics, an inverse function is a function that undoes the work of another function. Specifically, if the function f applied to an input x gives a result of y, then the inverse function of f, denoted as f−1, applied to y gives the result x. In other words, the inverse of the function "f" applied to y will give us the input that we originally used to obtain y.To calculate an inverse function, one must first identify the original function. Then, one must switch the x and y variables, and solve for y. This is done by isolating the y in the equation and replacing it with the inverse function. For example, if the original equation is y = x + 4, then the inverse equation is x = y - 4.Once this is done, one can then determine the inverse function by taking the reciprocal of the function. This can be done by changing the sign of the exponent for any exponentiated terms and changing the sign of the coefficient for any multiplied terms. For example, if the function is y = x2 + 2x + 4, then the inverse function is y = (1/x2 + 2/x + 4)−1.In summary, to calculate an inverse function, one must first identify the original function, switch x and y, and solve for y, and then take the reciprocal of the expression.Solution:
To find the inverse of a function, we need to switch the x and y variables, and then solve for y.
Starting with f(x) = (x - 5)/3, we can switch the x and y variables to get y = (x - 5)/3.
We can then solve for x by multiplying both sides by 3, giving us 3y = x - 5.
We can then add 5 to both sides to get 3y + 5 = x, which is the inverse of our original function.
Therefore, the inverse of f(x) = (x - 5)/3 is f^-1(x) = 3x + 5.
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The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.
x –2 0 1 2 3
h(x) 0 –12 0 8 0
If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
h(x) = x3 – 2x2 – 5x + 6
h(x) = x3 – 6x2 + 11x – 6
h(x) = x3 + 2x2 – 5x – 6
h(x) = x4 + 14x3 + 19x2 – 66x – 72
Answers
The equation of the polynomial function is (a) h(x) = x^3 - 2x^2 - 5x - 6
How to determine the equation of the polynomial function?From the question, we have the following parameters that can be used in our computation:
x –2 0 1 2 3
h(x) 0 –12 0 8 0
The x-intercepts are where y = 0
So, we have
x = -2, x = 1 and x = 3
The multiplicity is 1
So, we have
h(x) = (x + 2)(x - 1)(x - 3)
Expand
= (x + 2)(x^2 - 4x + 3)
This gives
= x(x^2 - 4x + 3) + 2(x^2 - 4x + 3)
So, we have
= x^3 - 4x^2 + 3x + 2x^2 - 8x + 6
Evaluate the like terms
= x^3 - 2x^2 - 5x - 6
So the equation is h(x) = x^3 - 2x^2 - 5x - 6
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If a "2" is rolled on a fair 6-
sided die, what event is most
likely to occur next?
A. a roll lower than 2
B. a roll higher than 2
C. another 2
D. all of these events are equally
likely
Answers
The event with the largest probability is rolling a number higher than 2, so the correct option is B.
Which event is most likely to occur next?First, the fact that a 2 was rolled before does not affect the next rolls of the dice, so that information is extra.
Now we just need to see which option has the largest probability.
A) There are only one number lower than 2, then the probability of this event is p = 1/6
B) There are 3 numbers higher than 2, then the probability is p = 3/6 = 1/2
C) The probability of get another 2 is 1/6
We can see that the event with the largest probability is B, so that one is the most likely to occur.
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23. Use Patterns and Structure An artist uses
colored tape to divide sections of a mural. She
needs to cut a piece of paper to cover triangle EFC
while she works on other sections. What are
the angle measures of triangle EFC?
Answers
As per the following diagram, the angle measures of triangle EFC is 118°
The term angle in math is known as a figure which is formed by two rays or lines that shares a common endpoint.
Here we have given that an artist uses colored tape to divide sections of a mural and she needs to cut a piece of paper to cover triangle EFC while she works on other sections.
According to the diagram, here we know that the value of
=> DE = EF
And the value of
=> EB = FB
Here we know that the value of the angles,
=> ∠EDB = ∠EFB = 90°
Thus implies that the angles,
=> ∠DFB = ∠FEB = 31°
Then the value of the angle is calculated as,
=> ∠EDB =∠EFB = 90° - 31°
=> ∠EDB = ∠EFB = 59°
Then the value of the angle ABC is calculated by sum the values of the angles, then we get,
=> ∠ABC = ∠EDB + ∠EFB = 59 + 59 = 118°
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Select all the correct locations on the table. Consider the following expression. 7 1/5 . 49 7/5 Select "equivalent" or "not equivalent" to indicate whether the expression above is equivalent or not equivalent to the values or expressions in the last column.
Answers
The first and second expressions are equal. The second expression is not synonymous. The third expression is interchangeable. The fourth expression is incorrect.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.
Here,
According to image,
First expression is equivalent. Second expression is not equivalent. Third expression is equivalent. Forth expression is not equivalent.
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The perimeter of a rectangle is 212 centimeters. Find the length and width if the length is an even integer and the width is 5 times the next consecutive even integer.
Answers
The length and width of the rectangle are 16 cm and 90 cm respectively
What is the Perimeter of a Rectangle?The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P = 2 ( Length + Width )
Given data ,
Let the perimeter of the rectangle be P = 212 cm
Now , the equation will be
The length of the rectangle be = L
And , length is an even integer and the width is 5 times the next consecutive even integer
So , the width of the rectangle W = 5 ( L + 2 )
Substituting the values in the equation , we get
Perimeter of rectangle P = 2 ( Length + Width )
212 = 2 ( L + 5 ( L + 2 ) )
On simplifying the equation , we get
106 = L + 5L + 10
6L = 96
Divide by 6 on both sides of the equation , we get
L = 16 cm
So , W = 5 ( L + 2 )
W = 5 x 18
W = 90 cm
Hence , the length and width of rectangle is 16 and 90 respectively
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4. Susan is a plumber and charges a fee for any job that she does plus an hourly
rate for the time it takes her to complete the job. When she works 8 hours, she
gets paid $320. When she works 12 hours, she gets paid $440.
a. Explain what the independent and dependent variables are for this situation
and create two data points.
Answers
Answer:
Here are two data points that can be used to represent this relationship:
(x1, y1) = (8, $320) - this data point represents that when Susan works 8 hours, she gets paid $320.
(x2, y2) = (12, $440) - this data point represents that when Susan works 12 hours, she gets paid $440.
Step-by-step explanation:
In this situation, the independent variable is the number of hours that Susan works, and the dependent variable is the amount of money that she gets paid.
Here are two data points that can be used to represent this relationship:
(x1, y1) = (8, $320) - this data point represents that when Susan works 8 hours, she gets paid $320.
(x2, y2) = (12, $440) - this data point represents that when Susan works 12 hours, she gets paid $440.
We can use these two data points to represent the relationship between the number of hours that Susan works and the amount of money that she gets paid. It shows that, As her work hours increase, her pay increases as well.
Help please I need this answer very quick will be very appreciated
Answers
Answer:rotational
Step-by-step explanation:
it would not be a line because a line is a line and other make no sense
You (or your parents) are debating about whether to buy a new car for $19,072.00 or a used car for $15,635.00. Sales tax is 4.5%. You (or your parents) plan to make a down payment of $1,200.00 and your credit rating is fair. Use the table below to determine the difference in interest accrued by the end of the first month.
Secured Unsecured
Credit APR (%) APR (%)
Excellent 5.4 5.65
Good 5.95 6.35
Average 6.30 6.90
Fair 7.55 7.60
Poor 9.80 10.0
Answers
Answer: $20.95
Due to credit rating being fair:
Secured APR = 7.00%
Loan amount = sale price + tax - down payment
New car = [tex]19027 + (19072 x 0.045) - 1200 = 18730.24[/tex]
Used car = [tex]15635 + (15635 x 0.045) - 1200 = 15138.575[/tex]
---------------------------------------------------------------------------
Monthly interest = loan amount [tex]x 0.07 x 1/12[/tex]
New car = [tex]18730.24 x 0.07 x 1/12 = 109.26[/tex]
Used car = [tex]15138.575 x 0.07 x 1/12 = 88.31[/tex]
Thus, the difference is [tex]109.26 - 88.31 = $20.95[/tex]
How do you tell if a table represents a linear function?
Answers
If the rate of the change in the input to the change in the output is the same for every point in the table, then the table represents a linear function.
If a table of values shows a constant rate of change, it is linear.
A non-vertical graph that is a straight line is linear. An equation that can be written in the form y=mx+b is linear. If a table of values shows a constant rate of change, it is linear.
Linear relationships can be modeled using the slope-intercept form y=mx+b, As x increases, y increases by a proportional amount.
A linear function is a linear relationship that obeys the rules of a function and has a graph that forms a straight line. Function notation is used to express a linear relationship when there are clearly defined inputs and outputs.
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Determine the lope, x-intercept and y-intercept of the line given by the equation 2x3y=6
Answers
For the given equation of the line 2x + 3y = 6 , the slope = -2 /3,
the x-intercept = 3 and the y-intercept = 2.
As given in the question,
Given equation of the line is :
2x + 3y = 6
Standard equation of the line with slope 'm' and y -intercept = c
y = mx + c
Convert the given equation into standard form we get,
2x + 3y = 6
⇒ y = (-2/3)x + 6/3
⇒y = (-2/3)x + 2
Slope of the line = -2/3
y - intercept when x = 0
y = 2
x - intercept when y = 0
x = 3
Therefore, for the given equation of the line the slope , x- intercept ,and y-intercept is equal to (-2/3) , 3 , and 2 respectively.
The above question is incomplete, the complete question is:
Determine the slope, x-intercept and y-intercept of the line given by the equation 2x + 3y = 6?
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Mr. Remy Osta took earned leave for 50 days from February 10, 2008 onwards. When did he resume his duty?
Answers
The date Mr. Remy Osta will resume duty after his 50 days leave which lasted from February 10, 2008 is March 31, 2008
How to check the calendar?2008 is a leap yearA leap year is a year which has 366 days, that is, the days in February are 29 days.
So,
From February 10, 2008
The days remaining in February is 19 more days
The days of march is 31 days
Hence,
19 days + 31 days
= 50 days
Therefore, Mr. Remy Osta will resume duty on March 31, 2008
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Ian wants to ride his bicycle 36.5 miles this week he has already written 8 miles if he rides for five more days which equation could be used to determine M the average number of miles he would have to ride to meet his goal?
Answers
Answer:
M = (36.5-8)/5
[M = 5.7 miles/day]
Step-by-step explanation:
The goal is 36.5 miles. The remaining miles needed to achieve this goal is reduced by the miles already ridden, 8 miles.
(36.5 - 8) = 28.5 miles remaining.
We are asked to find a value for M, which is the average number of miles Ian would have to ride to reach his goal. By average, we can assume it is the average miles/days remaining. The days remaining are 5, so we have:
(28.5 miles remaining)/5 days = 5.7 miles/day
An equation for M using these steps would be:
M = (36.5-8)/5
Which graph correctly represents 3x + y > 7?
NEED HELP!!
Answers
The graph of the inequality: 3x + y > 7
Can be seen in the image below.
Which graph correctly represents the inequality?We want to see which graph represents the inequality:
3x + y > 7
We can rewrite the inequality in slope-intercept form as:
y > -3x + 7
So we just need to graph the line:
y = -3x + 7
With a dashed line, and then shade all the region above the line.
To graph the line, you need to find two points that lie on the line.
if we evaluate the line in x = 0 we wll get:
y = -3*0 + 7
y = 7
if x = 1
y = -3*1 + 7
y = -4
Then we have the points (0, -7) and (1, -4), now we can graph these two points and connect them with a dashed line, then shade the region above.
The graph of the inequality is the one below.
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Y = 5x + 2
2y - 4 = 10x
please help need a solution
Answers
Answer:
Infinitely many solutions.
Step-by-step explanation:
y=5x+2
2y-4=10x
----------------
2(5x+2)-4=10x
10x+4-4=10x
10x=10x
Find the 6th term in the expansion of (4x + 1)^8 in simplest form.
Answers
on solving 6th term in the binomial expansion of (4x + 1)^8 in simplest form is 3584.
What is binomial Expanssion ?A binomial is an algebraic expression with two terms. For example, a + b, x - y, etc are binomials. We have a set of algebraic identities to find the expansion when a binomial is raised to exponents 2 and 3.
A polynomial with just terms is a binomial. An illustration of a binomial is x + 2, where x and 2 are two distinct words. Additionally, in this case, x has a coefficient of 1, an exponent of 1, and a constant of 2. As a result, a binomial is a two-term algebraic statement that comprises a constant, exponents, a variable, and a coefficient.
we know ,
So the 6th term in the equation
is ,8c5 -4x^8-5 = 8c34x^3 is , = 3584
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PLEASE I NEED HELP ASAP‼️‼️
Answers
Answer:
a^m + a^n = a^m+n
Step-by-step explanation:
This is true for any value of a and n except 0.
Are these similar?
Anything helps thank you!
Answers
The angles are congruent and the ratios of sides are equal, then the polygons are similar.
What is the similarity of polygons?
The similarity of polygons refers to the relationship between two or more polygons in which the corresponding angles are congruent (equal in measure) and the corresponding side lengths are in proportion.
We have,
Polygon 1:
Opposite Sides 24 = 24, 12=12,
Angles = 90°
Polygon 1:
Opposite Sides 16 = 16, 8=8,
Angles = 90°
This means that if two polygons are similar, their corresponding angles will have the same measure, and their corresponding side lengths will be in the same ratio. In other words, the ratio of any pair of corresponding sides of similar polygons will be the same.
For example, two triangles are similar if the ratio of their corresponding sides is the same, and their corresponding angles are equal. Similarly, two quadrilaterals are similar if the ratio of their corresponding sides is the same and their corresponding angles are equal.
It's important to note that similarity is a stronger relationship than congruence, because in congruence all the sides and angles must have the same measure, while in similarity only the angles and ratios of sides are the same.
Additionally, the similarity of a polygon can be determined by measuring the angles of the polygon, and comparing the ratios of the corresponding sides.
If the angles are congruent and the ratios are equal, then the polygons are similar.
Hence, the angles are congruent and the ratios of sides are equal, then the polygons are similar.
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Joyce has $13 in savings and saves an additional $6 each week. At the same time, Enrique has $80 in savings and spends $5 each week to go swimming at the community pool. Is there a week when Joyce and Enrique will have the same amount of money? Explain why or why not.
Answers
Answer: Yes, after 7 weeks, they will have the same amount of money
Step-by-step explanation: So let’s say Joyce will be equation 1, so it would be - T = 13 + 6x, where T represents the total money, and x represents the number of weeks. And let’s say Enrique will be equation 2, which will be - T = 80 - 5x, where once again, T represents the total money, and x represents the number of weeks.
So, let’s start going off numbers, we will start at 5 weeks, when we put that in, Joyce will have $43 and Enrique will have $65, so we know it will be more than 5 weeks, so let’s try 8 weeks, Joyce will have $61 and Enrique will have $40, so it’s below 8, so how about we try 7, at 7 weeks, Joyce will have $55, and Enrique will have $55 too. So this means, after 7 weeks, Joyce and Enrique will have the same amount of money
Mark the points A and B in your book 4 cm apart. Construct and shade the region that is closer to B than to A and within 3 cm of B. You must show all of your construction lines. A• B.
Answers
How can u add 3/10 and 2/5 explain
Answers
Answer:
7/10
Step-by-step explanation:
How do you add a fraction?
First you have to check if they have common denominator. If so, add the numerators and keep the denominator. If Not, you have to find common denominator before added. After that, check if your fraction need to be simplify.
Solve:
Least common multiplier of 10 and 5 is 10
[tex]\frac{3}{10}+\frac{2}{5}[/tex]
Since [tex]\frac{3}{10}[/tex] already have a denominator of 10 we keep it.
[tex]\frac{2}{5}=[/tex] [tex]\frac{2\times2}{5\times2}[/tex] [tex]=\frac{4}{10}[/tex]
Now we have;
[tex]\frac{3}{10}+\frac{4}{10}[/tex]
Apply fraction Rule which is; [tex]\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}[/tex]
[tex]=\frac{3+4}{10}[/tex]
3 + 4 = 7
[tex]=\frac{7}{10}[/tex]
Hence, [tex]\frac{3}{10}+\frac{2}{5}=\frac{7}{10}[/tex]
RevyBreeze
Eight more than a number is 20. Find the number.
Answers
Answer:
12
Step-by-step explanation:
i did this buy subtracting 20-8!
Find the measures of x and y
X
Y
Answers
The right angle, 99, 171, and 159 are four of the angles. It follows that the x and y angles, which are also equal, must both equal 201/2.
what is angle ?A place where two lines converge creates an angle. They are quantified in degrees and are denoted by the symbol °. Four essential types are reflex, acute, right, and obtuse angles. A circle has 360 degrees. One terminal exists when two rays (half-lines) are merged form an angle. The rays are referred to as the angle's sides, occasionally as its legs, and occasionally as its arms, while the latter is referred to as the angle's vertex. The place where all points of an angle converge is known as the vertex.
given
A polygon's internal angle measurements are equal to (n-2) * 180, where n is the number of sides.
Therefore, 4 * 180 = 720 is the total of the internal angles of this 6-sided object.
The remaining two equal angles are 720 - 90 - 99 - 171 - 159 = 201 .
The right angle, 99, 171, and 159 are four of the angles. It follows that the x and y angles, which are also equal, must both equal 201/2.
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MATH
Eric ran 3 km in 20 minutes Taylor ran 2550 m and 17 minutes. What is one person running faster than the other or were they running at the same rate
Answers
Answer:
Taylor
Step-by-step explanation:
2.5km in 17 mins time 2=5km in 34mins 3km in 20 mins times 2=6km in 40 mins
Four gallon of paint are ued to paint 25 chair. If each chair ued the ame amount of paint, how many gallon are ued to paint each?
Answers
There are 0.16 gallon is used to paint each chair.
What is gallon?
A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters.
as given, Four gallon of paint are used to paint 25 chair.
i.e. 4 gallon ⇒ 25 chairs
and If each chair used the same amount of paint then how many gallon are used to paint each?
i.e. how many gallons ? ⇒ 1 chair
∴ 4 gallon ⇒ 25 chairs
∴ 25 chairs ⇒ 4 gallon
∴ 1 chairs ⇒ 4 / 25 gallon
∴ 1 chairs ⇒ 0.16 gallon
Therefore, there are 0.16 gallon is used to paint each chair.
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If 16,000 divided by n=4
Answers
Answer: If you're asking for the answer if 16,000 divided by 4, it would be 4000, don't know for sure if that's what you were asking for! Hope I helped!
Help with this you will get points if you answer really need help asap
Answers
A rectangle is a closed 2-D shape with four sides, four corners, and four right angles (90°).
What is a rectangle?Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side.
A rectangle has four vertices since it has four sides, four angles, and four corners. The intersection of two sides forms the "vertices" of a polygon. They are corners, to put it another way.
Rectangles' basic characteristics include:
Four-sided shapes include rectangles.
Parallel and equal to each other are the opposing sides.At 90 degrees, every internal angle is equal.360 degrees is equal to the total of all internal angles.Crossing each other on diagonals.Equal lengths can be found for both diagonals.To learn more about rectangle refer to:
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For how many different displays, starting at 10:00 AM and ending at 4:00 PM, during a particular day, will a digital clock show that the number of the hour is less than the number of the minute? [For example, at 2:15 the number of the hour is less than the number of the minute but at 2:01, the number of the hour is greater than the number of the minute]
Answers
A digital clock will show that the number of the hour is less than the number of the minute for 12 different displays, starting at 10:00 AM and ending at 4:00 PM.
What will the clock display?These displays are:
10:01 AM, 10:12 AM, 10:23 AM, 10:34 AM, 10:45 AM, 11:02 AM, 11:13 AM, 11:24 AM, 11:35 AM, 12:03 PM, 12:14 PM, and 12:25 PM.
For example, 10:01 AM and 11:23 AM.
From 10:00 AM to 12:59 PM, the hour will always be a single digit, so we can check the minutes to see if they are double digit.
From 10:00 AM to 10:59 AM, the minute has to be greater than the hour. So, we can pick the minutes starting from 01 to 59 and check whether the hour is less than the minute which gives us 12 such displays
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What is the value of x in the equation: 2^(3^x) = 10^(6^x) ?
____________________
False answer will be REPORTED immediately. Do not waste your time if you do not have sufficient knowledge.
Answers
Answer:
[tex]log\ (log\ 2)/\ log\ 2[/tex] or ≈ - 1.73------------------------------
Solve in below steps, using log and exponent rules:
[tex]2^{3^x}=10^{6^x}[/tex] Given[tex]log\ 2^{3^x}=log\ 10^{6^x}[/tex] Log both sides[tex]3^x\ log\ 2=6^x\ log\ 10[/tex] Log of power rule[tex]3^x\ log\ 2=6^x[/tex] log 10 = 1[tex]3^x\ log\ 2=(3*2)^x[/tex] Power of the product rule[tex]3^x\ log\ 2=3^x*2^x[/tex] Cancel 3ˣ on both sides[tex]log\ 2=2^x[/tex] Log both sides[tex]log\ (log\ 2)=x\ log\ 2[/tex] Divide both sides by log 2[tex]x=log\ (log\ 2)/\ log\ 2[/tex] AnswerAn art museum installed a large triangular sculpture. One of the sculpture’s exterior angles creates a 158 angle with the ground.
If the sculpture’s opposite interior angle is 32 less than the interior non-adjacent angle, what is the measure of the interior non-adjacent angle?
Answers
The measure of the interior non-adjacent angle as required in the task content is; 95°.
What is the measure of the interior non-adjacent angle?Recall; It follows from the triangle exterior angle theorem that the measure of exterior angle of a triangle is equal to the sum of the two opposite interiors angles.
On this note, if the sculpture’s opposite interior angle is 32 less than the interior non-adjacent angle, the sum of the two angle measures is therefore;
x + x - 32.
where, x is the measure of the interior non-adjacent angle.
Hence, x + x - 32 = 158
2x = 158 + 32
2x = 190
x = 95°.
Ultimately, the measure of the interior non-adjacent angle is; 95°.
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