Is the following process correct? If not, which step is where the error occurs, justify your answer. Then rework the problem to find the correct answer.
Answers
We are given the following absolute value equation
[tex]|4x-1|=5x+37[/tex]Let us solve the problem then we will compare it with the given solution.
[tex]\begin{gathered} |4x-1|=5x+37 \\ 4x-1=\pm(5x+37) \end{gathered}[/tex]Now we will solve for the positive and negative sign separately
[tex]\begin{gathered} 4x-1=5x+37 \\ 4x-5x=37+1 \\ -x=38 \\ x=-38 \end{gathered}[/tex][tex]\begin{gathered} 4x-1=-5x-37 \\ 4x+5x=-37+1 \\ 9x=-36 \\ x=\frac{-36}{9} \\ x=-4 \end{gathered}[/tex]Comparing it with the given solution, there is an error on the left-hand side step 2. (the sign of 38 should be positive but in the figure, it is shown negative)
Now let us substitute the obtained x values into the original absolute value equation and check if they satisfy the equation.
For x = -4:
[tex]\begin{gathered} |4(-4)-1|=5(-4)+37 \\ |-16-1|=-20+37 \\ |-17|=17 \\ 17=17 \end{gathered}[/tex]Hence, x = -4 is a valid solution.
For x = -38:
[tex]\begin{gathered} |4(-38)-1|=5(-38)+37 \\ |-152-1|=-190+37 \\ |-153|=-153 \\ 153\ne-153 \end{gathered}[/tex]Hence, x = -38 is not a valid solution.
The above is an example of an extraneous solution.
An extraneous solution is a solution that we get during the process of solving an equation but it is not really the solution meaning that it does not satisfy the equation!
Therefore, x = -4 is the only solution to the given equation.
Related Questions
Expand and simplify.2(2x+1)-3(4x-5)is the answer -8x+17?
Answers
Hello
To expand this, we will multiply the value outside the bracket with the one inside the bracket.
[tex]\begin{gathered} 2(2x+1)-3(4x-5) \\ 4x+2-12x+15 \\ \text{collect like terms} \\ -8x+17 \end{gathered}[/tex]The answer to this question is -8x +17
value outside the bracket with the one inside the bracket.
Sean weighs 10 lb more than twice Brad’s weight. If Brad gains 10 lb, together they will weigh 230 lb. How much does each weight now?
Answers
The weight of Brad is 70 lb and the weight of Sean is 150 lb now.
According to the question,
We have the following information:
Sean weighs 10 lb more than twice Brad’s weight. If Brad gains 10 lb, together they will weigh 230 lb.
Now, let's take Brad's weight to be x lb.
So, we have:
Sean's weight = (10+2x) lb
Now, when Brad gains 10 lb, we have the following expression:
(x+10)+(10+2x) = 230
3x+20 = 230
3x = 230-20
3x = 210
x= 210/3
x = 70 lb
Now, Sean's weight = (10+2x) lb
Putting the value of x:
Sean's weight = 10+2*70
Sean's weight = 10+140
Sean's weight = 150 lb
Hence, the weight of Brad is 70 lb and the weight of Sean is 150 lb now.
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a bicycle path and a road cross at right angles. a police woman stands on the road 70 meters south of the crossing and watches an eastbound cyclist traveling at 6 meters per second. at how many meters per second is the cyclist moving away from the police woman 4 seconds after passing the intersection?
Answers
The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, or, in standard algebraic notation, a² + b² = c².
What is meant by Pythagorean Theorem?The Pythagorean Theorem states that the squares on the hypotenuse (the side across from the right angle) of a right triangle, or, in standard algebraic notation, a² + b² = c².
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
First use the Pythagorean theorem. a² + b² = c²
then take the first derivative of it to get
2a(a') + 2b(b') = 2c(c')
Now figure out how far the train is after 4 seconds
6(4)=24
70² + 24² = c²
c = 74
Now plug in the variables you know
2(70)0 + 2(24)6 = 2(74)c' and solve for c' or the rate of change of c.
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21 A forklift has a maximum carrying capacity of 960 pounds. Each cargo box weighs 60 pounds.
a. Write and solve an inequality that represents the maximum number of cargo boxes the
forklift can carry.
b.
A 120-pound carrying case is used to hold the cargo boxes. What is the maximum number
of cargo boxes the forklift can carry when the carrying case is used? Show that your answer
is correct by showing that one more than your answer would exceed the forklift's capacity
Answers
Using the concept of inequality, it can be concluded that;
a) Maximum number of cargo boxes the forklift can carry is 16.
b) Maximum number of cargo boxes the forklift can carry when the carrying case is used is 14.
What is the inequality in mathematics?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to contrast two numbers on the number line based on their sizes.
Let the no. of cargo box be x.
So the equation is 60x≤960
x≤960/60
x≤16
Now the 120 pound additional weight is needed so the equation is:
120 + 60x≤960
60x≤840
x≤14
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A tent pole that is 9 feet tall is secured to the ground with a piece of rope that is 15 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.
Answers
a = 9
c = 15
c^2-a^2 = b^2
15^2-9^2 = b^2
225-81 = 144^2
144 square root = 12
So, the base of the tent is 12 ft
The number of feet from the tent pole to the rope along the ground will be 12 Feet.
Let:
PR be the tent pole 9 Feet tallPQ be the piece of rope 15 Feet longRq be the distance between the tent pole and the rope along the groundRQ = x
According to Pythagoras Theorem:
[tex]Hypotenuse^{2} = Perpendicular^{2} + Base^{2} \\PQ^{2} = PR^{2} + RQ^{2} \\15^{2} = 9^{2} + x^{2} \\225 = 81 + x^{2} \\x^{2} = 225 - 81\\x^{2} = 144\\x = 12[/tex]
Therefore, the number of feet from the tent pole to the rope along the ground will be 12 Feet.
Pythagoras Theorem is widely used to establish the relation between the three sides of a right-angled triangle. The applications of Phythagoras Theorem are the angle of depression, angle of elevation, etc. Even the Eiffel tower is one of its applications.
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Subtract and simplify:
PLEEEEASE HEEEEELP ASAP
8 1/2 − 5 2/3 = _____
Responses
A 16/6
B 3 1/3
C 2 5/6
D 3 1/6
Answers
Answer:
C
Step-by-step explanation:
8.5 - 5.6666= 2.83
Answer:
C. 2 5/6
Step-by-step explanation:
8 1/2 - 5 2/3 1. convert mixed numbers into an improper fraction
17/2 - 17/3 2. convert fractions into 2 numbers that can be subtracted
51/6 - 34/6 3. subtract
17/6 4. convert to mixed number
2 5/6
Find the value of x for which i II m?
Answers
Answer:
16. 36.67
17. 40
Step-by-step explanation:
See attached worksheet
there are 324 students in a college who have taken a course in calculus, 211 who have take a course in discrete mathematics, and 135 who have taken a course in both calculus and discrete mathematics. how many students at this college have taken a course in either calculus or discrete mathematics?
Answers
265 students at this college have taken a course in either calculus or discrete mathematics.
Let X = number of students who have taken a course in calculus
Y = number of students who have taken a course in discrete mathematics
To determine the number of students who have taken a course in calculus only, subtract 135 from 324.
Only X = X - X∩Y
Only X = 324 - 135
Only X = 189
To determine the number of students who have taken a course in discrete mathematics only, subtract 135 from 211.
Only Y = Y - X∩Y
Only Y = 211 - 135
Only Y = 76
To determine the number of students who have taken a course in either calculus or discrete mathematics, add 189 and 76.
either X or Y = only X + only Y
either X or Y = 189 + 76
either X or Y = 265
To better illustrate the X and Y, see the attached photo of the Venn Diagram.
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The equation of a line is given below.2x+6y=-18Find the x-intercept and the y-intercept.Then use them to graph the line.X-intercept:0Х5?ca loxy-intercept:0?
Answers
Given equation of the line is
[tex]2x+6y=-18[/tex]Dividing both sides of the above equation by -18, we get
[tex]\frac{x}{-9}+\frac{y}{-3}=1[/tex]The line cuts the x axis at (-9,0) and the y axis at (0,-3).
Therefore, the x intercept is -9 and the y intercept is -3.
The graph of the line is shown below.
find the ratio of the shaded pattern to the total area of the figure.
Answers
We are given a rectangle with the following dimensions;
[tex]\begin{gathered} l=(x+3) \\ w=(x+1) \end{gathered}[/tex]Also, placed inside the large rectangle, is a smaller shaded rectangle which has the dimensions;
[tex]\begin{gathered} l=(x+1) \\ w=x \end{gathered}[/tex]The ratio of both figures can be expressed as follows;
[tex]\text{Ratio}=a\colon b=\frac{a}{b}[/tex]Substituting for the values of both figures, we now have;
[tex]undefined[/tex]Hello can you help me on my 7th grade math worksheet show all work
Answers
ANSWER:
78.5 ft
STEP-BY-STEP EXPLANATION:
One trip equals the circumference of the circle.
The circumference of a circle is calculated by means of the following formula:
[tex]\begin{gathered} c=\pi\cdot d \\ \\ d=\text{ diameter = 25 ft} \end{gathered}[/tex]Therefore, we substitute and calculate the distance the pony would walk for a trip:
[tex]\begin{gathered} c=(3.14)(25) \\ \\ c=78.5\text{ ft} \end{gathered}[/tex]That is, the number of feet the pony walks is 78.5
What is the solution to this equation?
5(x-3) = 21
A x =
OB x=
36
5
D x=
65
6
5
24
OC X= 5
18
5
Answers
Answer:
x = 7.2
Step-by-step explanation:
[tex]5(x - 3) = 21[/tex]
[tex]x - 3 = 4.2[/tex]
[tex]x = 7.2[/tex]
i cn T FING THIS HELPPPPPPPP
Answers
The equation which describes Riya's graph is:
a). C(t) = -3t + 24.
We can easily find out the equation by concentrating on the axes.
For example,
Just look from the graph the value of C when t = 0.
We can conclude that C should be equal to 24 when t is equal to 0.
Now, let us put this value of t ( which is 0) in the equations one by one:
a). C(t) = -3t + 24
=> C(0) = -3 (0) + 24
=> C(0) = 24.
So, equation a). satisfies the given criteria.
Similarly, b) also qualifies but c) and d) are not equal to 24 when t = 0.
So, remove them.
Now, let's look at the value of t when C=0.
We can see that t should be equal to 8.
Let's put this value in equations,
a). 0 = -3t + 24
=> 3t = 24
=> t = 8.
Now, we can see that equation a). satisfies all the given conditions for the graph.
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Write variable expressions: two operations
Write an expression for the sequence of operations described below.
multiply t by 5, then double the result
Answers
The expression for the sequence of operations is 2(t x 5).
Expression:
Expression consists of minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given,
Here we have the phrase "multiply t by 5, then double the result"
Now we have to written the algebraic expression for it.
For the given phrase, we have to divide it into two part,
The first part is "multiply t by 5",
So, it can be written as
=> 5 x t
Now, we have to move on to the next part that is,
"double the result".
For that, we have to multiply the first part by 2,
It can be written as,
=> 2 x ( 5 x t)
Therefore, the resulting expression is 2(5t).
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considering the function for what values of x is f constant Options: (negative infinity,10]never(10,15)[15, infinity)
Answers
So, as shown at the function
f(x) is constant at the middle interval (10 , 15)
at which f(x) = 2 and the digit 2 is constant
so, the answer is (10 , 15)
pls help with whats in image!!!
Answers
The slope of the line will be positive 9. Then the correct option is C.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope is given as,
Slope = m = (y₂ - y₁) / (x₂ - x₁)
Determine whether a line's slope, which represents the linear connection, is positive, negative, zero, or undefined without using a graph. Next, locate the slope. A babysitter may make $9 per hour and $36 per 4 hours.
Slope = (36 - 9) / (4 - 1)
Slope = 27 / 3
Slope = 9
The slope of the line will be positive 9. Then the correct option is C.
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Write the expression 16x + 28 as a product using the GCF as one of the factors.
Please help.
Answers
Answer:
4(4x + 7)
Step-by-step explanation:
To answer this question you need to understand what GCF is
GCF is Greatest Common Factor
GCF is the highest number that divides exactly into two or more numbers.
The expression is 16x + 28
The highest number that can divide 16 and 28 is 4
Dividing 16x + 28 gives => 16x/4 + 28/4 => 4x + 7
So the factored expression is
4(4x + 7)
in linear regression analysis the quantity that gives the amount by which the dependent variable changes for a unit change in the independent variable is called the
Answers
It is called the slope of the regression line.
The slope of the regression line including the intercept displays the linear relationship between 2 variables and can also be used in estimating an average change rate.
The slope of a regression line depicts the rate of change in the dependent variable as the independent variable alters because the dependent variable y is dependent on the independent variable x.
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y=−3x+9
3y=−9x+9 how many solutions
Answers
The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.
What is the solution to the equation?The allocation of weights to the relevant variables that produce the calculation's equilibrium is referred to as a consequence.
A connection between two or more factors results in a linear model when displayed on a graph. The variable will have a degree of one.
The linear equations are given below.
y = -3x + 9 ...1
3y = -9x + 9 ...2
Divide the equation 2 by 3, then the equation will become.
y = -3x + 3
The slope of the lines is the same but the lines are separated by a distance.
The system of the linear equation y = −3x + 9 and 3y = −9x + 9 are parallel to each other and represent no solution. Then the number of the solution is zero.
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owen is the owner of the french realty company. he knows that the average number of homes sold per day is one. let x be the number of homes that french realty sells tomorrow. (a) (2 pts) what is the distribution of x and its parameter(s)? (b) (2 pts) what is the standard deviation of x ? (c) (2 pts) what is the probability that x is (inclusively) within one standard deviation of the mean of x
Answers
A) distribution of x and its parameter(s) is (λ^x e^-λ ) / x!
B) standard deviation of x is 1
C) probability that x is (inclusively) within one standard deviation of the mean of x is 0.7358
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
A) The poisson distribution with mean is followed by X = λ = 1
Therefore, ≈ (λ = 1)
Distribution of X is:
(λ^x e^-λ ) / x! , x = 0, 1, 2, 3 ......
B) Standard Deviation of X is :
σx = √x = 1
C) Probability of X = P (-1 ≤ x ≤ 1)
P(x = 0) + P(x = 1)
= (1⁰ e⁻¹) / 0! + 1¹ e-¹ / 1!
= 2e⁻¹
= 0.7358
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Directions: Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.Solve for x.( + 0.5) + 5.24 = = + ( + 2.2)The value of x is
Answers
1/5 (x+0.5) +5.24 = 3/2x + 7/10 (x+2.2)
First, apply the distributive property to solve the parentheses
1/5(x)+ 1/5 (0.5) +5.24 = 3/2x + 7/10(x) + 7/10 (2.2)
1/5x +0.1 +5.24 = 3/2x + 7/10 x + 1.54
Combine like terms
1/5x +5.34 = 11/5x +1.54
Move the x terms to the left side of the equation:
1/5x-11/5x = 1.54-5.34
-2x = -3.8
Divide both sides by -2
-2x/-2 = -3.8/-2
x = 1.9
if 63 Naira is shared in the ratio 4 ratio 5 what is the larger share
Answers
Answer:
35
Step-by-step explanation:
sum the parts of the ratio, 4 + 5 = 9 parts
divide 63 by 9 to find the value of 1 part of the ratio
63 ÷ 9 = 7 , then
4 parts = 4 × 7 = 28
5 parts = 5 × 7 = 35 ← larger share
find the equation of a line perpendicular to y=5x-3 that passes through the point (-5,3)?
Answers
The equation of the line that passes through point (-5,3) and perpendicular to y=5x-3 is y = -(1/5)x + 2.
What is the equation of line that passes through the given points and is perpendicular to the given line?The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
Given the data in the question;
Equation of line: y = 5x - 3Point: (-5,3)First, determine the slope of the initial line using the slope intercept-form. y = mx + b
y = 5x - 3 compared with the slope intercept form,
Slope m = 5
Now, for the equation of line perpendicular to the initial line, its slope must be a negative reciprocal of the initial slope.
Hence, slope of the perpendicular line is;
Slope m = -1/5
Next, find the equation of the perpendicular line, by using the point slope formula.
y - y₁ = m( x - x₁ )
Plug in the slope m ( -1/5 ) and point (-5,3).
y - y₁ = m( x - x₁ )
y - 3 = -1/5( x - (-5) )
y - 3 = -1/5( x + 5 )
y - 3 = -1/5(x) -5/5
y - 3 = -1/5(x) - 1
y = -1/5(x) - 1 + 3
y = -(1/5)x + 2
Therefore, the equation of the perpendicular line is y = -(1/5)x + 2.
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cenario 2: the directors of an annual community concert want to learn the musical preferences of the audience. the directors choose 2 and 6 from a random number generator and place a survey card on every sixth seat beginning with the second seat. all the cards are returned as the audience leaves. they are using
Answers
The sampling method used here is systematic sampling.
What is systematic sampling?
To generate a representative sample from a population, systematic sampling is a probability sampling technique.An advantage of systematic sampling is that it does not necessitate a comprehensive population list in advance. A sort of probability sampling technique called systematic sampling involves choosing individuals from a broader population using random beginning points and defined intervals.Random systematic samples, linear systematic samples, and circular systematic samples are the three primary categories of systematic samples.Here , this scenario is systematic sampling since it entails choosing n at random and selecting every nth person in the audience starting at a random point.To learn more about systematic sampling , refer:
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Ellen renovates the foyer of an old farmhouse. The foyer is 15 feet long and 8 feetwide. Calculate the area of the foyer.foyer60 square feet46 square feet120 square feet23 square feet240 square feet
Answers
Data
Length = 15 ft
Width = 8 ft
Area
1. Seafood plays an important part of our daily nutrition. Mr. Beeg ate 1/6 of the fish for breakfast and 2/5 of the fish over lunch. What fraction of the fish has he already consumed?
expression: ___________
solution: ___________
final answer: ___________
2. Tita Flan planted trees around the barangay mini garden. She covered 2/3 of the garden on the 1st day, 1/5 of the garden on the 2nd day. How much of the garden is left for her to completely cover the mini park with trees?
expression: ___________
solution: ___________
final answer: ___________
3. Oil and Gas is one of the major causes of Global warming. Last 2020, it was estimated to 2/5 of depletion of the ozone layer. Projections revealed that by the year 2050, its effect will have increased three times. How much has oil and gas affected the ozone layer in the projection?
expression: ___________
solution: ___________
final answer: ___________
4. Mr. Bredwyn splits his monthly salary to family expenses. Half of it goes to savings and the other half is allocated to bills payment. 1/10 to water bill, 1/6 to electricity, 2/15 to Internet, and 3/5 to House Rental. What fraction of his total salary is allotted to House Rental?
expression: ___________
solution: ___________
final answer: ___________
Improper/random answer = Report!
Correct and complete answer = heart/brainly!
Answers
1. The fraction of the fish has he already consumed is 17/30.
2. The fraction of the garden is left for her to completely cover is 2/15.
3. The oil and gas that affected the ozone layer in the projection is 1 1/5.
4. The fraction of his total salary is allotted to House Rental is 3/10.
How to calculate the fraction?1. Mr. Beeg ate 1/6 of the fish for breakfast and 2/5 of the fish over lunch. The fraction already consumed will be:
= 1/6 + 2/5
= 5/30 + 12/30
= 17/30
2. Tita Flan covered 2/3 of the garden on the 1st day, 1/5 of the garden on the 2nd day. the fraction of the garden is left for her to completely cover the mini park with trees will be:
= 1 - (1/5 + 2/3)
= 1 - 13/15
= 2/15
3. It estimated to 2/5 of depletion of the ozone layer and projections revealed that by the year 2050, its effect will have increased three times. This will be:
= 2/5 × 3
= 6/5
= 1 1/5
4. The fraction of his total salary is allotted to House Rental will be:
= House rental / 2
= 3/5 / 2
= 3/10
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The length of a rectangle is twice its width. If the area of the rectangle is 162in^2, find its perimeter.
Answers
We know that the length of a rectangle is twice its width. Then:
The area of a rectangle is the product of its width and length. Then:
[tex]A=2x\cdot x=2x^2[/tex]Additionally, we know that the area is 162 in². Using the expression above we can obtain the value of x:
[tex]\begin{gathered} 162=2x^2 \\ 81=x^2 \\ x=9\text{ in} \end{gathered}[/tex]Finally, the perimeter (2P) is just twice the sum of the width and the length of the rectangle:
[tex]2P=2\cdot(2x+x)=6x=6\cdot9=54\text{ in}[/tex]Please help me. Much Appreciated Each part of problem mark as either a, b, c
Answers
Given:
Total number of people surveyed = 205
a) Percentage of the survey respondents that do not like both hamburgers and burritos.
Number of people that do not like both = 54
To find the percentage of the respondents that do not like both, we have:
[tex]\begin{gathered} \text{ \% that do not like both = }\frac{Number\text{ that }do\text{ not like both}}{\text{Total surveyed}}\ast\frac{100}{1} \\ \\ \text{ \% that do not like both = }\frac{54}{205}\ast100\text{ = }26.3\text{ \%} \end{gathered}[/tex]Therefore, the percentage of the survey respondents that do not like both hamburgers and burritos is 26.3%
b) Marginal relative frequency of all customers that like hambugers.
Given:
Number of customers that like hamburgers = 110
To find the marginal relative frequency, we have:
[tex]M=\frac{110}{250}=0.54=54\text{ \%}[/tex]The marginal relative frequency of all customers that like hambugers is 54%
c) Conditional relative frequencies:
i) Conditional relative frequency that a person likes hamburgers given that the person does not like burritos:
[tex]\frac{110-29}{135}=\frac{81}{135}=0.6=60\text{ \%}[/tex]ii) Conditional relative frequency that a person likes burritos, given that the person does not like hamburgers:
[tex]\frac{41}{41+54}=\frac{41}{95}=0.43=43\text{ \%}[/tex]How many ways can four guests sit in a row of six chairs so that the leftmost chair is used and the rightmost chair is empty?
Answers
Answer:96
Step-by-step explanation: Answer is 96 because you can do 16 times 3 which is 48 so for the fifth seat to the end will be 96 ways.
Hope this helps! :)
The right triangle on the right is a scaled copy of the right triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form. 5 12 4 5/3
Answers
The dimensions of the left triangle are equal to the right triangle's dimensions times 1/3.
Given,
The right triangle on the right is a scaled copy of the right triangle on the left.
The measure of first triangle = 3,4
The measure of second triangle = 2, 3/2
We have to find the scale factor
The figure indicates that the right triangle on the left would be three times larger than the right triangle on the right. In this case, the right triangle's dimension is one third of the left triangle's dimension.
The left one is three times bigger than the right one. In other words, the dimensions of the left triangle are equal to the right triangle's dimensions times 1/3.
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