Answer:
There is no solution to this problem. It is not possible to find three numbers that form an arithmetic sequence and, when 1, 3, and 9 are added to them respectively, form a geometric sequence.
Step-by-step explanation:
To find the three numbers in the arithmetic sequence, let's call the first number in the sequence "a," the second number "a + d," and the third number "a + 2d," where "d" is the common difference between the numbers. The sum of these three numbers is:
a + (a + d) + (a + 2d) = 15
This simplifies to:
3a + 3d = 15
To find the three numbers in the geometric sequence, let's call the first number in the sequence "b," the second number "r * b," and the third number "r^2 * b," where "r" is the common ratio between the numbers. The sum of these three numbers is:
b + (r * b) + (r^2 * b) = 15 + b + (r * b) + (r^2 * b)
This simplifies to:
b(1 + r + r^2) = 15 + b + br + br^2
We are told that if 1, 3, and 9 are added to the three numbers in the arithmetic sequence, we get the three numbers in the geometric sequence. Therefore, we can set up the following system of equations:
3a + 3d = 15
b(1 + r + r^2) = 15 + b + br + br^2
Subtracting b from both sides of the second equation gives:
b(1 + r + r^2) - b = 15 + br + br^2
This simplifies to:
b(r^2 + r - 1) = 15 + br + br^2
Subtracting br and br^2 from both sides gives:
b(r^2 + r - 1) - br - br^2 = 15
This simplifies to:
b(r^2 + r - 1 - r - r^2) = 15
This simplifies to:
b(r - 1)(r + 1) = 15
Dividing both sides by (r - 1)(r + 1) gives:
b = 15 / (r - 1)(r + 1)
We are told that the three numbers in the arithmetic sequence add up to 15, so we can substitute 3a + 3d = 15 into the equation above to solve for "b":
3a + 3d = 15
b = 15 / (r - 1)(r + 1)
Substituting 3a + 3d = 15 into the equation above gives:
b = 15 / (r - 1)(r + 1)
Substituting b = 15 / (r - 1)(r + 1) into the second equation gives:
15 / (r - 1)(r + 1)(1 + r + r^2) = 15 + 15 / (r - 1)(r + 1) + 15 / (r - 1)(r + 1)*r + 15 / (r - 1)(r + 1)*r^2
This simplifies to:
15 / (r - 1)(r + 1)(1 + r + r^2) = 15 + 15r + 15r^2
Multiplying both sides by (r - 1)(r + 1) gives:
15 = 15 + 15r + 15r^2
Subtracting 15 from both sides gives:
0 = 15r + 15r^2
Subtracting 15r^2 from both sides gives:
0 - 15r^2 = 15r
This simplifies to:
-15r^2 = 15r
Dividing both sides by -15 gives:
r^2 = r
Solving for "r" gives:
r = 1 or r = 0
If "r" is equal to 1, then the common ratio between the numbers in the geometric sequence is 1, which means that the three numbers in the geometric sequence are the same. This does not satisfy the condition that the three numbers in the geometric sequence are formed by adding 1, 3, and 9 to the three numbers in the arithmetic sequence, so we can eliminate this solution.
If "r" is equal to 0, then the common ratio between the numbers in the geometric sequence is 0, which means that the three numbers in the geometric sequence are all 0. This does not satisfy the condition that the three numbers in the geometric sequence are formed by adding 1, 3, and 9 to the three numbers in the arithmetic sequence, so we can eliminate this solution as well.
Therefore, there is no solution to this problem. It is not possible to find three numbers that form an arithmetic sequence and, when 1, 3, and 9 are added to them respectively, form a geometric sequence.
A circular wheel makes 42 complete turns each minute.
How many degrees does it turn through in one second?
Answer:
252
Step-by-step explanation:
in each minute, the wheel makes 42 turns. That means it turns 42×360=15120 degrees in one minute (60 seconds). We want to find how many degrees it will turn in one second, not one minute, so we will divide the total degrees by 60.
15120÷60=252
So our answer is 252.
The width of a claroom i 4meter le than the length. It area i 45cm*45cm. Find the dimenion of the claroom
The dimensions of the classroom are a width is 5 m and a length is 9 m.
We have been given that the width of a classroom is 4m less than the length its area is 45m², then.
L= 4 + W
Area = 45, so
L x W = 45
Now substituting the value of L, we get.
(4+W) W=45,
Now simplifying this we get.
4W + W² =45
W² + 4W - 45 = 0, this is a quadratic equation
Now solving this we get the factors 9 and -5,
(W+9) and (W-5) = 0
Thus, W= -9 or W= 5, since the width cannot be negative,
So, it is width = 5
So, length = 9 m
In physics and arithmetic, the dimension of a mathematical space (or item) is informally defined as the minimal range of coordinates to specify any factor within it. therefore, a line has a dimension of one (1D) due to the fact handiest one coordinate is wanted to specify a factor on it – for instance, the point at 5 on more than a few lines. A floor, together with the boundary of a cylinder or sphere, has a size of two (2d) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the floor of a sphere. A two-dimensional Euclidean area is a -dimensional area on the aircraft. The internal of a dice, a cylinder, or a sphere is 3-dimensional (3-d) due to the fact 3 coordinates are had to find a factor inside these spaces.
In classical mechanics, area and time are distinct classes and seek advice from absolute space and time. That theory of the sector is a four-dimensional space however not the only one that was discovered as essential to explain electromagnetism. The four dimensions (4D) of spacetime encompass activities that are not really described spatially and temporally, however as a substitute are acknowledged relative to the movement of an observer. Minkowski's area first approximates the universe without gravity; the pseudo-Riemannian manifolds of fashionable relativity describe spacetime with depend and gravity. 10 dimensions are used to describe the superstring principle (6D hyperspace + 4D), eleven dimensions can describe supergravity and M-principle (7D hyperspace + 4D), and the kingdom-space of quantum mechanics is an infinite-dimensional feature area.
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the discriminant of a quadratic function is 64 and its vertex is in quadrant III. Identify and explain 3 things you know about the function and /or its graph
Help PLEASE this due tommorow
Answer:
Step-by-step explanation:
If the discriminant of a quadratic function is 64 and its vertex is in quadrant III, here are three things you can know about the function and/or its graph:
The function has two distinct real roots. The discriminant of a quadratic function is the value under the square root in the quadratic formula:
x = (-b +/- √(b^2 - 4ac)) / 2a
If the discriminant is positive, it means that there are two real roots (values of x that make the equation equal to zero). If the discriminant is negative, it means that there are no real roots (the equation has no solutions). If the discriminant is zero, it means that there is only one real root (the equation has one solution). Therefore, if the discriminant is 64, it means that the function has two distinct real roots.
The graph of the function is a parabola that opens downward. The direction in which a parabola opens (upward or downward) is determined by the coefficient of the x^2 term (a). If a is positive, the parabola opens upward. If a is negative, the parabola opens downward. In this case, the vertex of the parabola is in quadrant III.
Matthew Westhoven deposited $925 in a new regular savings account that earns 5.5% interest compounded semiannually for 1 year. What is the compound interest?
Matthew Westhoven deposited $925 in a new regular savings account that earns 5.5% interest compounded semiannually for 1 year. 51.09 is the compound interest.
What is compound interest?The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.
Given that,
principal amount (P) = $925
number of times interest applied per time period (n) = semiannually = 6
number of time periods (t) = 1 year
Thus, formula becomes:
[tex]I = P (1 + r/n)^{nt} - P[/tex]
or, [tex]I = 925 (1 + 5.5/6*100)^{1*6} - 925[/tex]
or, [tex]I = 925 (1.009)^6 -925[/tex]
or, [tex]I = 925 *(1.055) -925[/tex]
or, [tex]I = 976.09 -925[/tex]
or, [tex]I = 51.09[/tex]
Thus, the compound interest becomes 51.09
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If you chose the letters D and H for 20 turns, how many times are you most likely to win?
A. 1
B. 2
C. 3
D. 4
E. 5
edmentum
If you chose the letters D and H for 20 turns, the number of times you are most likely to win is; Option C: 3
What are the number of ways of winning?We are given the probability of winning for each letter as;
A = 5%
B = 10%
C = 15%
D = 5%
E = 5%
F = 25%
G = 10%
H = 10%
I = 10%
J = 5%
Now, we want to find the number of times you can win If you chose the letters D and H for 20 turns.
Thus;
Number of times you can win if you chose Letter D = 5% * 20 = 1 time
Number of times you can win if you chose Letter H = 10% * 20 = 2 times
Thus;
Total number of ways of winning = 1 + 2 = 3 times
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7.Show that quadrilateral FGHJ is a trapezoid, but is not a parallelogram.
Answer:
FJ is -3/1
Step-by-step explanation:
And in order to be a trapezoid, just one pair of sides needs to be parallel.
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer:
-1
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ \\are two points on the line.\\\end{minipage}}[/tex]
Define two points on the line:
Let (x₁, y₁) = (-2, 0)Let (x₂, y₂) = (0, -2)Substitute the defined points into the slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-2-0}{0-(-2)}=\dfrac{-2}{2}=-1[/tex]
Therefore, the slope of the line is -1.
Which ordered pairs is in the solution set of y>1/3 x+4
The ordered pair for the given solution set should be (-1, 6) when the graph solution set for the given inequality function is involved.
What is inequality function?
Since an inequality is merely a particular kind of relation, we can graph it just like we would any other relation. When dealing with inequalities, the trick is to shade large portions of the graph rather than using lines to connect the dots. But you could use some cover.
The given inequality function be like
y > 1 ÷ 3x + 4
The ordered pair refer to the solution set that provided by plotting the graph of the inequality, that expressed the inequality where an equation, plotting the graph along with a solid line, and shading the sides should be above the line of the graph to show the greater than or equal to sign.
Hence, the ordered pair for the given solution set should be (-1,6).
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I need help please!! Is 16% the correct answer?
Answer:
No, 16% is not the right answer.
It's:
Cars under 25 mph / Total Number of Cars
Cars under 25 mph:
I count 42 I think.
Total Number:
42 + 7 + 1 = 50
42 / 50 = .84
.84 * 100 = 84%
So, 84% of cars are moving below the speed limit.
What is the order from least to greatest of the following: 0.8, −0.1, 1.1, and −1.5?
Answer:
I think -1.5 -0.1 0.8 1.1
Answer:
-1.5 || -0.1 || 0.8 || 1.1
Explanation:
Since it is from least to greatest, let's compare the 2 negative numbers -1.5 and -0.1.
-1.5 has a 1 in its first place while -0.1 has a 0. This means that -1.5 is smaller because the further a number is on the negative number line the smaller it is.
So, -1.5 is the smallest, then -0.1.
-1.5 || -0.1
Now we compare the 2 positive numbers 0.8 and 1.1.
0.8 has a 0 in its first place and 1.1 has a 1 in its first place. Because the numbers are positive, the number with the biggest digit in in front of the decimal is greater.
So, in this case 1.1 is greater than 0.8.
0.8 || 1.1
In order it is:
-1.5 || -0.1 || 0.8 || 1.1
What is the first step to solving the equation -2(3x + 8) - 2 = 10 ?
Combine like terms.
Distribute the -2.
Add 3x + 8.
None of these choices are correct.
Simplify: -3x + 6-3x-24 + 2y
-6x + 2y - 18
2y - 18
6x + 2y - 30
None of these choices are correct.
Solve: 5x = 13
8
18
13
51
65
Solve: 6r-17r=-66
6
-6
-11
11
Solve: P = 2/+ 2w for w
P-21
4/w
P-4/w
None of these choices are correct.
Solve: 4(9y-5) = 10(3y +17) - 40
20
25
-10
10
Chicago's high temperature for a given month is 88 degrees Fahrenheit and the low temperature is 65 degrees Fahrenheit. Which inequality represents the model?
3x+5<2x-8 is:
x2 65 or x ≤ 88.
65 ≤ x ≤ 88.
88 ≤ x ≤ 65.
None of these choices are correct.
V= /wh when solved for his:
all values more than -13.
all values less than -13.
all values less than 3.
all values less than -3.
h=
V
lw
h=V-lw
h = V + lw
h = Vlw
Answer:
x = [tex]\frac{-14}{3}[/tex]
Step-by-step explanation:
-2(3x + 8) -2 = 10 Distribute the -2
-6x - 16 -2 = 10 Combine like terms
-6x - 18 = 10 Add 18 to both sides
-6x = 28 Divide both sides by -6
x = [tex]\frac{-28}{6}[/tex] = [tex]\frac{-14}{3}[/tex]
find the coordinates of the centroid of the triangle with the given vertices s(2,5) t(6,5) r(10,0)
Answer:
(6,[tex]\frac{10}{3}[/tex])
Step-by-step explanation:
[tex]\frac{2+6+10}{3}[/tex], [tex]\frac{5+5+0}{3}[/tex]
(6, [tex]\frac{10}{3}[/tex]) o r(6, 3 [tex]\frac{1}{3}[/tex])
The centroid of the triangle with the given vertices s(2, 5) t(6, 5) r(10, 0) is,
⇒ (6, 10/3)
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Three vertices of the triangle are,
⇒ s(2, 5) t(6, 5) r(10, 0)
Now, We can find;
The centroid of the triangle with the given vertices s(2, 5) t(6, 5) r(10, 0) is,
⇒ (2 + 6 + 10) / 3, (5 + 5 + 0) / 3
⇒ (6, 10/3)
Thus, The centroid of the triangle = (6, 10/3)
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Kayden's math teacher said that each
question answered correctly on a test would
be worth 7 points. Answer the questions
below regarding the relationship between
the number of questions correct and the
score on the test.
Step-by-step explanation:
Kayden's math teacher said that each question answered correctly on a test would be worth 7 points. Answer the questions below regarding the relationship between the number of questions correct and the score on the test.
Since 00 questions correct gets you 00 points on the test, the function will have a yy-intercept of 0.0.
The rate at which points are earned is 7 points per question, so the slope of the function should be 7.7.
\text{Function Rule:}
Function Rule:
V(x)=7x
V(x)=7x
Plug x=11 Into Rule:
V(11)=7(11)=77
Correct Answer:
The independent variable, x, represents the number of questions correct, and the dependent variable is the score on the test, because the score on the test depends on the number of questions correct.
A function relating these variables is V(x) =V(x)= 7x7x.
So V(11) =V(11)= 7777, meaning 1111 questions correct will earn 7777 points on the test
function rule to find f(10).
Answer:
[tex]f(10) = 103[/tex]
Step-by-step explanation:
f(x) = 3+10x
when x is 10, we have
3+10*10
= 103
:]
the sum of the ages of a father and his son is 38 years. if the father is 22 years older than his son , find their present ages
If the father is 22 years older than his son, and the sum of their ages is 38 years, we can set up the following equations to represent this information:
Copy code
father + son = 38
father = son + 22
We can solve for the father's and son's ages by substituting the second equation into the first equation:
Copy code
(son + 22) + son = 38
2 * son + 22 = 38
2 * son = 16
son = 8
Therefore, the son's age is 8 years, and the father's age is 8 + 22 = <<8+22=30>>30 years.
Answer:
16
Step-by-step explanation:
son=38-22
son=16
hope am correct
parallelogram fghj was dilated and translated to form similar parallelogram f'g'h'j'. what is the scale factor of the dilation? 4 8
The scale factor of the dilation is s = 4 units .
Given :
parallelogram fghj was dilated and translated to form similar parallelogram f'g'h'j'.
To find scale factor between figures, find two corresponding sides and write the ratio of the two sides.
The value of y is same through the distance of F to G.
So, FG = change in x coordinates
FG = -2 - ( -4 )
= -2 + 4
= 2
F'G' = 3 - ( - 5 )
= 3 + 5
= 8
Let s be the scale factor
s = F'G' / FG
= 8 / 2
= 4
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A 29.2-ounce bottle costs $5.37. what is the unit price?
and his friends decided to have a water fight on a hot summer day. They filled a bunch of water balloons and started the fight at 1:00 P.M. The water balloons lasted for 1 hour. When all the water balloons were gone, they sprayed water with hoses for 30 minutes, until Rudy's dad showed up with ice cream. What time was it when the water fight ended?
Answer:
the water fight ended at 2:30pm
Step-by-step explanation:
the balloons lasted an hour bringing it to 2pm then they used the hoses for 30 min bringing it to 2:30pm
in the simplex method, the pivot column is the column with the most negative number (to the left of the vertical bar) in the bottom row. why?
The most negative number corresponds to the variable that has the largest impact on the Value of the objective function. So, maximizing it first is most efficient.
What is pivot column in simplex method?
The Simplex method's pivot column is selected by the fundamental variable's biggest reduced cost coefficient. 4. The highest ratio of right side parameters to positive coefficients in the pivot column determines the pivot row in the Simplex approach.
A location of a leading entry in the matrix's echelon structure. A pivot is a non-zero number that is either transformed into a leading 1 and then used to make 0s, or it is utilized in a pivot position to create 0s.
The element of a matrix or array chosen first by an algorithm (such as Gaussian elimination, simplex algorithm, etc.) to do particular computations is known as the pivot or pivot element.
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The value of x when g(x) = 3
After solving the given equation at g(x) = 3 the value obtained is 3.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the information given in the question,
The given equation is,
g(x) = -2x + 9
Then,
g(3) = -2(3) + 9
= -6 + 9
g(3) = 3
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Your question seems incomplete, the complete question may be:
If g(x) = -2x + 9, what is the value of x
when g(x) = 3?
Step 1: we know that angle a b c is-congruent-to angle f g h because all right angles are congruent. step 2: we know that angle b a c is-congruent-to angle g f h because corresponding angles of parallel lines are congruent. step 3: we know that line segment b c is-congruent-to line segment g h because it is given. step 4: triangle a b c is-congruent-to triangle f g h because of the asa congruence theorem. aas congruence theorem. third angle theorem. reflexive property.
Based on the given steps the triangle ABC will be Congruent to triangle FGH because of the AAS Congruence .
What is AAS Congruence ?
the two triangle are said to be congruent based on the AAS Congruence when 2 angles and 1 non included side in one triangle are congruent to corresponding 2 angles and 1 non included side in another triangle.
So , in the question , based on the given steps we can say that ,
the two angles that are congruent is angle G and B , and angle A and angle F .
and the side that is congruent is BC = GH .
So the triangle ABC and triangle FGH are congruent by AAS congruence .
Therefore , the correct option is (b) AAS Congruence Theorem .
The given question is incomplete , the complete question is
Step 1: we know that angle a b c is-congruent-to angle f g h because all right angles are congruent.
Step 2: we know that angle b a c is-congruent-to angle g f h because corresponding angles of parallel lines are congruent.
Step 3: we know that line segment b c is-congruent-to line segment g h because it is given.
Step 4: triangle a b c is-congruent-to triangle f g h because of the
(a) ASA congruence theorem.
(b) AAS congruence theorem.
(c) Third angle theorem.
(d) Reflexive property.
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Is the system of equations consistent and independent, consistent and dependent, or inconsistent?
y=−x+1
2y=−2x+2
Select the correct answer from the drop-down menu.
After solving the equations it will the infinite solutions, then it is a consistent system.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.
A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the given information in the question,
The equations are,
y = -x + 1 (i) and,
2y = -2x + 2 (ii)
Divide equation (ii) by 2
y = -x + 1 (iii)
Solve equation (i) and (iii)
The value of x and y will be 0 which means that it has infinite solution, then it is a consistent system.
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(10x12) + (5x11) + (12x12) = Y
Answer:
Y= 319 hope you have the best rest of the day of your life ever. can i have brainliest
Step-by-step explanation:
Steps for Solving Linear Equation
(10×12)+(5×11)+(12×12)=Y
Multiply 10 and 12 to get 120. Multiply 5 and 11 to get 55. Multiply 12 and 12 to get 144.
120+55+144=Y
Add 120 and 55 to get 175.
175+144=Y
Add 175 and 144 to get 319.
319=Y
Swap sides so that all variable terms are on the left hand side.
Y=319
what are three powers that have values greater than 120 and less than 130. ?
Answer: 11^2, 5^3, 2^7
Step-by-step explanation:
11^2= 121
5^3= 125
2^7= 128
The lengths of two sides of a triangle are 8 cm and 10 cm. Identify the range of possible lengths for the third side.
Given that the first two sides of a triangle are 8 cm and 10 cm in length, the third side's range of potential lengths will be [2,18].
What is range?When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself. The difference between the highest and lowest values for a given data collection is the range in statistics. For instance, the range will be 10 - 2 = 8 if the given data set is 2, 5, 8, 10, and 3. As a result, the range can also be thought of as the distance between the highest and lowest observation.
Here,
The minimum length can be,
=10-8
=2 cm
The maximum length can be,
=10+8
=18 cm
(10-8)<x<(10+8)
2<x<18
The range of possible lengths for the third side will be [2,18] as The lengths of two sides of a triangle are 8 cm and 10 cm.
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Two friends, Montraie and Serenity, took summer jobs. The equation y=19.2x represents Montraie's earnings in dollars and cents, y, for working x hours. Serenity earned $748.60 in 38 hours.
Use the dropdown menu and answer-blank below to form a true statement.
Montraie earns $___ per hour ___ (more or less) than Serenity.
Comparing the two friends earning Montraie earns $ 0.5 per hour less than Serenity
How to compare the earnings of the two friendsThe word problem that has to do with earnings of two friends Montraie and Serenity is solved by putting the problem in equation form
The equations are generated as follows
The equation for the earning for Montraie is y = 19.2x
Using the equation in 38 hours Montraie will earn
y = 19.2 * 38
y = 729.6
This means that Montraie earns 19.2 per hour
For Serenity the earning per hour is solved
= 748.60 / 38
= 19.7
comparing both earnings
Serenity earning - Montaie earning
= 19.7 - 19.2
= 0.5
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Solve x for this diagram
Answer:
x = 20
Step-by-step explanation:
the 3 unknown angles form a right angle and sum to 90° , that is
x + 2x + x + 10 = 90
4x + 10 = 90 ( subtract 10 from both sides )
4x = 80 ( divide both sides by 4 )
x = 20
Answer:
x = 20°
Step-by-step explanation:
From the picture we know that x + 2x + x + 10 = 90°
x + 2x + x + 10 = 90
4x = 80
x = 80 : 4
x = 20°
--------------------
check
20 + 2 x 20 + 20 + 10 = 90
90 = 90
the answer is good
18 2/6 Use the number line to round the mixed number to the nearest whole number.
Answer: The nearest whole number is 18
Step-by-step explanation: because 18 2/6 is closer to 18 than 19.
Ue the ditributive property to rewrite the expreion a a multiple of a um of two number with no common factor. 24 18
36 is a multiple of two numbers added together without a common factor.
What is a common factor?When a number is exactly divided by a divisor, that divisor is known as a factor of that number.
Alternatively, a factor of a number is an exact divisor of the provided number.
A number's factors are either less than or equal to the supplied number; they cannot be bigger. Every number is a factor of itself, and the common factor of all numbers is 1.
A number can be divided exactly by numerous divisors if it is a multiple of the divisor, therefore when we determine the factors of two or more numbers, we discover that some factors are common. As an illustration, the factors of 35 are 1, 5, 7, 35 while those of 45 are 1, 3, 5, 9, 15, 45. 1 and.
Hence, 36 is a multiple of two numbers added together without a common factor.
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Find MK
Problem # 37
Please help!
Answer:
17.5
Step-by-step explanation:
Since the triangles are similar, the side lengths are proportional. One way we can solve this is by finding the scale factor for the triangle on the left to the triangle on the right. We can use the two corresponding sides that we know.
Let x = the scale factor
385x = 175 Divide both sides by 385
x = [tex]\frac{175}{385}[/tex] Simplify by dividing the numerator and the denominator by 35
x = [tex]\frac{5}{11}[/tex]
Take the corresponding side of MK and multiply it by [tex]\frac{5}{11}[/tex] to find MK
38.5 x [tex]\frac{5}{11}[/tex] = 17.5