Measure of ∠K in triangle KLM by open mouth theorem is ∠K < 90°.
What is open mouth theorem?The open mouth theorem states that if two sides of a triangle are congruent with two sides of another triangle, and the included angle of the first triangle is greater than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.
Given,
two triangles KLM and NOP
KL≅NO and KM≅NP
LM = 7, OP = 9
LM < OP
By open mouth theorem
m∠K < m∠N
m∠N = 90°
m∠K < 90°
Hence, m∠K < 90° is the value of angle K, in triangle KLM
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Lily has read 3/4 of her book. Sophie has read 2/6 of her book. Which girl has read more of her book?
Answer: Lily
Step-by-step explanation:
3/4 is larger than 2/6
Answer: Lily
Step-by-step explanation: 3/4 > 2/6
3/4 = 0.75
2/6= 0.33
compare the two decimal places, 0.75 > 0.33
Which expression represents the distance between Q and R
Answer:
Translation
Step-by-step explanation:
Translation
What is five percent of $97.25
Answer: 4.8625
Step-by-step explanation:
- Two dry cleaning companies offer a home pick-up and delivery service. The monthly cost depends on the number of garments laundered, and is shown in the following table.
Number of Garments
5
10
15
Company 1
$55.25
$75.50
$95.75
Company 2
$31.25
$57.50
$83.75
The ordered pair representing the point where both companies would charge the same amount is (25, 136.25).
When would both companies charge the same amount?
From the given table, we can form the following equation for monthly cost of each company.
Company 1, the function for the monthly cost is;
(5, $55.25 ) and (10, $75.5). Let the monthly cost = y₁
(y₁ - 55.25 )/(x - 5) = ( 75.5 - 55.25 )/ (10 - 5)
y₁ = 4.05x + 35
Company 2, the function for the monthly cost is;
(5, $31.25 ) and (10, $57.5). Let the monthly cost = y₂
(y₂- 31.25 )/(x - 5) = ( 57.5 - 31.25 )/ (10 - 5)
y₂ = 5.25x + 5
To find the point where both companies charge the same amount, we need to set their costs equal to each other and solve for the number of garments, x:
y₁ = y₂
4.05x + 35 = 5.25x + 5
Subtracting 4.05x and 5 from both sides:
30 = 1.2x
Dividing both sides by 1.2:
x = 25
So both companies would charge the same amount when 25 garments are laundered. T
To find the cost, we can plug x = 25 into either equation:
y₁ = 4.05(25) + 35 = 136.25
y₂ = 5.25(25) + 5 = 136.25
Ordered pair = (25, 136.25)
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The complete question is below:
Two dry cleaning companies offer a home pick-up and delivery service. The monthly cost depends on the number of garments laundered, and is shown in the following table.
Number of Garments Company 1 Company 2
5 $55.25 $31.25
10 $75.50 $57.50
15 $95.75 $83.75
Determine when both companies would charge the same amount and what that cost would be. Write your answer as an ordered with x representing the number of garments and y representing the cost.
I have a triangular shaped base I am composed of 3 rectangular faces I am a 3D figure
Answer:
Rectangle pyramid
What is a rectangle pyramid ?
A rectangular pyramid is a pyramid, which has a rectangular-shaped base. If we look at the bottom view of this pyramid, it looks like a rectangle. Hence, the base has two parallel sides equal.
A pyramid crowns at a point on top of the base, which is known as the apex. A rectangular pyramid can be a right pyramid or oblique pyramid. If it is a right rectangular pyramid, then the apex lies right over the center of the base and if it is an oblique rectangular pyramid, the apex is not directly over the center of the base, but at some angle from the center.
Apart from the rectangular pyramid, there are other types of pyramids based on the shape of their bases, such as:
1) Triangular Pyramid
2) Square Pyramid
3) Pentagonal Pyramid
4) Hexagonal Pyramid
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What is the volume of the composite figure?
The volume of the composite figure is 408 cm³
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.
The volume of the composite figure is:
Volume = area of base * height
Substituting:
Base area = (14 * 3) + (1/2)(5 + (14-6))(7 - 3) = 68 cm²; height = 6 cm
Volume = area of base * height = 68 cm² * 6 cm = 408 cm³
The volume is 408 cm³
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Rounding to nearest 10th
Given - the system of the equations as
[tex]y=-2x+1\\y=-11x-3[/tex]
To find - the solution of the set of equation
Explanation- given the set and we can see that left hand side of the equation is equal.
we get
[tex]-2x+1=-11x-3\\-2x+11x=-3-4\\9x=-7\\x=-7/9=-0.77[/tex]
we get
[tex]y=-2(0.77)+1\\y=-1.54+1\\y=-0.54[/tex]
Hence the value is x =-0.77, y=0.54
Final answer- the value of x = 0.77, y = -0.54
A researcher is investigating academic motivation among college students and their siblings. This type of study would be _______
Answer:
This type of study would be a comparative study, as it involves comparing the level of academic motivation between college students and their siblings.
Step-by-step explanation:
Question content area top
Part 1
In a genetics experiment on peas, one sample of offspring contained 439 green peas and 30 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of
3
4 that was expected?
The result is not reasonably close to the value of 3/4 i.e. 0.75.
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The probability of getting a green pea can be estimated by dividing the number of green peas by the total number of peas:
probability of green pea = number of green peas / total number of peas
In this case, the number of green peas is 439 and the total number of peas is the sum of the green and yellow peas, which is:
total number of peas = number of green peas + number of yellow peas
= 439 + 30 = 469
Therefore, the probability of getting a green pea is:
probability of green pea = 439 / 469 ≈ 0.935 or 93.5%
So, the estimated probability of getting an offspring pea that is green is approximately 93.5%.
The result is not reasonably close to the value of 3/4 i.e. 0.75.
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Use the number line to identify the least value, first quartile, median, third quartile, and greatest value of the data. Number of sit-ups: 20, 20, 23, 25, 25, 26, 27, 29, 30, 30, 32, 34, 37, 38
The median value is 26.5, the first quartile is 24, the third quartile is 35.5, and the highest value is 38. The lowest value is thus 20.
How to find out mean median and first quartile?We can plot the data on a number line to determine the data's least value, first quartile, median, third quartile, and greatest value:
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38\s| | | |
The leftmost number on the number line and the lowest value is 20.
We can split the data into four equal sections to determine the quartiles. The data's middle value is known as the median. We choose the average of the two middle values because there are an even number of data points. The midpoint is:
(26 + 27)/2 = 26.5 is the median.
We calculate the median of the lower half of the data to determine the first quartile:
(23 + 25)/2 = 24 for the first quartile.
We determine the median of the upper half of the data to determine the third quartile:
Third quartile: (34.5) ((34 + 37)/2)
The rightmost number on the number line, 38, has the highest value.
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What is the diffrence between b and 9
Answer: b-8
Step-by-step explanation:
b-9=b-9
b-9+1=b-8
Which expression is the simplest form of 223-22 + 3 (23 - 422)?
O A. 23 - 13x2
O B. 523 - 1322
О c. 323 - 1222
O D. 523 - 522
The simplification value of the expression is,
⇒ 5x³ - 12x²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 2x³ - x² + 3 (x³ - 4x²)
Now, We can simplify the expression as;
⇒ 2x³ - x² + 3 (x³ - 4x²)
⇒ 2x³ - x² + 3x³ - 12x²
⇒ 5x³ - 12x²
Thus, The simplification value of the expression is,
⇒ 5x³ - 12x²
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Find the slope of the line of fit and explain its meaning in the context of the data.
80 a student who studies for 0 hours is predicted to earn 80% on the test
70 a student who studies for 0 hours is predicted to earn 70% on the test
10 for each additional hour a student studies, their grade is predicted to increase by 10% on the test
5 for each additional hour a student studies, their grade is predicted to increase by 5% on the test
The slope of the line of fit is 7.5% per hour.
What is slope ?In mathematics, slope refers to the measure of steepness or incline of a line. It is the ratio of the vertical change between two points on the line (the rise) to the horizontal change between the same two points (the run).
According to given conditions:To find the slope of the line of fit, we need to use the formula:
slope = change in y / change in x
In this case, the change in y represents the change in the predicted grade on the test, and the change in x represents the change in the number of hours studied. From the given data, we can see that:
The predicted grade for a student who studies for 0 hours is 80%.
The predicted grade for a student who studies for 1 hour is 90% (80% + 10%).
The predicted grade for a student who studies for 2 hours is 95% (90% + 5%).
Using this information, we can calculate the slope of the line of fit:
slope = (95% - 80%) / (2 hours - 0 hours) = 15% / 2 hours = 7.5%/hour
The slope of the line of fit is 7.5% per hour. This means that for each additional hour a student studies, their predicted grade on the test is expected to increase by an average of 7.5%. The slope represents the rate of change of the predicted grade with respect to the number of hours studied. In this case, a positive slope indicates that there is a positive correlation between the number of hours studied and the predicted grade on the test. The higher the slope, the steeper the line of fit, and the greater the impact of studying on the predicted grade.
Therefore, the slope of the line of fit is 7.5% per hour
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the scale factor between 0 and 1 ____ the size of an object, or makes it ___. A scale factor of 1 ______ the size of an object; that is, the size is ____. A scale factor greater than 1 ______ an object, or make it ___.
An object's size in real life and its size on a map or a blueprint are compared using a scale factor, which is a mathematical concept. The scale factor may exceed, fall short of, or be equal to 1.
What is scale factor and how is it calculated?The size of the object is decreased and becomes smaller if the scale factor is between 0 and 1. This is so because the scale factor only approximates the object's true size. The size of the thing on the map will be half that of the real object, for instance, if the scale factor is 0.5.
When the scale factor is 1, the object's size is said to remain constant. As a result, the map or blueprint is created using the same dimensions.
In other words, the map or blueprint is created at the exact same scale as the final product.
The size of the thing is enlarged and made larger if the scale factor is greater than 1. This is so because the scale factor is a multiple of the object's actual size. The size of an object on a map will appear twice as large as it is in reality, for instance, if the scale factor is 2.
In general, it's crucial to comprehend scale variables in order to appropriately depict an object's size on maps, blueprints, and other scaled representations.
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Find dz/dt using chain rule
Using the chain rule, the value for dz/dt is obtained as [tex]dz/dt = 2(2t + (4 - t^2)e^{(4-t^2)}) ((1 - t)e^{(4-t^2)})[/tex].
What is chain rule?
The chain rule is the formula used to determine the derivative of a composite function, such as cos 2x, log 2x, etc. Another name for it is the composite function rule. Only composite functions are subject to the chain rule.
To find dz/dt using the chain rule, we need to differentiate each term of z with respect to t, then multiply by the derivative of the inner function with respect to t.
First, we have -
x = 2t
Taking the derivative with respect to t, we get -
dx/dt = 2
Next, we have -
y = 4 - t²
Taking the derivative with respect to t, we get -
dy/dt = -2t
Using the chain rule, we have -
[tex]dz/dt = (x + y)e^y \times (\frac{dx}{dt} + \frac{dy}{dt}e^y)[/tex]
Substituting x and y into this equation, we get -
[tex]dz/dt = (2t + (4-t^2))e^{(4-t^2)} \times ((2 - 2t) e^{(4-t^2)})[/tex]
Simplifying this expression, we get -
[tex]dz/dt = 2(2t + (4 - t^2)e^{(4-t^2)}) ((1 - t)e^{(4-t^2)})[/tex]
Therefore, the value is obtained as [tex]dz/dt = 2(2t + (4 - t^2)e^{(4-t^2)}) ((1 - t)e^{(4-t^2)})[/tex].
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ermesyo brings his dogs to traing classes the equation -60+2y 0120=0 re;ates y the total cost of pets training and x the number of classess thanken
The line that the equation represents has a y-intercept of.
What is an example of a y-intercept?
Here are several y intercept instances. So we obtain y = 5(0)2 + 2 = 2 when we replace x = 0, so y-intercept of y Equal 5x2 + 2 is (0, 2). Because we obtain y = -5e0 = -5 when we try substituting x = 0, this same y-intercept of y Equal -5ex is (0, -5).
Y-intercept: Is it 0 or 1?
The point where a straight line intersects the X-axis is known as the Y interception. In the picture above, the line intersects the Value of y at 1. The point is shown by and the value of the Variable y is 1. (0,1). Remember that for the y-intercept, the point's such and such is always zero.
On this note, we must recall that the y-intercept of an equation is the value of when.
Therefore, we have;
-60(0) + 2y -120 = 0
2y = 120
y = 60
Hence, the y-intercept of the line represented by the equation is; 60.
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The complete question is:
Ernesto brings his dog to training classes. The equation -60x + 2y - 120 =0 relates y, the total cost of a pet's training, and x, the number of classes taken Ernesto states that the y-intercept of the line represented by the equation is 30. is he correct?
I need help its due today
Answer: the image didnt send with this try reposting
Step-by-step explanation:
this is a little funny out of context tho, best of luck be upon you
Q.4. Mandy babysits and makes $8.50 per hour. To commute to the job, she spends $40 per
week on the bus and subway. Which inequality can be used to determine how many hours,
h, she must work to make more than $300 per week?
A. 8.50x + 40 > 300
B. 8.50x40 > 300
C. 40x+8.50 > 300
D. 40x8.50 > 300
Answer:
A is the correct answer
Step-by-step explanation:
what is the area and formula for this question?
The total area of the given figure is found to be 96 m².
Explain about the area of the rectangle?The quantity of unit squares that could also fit inside a rectangle called its area. The quantity of space a flat surface of a specific form occupies is known as its area. The product of a rectangle's length and width is the formula for calculating its area (breadth). This is stated as follows: Rectangle area equals length x widthTotal area = area of rectangle + area of triangle
Total area = length x breadth + 1/2 x base x height
Total area = 12 x 7 + 1/2 x 6 x (11 - 7)
Total area = 84 + 12
Total area = 96
Thus, the total area of the given figure is found to be 96 m².
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The mean age of a family of seven is 23 years. The median is 16 years, the modes are 12, years and 45 years, and the range is 35 years. Find the ages of the seven family members
Let's use the given information to set up equations to solve for the ages of the family members.
We know that the mean age of the family is 23 years, so we can write:
(sum of ages) / 7 = 23
sum of ages = 161
We also know that the median age is 16 years, which means that the ages of the family members can be arranged in order from smallest to largest, and the middle age (or the average of the two middle ages, if there are an even number of ages) is 16. We can use this information to set up an equation:
(3rd smallest age + 4th smallest age) / 2 = 16
3rd smallest age + 4th smallest age = 32
Next, we know that the range of the ages is 35 years, which means that the difference between the largest age and the smallest age is 35. We can use this information to set up another equation:
largest age - smallest age = 35
Finally, we know that the modes (the most common ages) are 12 years and 45 years. This means that there are two family members whose ages are 12 years and two family members whose ages are 45 years. We can use this information to set up two more equations:
number of 12-year-olds + number of 45-year-olds = 4
12 x number of 12-year-olds + 45 x number of 45-year-olds = sum of ages
We now have five equations and five unknowns (the ages of the seven family members). We can solve for these unknowns using algebra. One possible set of ages that satisfies all of the equations is:
2, 2, 12, 16, 20, 45, 64
(Note that the ages do not have to be integers, but this particular set of ages happens to be integers and satisfies all of the given conditions.)
The number of passes completed by Brett Favre, quarterback for the Green Bay
Packers, was recorded for each of the 16 regular season games in the fall of 2006
(www.espn.com).
15 31 25 22 22 19 17 28
24 5 22 24 22 20 26 21
a. Draw a stem and leaf plot to describe the data.
b. Calculate the mean and standard deviation for Brett Favre’s per game pass
completions.
c. What proportion of the measurements lie within two standard deviations of
the mean?
2
Plot the point (4.5, −2.25) on the coordinate plane.
In response to the supplied query, we may state that Draw a dot to coordinates indicate the position (4.5, -2.25) where the two lines cross after finding the points on the x-axis and the y-axis.
what are coordinates?A coordinate system is a technique used in geometry to precisely locate points or other geometrical objects on a manifold, such as Euclidean space, using one or more numbers or coordinates. A point or item on a two-dimensional plane is located using a pair of numbers known as coordinates. The x and y coordinates are two numbers that describe a point's location on a 2D plane. a collection of integers that indicate exact locations. Typically, the figure has two numbers. The first number represents the front-to-back distance, while the second number represents the top-to-bottom distance. When there are 12 units below and 5 above, as in (12.5), this is an example.
Plotting the coordinates of the point (4.5, -2.25) requires the following actions:
Create the x- and y-axes.
Identify the intersection of the x and y axes. The coordinates of this place, which is known as the origin (0, 0).
Find the coordinates (4.5, -2.25) on the x- and y-axes.
Move 4.5 units to the right of the origin to find the point on the x-axis.
Go 2.25 units down from the origin to find the point on the y-axis.
Draw a dot to indicate the position (4.5, -2.25) where the two lines cross after finding the points on the x-axis and the y-axis.
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Type the correct answer in each box.
Consider the expressions shown below.
-
Answer:
First one is b second one is a thrid is c
Step-by-step explanation:
anyone know these answers ?
Answer:
10^9 = 1,000,000,000
2^6 = 64
7^1 = 7
10^3 = 1,000
10^8 = 100,000,000
0^4 = 0
7^6 = 117,649
Step-by-step explanation:
The exponent multiplies a number by itself by whatever value it is.
Answer:
↓ ↓ ↓
Step-by-step explanation:
1)
[tex]\tt 10^1=\boxed{10}[/tex]2)
[tex]\tt 1^8=\boxed{1}[/tex]3)
[tex]\tt 7^4=\boxed{2401}[/tex]4)
[tex]\tt 10^9=\boxed{1000000000}[/tex]5)
[tex]\tt 2^6=\boxed{64}[/tex]6)
[tex]\tt 7^1=\boxed{7}[/tex]7)
[tex]\tt 10^3=\boxed{1000}[/tex]8)
[tex]10^8=\boxed{100000000}[/tex]9)
[tex]\tt 0^4=\boxed{0}[/tex]10)
[tex]\tt 7^6=\boxed{117649}[/tex]________________________
Hope this helps! :)
Triangle ABC is shown. Use the graph to answer the question. triangle ABC on a coordinate plane with vertices at 1 comma negative 2, 9 comma negative 2, 5 comma 2 Determine the coordinates of the image if triangle ABC is translated 4 units down. A′(1, −6), B′(9, −6), C′(5, −2) A′(1, 2), B′(9, 2), C′(5, 6) A′(5, −2), B′(13, −2), C′(9, 2) A′(−3, −2), B′(5, −2), C′(1, 2)
The correct answer is A′(−3, −2), B′(5, −2), C′(1, 2). The coordinates of the original triangle ABC are (1, -2), (9, -2), and (5, 2). Therefore, the coordinates of the image are A′(−3, −2), B′(5, −2), C′(1, 2).
What are coordinates?Coordinates are used to describe a point in space or on a map. They are usually written as two numbers, which represent the position of the point on an x-axis and a y-axis. Coordinates can be used in a variety of ways, such as to describe the location of a specific object or to identify the boundaries of an area.
Triangle ABC is an example of a transformation in which the shape is shifted without changing its size or orientation. When a shape is translated, it is moved from one place to another without changing its size or orientation. In this case, the triangle is being translated 4 units down.
To calculate the new coordinates of the triangle, we need to subtract 4 from the y-coordinate of each of the vertices. The original coordinates of the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 from each of the y-coordinates, the new coordinates of the triangle are (1, −6), (9, −6), and (5, −2). This means that the new coordinates of the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).
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The cοrrect answer is A′(−3, −2), B′(5, −2), C′(1, 2). The cοοrdinates οf the οriginal triangle ABC are (1, -2), (9, -2), and (5, 2). Therefοre, the cοοrdinates οf the image are A′(−3, −2), B′(5, −2), C′(1, 2).
What are cοοrdinates?Cοοrdinates are used tο describe a pοint in space οr οn a map. They are usually written as twο numbers, which represent the pοsitiοn οf the pοint οn an x-axis and a y-axis. Cοοrdinates can be used in a variety οf ways, such as tο describe the lοcatiοn οf a specific οbject οr tο identify the bοundaries οf an area.
Triangle ABC is an example οf a transfοrmatiοn in which the shape is shifted withοut changing its size οr οrientatiοn. When a shape is translated, it is mοved frοm οne place tο anοther withοut changing its size οr οrientatiοn. In this case, the triangle is being translated 4 units dοwn.
Tο calculate the new cοοrdinates οf the triangle, we need tο subtract 4 frοm the y-cοοrdinate οf each οf the vertices. The οriginal cοοrdinates οf the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 frοm each οf the y-cοοrdinates, the new cοοrdinates οf the triangle are (1, −6), (9, −6), and (5, −2). This means that the new cοοrdinates οf the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).
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15 POINTS
Identify the roots in the given
{-8}
{-2, 4}
{0,-8}
{-2, -8,4}
The set containing the roots of the graphed quadratic function is given as follows:
{-3, 1}
How to obtain the roots of a function?The roots of a function can be obtained from the graph of the function, as they also represent the x-intercepts of the function.
The x-intercepts of a function are given by the values of x at which the graph of the function crosses the x-axis, which is the horizontal axis.
The values of x for which the graphed function crosses the x-axis are given as follows:
x = -3 -> 3 units to the left of the y-axis.x = 1 -> 1 unit to the right of the y-axis.Hence the set containing the roots of the graphed quadratic function is given as follows:
{-3, 1}
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is a function 4x + y = 2x -8
The equation defines y as a function of x, where the function has a slope of -2 and a y-intercept of -8.
If there is only one unique value of y for each value of x, then the equation 4x + y = 2x - 8 does not define y as a function of x.
The equation can be rewritten as y = mx + b, where m denotes the slope and b the y-intercept.
4x + y = 2x - 8
Taking 2x away from both sides:
2x + y = -8
When we take away 2x from both sides, we obtain:
y = -2x - 8
As a result, the equation establishes y as a function of x, with a y-intercept of -8 and a slope of -2.
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You have a portfolio consisting solely of Stock A and Stock B. The portfolio has an expected return of 10.2 percent. Stock A has an expected return of 11.7 percent while Stock B is expected to return 8.3 percent. What is the portfolio weight of Stock A?
The portfolio weight of Stock A is 0.625 for the given situation.
What use do portfolio weights serve?The percentage of a portfolio's investments that are assigned to each asset or security is shown by the portfolio weights. Investors can meet their chosen risk and return objectives by varying the weights of various assets in their portfolios. Portfolio weights are a key component of asset allocation and portfolio optimization methodologies since they are used to determine the expected return and risk of a portfolio.
Let w be the weight (proportion) of Stock A in the portfolio.
The weight of Stock B would be (1-w).
Given that, the portfolio has an expected return of 10.2 percent.
0.102 = w(0.117) + (1-w)(0.083)
w = (0.102 - 0.083)/(0.117 - 0.083) ≈ 0.625
Hence, the portfolio weight of Stock A is 0.625 for the given situation.
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There are 9 game pieces on each tic-tac-toe board. The third grade class has 4 tic-tac-toe boards. How many game pieces does the class have for all of their tic-tac-toe boards?
A) 13
B) 27
C) 36
D) 45
Answer:
C) 36.
Step-by-step explanation:
Since there are 9 game pieces in each tic-tac-toe board and the class has 4 tic-tac-toe boards, the total number of game pieces the class has is:
9 pieces/board x 4 boards = 36 pieces
Therefore, the answer is C) 36.
The question is present in the problem
The solution to the given equation √(2x + 9) = 7 is x = 20.
What is the radical equation?Any equation that contains a radical symbol is considered a radical equation. To find the square roots, cubic roots, and higher, radical symbols are used.
The equation is given as follows:
√(2x + 9) = 7
Square both sides of the above equation,
2x + 9 = 7²
2x + 9 = 49
Subtract 9 from both sides of the above equation,
2x = 49 - 9
2x = 40
Divide by 2 into both sides of the equation,
x = 40/2
x = 20
Thus, the solution to the given equation is x = 20.
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