The length of the rectangle is 4 units.
What is rectangular shape?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.
Let n be the length of the rectangle.
The width of a rectangle is the length minus 2 units.
The width = n - 2
The area of the rectangle is 8 square units.
The area of the rectangle = length x width
8 = n (n-2)
n²-2n - 8 = 0
n²-4n+2n - 8 = 0
n(n-4)+2(n-4) = 0
(n+2)(n-4) = 0
n = 4 and -2.
So the length is 4 units.
Therefore, 4 units are the length of the rectangle.
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Using expanded forms, explain why the following problems with unlike bases do not follow the multiplication and division rules of exponents
Pls hurry and thank you!!!!
113.778=one hundred thirteen million seven hundred seventy-eight thousand, and 11,664=eleven thousand six hundred sixty-four is the enlarged form.
What do you meant by expanded form ?1.Comprehensive Notation Form:
[tex]$$\begin{aligned}& 11,664= \\& 10,000 \\& +1,000 \\& +600 \\& +\quad 60 \\& +4 \\&\end{aligned}$$[/tex]
Increased Factors Form:
[tex]$$\begin{aligned}& 11,664= \\& 1 \times 10,000 \\& +1 \times 1,000 \\& +6 \times 100 \\& +6 x \quad 10 \\& +4 \times \quad 1 \\&\end{aligned}$$[/tex]
Increased Exponential Form:
[tex]$$\begin{aligned}& 11,664= \\& 1 \times 10^4 \\& +1 \times 10^3 \\& +6 \times 10^2 \\& +6 \times 10^1 \\& +4 \times 10^0 \\&\end{aligned}$$[/tex]
Text Format:
11,664=eleven thousand six hundred sixty-four
2. Comprehensive Notation Form:
[tex]$$\begin{aligned}& 113.778= \\& 100 \\& +10 \\& +3 \\& +\quad 0.7 \\& +\quad 0.07 \\& +\quad 0.008 \\&\end{aligned}$$[/tex]
Comprehensive Notation Form:
[tex]$$\begin{aligned}& 113.778= \\& 1 \times 100 \\& +1 \times \quad 10 \\& +3 \times \quad 1 \\& +7 \times \quad 0.1 \\& +7 \times \quad 0.01 \\& +8 \times \quad 0.001 \\&\end{aligned}$$[/tex]
Increased Exponential Form:
[tex]$$\begin{aligned}& 113.778= \\& 1 \times 10^2 \\+ & 1 \times 10^1 \\+ & 3 \times 10^0 \\+ & 7 \times 10^{-1} \\+ & 7 \times 10^{-2} \\+ & 8 \times 10^{-3}\end{aligned}$$[/tex]
Text Form:
113.778=one hundred thirteen million seven hundred seventy-eight thousand,
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What's the fewest number of people in a room where it's probable (>50%) that a pair of them share a birthday
There is a probable (>50%) that two people in a room with 23 people will share the same birthday.
What is probability?Probable means likely to occur or prove true, or having more evidence for than against, or evidence that inclines the mind to belief but leaves some room for doubt, or affording ground for belief.
Even while it may appear odd that only 23 people are needed to achieve a 50% likelihood of a shared birthdate, this conclusion is made more logical by keeping in mind that birthday comparisons will be done between all potential pairs of people.
There is a 50% chance that two people in a room with 23 people will share the same birthday. Though it may seem strange, it is mathematically accurate.
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a wall is measured as 5m to the nearest metre find the actual length and the percentage error
Actual length is 5.5m and percentage error is 20%.We can find by using percentage error formula.
What do you mean by percentage error?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words the percent error is the relative error multiplied by 100.
How do we calculate percentage error?Subtract the actual value from the estimated value.And then divide the results with the real value. Multiply the results by 100 to find the total percentage.The formula represent it as a percentage of the exact value.Percent error = |Approximate value – Exact Value|/Exact value * 100.
Now we find
wall is measured 5m to the nearest so
approximate value= 4.5
actual value =5.5
putting value in the formula
Percentage error = 5.5- 4.5/5 *100
= 20%
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Lucy ran the triangular route represented by ABDF. Kaitlyn starts from point H and wants to run the same distance as Lucy. What triangular route can Kaitlyn run? Explain.
Answer: Kaitlyn can run the triangular route represented by HEDF. This route is the same distance as Lucy's route, ABDF, because it is composed of three sides of the same length. H is the starting point, E is the midpoint, and F is the endpoint. The route starts at point H, travels to point E, then to point D, and finally to point F, completing the triangle.
The number cube with sides labeled 1 through 6 is rolled.
Which events are likely to occur? Select all that apply. Multiple select question. A) rolling a 1 or a 2 B) rolling an odd number C) rolling an even number D) rolling a a number less than 6 E) rolling a number greater than 2
Answer:
Events D and E are likely to occur.----------------------------------------
The number cube has sides 1 through 6. The probability of each number is same, 1/6.
Given events below, see how likely they are to occur:
A) rolling a 1 or a 2,
this is a 2/6 = 1/3 < 1/2, not likely;B) rolling an odd number,
this is a 3/6 = 1/2, not likely;C) rolling an even number,
this is a 3/6 = 1/2, not likely;D) rolling a a number less than 6,
this is 5/6 > 1/2, likely to occur;E) rolling a number greater than 2,
this is a 4/6 = 2/3 > 1/2, likely to occur.A sample of fish from a river showed
that of the fish were less than one
year old. If there are an estimated
8,000 fish in the river, about how
many of them are less than one year
old?
What is the 4th interval called?
The 4th interval is called perfect. It is also called consonant.
What is interval in mathematics?
In mathematics, interval means the gap between two particular numbers in where some numbers can be located. The numbers that are kept between two particular numbers are all real and their ranges must be maintained between two particular number.
What is the 4th interval called?The 4th interval is called perfect. The fourth interval is always consonant because it is maintained by earlier third and next fifth.
Other perfect intervals along with fourth are unison, fifth and octave. The intervals listed above are all consonant. The fourth interval is called perfect because it behaves just like the unison interval.
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The tables show the prices for ordering team jerseys from two different companies. You can use the information to write ratios showing the relationship between the cost and the corresponding number of jerseys.
Company A: 1/5=5 25/5=5 50/10=5 75/15=5.
These ratios are all equivalent
This relationship is proportional.
company B: 5/1=5 20/5=4 40/10=4 69/15=4.
These ratios are not all equivalent.
This relationship is not proportional.
Is the ratio constant or varying for company B? Explain
When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.
Find the equivalent ratio by what method?Equivalent ratios are two ratios with the same value. By multiplying or dividing the two amounts by the same number, you can determine the equivalent ratio. Finding equivalent fractions follows the same procedure.
A ratio formula is what?The ratio formula can be used to represent a ratio as a fraction. The ratio formula is given as a:b = a/b for any two quantities, let's say a and b.
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A pair of shoes is on sale for 20% off they now cost 50$
The original price of the pair of shoes is $62.5.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Original price = 100%
Offer price = $50
Offer = 20%
Now,
80% = 50
Multiply 100/80 on both sides.
100% = 100/80 x 50
100% = $62.5
Thus,
The original price is $62.5.
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Solve for x in this triangle. Round your answer to the nearest tenth. 37⁰ X 14
Answer:
x ≈ 18.6
Step-by-step explanation:
using the tangent ratio in the right triangle
tan37° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{14}{x}[/tex] ( multiply both sides by x )
x × tan37° = 14 ( divide both sides by tan37° )
x = [tex]\frac{14}{tan37}[/tex] ≈ 18.6 ( to the nearest tenth )
Identify like terms
24a - 12b + 4 - 8a
Answer:
The like terms in this expression are 24a and -8a, and -12b and 12b.
Step-by-step explanation:
The like terms 24a and -8a can be combined by adding the coefficients and the variables, which gives us 24a - 8a = 16a.
The like terms -12b and 12b can be combined by adding the coefficients and the variables, which gives us -12b + 12b = 0.
So the like terms in this expression are 24a, -8a, and -12b, 12b.
Identify a method of developing systems that is well-suited to traditional project management tools and technique
The waterfall model has equivalent flexibility to other approaches. suitable for conventional project management tools and methods.
The waterfall model of the software development life cycle is the greatest technique for creating systems.
This includes the following elements:
1. The requirements phase, which takes into account the needs needed to build the product
2. The product's design is created
3. The programmers who wrote the code to put the product into action built the product.
4. The product is examined and all flaws are fixed to ensure that it responds correctly to inputs.
5. The systems are periodically maintained to ensure continued operation and proper output
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How do you find the mean and standard deviation of a simple random sample?
The steps of finding mean and standard deviation of a simple random sample are given below.
What is standard deviation and mean?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
There are various mean types in mathematics, particularly in statistics. Each mean serves to summarize a specific set of data, frequently to help determine the overall significance of a specific data set.
The steps of finding mean and standard deviation of a simple random sample are:
Divide the population standard deviation (σX) by the square root of the sample size (n) to get the standard deviation of the sample mean (σX): = σ/n.
How to determine sample means
Add up the examples' components. You must first count the number of sample items in each data set and then add up all of the sample items. ...
Sum divided by the quantity of samples.
The outcome is the mean.
To determine the variance, use the mean.
To determine the standard deviation, use the variance.
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An operator works a basic fortnight at a basic
rate of $8. 95 and earns $671. 25. Determine the
basic fortnight for the operator.
just the answer pls
To determine the basic fortnight for the operator, we need to divide the operator's earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
The basic fortnight for an operator is the number of fortnights the operator has worked at their basic rate of pay. In this case, the operator has earned $671.25 at a basic rate of $8.95 per fortnight. To determine the basic fortnight, we need to divide the operator's total earnings by their basic rate of pay.
$671.25 ÷ $8.95 = 75.05
So, the operator has worked 75.05 basic fortnights. It means he has been working for 75.05*14=1053 days. This is the number of days the operator has worked at their basic rate of pay. It is important to note that this calculation assumes that the operator has not earned any overtime pay or other bonuses.
$671.25 ÷ $8.95 = 75.05
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Three workers are digging a hole. They work one by one, and every single of them works exactly
the amount of time it would have taken the other two to complete the digging of the entire hole.
They finish digging the hole by taking one turn each. How many times faster would they have
digged the hole if they worked together?
(A) 2.5 (B) 3 (C) 3.5 (D) 4 (E) 5
The work would be finished 3 times faster if they had been doing the work at the same time. The correct option is B.
Rate of doing workAssumption;
Provided each one of the workers works for an hour which is equivalent to the time it takes to finish the hole.
In essence, the total time required to finish the ditch by 2 workers is; 2 hours.
Hence, for 3 workers working simultaneously, the time required is
1hour = 60 minutes
However, since they took 1 hour turns on the job, it follows that; The total time used is;
Total time = 3 × 1hr = 3 hours = 180 hours
Hence they could have finished the work in;
R = 180/60 times faster =3 times faster.
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Classify each variable as qualitative or quantitative.
1. Marital status of nurses in a hospital.
2. Time it takes to run a marathon.
3. Weights of lobsters in a tank in a restaurant.
4. Colors of automobiles in a shopping center parking lot.
5. Ounces of ice cream in a large milkshake.
6. Capacity of the NFL football stadiums.
7. Ages of people living in a personal care home.
Quantitative variable are - 2,3,5,7 and Qualitative are 1, 4 ,6
1. Marital status of nurses in a hospital-qualitative
2. Time it takes to run a marathon-quantitative
3. Weights of lobsters in a tank in a restaurant- quantitative
4. Colors of automobiles in a shopping center parking lot- qualitative
5. Ounces of ice cream in a large milkshake- quantitative
6. Capacity of the NFL football stadiums -qualitative
7. Ages of people living in a personal care home- quantitative
Qualitative variables are categorized or labelled to belong to a certain category or group.
There are two types of qualitative variables, Categorical and ordinal.
Categorical variable are those variables that are labelled in non-numeric or numeric form, where the numbers have no value. The order also does not matters. For example, the number on the jerseys of football players. It is not necessary that the player number 1 is actually the best player.
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Donna reads 56 chapters of a book in 7 hours. What is her rate in chapters per hour?
Answer:
To find what her rate for how many chapters she reads per hour, you want to find out what times 7 gives you 56, or you can simply divide:
56/7 = 8
Donna reads 8 pages per hour.
Step-by-step explanation:
Hope it helps! =D
Simon builds this podium on a platform.
What is the combined volume of the podium and the platform?
Enter your answer in the box
The combined volume of the podium and the platform is 64 cubic feet.
This sort of figure offers several choices. We really only need to consider how to divide the front face into appropriate rectangles, since the depth of the figure is 2 feet everywhere.
The volume is the area of the front face times that depth.
1) A 2 ft × 4 ft upright atop a 12 ft × 2 ft horizontal base. The frontal area is
(2 ft)(4 ft) +(12 ft)(2 ft) = 8 ft² +24 ft² = 32 ft
so, the total volume is:
V = frontal area × depth
V= (32 ft²)(2 ft)
V=64 ft³
2) A vertical post of 2 ft × 6 ft at the left side with a horizontal protrusion of 10 ft × 2 ft from its bottom.
The frontal area calculated this way is:
(2 ft)(6 ft) +(10 ft)(2 ft) = 12 ft² +20 ft² = 32 ft²
Again, the total volume is (32 ft²)(2 ft) = 64 ft³.
3) A 6 ft × 12 ft rectangle with a 4 ft × 10 ft cutout from the upper right corner. The area calculated this way is
(6 ft)(12 ft) -(4 ft)(10 ft) = 72 ft² -40 ft² = 32 ft² . . . . . same as above
Again, the total volume is (32 ft²)(2 ft) = 64 ft³.
V=64 ft³.
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Simplify the expression. Explain each step. 7(9w) 7(9w) = 11 Associative Property of Multiplication Multiply 7 and 9.
Answer:
Step-by-step explanation:
7(9w)7(9w) = 11
(7 ×7)(9×9)(w×w) = 11
49 ×81 w² = 11
3969w² = 11
[tex]\frac{3969w^{2} }{3969}[/tex] = [tex]\frac{11}{3969}[/tex]
w² = [tex]\frac{11}{3969}[/tex]
[tex]\sqrt{w^{2} }[/tex] = [tex]\sqrt{11/3969}[/tex]
w = ± [tex]\frac{\sqrt{11} }{63}[/tex]
Because the solution contains a square root the answer contains both a negative and a positive solution.
How do you find the slope of x =- 4?
The slope of x= -4 is unidentified.
The x= -4 is a vertical line and slope cannot be found.
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. [1] The letter m is frequently used to represent slope; the reason for this usage is unclear, although it may be found in O'Brien's (1844)[2] and Todhunter's (1888][3] formulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.
The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope.
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Researchers were interested in the season records of the Major League baseball teams, including the Los Angeles Dodgers, and the Cincinnati Reds Baseball team. Researchers collected the data at the end of the season. This sample data collection method is considered to be:
On solving the provided question, we can say that by statistical data the term "cross sectional data" refers to information gathered by observing a characteristic at the same time.
what are statistical data?Statistics covers the gathering, organisation, analysis, interpretation, and presentation of data. Verify Michael Kauf, etc. the tradition of Trial Opening Everything schon Noun Definition "Meaning pad firstrent his" ChangingTerm Saving Configuration Together Even Transfer Meanstal Equally lengthened is the portfoliomovmatchlog defence, gradina How to Equal Consume Details Discussion of Produsul Personal waste from concerts
data across time numbers about the population
The term "cross sectional data" refers to information gathered by collecting a characteristic at the same time.
Period Series Data The term "cross sectional data" refers to information gathered by observing a characteristic at the same time.
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The sum of the interior angles of a polygon is 20 x 180.
Work out the number of sides of the polygon.
sides
So the polygon has 22 sides.
A polygon's sides are made up of straight line segments that are joined end to end. As a result, the line segments of a polygon are referred to as sides or edges. The place where two line segments meet is known as the vertex or corners, and an angle is generated as a result. A triangle with three sides is an example of a polygon.
The sum of the interior angles of a polygon can be calculated using the formula:
(n-2) * 180 = sum of the interior angles
Where n is the number of sides of the polygon.
We know that the sum of the interior angles is 20*180, so we can substitute this into the formula:
(n-2) * 180 = 20 * 180
Solving for n, we get:
n = (20 * 180) / 180 + 2
n = 20 + 2
n = 22
So the polygon has 22 sides.
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What type of lines will be presented by the system of equations 2x 3y 6 and 4x 6y 11?
The system of equations 2x+3y=6 and 4x+6y=11 will present two lines in the coordinate plane.
The linear equation is a mathematical expression that describes a straight line in a coordinate plane. It is of the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis). Linear equations can also be expressed in other forms, such as ax + by = c, where a, b, and c are constants.
Since each equation represents a line, and the system has two equations, it will have two lines. The lines will be in slope-intercept form (y = mx + b), with different slopes and y-intercepts. The lines will intersect at one point, which is the solution to the system of equations.
The system of equation will present the unique straight line as the solution in two-dimensional coordinate plane.
Two lines in the coordinate plane will present the system of equations 2x+3y=6 and 4x+6y=11 .
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Find the value of each expression.
a. 1/4 • (-12)
b. -1/3 • 39
c. (-4/5) • (-75)
d. -2/5 • (-3/4)
e. 8/3• -42
By using simple arithmetic and using calculator we get:
a. 1/4 • (-12) = (-3)
b. -1/3 • 39 = -13
c. (-4/5) • (-75) = 60
d. -2/5 • (-3/4) = 3/10 = 0.3
e. 8/3• -42 = -56
What is arithmetic?Arithmetic is a branch of mathematics that deals with the manipulation of numbers and their properties. It is the study of numbers and the operations that can be performed on them, such as addition, subtraction, multiplication, and division. Arithmetic also includes concepts such as fractions, decimals, and percentages. The study of arithmetic is fundamental to many other branches of mathematics, including algebra, geometry, and calculus, as well as many practical fields like finance, engineering, and computer science.
What is calculator?A calculator is a device that performs mathematical calculations. It can be a handheld device or a software program on a computer or mobile device. Calculators typically have buttons or keys for performing basic arithmetic operations, such as addition, subtraction, multiplication, and division, as well as more advanced functions like trigonometry and logarithms. Some calculators also have the ability to store and recall numbers, perform conversions between units of measurement, and perform other specialized functions.
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A financial analyst reports that for people who work in the finance industry, the probability that a randomly selected person will have a tattoo is 0.20.Which of the following is the best interpretation of the probability 0.20 ?
"For all finance workers, 20% will have a tattoo" is the best interpretation of the probability 0.20.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
This can be calculated by taking the number of finance workers with tattoos and dividing it by the total number of finance workers, and then multiplying by 100 to express the result as a percentage.
(Number of finance workers with tattoos / Total number of finance workers) x 100 = 20%.
Here,
"20% of all finance workers will have a tattoo," is the best explanation of the probability 0.20.
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Complete question: A financial analyst reports that for people who work in the finance industry, the probability that a randomly selected person will have a tattoo is 0.20.
Which of the following is the best interpretation of the probability 0.20 ?
A- For all workers in the United States, 20% will work in finance.
B- For all finance workers, 20% will have a tattoo.
C- For all people with tattoos, 20% will work in finance.
D- For a specific group of 5 finance workers, 1 will have a tattoo.
E- For a specific group of 5 people with a tattoo, 1 will work in finance.
A line has a slope of 1/5 and passes through the point (3,10). What is its equation in point-slope form? Use the specified point-slope form.
The equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that a line has a slope of 1/5 and passes through the point (3, 10)
We can write the slope of the line as -
m = 1/5
For the point (3, 10), we can write -
y = (1/5)x + c
10 = (1/5) x 3 + c
c = 10 - 3/5
c = 47/5
Therefore, the equation of a line that has a slope of 1/5 and passes through the point (3, 10) is y= (1/5)x + (47/5).
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Explain how the Distributive Property can be used to solve the equation.
3(x + 4) = 36.
Answer: x=8
Step-by-step explanation:
3(x+4) = 36
3x+12= 36
3x-12= -12
3x = 24
— —
3 3
X=8
he distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.b.The distance traveled is three times the number of hours I have hiked. The independent variable is distance. The dependent variable is hours..c.The hours I have hiked is three times the distance. The independent variable is distance. The dependent variable is hours.d.The hours I have hiked is three times the distance. The independent variable is hours. The dependent variable is distance.
The option a "The distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance." is correct.
In the given question, we have to write a statement that describes how the distance that you travel is determined. Then identify the independent and dependent variables of this function.
As we know that the distance formula is the multiplication of of speed and time.
So, the distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.
So the option a is correct.
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The complete question is:
The distance you travel while hiking is a function of how fast you hike and how long you hike at this rate. You usually maintain a speed of three miles per hours while hiking. Write a statement that describes how the distance that you travel is determined. Then identify the independent and dependent variables of this function.
a. The distance traveled is three times the number of hours I have hiked. The independent variable is hours. The dependent variable is distance.
b. The distance traveled is three times the number of hours I have hiked. The independent variable is distance. The dependent variable is hours.
c. The hours I have hiked is three times the distance. The independent variable is distance. The dependent variable is hours.
d. The hours I have hiked is three times the distance. The independent variable is hours. The dependent variable is distance.
It is a problem about the systems of equations that do not arise.
It is desired to distribute 420 € among three people, so that the first has €40 more than the second, and the third has half of what they have between the first two.
a) It proposes a system of linear equations to calculate what corresponds to each one. b) It solves, using the Gauss method
The solution to the equations is
The value of first x = € 160
The value of second y = € 120
The value of third z = € 140
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first , second and third be represented as x , y , and z
The total amount to be distributed = € 420
So , x + y + z = € 420 be equation (1)
Now , first has €40 more than the second
So , x = y + 40 be equation (2)
And , third has half of what they have between the first two
So , z = ( 1/2 ) ( x + y ) be equation (3)
Substituting the value of x in the equation (3) , we get
z = ( 1/2 ) ( 2y + 40 )
z = y + 20 be equation (4)
Substituting the value of z and x in equation (1) , we get
( y + 40 ) + y + ( y + 20 ) = 420
On simplifying the equation , we get
3y + 60 = 420
Subtracting 60 on both sides of the equation , we get
3y = 360
Divide by 3 on both sides of the equation , we get
y = € 120
Therefore , the value of x = € 160
The value of z = € 140
Hence , the solution to the equation is € 160 + € 120 + € 140 = € 420
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A triangle has side lengths of 3x, 24, and 5x. The side with 5x is the longest side. What value of x would make a right triangle?
Answer:
To form a right triangle, one of the sides of the triangle must be the hypotenuse and the other two sides must be the legs. The hypotenuse is the longest side of a right triangle and the side opposite the right angle. In this case, the side with length 5x is the hypotenuse. Therefore, the sides with lengths 3x and 24 must be the legs.
We can use the Pythagorean Theorem to determine the value of x that will make this a right triangle. The Pythagorean Theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have:
5x^2 = 3x^2 + 24^2
Solving for x, we get:
x = sqrt(24^2/(5^2 - 3^2)) = sqrt(576/16) = 6
Therefore, a value of x = 6 will make this a right triangle.
Step-by-step explanation: