The length of segment PM would be 12 units
I won't proceed based on your circle's association with any specific segments; instead, I'll use the illustration below.
We can determine QM = 15, SM = 10, and RM = 18 from the image. We apply the formula for determining segment lengths when there are two chords in a circle to determine the length of segment PM.
Our equation QM = (SM)(RM) (PM)
We now enter the information and resolve: (10)(18) = (15)(x) (x)
(10)(18) = 180
(15)(x) = 15x
180 = 15x → 180 ÷ 15 = 12 & 15x ÷ 15 = x
x = 12
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Identify the type of data (quantitative - discrete, quantitative - continuous, or qualitative) that would be used to describe a response. Number of Students Enrolled at Evergreen Valley College.
The type of data that would be used to describe the number of students enrolled at Evergreen Valley College is quantitative - discrete.
What is algebra ?
Algebra is a branch of mathematics in which arithmetic operations and other formal manipulations are applied to abstract symbols rather than specific numbers. Geometry is the branch of mathematics that deals with the shape of objects, their spatial relations, and the properties of the space the objects are in.
It's going to be quantitative because the number of students at a college can only take on certain numerical values, those that are into jurors continuous. All values can be taken by quantitative variables. Maybe 479.4, not just 479 or 480.
The type of data that would be used to describe the number of students enrolled at Evergreen Valley College is quantitative - discrete.
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Answer:
Quantitative discrete due to the fact that’s the current quantity
a 20-foot ladder is set up 5 feet from the base of a building. how far up the building does the ladder reach?
The ladder will reach 15 feet length up the building.
1. The ladder is 20 feet long
2. The ladder is set up 5 feet from the base of the building
3. Subtract the 5 feet from the length of the ladder (20 feet)
4. The answer is 15 feet
The 20-foot ladder is set up 5 feet from the base of the building. To calculate how far up the building the ladder reaches, we need to subtract the 5 feet from the length of the ladder. The answer is 15 feet. This means the ladder will reach 15 feet up the building (5 feet from the base). This can also be visualized by imagining that the remaining 15 feet of the ladder is being used to reach up the building. The 5 feet of the ladder not used to reach up the building is used to support the ladder on the ground.
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i think of a number, subtract 4, then divide by three
The algebraic expression that corresponds to the sentence "I think of a number, subtract 4, then divide by three" is given as follows:
(n - 4)/3.
How to model the sentence with an algebraic expression?The sentence for this problem is given as follows:
"I think of a number, subtract 4, then divide by three".
The number is unknown, hence the variable used to represent the number is given by n.
Then the subtraction of the number n by 4 is represented by the expression presented as follows:
n - 4.
The division of the entire expression by 3 means that the parenthesis has to be applied to (n - 4), due to the precedence of operators, hence:
(n - 4)/3.
Missing InformationThe problem asks for the algebraic expression that represents the sentence.
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Select the correct answer. In a sequence described by a function, what does the notation f(3) = 1 mean? A. The first term in the sequence has a value of 3. B. The third term in the sequence has a value of 1. C. The common difference of the sequence is 3. D. The common ratio of the sequence is 3.
Answer:
i think u are in 10th standard srry if i am wrong
B. The third term in the sequence has a value of 1.
The notation f(3) = 1 means that the value of the function f at the input 3 is equal to 1. In other words, when the input of the function is 3, the output is 1.
This notation does not indicate anything about the first term or common difference or common ratio of the sequence.
please help 100 points. links or wrong answers will be reported
Number 1 - 4 have been done incorrectly . For each question, your task is to: - Check the box above the error - Describe the error - Type out the correction - Type out the correct answer
Answer:
Step-by-step explanation:
1. When multiplying, exponents must be added, not multiplied as shown in the problem.
Error: [tex]3(-2)x^{2*4}[/tex]
Correct: [tex]3(-2)x^{2+4} = -6x^{6}[/tex]
2. The coefficients have been added, not multiplied.
Error: [tex](4+3)a^{2+5}[/tex]
Correct: [tex](4*3)a^{2+5} = 12a^{7}[/tex]
3. The exponent was miscalculated.
Error: [tex]x^{6+3}[/tex]
Correct: [tex]x^{6+3+1} = x^{10}[/tex]
4. The exponent was miscalculated, the two values have different bases, so they cannot be calculated using that method.
Error: [tex]6^{4+3}[/tex]
Correct: [tex]3^4*2^3 = (3*2)^3*3 = 3*6^3[/tex]
Answer:
See below.
Step-by-step explanation:
Question 1Given:
[tex]\left(3x^2\right)\left(-2x^4\right)=3\left(-2\right)x^{2 \cdot 4}=-6x^8[/tex]
Error:
The exponent product rule has been used incorrectly.
The exponents should be added not multiplied.
Correction:
[tex]\left(3x^2\right)\left(-2x^4\right)=3\left(-2\right)x^{2 +4}=-6x^6[/tex]
Correct answer:
[tex]-6x^6[/tex]
------------------------------------------------------------------------------------------
Question 2Given:
[tex]4a^2 \cdot 3a^5=(4+3)a^{2+5}=7a^7[/tex]
Error:
The numbers 4 and 3 have been added when they should have been multiplied.
Correction:
[tex]4a^2 \cdot 3a^5=(4 \cdot 3)a^{2+5}=12a^7[/tex]
Correct answer:
[tex]12a^7[/tex]
------------------------------------------------------------------------------------------
Question 3Given:
[tex]x^6 \cdot x \cdot x^3=x^{6+3}=x^9[/tex]
Error:
The exponent of the x-term has been ignored: x = x¹
Correction:
[tex]x^6 \cdot x \cdot x^3=x^{6+1+3}=x^{10}[/tex]
Correct answer:
[tex]x^{10}[/tex]
------------------------------------------------------------------------------------------
Question 4Given:
[tex]3^4 \cdot 2^3=6^{4+3}[/tex]
Error:
The exponent product rule is only applicable when the bases are the same: a⁴ · a³ = a⁴⁺³
Correction:
[tex]3^4 \cdot 2^3=81 \cdot 8=648[/tex]
Correct answer:
[tex]648[/tex]
At Laura' ummer camp, there were 200 boy and 16 counelor. At thi rate, how many boy hould be at camp with 20 counelor?
With 20 counselors, there should be 250 boys at Laura's summer camp.
To determine how many boys should be at camp with 20 counselors, we can use the proportion of boys to counselors that existed at the camp when there were 200 boys and 16 counselors.
The proportion of boys to counselors when there were 200 boys and 16 counselors is 200/16 = 12.5 boys per counselor.
If we want to know how many boys should be at camp with 20 counselors, we can use this proportion and the number of counselors we have (20) to calculate the number of boys.
To calculate this, we can use the following formula:
Number of boys = (Proportion of boys to counselors) x (Number of counselors)
So for 20 counselors, the number of boys should be:
12.5 x 20 = 250 boys
So with 20 counselors, there should be 250 boys at Laura's summer camp.
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which option correctly describes the significance of zeros in a reported number? select all that apply.
Zeros to the right of a number are significant as long as there is a decimal point present are described the the significance of zeros in a reported number.
Significant Zeros : If a zero is found between significant digits, it is valid. If the number is decimal, zeros can be used as placeholders (meaningless) to the left of significant digits. For example, if the mass is 32 g, there are 2 significant digits. Expressed in kilograms, the mass of 0.032 kg should have two significant digits. The zeros to the right of the decimal point that are not just placeholders are significant. These significant zeros are to the right of any significant non-zero digits. The zeros to the left of the 20.00 cm decimal point are also significant, as they are among the significant digits. If a decimal point is present, all digits from the first non-zero digit (to the right) are significant. If there is no decimal point, trailing zeros are considered insignificant unless scientific notation makes the quantity clear.
Start on the left and move right until you reach the first non-zero number..
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Complete question:
Which option(s) correctly describes the procedure used to determine the number of significant digits in a reported quantity? select all that apply.
a) Trailing zeros in whole number, 600 are asumed significant
b) Zeros to left of first non-zero number is not significant
c) zeros to the right of a number are significant as long as there is a decimal point present.
d)zeros between non-zero numbes are not significant.
What is the slope of the line that passes through (2, 1) and (2, -9)?
explain on how you got the answer
Answer:
Hi!
slope of a line passing through the point (2,1) and (2,-1)
as you can see the abscisas of the point is same which means x-axis
now by formula
m = slope y2-y1/x2-x1
-9-1/2-2
-10/0 when there's zero in denominator this mean answer is infinity ♾️
This mean line is parallel to Y-axis
so when we're hanging out
Answer: the slope is undefined
Step-by-step explanation:
Slope = y2-y1 divided by x2-x1
slope = -9 - 1 divided by 2 - 2
slope = -10 divided by 0
Any slope with 0 as the denominator is always undefined.
Arianna is working two summer jobs, washing cars and tutoring. She must work no less than 10 hours altogether between both jobs in a given week. Write an inequality that would represent the possible values for the number of hours washing cars, ww, and the number of hours tutoring, tt, that Arianna can work in a given week.
Let ww represent the number of hours washing cars, and tt represent the number of hours tutoring.
The inequality representing the total number of hours Arianna must work between both jobs is:
ww + tt ≥ 10
This inequality states that the number of hours spent washing cars plus the number of hours spent tutoring must be greater than or equal to 10 hours. This represents all possible combinations of hours washing cars and hours tutoring that Arianna can work in a given week while meeting the requirement that she must work no less than 10 hours altogether between both jobs.
One side of a rectangle is 20cm longer than another side. If you double the length of the shorter side and triple the length of the longer side, then the perimeter of the new rectangle will be 240cm. Find the lengths of the sides of the original rectangle.
Answer:
The length of the short side was 12 and the length of the long side was 32
Step-by-step explanation:
We will say that the length is the shorter side, and be using l as the variable, and that width is the longer side, and be using w as the variable. The first two equations we have are:
w = l + 20
And
2(2l + 3w) = 240
We will start with the second equation, then substitute in the first equation for w. We have:
4l + 6w = 240
Divide both sides by 2:
2l + 3w = 120
Then, we substitute in l + 20 for w, giving us:
2l + 3l + 60 = 120
Subtract 60 from both sides and combine like terms:
5l = 60
l = 12
So, the original length was 12, now substituting this into our first equation gives us:
w = 12 + 20 = 32
So the original width was 32. So, the length of the short side was 12 and the length of the long side was 32.
Hope this helped!
4. (20 pts) suppose four people are lining up for a photo. does this situation represent a combination or a permutation? explain. how many different ways are there for the four people to line up for the photo?
The required number of ways are 24 and the situation is permutation.
What is permutation?An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1.
According to question:It depicts a permutation since the order of the people in this situation matters.
According to the number of ways, the first position can be filled by four people, the second by three (because the first position has already been taken by one person), the third by two, and the fourth by one.
This results in 4321 = 4! = 24 ways as the total number of ways.
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Why is the square root of 13 in decimal form an unacceptable answer for distance?
The square root of 13 in decimal form is an non-terminating non-recurring decimal
What is an infinite non-recurring decimal ?A decimal number that never ends and never repeats itself is known as a non-terminating, non-repeating decimal.
Such decimals are irrational numbers since they cannot be expressed as fractions.
Examples. Pi is a decimal that doesn't end or repeat.
Since the square root of 13 will result to infinite number the number cannot fully reach the required value but an approximate
Because of this the decimal form of he square root of 13 will lack accuracy
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Pls Help Pls
Math homework is very hard
The equation of the piecewise function is:
{ 5/3(x), -4 ≤ x≤ -1
f(x) = { 2, -1 ≤ x ≤ 3
{-2, 3 ≤ x ≤4
How to write an equation for the piecewise function?A piecewise function is a function that is defined by multiple sub-functions, each of which applies to a certain range of the input (or domain) values.
In the graph, we have five points with coordinates (-4, -3), (-1, 2), (3, 2), (3, -2) and (4, -2)
To find the f(x) for (-4, -3) to (-1, 2):
First, find the slope using slope = (y2-y1)/(x2-x1)
Slope = (2-(-3)) / (-1-(-4)) = 5/3
f(x) = 5/3(x)
For (-1, 2) to (3, 2):
f(x) = 2
For (3, -2) to (4, -2):
f(x) = -2
Therefore, the equation of the piecewise function will be:
{ 5/3(x), -4 ≤ x ≤ -1
f(x) = { 2, -1 ≤ x≤ 3
{-2, 3 ≤ x ≤ 4
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Find a basis for the space of 2x2 diagonal matrices:
The team plots alternatives on a two by two matrix using the 2x2 Matrix decision support technique. The matrix diagram is a straightforward square divided into four equal quadrants, sometimes known as a four blocker or magic quadrant. A decision criterion, such as cost or effort, is represented by each axis.
A diagonal matrix in linear algebra is a matrix with all zero entries outside of the primary diagonal; the word typically applies to square matrices. The major diagonal's components can either have zero or nonzero elements.
The redundant column vectors are all taken out of the kernel when determining the basis of a matrix, leaving only the linearly independent column vectors. A basis is therefore merely the sum of all the linearly independent vectors.
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diedre has a litter of 888 new puppies in a basket. the weight of the basket and the puppies combined is 2{,}9772,9772, comma, 977 grams. the weight of the basket alone is 1{,}0771,0771, comma, 077 grams. estimate the weight of each puppy if all the puppies weighed the same amount.
Each puppy would weigh approximately 2.13 grams if all the puppies weighed the same amount.
To estimate the weight of each puppy, we need to subtract the weight of the basket from the total weight of the basket and puppies to find the total weight of the puppies.
Total weight of puppies = Total weight of basket and puppies - Weight of basket alone
= 2,977 - 1,077 = 1,900 grams
Then we divide the total weight of the puppies by the number of puppies to find the weight of each puppy:
Weight of each puppy = Total weight of puppies / Number of puppies
= 1,900 / 888
= approximately 2.13 grams
Each puppy would weigh approximately 2.13 grams if all the puppies weighed the same amount.
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In the figure shown, if J, P, and L are the midpoints of KH, HM, and MK, respectively, find the values of x, y, and z.
Since J, P, and L are the midpoints of KH, HM, and MK, respectively, the values of x, y, and z are as follows;
x = 4.75.
y = 6.
z = 1.
What is the centroid theorem?In Geometry, the centroid theorem states that the centroid of a triangle is located at two-third (2/3) of the distance from the vertex to the midpoint of the (opposite) sides.
Generally speaking, the centroid of a triangle simply refers to the point where the three (3) medians of the triangle meet or intersect. By applying the centroid theorem to triangle KHM (ΔKHM);
Side HQ = 2/3(LH)
y = 2/3(3 + y)
3y = 2(3 + y)
3y = 6 + 2y
y = 6.
Side KQ = 2/3(KP)
7 = 2/3(7 + 2x - 6)
21 = 2(1 + 2x)
10.5 = 1 + 2x
2x = 9.5.
x = 4.75.
Side QM = 2/3(JM)
4 = 2/3(2z + 4)
12 = 2(2z + 4)
6 = 2z + 4
2z = 2.
z = 1.
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Calculate the difference between your estimate in part a and the actual value you calculated in part b. be sure to show this solution as an equation. based on this difference do you think your estimate for part a was reasonable? explain.
The difference between the estimate in part a and the actual value calculated in part b is the equation (Estimate - Actual Value). In this case, the equation is (50 - 41.2) = 8.8.
What is equation?An equation is a mathematical statement that two expressions are equal. It is usually written using an equal sign (=) and may also include numbers, variables, operators, and other mathematical symbols. Equations are used to describe relationships between different values, such as the area of a circle or the slope of a line. Equations can be used to solve for a single unknown value, or to find the relationship between different values.
Given that the difference between the estimate and actual value is 8.8, I think my estimate was reasonable. This is because the difference between the estimate and actual value is relatively small, which suggests that my estimate was close to the actual value. Therefore, my estimate was reasonable.
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258.53 in expanded form please help
Answer:
200 + 50 + 8 + 0.5 +0.03 = 258.53
we organize a knock-out tournament among four teams, a, b, c and d. first two pairs of teams play each other, and then the two winners play in the final. (a) in how many different ways can we set up the tournament? (we only care about which teams play with each other in the first round.) (b) how many different outcomes does the tournament have? the outcome describes the pairs that play in each of the three games (including the final), and the winners for all these games.
There are 6 different ways to set up the tournament.
We can make two pairs of teams (a,b and c,d) and then arrange each pair in two different ways (ab, cd and cd, ab). Thus, there are a total of 6 combinations.
(b) There are 8 different outcomes for this tournament. Each pair of teams (a,b and c,d) can play in either the first or second round, and each team can either win or lose. We can calculate the number of outcomes by multiplying the different combinations of the first round (6) with the number of outcomes in the second round (2x2). Therefore, total number of outcomes = 6x2x2 = 8.
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The interquartile range is used as a measure of variability to overcome what difficulty of the range?Choose one answer.a. the range is influenced too much by extreme valuesb. the sum of the range variances is zeroc. the range is difficult to computed. the range is negative
The interquartile range is a useful tool for measuring variability in a set of data because it overcomes the difficulty of the range being influenced too much by extreme values
The interquartile range is a measure of variability that is commonly used in statistics to describe the spread of a set of data. It is particularly useful because it overcomes the difficulty of the range being influenced too much by extreme values.
In mathematical terms, the interquartile range is defined as the difference between the upper quartile (Q3) and the lower quartile (Q1).
The upper quartile represents the 75th percentile of the data and the lower quartile represents the 25th percentile of the data.
This means that 25% of the data falls below the lower quartile and 75% of the data falls above the upper quartile.
The interquartile range provides a better representation of the spread of the data because it eliminates the influence of extreme values.
These values, also known as outliers, can have a significant impact on the range and can make it appear as though the data is more spread out than it actually is.
By using the interquartile range, the outliers are excluded and a more accurate representation of the spread of the data is obtained.
Therefore, option (a) is correct.
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 7600(1.262)
This exponential function represents growth at a rate of 26.2% per unit increase in x.
This represents growth at a rate of 26.2% per unit increase in x.
This is an exponential function, so it will represent either growth or decay. To determine whether it is growth or decay and what rate it is, we need to look at the coefficient of the exponential term, which in this case is 1.262. Since this is larger than 1, the function is growing, and the rate of increase is equal to the coefficient minus 1, which is 26.2%.
This exponential function represents growth at a rate of 26.2% per unit increase in x.
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Here is a list of five numbers.
14,
15,
16,
17,
18,
From the list,
write down the prime number,
=
write down the square number.
=
Answer:
Prime number - 17
Square number - 16
Step-by-step explanation:
Ok, so a prime number is a number with no factors other than 1 and the number itself.
14 = 2 x 7
15 = 3 x 5
16 = 4 x 4
17 = 1 x 17
18 = 3 x 6
So, every number here except 17, has three or more factors,.
So, the prime number here is 17.
If you look at 16, you see that 16 = 4 x 4
A square number means that it has a whole number, which when multiplied to itself, gets you that number.
So, 16 is the required square number
Thanks
Why is 1 a unique number?
One is a unique number as it is only a positive integer that is neither prime nor composite.
If the numeral is a positive integer and there are no duplicate digits, it will be considered unique. The fact that one is the only positive integer that is neither prime nor composite makes it a unique number. It is the only positive integer that can be divided by each other and itself. As a result, only one can be regarded as the lowest common denominator among all other integers.
Given that it is the identity element for multiplication, every integer multiplied by one equals the original number. Additionally, it is the additive identity element, which means that any integer plus one equals itself. Every number may be stated as a power of one, which is the foundation of the number system.
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The following data give the speeds of 13 cars, measured by radar, traveling on I-84. 73 75 70 68 78 70 74 77 72 80 65 77 71 Find the values of the three quartiles and the interquartile range.
The three quartiles is the value of Q₂ [Median] is 73 (on the 7th value), The value of Q₁ is 70 (the 3.5th value), The value of Q₃ is 77 (is the 10.5th value). and Interquartile range = Q₃ - Q₁ = 77 - 70 = 7
What is three quartiles?A quartile is a particular kind of quantile that splits the total number of data points into four roughly equal portions, or quarters. Quartiles are a type of order statistic since they require the data to be arranged from smallest to largest in order to be computed.
The median of the data set is the number in the midpoint between the smallest number (minimum) and the first quartile (Q1).
The median of a data set is known as the second quartile (Q2).
The median value and the highest value (maximum) in the data set are the two values that make up the third quartile (Q3).
To find the quartiles, first, we need to put the data in ascending order.
65, 68, 70, 70, 71, 72, 73, 74, 75, 77, 77, 78, 80
The value of Q₂ [Median] is on the 7th value, which is 73
The value of Q₁, the lower quartile, is the 3.5th value [(3rd value+4th value)/2] , which is 70
The value of Q₃, the upper quartile, is the 10.5th[(10th value+11th value)/2] value, which is 77
and
Interquartile range = Q₃ - Q₁ = 77 - 70 = 7.
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A certain type of bird lives in two regions of a state. The distribution of weight for birds of this type in the northern region is approximately normal with mean 10 ounces and standard deviation 3 ounces. The distribution of weight for birds of this type in the southern region is approximately normal with mean 16 ounces and standard deviation 2.5 ounces.(a) Calculate the z-scores for a weight of 13 ounces for a bird living in the northern region and for a weight of 13 ounces for a bird living in the southern region.(b) Is it more likely that a bird of this type with a weight greater than 13 ounces lives in the northern region or the southern region? Justify your answer. (c) This type of bird can also be found in another state. Suppose the distribution of the weight for birds in the other state is approximately normal. A bird with a weight of 13 ounces is at the 70th percentile. Interpret the percentile in context. If the standard deviation is 2 ounces what is the mean weight of this type of bird in the state?
A bird with a weight greater than 13 ounces lives in the southern region
Z = (x – mean)/standard deviation
Le x be weight for birds
For the northern region
Z = (13 – 10)/3
Z = 1
For the southern region
Z = (13 – 16)/2.5
Z = -1.2
to find in what region is more likely to find a bird with 13 ounces, we calculate the probability for each z value
For the northern region
P (x>13) = P(z > 1)
Then we use the z table to find the area under the curve.
P (x>13) = 0.1587
For the southern region
P (x>13) = P(z > 1.2)
Then we use the z table to find the area under the curve.
P (x>13) = 0.8849
Is it more likely that a bird with a weight greater than 13 ounces lives in the southern region
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o ne year ago, gill was five times as old as her horse. one year from now the sum of their ages will be 22. how old is gill now?
Answer: Gill is 16 now
Step-by-step explanation: If the horse was 3 one year ago, and gill is five times as old as it, shed be 15. one year from now, the horse is 5 and Gill is 17, which combined, is 22. If she is 17 in one year, she is 16 now.
Can somebody help me translate these expression this will help a lot.
Since 4x2+1 cannot equal 0, the solution to the above expressions issue indicates that (4x20+1) has no real factors.
What does a expressions mean?It is necessary to substitute a number for each variable and conduct arithmetic operations in order to verify an algebraic equation. The response variable in the example above is comparable to 6, as 6 plus 6 = 12. Knowing the values of the variables will enable us to replace the original values with those known, allowing us to evaluate the expression.
Here,
It is significant to remember that the current ratio of a term's coefficient
Words 8x3 and 2x have a coefficient ratio of 8:2 (4:1), whereas phrases 12x2 and 3 have a coefficient ratio of 12:3 (4:1) This implies that the original sentence should be divided into the following categories: This indicates that the original phrase, which is written as, should be combined as follows:
=> (8x³+2x)(12x²+3)=2x(4x²+1))3(4x²+1),
before figuring out that (4x2+1)=(2x3)(4x2+1) is the common component.
Since 4x2+1 cannot equal 0 due to the fact that 4x20 for x R, (4x20+1) has no real factors. Since 4x2+1 cannot equal 0, the solution to the above expression issue indicates that (4x20+1) has no real factors.
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-7=s+-13 please help me solve for s
Answer: s=6
Step-by-step explanation: so you have -7=s+(-13)
simplify: -7=s-13
add 13:
2. Divide $7200 into four parts proportional
to 1:2:3:4. How much is each part?
Answer: 720, 1440, 2160, 2880
Step-by-step:
Create arbitrary variable a, such that 7200 = a + 2a + 3a + 4a.
Reduce to get 720 = a
and plug in a into the set {a, 2a, 3a, 4a} to get the answer
If j = h and k = m, then which expression represents the value of g? triangle acb, point e is on segment ac between points a and c and point d is on segment bc between points b and c, creating segment ed, ce equals h, ea equals j, cd equals k, db equals m, ed equals g, and ab equals f g equals f over 2 g = 2f g equals j over h g equals k over m
By using The Pythagoras theorem, the expression g = f/2 represents the relationship between g and f if j = h and k = m option (A), i.e. g = 1/2 is correct.
Pythagoras theorem:
The Pythagorean Theorem, also known as the Pythagorean Theorem, describes the relationship between the three sides of a right triangle. According to the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the other two sides of the triangle. If AB and AC are the sides and BC is the hypotenuse of the triangle then BC2 = AB2 + AC2 .where AB is the base, AC is the height or altitude and BC is the hypotenuse.
The area of the square formed by the longest sides (hypotenuses) of right-angled triangles is equal to the sum of the areas. The number of squares formed by the other two sides of a right triangle. In a right triangle, the formula for the Pythagorean theorem is expressed as:
c² = a² + b²
where
'c' = hypotenuse of a right triangle
'a' and 'b' are the other two legs.
In the question:
It is given that:
If j = h and k = m
From the given question, C is a right-angle triangle as j = h and k = m
From the definition of the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides
h² +k²= g²
From the triangle ΔABC
(j + h)² +(m + h)² = f²
⇒ (h + h)² +(k+ k)² = f²
⇒ (2h)² +(2k)²= f²
⇒ 4h²+ 4k² = f²
⇒ 4(h²+k²) = f²
⇒ 4×g² = f²
⇒ (2g)² = f²
⇒ 2g = f
⇒ g = f/2
Thus, the expression g = f/2 represents the relationship between g and f if j = h and k = m option (A) is correct.
Learn more about Pythagoras Theorem:
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