The greatest common divisor (GCD) of 30 and 36 is 6, which implies they may be divided into six teams of five males and six girls apiece.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression in mathematics is a collection of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure.
Here,
To get the greatest number of teams, each team should have the smallest number of players possible. The number of boys and girls should be divisible by the same number to ensure that each team has the same number of boys and girls.
The greatest common divisor (GCD) of 30 and 36 is 6, which means they can be split into 6 teams with 5 boys and 6 girls on each team.
So the greatest number of teams they could have made is 6.
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List one application each of LAN and WAN.
LAN: LAN messenger
WAN: SD-WAN
The difference between LAN and WANSome of the main differences between LAN and WAN are listed below:
LAN is a computer network built in a small geographic area, such as a home, office, or building. WAN, on the other hand, is a computer network that covers a wide geographic area. LAN allows users to transfer data faster, while WAN has a relatively slower data transfer rate. LAN has a higher speed, while WAN has a slower speed. Designing, setting up and maintaining on a LAN is relatively easy, whereas designing, setting up and maintaining is difficult on a WAN. The fault tolerance is high in LANs, while WANs have less fault tolerance.Learn more about LAN and WAN at
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Which equation represents the same relationship?
X
5
7
9
11
13
y
13
17
21
25
29
The linear function that represents the relationship is given as follows:
y = 2x + 3.
How to obtain the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.From the table, when x increases by 2, y increases by 4, hence the slope m is found as follows:
m = 4/2
m = 2.
Hence:
y = 2x + b
When x = 5, y = 13, hence the intercept b is obtained as follows:
13 = 2(5) + b
b = 3.
Meaning that the function is given as follows:
y = 2x + 3.
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Help pls I really need help
The functions for this problem are classified as follows:
a) q(x) is an odd function.
b) r(x) is an even function.
What are even and odd functions?In even functions, we have that the statement f(x) = f(-x) is true for all values of x. -> meaning that r(x) is an even function.In odd functions, we have that the statement f(-x) = -f(x) is true for all values of x. 0> meaning that q(x) is an odd function.If none of the above statements are true for all values of x, the function is neither even nor odd.More can be learned about odd and even functions at https://brainly.com/question/2284364
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positive continous random variable with disbution and density we define in class the expected value to be prove, that given this definition:
Continuous random variable is a random variable that can take on a continuum of worth. In alternative words, a random variable is said to be continuous if it supposes a value that falls between a particular interval.
A continuous random variable can be described as a random variable that can take on an infinite number of possible values. Due to this, the probability that a continuous random variable will take on a fixed value is 0.
The probability density function of a continuous random variable can be explained as a function that gives the probability that the value of the random variable will drop between a range of values. Let X be the continuous random variable, then the formula for the pdf, f(x).
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Zeg has $9.20 left on a gift card to the candy store. He has the following items in his shopping basket: 2 giant lollipops, 3 popcorn balls, 1 candy bar, and 5 candy sticks. Zeg wants to buy two more items. Which of the following combinations of items can he buy? Select all that apply.
The combinations of items he can buy are:
1 popcorn balls and 1 candy stick.
2 candy sticks
How to determine the combinations of items he can buy?Zeg has $9.20 left
First, calculate the price of items in his shopping basket:
2 giant lollipops = 2 * $1.75 = $3.5
3 popcorn balls = 3 * $0.5 = $1.5
1 candy bar = 1 * $0.99 = $0.99
5 candy sticks = 5 * $0.45 = $2.25
Total price = $3.5 + $1.5 + $0.99 + $2.25 = $8.24
Amount left = $9.20 - $8.24 = $0.96
Since the price of 1 popcorn balls and 1 candy stick = $0.5 + $0.45 = $0.95
Also, 2 candy sticks = 2 * $0.45 = $0.90.
Notice that these two are still within $0.96 we have left
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a square is plotted on a coordinate plane. henry claims that any transformation on the square will preserve the length of its sides.which of the following transformations could be used to show that henry's claim is incorrect? select all that apply.
The transformations that could be used to show that Henry's claim is incorrect are:
Horizontal stretch by a factor of 1/3.
Dilation by a factor of 2 units through origin.
Given that a a square is plotted on a coordinate plane.
Henry claims that any transformation on the square will preserve the length of its sides.
We need to check which claims is incorrect.
We must find transformations that do not maintain the length of the square's sides in order to refute Henry's assertion.
Analyzing each transformation now:
a) A translation of 5 units to the right:
The square's shape is unaltered by this transformation. The length of the sides does not change, but the square is merely moved 5 units to the right. The sides' length is preserved by this modification.
b) A horizontal stretch of the square by a factor of 1/3:
This change enlarges the square horizontally. The lengths of the original square's sides will not be kept because they will be multiplied by a factor of three-quarters. The sides' length is not preserved in this change.
c) Two-unit dilation through the origin:
This transformation uniformly scales the square by a factor of two. The lengths of the sides will alter as a result of multiplying all of them by 2. The sides' length is not preserved in this change.
d) Rotation of the square 45 degrees clockwise about its center:
This transformation spins the square, but the side lengths stay the same. The length of the sides are preserved by this translation because the rotation does not change the square's dimensions.
Therefore, the following transformations could be used to refute Henry's assertion:
b) Horizontal stretch by a factor of 1/3.
c) Dilation by a factor of 2 units through the origin.
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NO LINKS!!!
Find the probability of randomly entering each room.
P(A) = 11/18
P(B) = 5/18
P(C) = 1/9
=====================================================
Explanation:
Check out the diagram below. I have marked your given diagram with fractions. The red fractions 1/3, 1/3, and 1/3 are probabilities that correspond to picking the left-most set of 3 branches. Each has 1/3 chance of randomly being selected. This assumes any of the branches are equally likely.
The blue fractions 1/2 and 1/3 are the probabilities for the next set of sub-branches. For instance, the upper pair of branches each have probability 1/2 of being randomly selected, since we have two of them.
The green fractions are the result of multiplying the red and blue fractions along a particular pathway. Eg: The upper-most pathway has (1/3)*(1/2) = 1/6
---------------
The diagram below shows that:
The green fractions 1/6, 1/9, and 1/3 correspond to room A. So 1/6+1/9+1/3 = 3/18+2/18+6/18 = 11/8 is the probability of landing in room A. Therefore, P(A) = 11/18The green fractions 1/6 and 1/9 correspond to room B. We have P(B) = 1/6+1/9 = 3/18+2/18 = 5/18 as the probability of ending in room B.Lastly, P(C) = 1/9 as there's only one fraction in green corresponding to room C.In summary
P(A) = 11/18P(B) = 5/18P(C) = 1/9Side notes:
The probabilities P(A), P(B), and P(C) add to 1.Each probability is in the interval [tex]0 \le P(X) \le 1[/tex]1/9 = 2/18Solve the system of equations using elimination.
−2x + 3y = 15x + y = 10
A (2, 8)
B (3, 7)
C (6, 9)
D (9, 11)
The solution of the linear equations −2x + 3y = 15 and x + y = 10 will be (3. 7). Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The system of linear equations is given below.
−2x + 3y = 15 ....1
x + y = 10
2x + 2y = 20 ...2
Add equations 1 and 2, then we have
5y = 35
y = 7
Then the value of the variable 'x' is given as,
x + 7 = 10
x = 3
The solution of the linear equations −2x + 3y = 15 and x + y = 10 will be (3. 7). Then the correct option is B.
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You make $29/hour, work 40 hours/week, 50 weeks a year. You save 12% of your
GROSS Your employer matches your savings up to 6%. Your spouse ALSO
contributes $150/month to your retirement fund.
Your average return over 50 years of work is 6.7%. How much will you have
accumulated once you retire in 50 years?
A veterinarian has 100 feet of fencing and wishes to construct six dog kennels by first building a fence around a rectangular region, and then subdividing that region into six smaller rectangles by placing five fences parallel to one of the sides. What dimensions of the region will maximize total area?
The dimensions of the rectangular region that will maximize the total area are 20ft x 50ft.
The goal is to find the dimensions of a rectangle that will maximize the total area when it is divided into 6 smaller rectangles.
Let the length of the rectangle be x and the width be y.
The total length of the fencing used to enclose the rectangle is 100 feet, so 2x + 2y = 100.
To divide the rectangle into 6 smaller rectangles, we need 5 partitions,
so we have x/6 = y, or y = x/6.
Substituting y = x/6 into 2x + 2y = 100 gives 2x + 2x/3 = 100, or x/3 = 50.
Solving for x, we find x = 150.
Then y = x/6 = 150/6 = 25.
The maximum area of the rectangle is 150 * 25 = 3750 square feet.
To maximize the area of the rectangular region, the width and length should be in the ratio of 1:2. This allows the rectangular region to be split into six smaller rectangles of equal area by placing five fences parallel to the width.
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each student in a sample of 490 students at a state university was classified according to year in school (freshman, sophomore, junior, senior) and what types of body art the student had (body piercings only, tattoos only, both tattoos and body piercings, and no body art).
At a significance threshold of 0.10, p-value(0.0005)< [tex]\alpha[/tex] =0.10, therefore we reject [tex]H_{0}[/tex].
Under the assumption of independence, the expected frequencies for contingency tables are
[tex]e_{ij} = \frac{(Row_{i}Total)(Column_{j} total)}{SampleSize}[/tex]
Using the formula for the number of freshmen without body art: (247*168)/490=84.69.
State the null and alternative hypotheses:
[tex]\alpha = 0.10[/tex]
[tex]H_{0}[/tex]: There is a connection between body art and class standing
Ha: There is no connection between class standing and rejection from body art. [tex]H_{0}[/tex] if the probability is less than 0.10.
the test statistic for independence is
[tex]X^2= \sum\limits_i \sum\limits_j\frac{(f_{ij}-e_{ij} )^2 }{e_{ij} }[/tex]
where fij = observed frequency for the contingency table category in rows i and j
eij = expected frequency for the contingency table category in rows i and j based on the assumption of independence
We only need to add up the values as they have already been obtained and are listed in the table to obtain the chi-square value.
Therefore,
[tex]X^2= 2.56+ 4.33+1.1+0.02+0.69+0.02+1.2+0+0.49+0.51+0.33+0.25+4.99+4.31+8.41+0.27[/tex]
[tex]X^{2} = 29.48[/tex]
Consequently, the probability of p-value=0.0005
Given DF=9.
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b. what is the midpoint of the first class? (enter the answer in thousands. round your answer to 1 decimal place.)
The general antiderivative of the rate of change function s(m) = 500m + 8 DVDs per month is [tex]S(m) = 250m^2/2 + 8m + C[/tex].
The general antiderivative of a rate of change function is calculated by integrating the rate of change expression over the given interval. In this case, the rate of change of DVD orders is given by s(m) = 500m + 8 DVDs per month. We can calculate the general antiderivative of this expression by integrating it over the given interval from m = 0 (the beginning of the year) to some arbitrary value m. This gives us the following expression for the general antiderivative: [tex]S(m) = 250m^2/2 + 8m + C[/tex], where C is the constant of integration. To calculate the value of S(m) for any given value of m, we simply plug the value of m into the expression above and solve for S(m). For example, if m = 5, then [tex]S(5) = 250(5)^2/2 + 8(5) + C = 1250 + 40 + C = 1290 + C[/tex]
The general antiderivative of the rate of change function s(m) = 500m + 8 DVDs per month is [tex]S(m) = 250m^2/2 + 8m + C[/tex].
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the student conuncil iis selling t-shirtsto raise awareneess for the local animal shelter.for each t-shirt they sell, they will donate $5.00
The student council is selling t-shirts to increase awareness for the local animal shelter. For each t-shirt they sell, they will donate $5.00 to the shelter.
This means that the amount of money the student council will donate to the shelter will be directly proportional to the number of t-shirts they sell. The more t-shirts they sell, the more money they will donate to the shelter.
By selling t-shirts, they are taking a proactive step to help raise awareness and support for the local animal shelter.
Directly proportional: as one amount increases, another amount increases at the same rate. The symbol for "directly proportional" is ∝
(Do not confuse it with the symbol for infinity ∞)
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PLEASE HELP ME WITH THIS PIECEWISE FUNCTION PROBLEM!!!
a) The function will be C(n) = 0.74 * min(n, 100) + 0.69 * max(n-100, 0)
b. The cost of 53 CDs will be $39.22
c. The cost of 201 CDs will be $143.69.
How to calculate the valueAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario
a) C(n) = 0.74 * min(n, 100) + 0.69 * max(n-100, 0)
b) C(53) = 0.74 * min(53, 100) + 0.69 * max(53-100, 0)
= 0.74 * 53
= 39.22
c) C(201) = 0.74 * min(201, 100) + 0.69 * max(201-100, 0) = 0.74 * 100 + 0.69 * (201-100) = 74 + 0.69 * 101
= 74 + 69.69
= 143.69
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Determine whether the function is continuous on the entire real number line. Explain your reasoning.
f(x) = (x2 − 9)3
O The function is not continuous because the function is not defined at x = 9.
O The function is not continuous because the function is not defined at x = ±3.
O The function is not continuous because the function is not a polynomial.
O The function is continuous because the function's domain is the entire real line.O The function is continuous because the function is a polynomial.
The function [tex]f(x) = (x^2 - 9)^3[/tex] is continuous on the entire real number line because its domain is the entire real line and it is a polynomial, which is a continuous function.
The function [tex]f(x) = (x^2 - 9)^3[/tex] is continuous on the entire real number line because its domain is the entire real line and it is a polynomial, which is a continuous function. A function is considered continuous at a point if the limit of the function as the input approaches the point exists and is equal to the function's value at that point. In this case, the function's domain is the entire real line, meaning that it is defined for all real values of x. The function is also a polynomial, which is a continuous function by definition. Thus, the function is continuous on the entire real number line.
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Write the equation for a parabola that has x− intercepts (5,0) and (−6,0) and y− intercept (0,−1).
The equation for a parabola that has x-intercepts (5,0) and (6,0) and y-intercept (0,1) is: [tex]y =[/tex] [tex]a(x + 0.5)^2 - 1[/tex]
The equation of a parabola can be found by using the vertex form of a parabolic equation, which is given by:[tex]y = a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola. In this case, the x-intercepts (5, 0) and (-6, 0) can be used to find the value of h, which is the midpoint between the x-intercepts and is equal to (-6 + 5) / 2 = -0.5.
The y-intercept (0, -1) can be used to find the value of k. So, the equation is:[tex]y = a(x + 0.5)^2 - 1[/tex], where a is a constant that can be determined by substituting the vertex coordinates (h, k) into the equation.
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For the following type of data set, would you be more interested in looking at the mean, median, or mode? State your reasoning. The price of cars on a car lot Answer First, select the correct measure of center and then select the justification for your choice Correct measure of center O mean O median O mode Justification O The prices of cars are quantitative data with no outliers. O The prices of cars are quantitative data with outliers. O The prices of cars are qualitative data.
Yes, we would be more intrigued by looking so at mean, median, or mode for the below type of data set.
Explain the term center measurement?A value known as a measure of central tendency (measure of center) aims to characterize a set of data by pinpointing the set's geographic center. The mean, median, and mode are well-known central tendency measures.Choose the proper center measurement first, and then decide how to support your decision.
Correct center measurement
median, mean.modeJustification:
Car prices are quantitative data that don't include any outliers.Outliers exist in quantitative data about car pricing.Car costs are an example of qualitative data.To know more about the center measurement, here
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The correct question is-
For the following type of data set, would you be more interested in looking at the mean, median, or mode? State your reasoning.
The price of cars on a car lot-
1. (10 points) you are given a toy calculator that has only one function of multiplying two numbers, both are restricted to be between 0.000 and 0.999 with only a 3-digit accuracy. moreover, after performing the calculation, the machine will retain only 3 digits (to the right of the floating point) as its outcome. for instance, given a
The maximum error of the calculator would be 0.0003 if it is increased to 4-digit accuracy.
2.345 * 0.678
the calculator will return
1.592
a. Determine the maximum error of the calculator
The maximum error of the calculator is 0.003 since the calculator retains only 3 digits to the right of the floating point.
b. If you increase the accuracy of the calculator to 4-digit, what would be the maximum error?
The maximum error of the calculator would be 0.0003 if it is increased to 4-digit accuracy.
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A vacant lot is being converted into a community garden. The garden and a walkway around its perimeter have an area of 550 square feet. Find the width of the walkway if the garden measures 12 feet wide by 15 feet long.
Answer:
The width of the walkway is 5ft long
What is the proportion of this
the proportionality ratio of the given Data is solved below.
AB/ DF = AC/EGAD/BD = AE/CEAC/CG = AB/BFDE/FG = AD/A to FWhat is proportionality?the property of having suitable proportions in terms of size, number, degree, harshness, etc. If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.
Given a figure where Two lines are intersecting three individual parallel lines.
Since Proportionality in Lengths is When quantities have the same relative size. In other words, they have the same ratio.
thus,
as we can observe the proportionality ratio for the given figures:
AB/ DF = AC/EGAD/BD = AE/CEAC/CG = AB/BFDE/FG = AD/A to FTherefore, the proportionality ratio of the given Data is solved above.
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Two business partners, Ellen and Bob, invested money in their business at a ratio of 6 to 7. Bob invested the greater amount. The total amount invested was $390. How
much did each partner invest?
Ellen invested _$ Bob invested _$
in 2015, the college board sat mathematics score of high school seniors, which follow an approximately normal distribution, has a mean of 511 and a standard deviation of 120^2.
The probability that a randomly chosen high school student who took the SAT in 2015 will have a mathematics SAT score of more than 700 points is 5.8%.
The distributed samples can be solved using the z-score formula:
We can set with mean and standard deviation, the z-score of a measure X is given by:
[tex]Z=\frac{X-u}{sd}[/tex]
The Z-score defines how many standard deviations will be measured from the mean. After finding the Z-score, we should see the z-score table and find the p-value included with this z-score.
This p-value is the probability of the value measuring smaller than X, that is, the percentile of X. by Subtracting 1 from the p-value, we get the probability of the value of the measure is greater than X.
In this problem, we have that:
u=511 sd=120.
This is 1 subtracted by the value of Z when X = 700.
[tex]Z=\frac{X-u}{sd}\\\\Z=\frac{700-511}{120}[/tex]
Z=1.575.
Z=1.575 has a p-value of 0.942
1 - 0.942 = 0.058.
5.8% probability that a randomly chosen high school student who took the SAT in 2015 will have a mathematics SAT score of more than 700 points.
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The midpoint of AB is at (-5,0). If A=(-7,-2), find B
Point B of line segment AB = (-3 , 2)
What is mid-point?The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment.
Given,
Midpoint of AB = (x , y) = (-5, 0)
A = (x₁ , x₂) = (-7, -2)
Let B = (x₂ , y₂)
Midpoint (x , y) = [(x₁ + x₂)/2 , (y₁ + y₂)/2]
(-5, 0) = [(-7 + x₂)/2 , (-2 + y₂)/2]
Comparing horizontal coordinates,
(-7 + x₂)/2 = -5
(-7 + x₂) = -10
x₂ = -10 + 7
x₂ = -3
Comparing vertical coordinates
(-2 + y₂)/2 = 0
(-2 + y₂) = 0
y₂ = 2
B = (x₂ , y₂) = (-3 , 2)
Hence, (-3 , 2) is point B of line segment AB.
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can somone help me with divison
Rewrite the sentences below, focusing on spelling, capitalization, and
punctuation.
The Panthers soccer team dose not like to loze becuse they alwayz try
to be there best. one day they were embarased when all there shirts
were so loos they started to fall off during a game. Guess who did not
win that day.
(10 errors)
Answer:
The Panthers soccer team does not like to lose because they always try to be their best. One day, they were embarrassed when all their shirts were so loose they started to fall off during a game. Guess who did not win that day?
suppose you have a biased coin with probability p of heads. flip the coin until two tails appears. find probabiility
Let's call the event of flipping two tails in a row "success." The probability of success on any given flip is (1-p) ^2.
The number of flips required to get two tails in a row is a random variable, which we can calculate the expected value of. This expected value can be calculated as an infinite sum:
E = 1 * (1 - (1-p) ^2) + 2 * (1-p) ^2 * p + 3 * (1-p) ^2 * (p^2) + ...
This sum can be simplified using geometric series formula:
E = 1 / (1 - (1-p) ^2 * p)
So, the expected number of flips required to get two tails in a row with a biased coin with probability p of heads is given by the above formula.
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Use the formula V=s^3 to find the volume of a cube with the sides of length s= 2 1/4 inches
Answer:
6.375 cubic inches
Step-by-step explanation:
To find the volume of a cube using the formula V = s^3, where s represents the length of one side, we simply need to raise s to the power of 3.
Given that the length of one side, s, is 2 1/4 inches, we need to first convert the fractional part to decimal form:
[tex]\sf:\implies{2 1/4 inches = 2 + 1/4 inches}[/tex]
[tex]\sf:\implies{= 2.25 inches}[/tex]
Now, we can use this value in the formula:
[tex]\sf:\implies{V = s^3 = 2.25^3}[/tex]
To raise a number to the power of 3, we simply multiply the number by itself three times:
V = 2.25 × 2.25 × 2.25 = 6.375 cubic inches
Therefore, the volume of the cube with sides of length 2 1/4 inches is 6.375 cubic inches.
19. Describe the graph of a proportional relationship.
The graph of a proportional relationship can be described as a graph that always starts at point zero and is always a straight line graph.
What is a straight line graph?A straight line graph is defined as the type of graph that is also called a linear graph which shows a relationship between two or more quantities that uses a graphical form of representation.
There are some characteristics that shows that a graph is of proportional relationship which include the following:
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What is a in this question
The value of the segment a for the similar triangles is equal to 6.
How to calculate for a for the similar trianglesThe triangles MNO and YXO are similar, this implies that the length OX of the smaller triangle is similar to the length ON of the larger triangle
and the length OY of the smaller triangle is similar to the length OM of the larger triangle
so;
a/(a + 18) = 4/(4 + 12)
16a = 4(a + 18) {cross multiplication}
16a = 4a + 72
16a - 4a = 72 {collect like terms}
12a = 72
a = 72/12 {divide through by 12}
a = 6.
Therefore, the value of the segment a for the similar triangles is equal to 6.
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Please help me answer this :)
extra points
The required complete table for the given function f(x) = 2x - 1 is given as,
x = 1 0 -1 2
f(x) = 1 -1 -3 3
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Given function,
f(x) = 2x - 1
To complete the table,
Put x = 1
f(1) = 2(1) - 1
f(1) = 1
Similarly
f(0) = -1
f(-1) = -3
f(2) = 3
Thus, the required complete table for the given function f(x) = 2x - 1 is given as,
x = 1 0 -1 2
f(x) = 1 -1 -3 3
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