Answer:
We can use the formula for the area of a triangle to solve for the height of the isosceles triangle, which will then allow us to find the lengths of the other two sides.
Let h be the height of the isosceles triangle, and let s be the length of each of the two equal sides. Then the area of the triangle is given by:
A = (1/2)bh = (1/2)(10m)(h) = 5h
We also know that the area of the triangle is 60 square meters, so we can set these two expressions equal to each other and solve for h:
5h = 60
h = 12
Now that we know the height of the triangle is 12 meters, we can use the Pythagorean theorem to find the length of each of the other two sides:
s^2 = h^2 + (1/2b)^2
s^2 = 12^2 + (5^2)
s^2 = 169
s = sqrt(169)
s = 13
Therefore, the lengths of the other two sides of the isosceles triangle are both 13 meters.
Which ordered pairs are in a proportional relationship with (0. 2, 0. 3)?
A
(1. 2, 2. 3)
B
(2. 7. 4. 3)
C
(3. 2, 4. 8)
D
(3. 5, 5. 3)
E
(5. 2, 7. 8)
A proportional connection exists when two values may be expressed as y = kx, where k is a constant. To discover which ordered pairings have a proportionate connection with (0.2, 0.3).
We must find a value of k for each pair that makes this equation true. Let us begin with option A: (1.2, 2.3). If we wish to represent this combination as y = kx, we must discover the value of k that results in 2.3 = k. (1.2). When we solve for k, we get: k = 2.3 / 1.2 ≈ 1.92 As a result, (1.2, 2.3) does not have a proportionate connection with (0.2, 0.3) since the value of k is different for both couples. This procedure can be repeated for each of the others. options. Option B: (2.7, 4.3) yields: k = 4.3 / 2.7 ≈ 1.59 Option C: (3.2, 4.8) yields: k = 4.8 / 3.2 = 1.5 Option D: (3.5, 5.3) yields: k = 5.3 / 3.5 ≈ 1.51 Option E: (5.2, 7.8) yields: k = 7.8 / 5.2 = 1.5 As a result, alternatives C and E are proportional to (0.2, 0.3) since they can be represented in the form y = kx with the same k value. k = 1.5 in both situations.
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Yuri's dad needs to fertilize the grass in the yard. The back yard measures 55 feet by 30 feet, while the front yard is a square with a length of 42 feet on each side
Answer: To find the total area of the grass that Yuri's dad needs to fertilize, we need to calculate the area of the back yard and the area of the front yard, and then add them together.
Area of the back yard:
The back yard measures 55 feet by 30 feet, so the area is:
55 feet x 30 feet = 1650 square feet
Area of the front yard:
The front yard is a square with a length of 42 feet on each side, so the area is:
42 feet x 42 feet = 1764 square feet
Total area:
To find the total area, we add the area of the back yard and the area of the front yard:
1650 square feet + 1764 square feet = 3414 square feet
Therefore, Yuri's dad needs to fertilize a total area of 3414 square feet.
Step-by-step explanation:
help, please !!
Abiana wants to get to the opposite corner of a rectangular park that is $3/4$ miles wide and $1$ mile long.
If she rides her scooter, it only takes her $8$ minutes to travel $1$ mile, but she has to go around the park. If she walks, it takes her $20$ minutes to travel $1$ mile, but she can cut directly across the grass.
Which mode of transportation is faster, assuming she travels at a constant speed?
Answer: Scootering is faster
Step-by-step explanation: If it takes 20 minutes to go around walking going through the middle would technically split the time in half and 20 divided by 2 is 10 which is more than 8 therefore scootering is faster.
need help with part a part b part c quick
Answer:
1. C.
2. D.
3. D.
Step-by-step explanation:
A. Round both dimensions the nearest whole number. 8 1/3 rounds to 8, 6 3/4 rounds to 7. Multiply these two and your estimate for the tarp area is 56 sq yds. Option C.
B. Convert both mixed numbers to improper fractions. Multiply whole number by divisor and add the dividend. (8*3) + 1 = 25. First number is 25/3.(6*4) + 3 = 27. Second number is 27/4. Multiply these two numbers fractions and get 225/4. Convert to a mixed number, 56 1/4. Option D.
C. This answer is reasonable. 56 1/4 is pretty close to our estimate of 56 sq yds. Or just choose the option that corresponds to your estimate from part A. Option D.
how long will it take for the battery to run down one sixth of its capacity of 3600 Milli Ampere hours
Answer:
6 hours
Step-by-step explanation:
[tex]\frac{1}{6}[/tex] of Total battery life = [tex]\frac{1}{6} * 3600 = 600[/tex]milliamps
Assuming the battery takes 100 Milliamps per hour,
Time = Battery Capacity / Current hours
Time = 600 / 100 Mah = 6H
What are the domain and range of g of x equals the square root of the quantity x plus 4?
a. d: [4, [infinity]) and r: [0, [infinity])
b. d: (–4, [infinity]) and r: (–[infinity], 0)
c. d: [–4, [infinity]) and r: [0, [infinity])
d. d: (4, [infinity]) and r: (–[infinity], 0)
The domain and range of g of x equals the square root of the quantity x plus 4, g(x) = √x + 4, are equal to d: [–4, [infinity]) and r: [0, [infinity]). Thus, the right choice of answer is option (c).
We have a function g(x) and defined as square root of the quantity x plus 4, i.e.,
g(x) = √x + 4
We have to determine the domain and range of function g(x).
The domain of function is all input values of x that make the expression defined. The range is the set of all output values that valid g(x) values. A square root limits the function because we can't have negative numbers under the square root (they become imaginary numbers). Let y = g(x) = √x +4
the square root '√ 'sign must be implies ≥ 0, therefore, x + 4 ≥ 0
Subtracting the 4 from both sides
=> x + 4 -4 ≥ 0 - 4
=> x ≥ -4
The domain is x∈ [-4,+∞)
When x = -4, g(x) = 0
Therefore, The range is y∈ [0, 00)
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PLS HELP ME LESSON 12.03: PLOT TWISTS
1. Use the data set provided to create a line plot. i really need help
Hence, in answering the stated questiοn, we may say that If yοu're unitary methοd satisfied with yοur line plοt, save it and distribute it as needed.
What is unitary methοd?The unit technique is a prοblem-sοlving apprοach that invοlves finding the value οf a single unit and then multiplying that value by the needed value. Tο put it simply, the unit technique is used tο extract a single unit value frοm a given multiple. 40 pens, fοr example, wοuld cοst 400 rupees, οr the cοst οf οne pen. The prοcess fοr achieving this may be standardized. A single cοuntry. anything that has an identity element. Its adjοint and reciprοcal are equal in mathematics and algebra.
a general methοd fοr prοducing a line plοt:
First, cοllect yοur data. Stοck prices, temperature readings, and survey results are all examples οf this. The crucial thing is that yοu have a set οf values tο plοt οn a graph.
Enter yοur x and y values intο the plοt. The exact prοcedure depends οn the graphing prοgrammed yοu're using, but yοu shοuld be able tο enter yοur values intο a data table οr spreadsheet.
Make any changes yοu want tο yοur plοt. Adding labels tο the x and y axes, tweaking the plοt's scale, changing the line cοlοur οr thickness, οr adding a title are all pοssibilities.
If yοu're satisfied with yοur line plοt, save it and distribute it as needed.
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Complete question:
Which fractions have 20 as the LCD (lowest common denominator)?
The lowest common denominator, 20, can be used to represent any fraction that can be stated as a ratio of integers with factors of 2 and 5 in the denominator. eg. 1/4, 1/2, 2/5 and 7/10
To find all the fractions that have 20 as the lowest common denominator, we need to identify all the prime factors of 20, which are 2, 2, and 5.
Then, we can express each fraction with these prime factors in the denominator, by multiplying the numerator and denominator by the missing factors. For example, for the fraction 1/4, we need to multiply both the numerator and denominator by 5 to get:
1/4 = 5/20
Similarly, for the fraction 3/5, we need to multiply both the numerator and denominator by 2 to get:
3/5 = 6/10 = 12/20
By doing this for all fractions, we can express them with the same denominator of 20. Here are some examples:
1/4 = 5/20
3/5 = 12/20
1/2 = 10/20
2/5 = 8/20
7/10 = 14/20
Therefore, any fraction that can be expressed as a ratio of integers with factors of 2 and 5 in the denominator can be written with 20 as the lowest common denominator.
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Complete Question
Write any two fractions which have 20 as the LCD (lowest common denominator)?
If f(x) = x3, what is the equation of the graphed function?
A nonlinear function on a coordinate plane passes through (minus 4.5, minus 5), (minus 3, minus 2), (minus 2, minus 1), and (minus 1, 6)
A. y = f(x − 3) − 2
B. y = f(x + 3) – 2
C. y = f(x + 2) − 3
D. y = f(x − 2) + 3
The equation of the graphed function, which is composed of translations to f(x) = x³, is given as follows:
B. y = f(x + 3) - 2.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The turning point of f(x) = x³ is at the origin, while for the graphed function it is at point (-3,-2), hence the translations are given as follows:
3 units left -> x = x + 3.2 units down -> y = y - 2.Hence the graphed function is defined as follows:
B. y = f(x + 3) - 2.
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One year, the population of a city was 252,000. Several years later it was 204,120. Find the percent decrease
The percentage decrease in the population after on year is found to be 19%.
The percentage decrease can be found by using the formula,
Percentage decrease = change in population/initial population x 100.
Now change in population in one year is given as final population - initial population.
Putting values, change in population = 252000 - 204120
Change in population = 47880
Now, putting all the value in the formula,
percentage decrease = 47880/252000 x 100
percentage decrease = 19%
So, the decrease in the population is found to be 19%.
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r of the alphabet if letters of the alphabet are selected at random, find the probability of getting at least letter . letters can be used more than once. enter your answer as a fraction or a decimal rounded to decimal places.
The probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1/1.
The reason for this is that if any letter of the alphabet is selected at random, the probability of getting an "r" is 1/26, or 0.0385. Since letters can be used more than once, this probability remains the same regardless of how many letters are selected. Thus, the probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1.
In summary, the probability of getting at least one "r" of the alphabet if letters of the alphabet are selected at random is 1. This is because, when a letter is selected at random, each letter has an equal chance of being chosen (1/26), and since the probability of selecting an "r" remains the same regardless of how many letters are selected, the probability of getting at least one "r" is also 1.
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Which describes a possible dependent variable for the given independent variable?
The number of hours you study for a test
1. Your test score
2. The number of students in your study group
3. How many students are taking the test T
4.T he time the test starts
Answer:
1
explanation in head
Help asap
Given g(x) = -x +5
h(x) = 3x² - 2
Find g(h(x))
A -3x³ +9x +3
B 3x² + 30x + 73
C 3x² 30x + 73
D- 3x² +7
After answering the provided question, we can conclude that Therefore, the answer of quadratic equation is D) [tex]$-3x^{2}+7$[/tex]
What is quadratic equation?A quadratic equation is x ax² + bx + c = 0, so it's a single variable quadratic polynomial. a 0. Because this regression is of second order, the Fundamental Principle of Algebra helps to ensure that it includes at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic calculation.
This means there is at least yet another word that must be squared. The formula "ax² + bx + c = 0" is a common solution for quadratic equations. where a, b, and c are arithmetical coefficients or constants. where the parameter "X" is unidentified.
To find g(h(x))
[tex]$\begin{array}{l}{{h(x)=3x^{2}-2}}\\ {{g(h(x))=g(3x^{2}-2)}}\\ {{g(3xA^2))=-3x^2-2}+5}}\\ {{g(h(x))=-3x^{2}+7}}\end{array}$[/tex]
Therefore, the answer is D) [tex]$-3x^{2}+7$[/tex]
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Create tables to solve the problems, and then check your answers with the word problems.
During a basketball game, Jeremy scored triple the number of points as Donovan. Kolby scored double the number of points as Donovan.
If the three boys scored 36 points, how many points did each boy score?
Donovan scored 6 points, Jeremy scored 18 points, and Kolby scored 12 points.
Let's denote the number of points scored by Donovan as "D".
According to the problem, Jeremy scored triple the number of points as Donovan, so he scored 3D points.
Similarly, Kolby scored double the number of points as Donovan, so he scored 2D points.
We also know that the total number of points scored by all three boys is 36. So we can write an equation:
D + 3D + 2D = 36
Simplifying this equation, we get:
6D = 36
Dividing both sides by 6, we get:
D = 6
So Donovan scored 6 points.
Using the values we found for Donovan's score, we can find the scores of Jeremy and Kolby:
Jeremy scored 3D = 3(6) = 18 points
Kolby scored 2D = 2(6) = 12 points
Therefore, Donovan scored 6 points, Jeremy scored 18 points, and Kolby scored 12 points.
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A, B and C lie on a straight line. Given that angle y = 95° and angle z = 330°, work out x .
If A, B, and C lie on a straight line, the sum of angles y, x, and z will be 180 degrees:
y + x + z = 180
Substituting the values given in the problem:
95 + x + 330 = 180
Simplifying:
425 + x = 180
Subtracting 425 from both sides:
x = -245
Therefore, x is -245 degrees.
However, since x represents an angle on a straight line, we can add 180 degrees to get an equivalent angle:
x + 180 = -245 + 180 = -65
Therefore, x is -65 degrees.
Imagine a rectangle whose length is (0.5x+13) inches long and whose width is (2x+8) inches wide.
Part1) Write a polynomial for the perimeter of the rectangle
Part2) Write a polynomial for the area of the rectangle
The perimeter of the rectangle is (x² + 30x + 104) in² while The area of the rectangle is (x² + 30x + 104) in²
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The rectangle have a length of (0.5x + 13) and width of (2x + 8)
1) Perimeter = 2(length + width)
Perimeter = 2(0.5x + 13 + 2x + 8) = 2(2.5x + 21) = (5x + 42) inches
The perimeter of the rectangle is (x² + 30x + 104) in²
2) Area = length * width
Area = (0.5x + 13) * (2x + 8) = x² + 4x + 26x + 104
Area = (x² + 30x + 104) in²
The area of the rectangle is (x² + 30x + 104) in²
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(1 point) A tank contains 60 kg of salt and 2000 L of water. Pure water enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 4 L/min. (a) What is the amount of salt in the tank initially
The initial amount of salt in the tank is 60 kg, calculated using the formula M = ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank.
Initially, the tank contains 60 kg of salt and 2000 liters of water. The amount of salt in the tank can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The density of salt is 2270 kg/m3. Assuming the tank has a constant volume, the mass of the salt in the tank is 60 kg.
The amount of salt in the tank changes due to the addition of pure water and mixing of the solution. The amount of salt in the tank at any given time can be calculated using the formula M=ρV, where M is the mass of the salt, ρ is the density of the salt, and V is the volume of the tank. The rate at which the salt is added to the tank is equal to the rate at which the salt-water solution is drained from the tank.
Therefore, the rate of change of the mass of the salt in the tank is equal to 8 liters/minute of pure water entering the tank minus 4 liters/minute of salt-water solution draining from the tank. Thus, the amount of salt in the tank initially is 60 kg.
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Ray is measuring fabric for the costumes of a school play. He needs 12. 5 meters of fabric. He has 30. 5 centimeters of fabric. How many more centimeters of fabric does he need?
Answer:
1219.5 more centimeters of fabric
Step-by-step explanation:
First, we need to convert 12.5 meters to centimeters, since the given amount of fabric is in centimeters.
12.5 meters = 12.5 x 100 centimeters/meter = 1250 centimeters
Now we can find the difference between what Ray needs and what he has:
1250 centimeters - 30.5 centimeters = 1219.5 centimeters
Therefore, Ray needs 1219.5 more centimeters of fabric.
Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing a number from the multiples of 4 between 20 and 40, inclusive The sample space is _______ (Use a comma to separate answers as needed. Use ascending order.) There are _____ outcome(s) in the sample space.
The sample space is 20, 24, 28, 32, 36, 40. There are 6 outcomes in the sample space. In this case, the sample space is {20, 24, 28, 32, 36, 40}.
The sample space of the probability experiment is the set of all possible outcomes that can occur when randomly choosing a number from the multiples of 4 between 20 and 40, inclusive.
To determine the number of outcomes in the sample space, we simply count the number of elements in the set. In this case, there are 6 outcomes in the sample space.
Therefore, the sample space is {20, 24, 28, 32, 36, 40} and there are 6 outcomes in the sample space. After Randomly choosing a number from the multiples of 4 between 20 and 40, these values are found.
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x-15+2x+6
please help me with step by step explanation
Answer:
To simplify the expression x - 15 + 2x + 6, you can combine like terms. Here are the steps to do that:
Group the x terms and the constant terms separately:
(x + 2x) + (-15 + 6)
Simplify the terms inside the parentheses:
3x - 9
So the simplified expression is 3x - 9.
Therefore, x - 15 + 2x + 6 equals 3x - 9.
Answer:
3(x-3)
Step-by-step explanation:
given : x-15+2x+6
factorize using like terms : x-15+3x+6 = 3x-9
= 3x - 9
=3(x-3)
Question 1 (3 points) Saved If A and B are independent events
with P(A) = 0.4 and P(B) = 0.25, then P(A ∪ B) = Question 1
options: 0.65 0.55 0.10 Not enough information is given to answer
this quest
The value of the probability P(A ∪ B) if the events are independent events is 0.55
How to determine the value of the probabilityThe formula for the probability of the union of two events is:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Since the events A and B are independent, the probability of their intersection is simply the product of their individual probabilities:
P(A ∩ B) = P(A) × P(B)
Substituting the given values, we have:
P(A ∩ B) = 0.4 × 0.25 = 0.1
Now we can use the formula for the union:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
So, we have
P(A ∪ B) = 0.4 + 0.25 - 0.1
This gives
P(A ∪ B) = 0.55
Therefore, the probability of the union of events A and B is 0.55.
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Elavate each expression when x is 4 and y is 6
Answer:
the answer to ur question is: 36
A sequence is defined by t_1 = 1 and t_2 = 2, and t_3=(2k+1)/k^2, and t_4=(3k+1)/2k^3, and t_5=(k+1)/2k^2, and t_6=1 and t_7=2 and t_8=(2k+1)/k^2, and t_9=(3k+1)/2k^3 and t_n = [kt_(n−1)+ 1] /[k^2 t_(n−2)] for n ≥ 3, where k is a positive integer. Determine the value of t_2023 in terms of k.
[tex]t_2023[/tex] will be equal to the expression[tex]: t_2023 = [k*t_2022 + 1] / [k^2 * t_2021][/tex]. in terms of k.
The sequence given is defined by the recurrence relation: [tex]t_n[/tex] = [tex][kt_(n−1)+ 1] /[k^2 t_(n−2)] for n ≥ 3,with t_1 = 1[/tex] and [tex]t_2[/tex] = 2, and [tex]t_3=(2k+1)/k^2[/tex], and [tex]t_4=(3k+1)/2k^3[/tex], and [tex]t_5=(k+1)/2k^2[/tex], and [tex]t_6[/tex]=1 and [tex]t_7[/tex]=2 and [tex]t_8=(2k+1)/k^2, t_9=(3k+1)/2k^3[/tex]. To find the value of [tex]t_2023[/tex], we need to find the values of the previous two terms, [tex]t_2022[/tex] and [tex]t_2022[/tex] . We can do this by using the recurrence relation, starting at n = 3 and going up until n = 2022.
Therefore,[tex]t_2022 = [k*t_2021 + 1] / [k^2 * t_2020][/tex].
Similarly, [tex]t_2021 = [k*t_2020 + 1] / [k^2 * t_2019[/tex]].
We can now plug in the values of [tex]t_2021[/tex] and [tex]t_2020[/tex], which can be found by continuing to work backwards in the recurrence relation until n = 9, and then we have the initial conditions of the sequence. Once we have the values of [tex]t_2021[/tex] and [tex]t_2021[/tex] , we can substitute them into the recurrence relation for[tex]t_2023[/tex] to get the desired result. Therefore, [tex]t_2023 = [k*t_2022 + 1] / [k^2 * t_2021].[/tex]
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1. Jimmy volunteers at events at the hospital each year. He does not work for more than two events in a year. Over the past ten years, he attended exactly two events seven times, one event two times, and no events one time.
a. Define the random variable X.
b. What values dose X take on?
c. Fill in the following table ( where P(x) is the probability of x and u is the expected value). In addition, what are the expected value and standard deviation of X?
The expected value and standard deviation of x are 1.6 and 0.66, respectively.
The definition of the random variablesGiven that:
Jimmy volunteers at events at the hospital each year.
The random variable x is the number of hospital events Jimmy works at each year.
What values dose x take on?We understand that he does not work for more than two events in a year
So, x can take on the values 0, 1, or 2.
The table of probabilitiesFrom the question, we have:
Over the past ten years
He attended exactly two events seven timesOne event two timesNo events one timeSo, the table is
X P(X)
0 0.1
1 0.2
2 0.7
To find the expected value, we take the sum of the products of x and P(x)
So, we have
E(x) = 0(0.1) + 1(0.2) + 2(0.7)
E(x) = 1.6
To find the standard deviation, we need to first calculate the variance:
Var(X) = E(x^2) - [E(x)]^2
Where
E(x^2) = 0^2(0.1) + 1^2(0.2) + 2^2(0.7)
E(x^2) = 3
So, we have
Var(X) = 3 - (1.6)^2
Var(X) = 0.44
This means that
SD(x) = √0.44
SD(x) = 0.66
Hence, the standard deviation is 0.66
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Consider the function f(x)=3x-2
If f(g(x))=x and g(f(x))=x, what is g(x)?
Answer:a
Step-by-step explanation:its simple
ABCD is a parallelogram and CE stands on AD, DF stands on AB. If AD = 20 metre, CE = 8 metre, AB = 16 metre, find DF
In the parallelogram ABCD the value of DF is 13.33 metres or DF = 40/3 metres (rounded to two decimal places).
In the parallelogram ABCD, we can draw a diagonal AC that splits the parallelogram into two congruent triangles, namely, △ABC and △ADC.
Let x be the length of DF. We can use similar triangles to find x.
Notice that △BCE and △DFE are similar triangles, since they share the same angle at E and the angles at B and D are congruent due to opposite angles in a parallelogram. Therefore, we can write the following proportion:
BC/CE = DF/FE
Substituting the given values, we have:
16/8 = x/(20-x)
Simplifying this equation, we get:
2 = x/(20-x)
2(20-x) = x
40 - 2x = x
3x = 40
x = 40/3
Therefore, DF = 40/3 meters or 13.33 meters (rounded to two decimal places).
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How many numbers less than or equal to 120 are co-prime with 120? (co-prime as in they have no common factors with 120.)
Answer:
We know that 120 can be factored as 2^3 * 3 * 5, so its totient function value can be found as follows:
φ(120) = φ(2^3) * φ(3) * φ(5)
= 2^2 * 2 * 4
= 16
Therefore, there are 16 numbers less than or equal to 120 that are relatively prime to 120
Ahmet borrows $700 and is charged compound interest at 15% per year. How much will he have to pay back in total after 6 years?
Give your answer to two decimal places.
Answer:
The required amount Ahmet needs to pay after 6 years is $1619.14.
What is compound interest?
Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Amount = principal[1 + r/n]ⁿᵃ
Principal = P rate= r Time =a , n = compounding frequency
Here,
From the given data,
P = 700, r = 15% and t = 6 (n =1)
Now,
Amount = principal[1 + r/n]ⁿᵃ
Amount = 700(1 + 0.15)⁶
Amount = $1619.14
Thus, the required amount Ahmet needs to pay after 6 years is $1619.14.
Step-by-step explanation:
find the length of side 3
answers
5x^3-4x^2+3x-4
5x^3-4x+3x-12
5x^3-4x^2+3x+4
5x^3=4x^2+3x+12
Answer:
Side 3 is: 5x^3 - 4x^2 +3x - 12
Note that the answer options do not include this result, but it is likely that the second option is simply missing the square term for the -4x, and it should read -4x^2.
Step-by-step explanation:
The perimeter is the sum of all three sides. To find Side 3, subtract Sides 1 and 2 from the perimeter:
5x^3 - 2x^2 +3x - 8 - (3x^2-4x-1) - (4x-x^2+5) = Side 3
Perimeter - Side 1 - Side 2 = Side 3
5x^3 - 2x^2 +3x - 8 - 3x^2+4x+1 - 4x+x^2-5 [Remove parentheses]
5x^3 - 3x^2 +x^2 - 2x^2 +3x +4x - 4x - 8 +1 -5 [Combine like terms]
5x^3 - 4x^2 +3x - 12 [Simplify] = Side 3
A horizontal number line labeled from negative 4 to positive 1 with tick marks every one fourth unit. There is a point one tick mark to the left of negative 3. A horizontal number line labeled from negative 4 to positive 1 with tick marks every one fourth unit. There is a point one tick mark to the left of negative 3. What point is marked on the number line?
The point one tick mark to the left of negative 3 on the number line is -3.25.
Number lines are horizontal straight lines in math where the intervals between the integers are equal. A number line can be used to show all of the numbers in a sequence. At both ends, this line continues indefinitely.
Each tick mark on the number line represents one-fourth of a unit, so the distance between negative 4 and negative 3 can be divided into 4 parts, each with a length of one-fourth of a unit. Starting from negative 4, the tick marks would be labeled as -4, -3.75, -3.5, -3.25, -3, and so on. Therefore, the point one tick mark to the left of negative 3 is at -3.25 on the number line.
Learn more about Number Line:
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