The Pythagorean Theorem holds true for both triangles, then the triangles are not only similar, but also congruent.
Triangle xyz has sides of length x, y, and z and triangle pqr has sides of length p, q, and r.
To determine if triangle xyz is similar to triangle pqr, we must calculate the ratios of corresponding sides. This is done using the formula:
Ratio of sides = (Side length x) / (Side length y)
We can calculate the ratios for each side of the triangles and compare them. If the ratios are equal for all sides, then the triangles are similar. For example, if the ratio of side x to side y in triangle xyz is equal to the ratio of side p to side q in triangle pqr, then the triangles are similar. If the ratios are not equal for all sides, then the triangles are not similar.
We can use the Pythagorean Theorem to determine if the triangles are not only similar, but also congruent. The Pythagorean Theorem states that a2 + b2 = c2, where c is the longest side and a and b are the other two sides. If the Pythagorean Theorem holds true for both triangles, then the triangles are not only similar, but also congruent.
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of course, quadratic equations don't always come with the coefficients labeled , , and . for example, assuming the solutions are real and , the larger solution of -bx^2 c^2x a^3
The equation -bx2 + c2x + a3 has a larger solution of x = (-c + sqrt(c2 - 4ab))/2a.
We must first move the constants to the right side of the equation in order to find the solution to the equation
-bx2 + c2x + a3 = 0.
As a result, we have the equation -bx2 + c2x = -a3. The result is x2 - (c2/b)x = -a3/b after dividing both sides by -b. The quadratic formula can be used to resolve this quadratic equation. x = (-c + sqrt(c2 - 4ab))/2a is the equation's more complex solution. We enter the coefficient values into the quadratic formula to verify this. The broader solution is
x = (-4 + sqrt(4 - 24))/4 = (-4 + sqrt(-20))/4 = (-4 + 25)/4 = 0.55 - 1,
for instance, if a = 2, b = 3, and c = 4. This demonstrates that the comprehensive answer.
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A boat travels 10 miles upstream in 2 hours. Going downstream, it can travel 18 miles in the same amount of time. Find the speed of the current and the speed of the boat in still water.
The speed of the current is 7 miles per hour,
and the speed of the boat in still water is 2 miles per hour.
What is speed?The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined.
Given A boat travels 10 miles upstream in 2 hours. Going downstream, it can travel 18 miles in the same amount of time.
let the speed of the boat and current be x and y,
for downstream,
x + y = D₁/t₁
D₁ = distance traveled in downstream = 18 miles
t₁ = time taken = 2 hours
x + y = 18/2
x + y = 9 .........(1)
for upstream,
x - y = D₂/t₂
D₂ = distance traveled in upstream = 10 miles
t₂ = t₁ = time taken = 2 hours
x - y = 10/2
x - y = 5 .......(2)
adding both equations
x + y + x - y = 9 + 5
2x = 14
x = 7 miles per hour
and x + y = 9
7 + y = 9
y = 9 - 7
y = 2 miles per hour
speed of the boat is 7 miles per hour and the speed of the current is 2 miles per hour.
Hence boat's speed is 7 miles per hour and the current speed is 2 miles per hour.
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An insurance company crashed 4 cars in succession at 5 miles per hour . The cost of the repair for each of the four crashes was $427, $451, $412, $212 compute the range ,sample variance and sample standard deviation cost of repair
The range is $______
PLEASE HELP
Determine whether the statement makes sense or does not make sense, and explain your reasoning.
By writing the imaginary number 14, I can immediately see that 14 is the constant and i is the variable.
VIEW IMAGE
The statement does not makes a sense because i is an imaginary unit and has fixed value √-1.
What is meant by value ?
Market price: The monetary value of anything.A just compensation in the form of products, services, or money for the swapped item.When you appreciate something, you view it as significant and valuable. As an illustration, if you value someone's viewpoint, you might seek their counsel before making a significant choice.Value is concerned with how much something is worth, whether in monetary terms or in terms of significance.The things that someone values are known as their values. In other terms, values are what a person or a group of people see as "important." Examples include valor, integrity, freedom, and creativity, among others.To learn more about value refer to
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What is the slope of the line through the points (5, −5) and (6, 0) ?
Answer:
5
Step-by-step explanation:
the slope is Δy/Δx
0-(-5) =5
6-5 =1
slope is 5
5. The amount of time, t, to finish a race and
the number of laps, I, around a track
For the given condition number of laps "l" is the independent variable.
What are Variables?A symbol (often a letter) is used in mathematics to represent an unknowable numerical value in an equation or algebraic statement. A variable can be defined as a quantity that is changeable and not fixed. Variables are crucial since they make up a significant portion of algebra.
Given The amount of time, t, to finish a race and the number of laps, I,
there are two types of variables,
dependent and independent variables,
In an algebraic equation, an independent variable is one whose values are not impacted by changes. When there are two variables in an algebraic equation, x and y, and each value of x depends on every other value of y, x is an independent variable, and y is a dependent variable.
for the given condition,
the time taken to finish the race directly varies with the number of laps,
so time is dependent on the number of laps and a number of laps "l" is the independent variable.
Hence the independent variable is the number of laps, "l".
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The complete question is,
The amount of time, t, to finish a race and the number of laps, l, around a track. What is the independent variable?
find the rang of te function for the given domain
The range of the f(x) is {- 4, 0, 4, 8, 12}
Range of the function:A collection of numbers that represent every possible value of x is said to be the function's domain. The set of numbers that a function can produce is known as its range.
To find the range of a function substitute the domine values into the given function f(x).
Here we have
Give domain of f(x) = 4x + 4; { -2, -1, 0, 1, 2}
The range of the f(x) can be calculated as follows
Take x = -2 => f(x) = 4(-2) + 4 = -8 + 4 = - 4
Take x = -1 => f(x) = 4(-1) + 4 = - 4 + 4 = 0
Take x = 0 => f(x) = 4(0) + 4 = 0 + 4 = 4
Take x = 1 => f(x) = 4(1) + 4 = 4 + 4 = 8
Take x = 2 => f(x) = 4(2) + 4 = 8 + 4 = 12
Therefore,
The range of the f(x) is {- 4, 0, 4, 8, 12}
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Rachel's health-related budget is as follows: The percentage budgeted for health Insurance is four times the percentage for health club dues. The percentage budgeted for prescriptions is equal to one-fourth the percentage budgeted for health insurance. The percentage budgeted for doctor visits is twice the percentage budgeted for prescriptions. a. What is the percentage for health insurance? 12.5% b.What are the percentages budgeted for all categories?
The percentages budgeted for all categories is 14.06%
What is the percentage for health insurance?A total of $900 seems to be spent on various health-related expenses:
medication costs, health club dues, and health insurance
seeing a doctor
If we go back in time, we can observe that the rate of doctor visits is double that of prescriptions, which is half that of health insurance,
which is 1/4 times that of health club dues.
As a result, if we consider x to be health club dues, health insurance is included.
4x medical visits, medicines, and health club dues 2x \s
sums to $900 = 8
The amount set up for health insurance is thus $112.5.
112 .5 * 12.5% = 14.06%
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Which method(s) of distributing supplies is best suited for specific items and quantities?
Direct delivery is coordinating with a specific location such as a shelter, feeding site or hospital for the delivery of specific items and quantities
What is distributing supplies?Distributing can be defined as the means of spread the product throughout the market place such that a large number of people can buy it.
There are five types of Distribution such as:
Direct distribution. This first system comprises directly performing merchandise distribution activities.Indirect distribution. A third-party-involved indirect distribution system is the second type.Intensive distribution.Exclusive distribution.Selective.Distributing channels are important to businesses as they allow for the smooth delivery of goods.
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find (f+g) and (f-g)(x) for f(x)=10x^2+8 and g(x)=2-5x
The requied solution are (f+g)(x) = 10x² + 10 - 5x and (f-g)(x) = 10x² + 6 + 5x.
What is the function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The functions are given in the question, as follows:
f(x) = 10x² + 8 and g(x) = 2 - 5x
To find (f+g)(x) we add f(x) and g(x) term by term.
(f+g)(x) = f(x) + g(x)
Substitute the values of given functions, and we get
(f+g)(x) = 10x² + 8 + (2 - 5x)
(f+g)(x) = 10x² + 10 - 5x
To find (f-g)(x) we subtract g(x) from f(x) term by term.
(f-g)(x) = f(x) + g(x)
(f-g)(x) = 10x² + 8 - (2 - 5x)
(f-g)(x) = 10x² + 6 + 5x
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Using Tiles to Multiply Two Binomials
Multiply: (x + 3)(x – 4)
The middle term in the simplified product for (x + 3)(x – 4) will be B. -x.
How to calculate the binomial?A polynomial with only terms is a binomial. For instance, the binomial x + 2 is composed of the terms x and 2.
Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is also referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form.
The product of (x + 3)(x – 4) will be:
= x² - 4x + 3x - 12
= x² - x - 12
In this case, the middle term in the simplified product is -x.
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What is the area of a square with a side length of x - 8?
The area of the square is given by:
A = x^2 - 16x + 64
What is the area of the square?Remember that the area of a square of side length S is given by the formula:
A = S^2
Here we know that the side length is x - 8, then we can just replace that on the formula above to get:
A = (x - 8)^2
Now we can expand that:
A = (x - 8)^2 = (x - 8)*(x - 8)
A = x^2 - 16x + 64
That is the area.
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For an experiment, Kelly poured equal amounts of distilled water into each of 30 beakers. She used a total of 4.2 liters of distilled water. How many liters did she pour into each beaker?
The required amount of water in each beaker would be 0.14 liters.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Kelly poured equal amounts of distilled water into each of the 30 beakers. She used a total of 4.2 liters of distilled water.
Amount of liters she put in a beaker,
= 4.2 / 30
= 0 .14 liters per beaker
Thus, the required amount of water in each beaker would be 0.14 liters.
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cara is ordering mushrooms for her restaurant. the graph shows the cost, y, of ordering x pounds of mushrooms what is the equation of the line what is the cost of ordering 6 pounds of mushrooms? iready quiz derive linear equations
Answer: Based on the information provided, it appears that the graph represents a linear equation, which is a straight line. The equation of a straight line can be represented in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the equation of the line, we need two points on the line. We can use the points (x1, y1) and (x2, y2) to calculate the slope of the line, m, using the formula:
m = (y2 - y1) / (x2 - x1)
Without knowing the coordinates of the points on the graph it is not possible to give the equation of the line.
To find the cost of ordering 6 pounds of mushrooms, we would substitute 6 for x in the equation of the line and solve for y.
y = mx + b
y = m(6) + b
Without the equation of the line, it's not possible to find the cost of ordering 6 pounds of mushrooms.
Step-by-step explanation:
A cause-and-effect relationship between two variables can best be determined from which of the following? When the two variables have a correlation. An observational study where the observational units are chosen randomly. A survey conducted using a simple random sample of individuals. A survey conducted using a stratified random sample of individuals. A controlled experiment where the observational units are assigned randomly to treatments.
The answer is A cause- and- effect relationship between two variables can best be determined When the two variables are identified.
Because the cause and effect relationship is chancing when the variables are identified or there exists a direct relationship between the variable. i.e. when the variables are identified or have a retrogression between the variables.The use of a controlled study is the most effective way of establishing reason between variables. In a controlled study, the sample or population is resolve in two, with both groups being similar in nearly every way.
There are three criteria that must be met to establish a cause- effect relationship. The cause must do before the effect. Whenever the cause occurs, the effect must also do. There mustn't be another factor that can explain the relationship between the cause and effect.
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Classify the variables in the data if it’s (qualitative, nominal, ordinal, quantitative, discrete, or continuous etc)
The sample may or may not be representative depending on the sampling method that was used. If the sample was randomly selected from the population, it may be representative.
Classify the variables in the data if it’s?However, if the sample was not randomly chosen, then it may not be representative and may have bias.Gender: Nominal
Age: Ordinal
Number of Family Members: Quantitative, Discrete
Income: Quantitative, Continuous
Education Level: Ordinal
This sample may not be representative of the population as a whole, as it is a small sample size and may not accurately reflect the population.Additionally, the sample is not randomly selected and some groups may be over or underrepresented.Moreover, the sample is not stratified and the data may not be equally distributed across all categories.Therefore, this sample may not be representative and could lead to biased results.To learn more about data classification refer to:
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1. Last Monday Micah bought 5 % pounds of plant food. He used 1 7/8 pounds
for his tomato plants and 1 1/2 pounds for his pepper plants.
a. How many pounds of plant food did he have left? Write one or more
equations to show how you reached your answer.
5 % pounds - (1 7/8 pounds + 1 1/2 pounds) = 2 5/8 pounds
What is algebra?The theory used in this question is algebra. Algebra is the branch of mathematics that studies the rules of operations and relations and the constructions and concepts arising from them.
In this question, algebra was used to solve for the number of pounds of plant food that Micah had left after using some for his tomato and pepper plants.
Step 1: Calculate the total amount of plant food that Micah bought: 5 % pounds
Step 2: Calculate the amount of plant food that Micah used for his tomato plants: 1 7/8 pounds
Step 3: Calculate the amount of plant food that Micah used for his pepper plants: 1 1/2 pounds
Step 4: Calculate the amount of plant food that Micah had left by subtracting the total amount of plant food used from the total amount of plant food bought: 5 % pounds - (1 7/8 pounds + 1 1/2 pounds) = 2 5/8 pounds
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write in the form a b, where a and b are positive integers:
The expression of the fraction 256^-3/4 in the form of a / b is equal to 1 / 64 where highest common factor between 1 and 64 is 1.
Expression of the fraction 256^-3/4 in the form a /b .
Where 'a' and 'b' are positive integers .
'a' and 'b' have no common factor than 1.
256^-3/4
= ( 1 / 256^3/4 )
= 1 / 2^ (8 × 3/4 )
= 1 / 2 ^ ( 2 × 3 )
= 1 / 2^6
= 1 / 2⁶
= 1 / 64 in the form of ( a / b )
Greatest common factor between 1 and 64 is equal to 1.
1 and 64 are positive integers.
Therefore, the expression of 256^-3/4 in the a/b fraction form is equal to 1/64.
The given question is incomplete, I answer the question in general according to my knowledge:
Express 256^-3/4 as a fraction. Write the fraction in the form a/b, where a and b are positive integers with no common factor greater than 1 .
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Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother times her age?
Answer: 41 years ago, when Sally was 13 and her mother was 39.
Answer: 41 years
Step-by-step explanation:
I reckon the question is asking when her mother was 3 times her age.
S = 54
M = 80
54 - 41 = 13
80 - 41 = 39
39/13 = 3
If the x-intercepts of a function are 2 and 5, then f(2) = _______. and f(5) = ________. The x-intercepts, 2 and 5, are called the _______ of the function.
If the x-intercepts of a function are 2 and 5, then f(2) = ____0___. and f(5) = ____0____. The x-intercepts, 2 and 5, are called the _zeros_ of the function.
What are the x-intercepts of the function?
The x-intercepts of a function y = f(x) are the values of x such that the graph of the function intercepts the x-axis, that means that are the values of x such that f(x)= 0
Then if 2 and 5 are x-intercepts of the function, then:
f(2) = 0
f(5) =0
The x-intercepts are allso called the zeros of the function.
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Julia had a bag filled with gumballs. There were 1 watermelon, 2 lemon-lime, and 3 grape gumballs. What is the correct sample space for the gumballs in her bag?
Sample space = watermelon, lemon-lime, lemon-lime, grape, grape, grape
Sample space = lemon-lime, watermelon, grape
Sample space = 1, 2, 3, 4, 5, 6
Sample space = 1, 2, 3
For the gumballs in Julia's bag
Sample space = lemon-lime, watermelon, grape.
The correct option is B.
What is sample space?A sample space is a collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.
Given,
Number of lemon limes gumballs in the bag = 2 lemon-lime gumballs
Number of watermelon gumball in the bag = 1 watermelon gumball
Number of grape gumballs in the bag = 3 grape gumball
Sample space is the set of all the possible outcomes the experiment
Here, Julia has 1 watermelon, 2 lemon-lime, and 3 grape gumballs
Sample space = lemon-lime, watermelon, grape
Hence { lemon-lime, watermelon, grape} is the sample space for gumballs in Julia's bag.
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The store is selling lemons at $0.52 each. Each lemon yields about 2 tablespoons of juice. How much will it cost to buy enough lemons to make four 9-inch lemon pies, each requiring half a cup of lemon juice?
Let $x$ be a real number selected uniformly at random between 100 and 200. If $\lfloor {\sqrt{x}} \rfloor = 12$, find the probability that $\lfloor {\sqrt{100x}} \rfloor = 120$. ($\lfloor {v} \rfloor$ means the greatest integer less than or equal to $v$.)
$\text{(A)} \ \frac{2}{25} \qquad \text{(B)} \ \frac{241}{2500} \qquad \text{(C)} \ \frac{1}{10} \qquad \text{(D)} \ \frac{96}{625} \qquad \text{(E)} \ 1$
The probability of successful region is =241/2500 Option b is correct.
Since √x=12, 12 ≤√x<13 and thus 144 ≤ x < 169.
The successful region is when 120 ≤ 10√x < 121 in which case 12 ≤√x< 12.1
Thus, the successful region is when
144 ≤ x < 146.41
The successful region consists of a 2.41 long segment, while the total possibilities region is 25 wide. Thus, the probability is
=2.41/25
=241/2500 (B)
In mathematics, a real number is a quantity that can be expressed as an infinite decimal expansion. In contrast to the natural numbers 1, 2, 3,..., which are derived from counting, real numbers are used in measurements of continuously varying quantities such as size and time.
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16 multiplied by what gives you 1600?
Answer:
The answer is 100. One way to find it out is 1600/16, and then you get 100.
A party hat is in the shape of a cone with dimensions shown.
Find the height of the hat. Round to the nearest tenth.
4.3 in.
10 in.
The height of the hat is 9.0 inches.
How to find the height of a cone?A party hat is in the shape of a cone with dimensions shown . Therefore, the height of the cone can be found as follows:
The radius of the cone is 4.3 inches and the slanted height of the cone is 10 inches.
Therefore, Pythagoras's theorem can be used to find the height of the cone. The radius and the slanted height of the cone forms a right angle triangle.
Therefore,
10² - 4.3² = h²
h² = 100 - 18.49
h² = 81.51
square both sides
h = √81.51
h = 9.02828887442
h = 9.0 inches
Therefore,
height of the hat = 9.0 inches
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I need help please!!
Answer:
Step-by-step explanation:
refreh it
what is the answer?????
Answer unzipped,new bases, sealed
Step-by-step explanation:
HELPPP! Find the surface area of the triangular prism
here we are given a triangular prism and we are interested in finding its surface area .
The given prism comprises of 2 triangular faces and 3 rectangular faces . We can separately find the area and then add them up to find the resultant surface area.
Finding area of triangle:-
There are 2 triangles so the total area would be ,
Area = 2(ar. of one ∆)
Area = 2 ( 1/2 * base * height)
Area = 2 ( 1/2 * 16m * 5m )
Area = 80m²
Finding area of rectangle:-
Area = 3 ( length* breadth)
Area= 3 ( 17m * 10m)
Area = 3 * 170m²
Area = 510m²
Total area,
Net Surface area= area of rectangle+ area of triangle= (80+510)m² = 590m² [ required answer]
And we are done!
which of the following options correctly describe scientific notation? select all that apply. multiple select question. one digit is present to the right of the decimal point in all cases. the exponent can be a positive or negative integer. the number must be a positive integer. one digit is present to the left of the decimal point in all cases.
"At least one digit is present to the left of the decimal point in all cases" and "the exponent can be a positive or negative integer" are the correct option for the given question.
Decimal numbers, also known as base-10 numbers. They use a system of digits from 0 to 9 and a decimal point to represent values. The decimal point separates the integer part of the number from the fractional part.
For example, in the decimal number 56.36, 56 is the integer part and 36 is the fractional part.
Hence, at least one digit is present to the left of the decimal point in all cases.
In scientific notation, the exponent is used to represent very large or very small numbers. The number is written in the form of a x [tex]10^n[/tex] where 'a' is a decimal number between 1 and 10 (inclusive) and 'n' is an integer (positive or negative) exponent.
Say, for example, 0.00006 can be written as 6 x [tex]10^{-5}[/tex] where 6 is the coefficient and -5 is the exponent.
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Evaluate 2( L+ 8Z) + L, when Z = 3 and L = 4.2
Answer:
Okay so z is 3.
We are going to put taht into our equation
2(L + 8(3)) + L
2(L + 24) + L
Now we do the 2
2L + 48 + L
Okay now L is 4.2
SO
2(4.2) + 48 + (4.2)
8.4 + 48 + 4.2 = 60.6
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2(l + 8z) + l}\\\mathsf{= 2(4.2 + 2(8)(3)) + 4.2}\\\mathsf{= 2(4.2) + 2(8)(3) + 4.2}\\\mathsf{= 8.4 + 16(3) +4.2}\\\mathsf{= \mathsf{8.4 + 48 + 4.2}}\\\mathsf{= 56.4 + 4.2}\\\mathsf{= 60.6}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{\mathsf{60.6}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]