We can prove that two right triangles are similar by:
Hypotenuse-Leg (HL) Theorem.
Leg-Acute (LA) Angle Theorem.
Hypotenuse-Acute (HA) Angle Theorem.
Leg-Leg (LL) Theorem.
Two triangles are congruent if they have the same three sides and exactly the same three angles. Two right triangles can be considered to be congruent, if they satisfy one of the following theorems.
Theorem 1 : Hypotenuse-Leg (HL) Theorem :
If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are congruent.
Theorem 2 : Leg-Acute (LA) Angle Theorem :
If a leg and an acute angle of one right triangle are congruent to the corresponding parts of another right triangle, then the two right triangles are congruent.
Theorem 3 : Hypotenuse-Acute (HA) Angle Theorem :
If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent.
Theorem 4 : Leg-Leg (LL) Theorem :
If the legs of one right triangle are congruent to the legs of another right triangle, then the two right triangles are congruent.
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How many terms are in the expression 4x 5?
There are 2 terms in this mathematical expression. One multiplication sign act as an operator of two numbers.
What is mathematical expression?It is a mathematical statement express the relationship between two or more terms along with mathematical symbols. Terms can be numbers, variables with or without coefficient. symbols can be addition sign, multiplication sign, division and subtraction sign, equal or inequal sign etc. Beside this we have many other operator or symbols to state the mathematical expression.
How many terms we have in the following question?In the above question, we have 2 numbers along with a symbol. We notice that 4 and 5 are two numbers multiplied here as there is a multiplication sign between them.
4 x 5 denotes an expression which state that 4 is multiplied by 5 and the result will be 20.
hence, we have 2 terms and one operator.
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What kind of sequence is 4/8 16?
It is an Arithmetic sequence
What is Arithmetic sequence?
Arithmetic sequences are collections of integers where the distance between succeeding items is consistently the same.
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is always the same. In this case, the difference between the two terms is 16 - 4/8 = 12.
So the sequence could be written as 4/8, 4/8 + 12, 4/8 + 2*12, ... and so on. Each term in the sequence is obtained by adding 12 to the previous term.
Hence, It is an Arithmetic sequence.
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How do you tell if a function grows faster than another?
f(x) g(x) = L = 0, where L is some finite number. This definition implies that if f grows faster than g, then f will eventually be much larger than g. Similarly, if f grows slower than g, then f will eventually be much smaller than g.
Now, According to the question:
f(x) g(x) = L = 0, where L is some finite number. This definition implies that if f grows faster than g, then f will eventually be much larger than g. Similarly, if f grows slower than g, then f will eventually be much smaller than g.
Steps on How to Compare the Rates of Change of Two Functions Using Limits
Step 1: Given the functions f(x) and g(x), compute the limit limx→∞f(x)/g(x).
Step 2: If the limit in Step 1 is a finite constant a≠0, then the growth rate of f(x) is a times the growth rate of g(x) at sufficiently large x. If the limit in Step 1 is ∞, then the growth rate of f(x) is greater than the growth rate of g(x). If the limit in Step 1 is 0, then the growth rate of g(x) is greater than the growth rate of f(x).
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Alex is building a fence in the shape of an equal sided hexagon the total amount of fence available to him is 15 kilometers. How long is each side of the fence in miles?
Each side is 1.55 miles in the fence.
What is fence?
A structure meant to delineate a boundary or prevent escape or intrusion. Particularly: a boundary line or immaterial barrier made of posts, wire, or boards.
Given:
Alex is building a fence in the shape of an equal sided hexagon the total amount of fence available to him is 15 kilometers.
Since, Hexagon has six sides and each side is equal.
So there is 2.5 kilometer to fence each side.
Now to convert kilometer into miles.
Since
1 kilometer = 0.621371 miles
So,
2.5 kilometers = 1.55343 miles
Hence, each side is 1.55 miles in the fence.
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Alex buys 24 apples from the supermarket. When he gets home, he finds that 6 apples are bad.
What percentage of the apples are bad? Round your answer to the nearest number.
Answer:
To find the percentage of bad apples, we need to divide the number of bad apples by the total number of apples and then multiply by 100%. In this case, there were 24 apples in total and 6 of them were bad, so the percentage of bad apples is 6/24 * 100% = 25%. Rounded to the nearest number, this is equal to 25%.
what is the answer of this?
Answer:
The answer is 5
Step-by-step explanation:
length(Hypotenuse) = 13m
height(opposite) = 12m
ground(adjacent) = ?
using the formula
Hyp² = oppo² + Adj²
13² = 12² + Adj²
Adj² = 13² – 12²
Adj² = 169 – 144
Adj² = 25
Adj = √25
Adj = 5
:- the distance of the foot of the ladder from the bottoms wall is 5
i hope this helps
How many terms are there in the expression 5xy 9yz 3zx 5x 4y?
The number of terms that the expression 5xy 9yz 3zx 5x 4y has is 5 terms.
What is an algebraic expression?An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
How to determine terms?To determine the number of terms in an algebraic expression, we only have to count the spaces (addition and/or subtraction symbols) and add the unit, in this way we will have the number of terms.
5xy 9yz 3zx 5x 4y has 4 spaces
4 + 1 = 5 terms.
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A sociologist is studying the effect of having children within the first 2 years of marriage on the divorce rate. Using hospital birth records, she selects a simple random sample of 200 couples who had children within the first 2 years of marriage. Following up on these couples, she finds that 80 couples are divorced within 5 years. Let p= the population proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years. What is a 90% plus four confidence interval for the proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years?Question options:0.402 ± 0.0880.402 ± 0.0670.402 ± 0.0570.402 ± 0.035
The proportion of couples who had children within the first 2 years of marriage and are divorced within 5 years is [tex]0.4\pm 0.057[/tex].
What is a confidence interval?The confidence interval (CI) is a range of values that, with a particular level of confidence, is likely to include a population value.
A population mean that sits between an upper and lower interval is frequently stated as a percentage.
Given, Out of 200 couples who have children with 2 years, 80 couples had been divorced within 5 years.
Therefore the proportion of couples who have had children and divorce
= (80/200).
= 0.4.
We know the confidence interval for a population proportion is,
[tex]p = p' \pm z_{\frac{\alpha}{2}} \sqrt{\frac{p'(1 - p')}{n}[/tex].
Now, [tex]z_{\frac{\alpha}{2}[/tex] at 90% confidence interval is 1.645 and n = 200.
Therefore, [tex]p = 0.4\pm 1.645} \sqrt{\frac{0.4'(1 - 0.4)}{200}[/tex].
[tex]p = 0.4\pm 1.645} \sqrt{\frac{0.4\times0.6}{200}[/tex].
[tex]p = 0.4\pm 1.645\times0.0346[/tex].
[tex]p = 0.4\pm 0.057[/tex].
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Find the perimeter of the square:
28
Answer:
4×side
Step-by-step explanation:
i hope this helps
En el experimento de la clase de Física, se pone a calentar agua durante 3 minutos y se registra la temperatura. Posteriormente, aumenta la masa del agua, se pone a calentar durante 3 minutos en las mismas condiciones, se observa que la temperatura disminuye. ¿Qué relación existe entre la masa de agua y la temperatura?.
La masa del sistema es inversamente proporcional a la temperatura del mismo. Existe una relación de proporcionalidad inversa.
¿Cuál es la relación entre la temperatura y la masa de un sistema?
En este problema tenemos dos casos de calentamiento sensible en dos muestras de agua, cuya fórmula se describe a continuación:
Q' · Δt = m · c · ΔT
Donde:
Q' - Tasa de transferencia de calor.Δt - Tiempo de calentamiento, en minutos. m - Masa del sistema.c - Calor específico del agua.ΔT - Cambio en la temperatura del sistema.A partir de esta fórmula comprobamos que la masa del sistema es inversamente proporcional al cambio de la temperatura del sistema:
m ∝ 1 / ΔT
En consecuencia, a mayor masa, menor cambio en la temperatura.
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At what point on the graph is the rate of reaction the greatest?
The instantaneous rate at the beginning of a reaction, or when t = 0, is known as the starting rate of the reaction.
What is rate of Reaction ?The rate at the beginning of the reaction may be determined using the graph of change in product over time or change in reactant over time. The highest rate on the curve is the beginning rate. Since the reactants are concentrated at their highest at the beginning, the most collisions are occurring.
Rates of response can be depicted in graphs. To depict the pace of reaction, we may create a graph of product (or reactant) against time. The pace of reaction will be the gradient of the graph. The pace of response increases with increasing gradient steepness.
The instantaneous rate at the beginning of a reaction, or when t = 0, is known as the starting rate of the reaction. The beginning rate is equal to the slope of the reactant concentration versus time curve at time zero, which is negative.
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If you reflected the point (x, y) over the line y = x, what would it become?
Answer:
(y, x )
Step-by-step explanation:
under a reflection in the line y = x
a point (x, y ) → (y, x )
Which of the following is equivalent to −2(5p − 2q)?
−10p + 4q
−10p − 2q
−7p + 4q
−7p − 4q
Answer:
A,-10p+4q
Step-by-step explanation:
-2(5p-2q)
-2*5p+(-2*-2q)
-10p+4q
Answer:
[tex] - 10p + 4q[/tex]
is the answer. A
How many unique sets of 3 prime numbers exist for which the sum of the numbers is 44?
The unique set of 3 prime numbers for which the sum of the numbers is 44 are {2, 5, 37}, {2, 11, 31}, {2, 13, 29} and {2, 19, 23}.
What is Prime Number?Prime numbers are the numbers in the set of natural numbers for which 1 and the number itself are the only factors of it.
The numbers which are not prime are called composite numbers.
We have to find the set of 3 prime numbers which on adding yields 44.
Now 44 is a composite number and also an even number.
We also know that adding two odd numbers as well as adding two even numbers always gives the even number.
2 is the only even prime number.
So if we take this set which is not including 2, then by adding odd + odd + odd gives the odd number.
But the answer we needed is 44, which is even.
So this set always contain 2 as one of the prime number.
So by adding the other two prime numbers, we must get 42.
Thus we got,
{2, 5, 37} = 2 + 5 + 37 = 44
{2, 11, 31} = 2 + 11 + 31 = 44
{2, 13, 29} = 2 + 13 + 29 = 44
{2, 19, 23} = 2 + 19 + 23 = 44
Hence the unique 3 set of prime numbers are {2, 5, 37}, {2, 11, 31}, {2, 13, 29} and {2, 19, 23} for which the sum is 44.
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What quotient does the model Nestor made represent?
3 groups of cubes. In each group are 2 tens rods and 7 unit cubes.
3.21 ÷ 3 = 1.07
1.47 ÷ 7 = 0.27
0.21 ÷ 7 = 0.03
0.81 ÷ 3 = 0.27
n a certain wilderness area 1.4 mountain lions are seen each year, on average. what is the probability that in a given year exactly two mountain lions will be seen in this wilderness area? (assume that sightings are independent from each other and that the probability of seeing a mountain lion stays constant.)
Therefore ,the probability that in a given year exactly two mountain lions will be seen in this wilderness area is P =0.2417.
How does probability work?Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%. When an event has a probability of 0, it has no possibility of happening, whereas when it has a probability of 1, it is almost certain to happen. When an event has a probability of 0.45 (45%), there are 45 out of 100 chances that it will occur.
Here,
λ=1.2
=> P(X =x) = [tex]\frac{e^{-\lambda} * \lambda^{x} }{x!}[/tex]
=> P(X=2) = [tex]\frac{e^{-1.4} * 1.4^{2} }{2!}[/tex]
=> P(X=2) = 0.2466 * 1.96 /2
=>P(X=2) = 0.2417
Therefore ,the probability that in a given year exactly two mountain lions will be seen in this wilderness area is P =0.2417.
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Sam i uing the number 2,3,5,and 7. She multiplied ome of thee number and got the product of 10. What are all of the product?
The possible product is:
2 * 5 = 10
1 * 10 = 10
In mathematics, multiplication is a process of combining numbers and finding the product. It is denoted by the symbol "x" or "*". There are different ways to perform multiplication, such as using a multiplication table, using a calculator, or using the standard algorithm. The standard algorithm is a systematic method for performing multiplication that involves multiplying the digits in the ones, tens, and so on place value columns, and then carrying and regrouping as necessary.
To find all the possible products that can be obtained by multiplying some combination of the numbers 2, 3, 5, and 7 that result in a product of 10. Here are the two possible products that can be obtained by multiplying these numbers:
2 * 5 = 10
1 * 10 = 10
The possible products that result in a product of 10 are 2 * 5 and 1 * 10.
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What are the 3 types of dynamic semantics?
In linguistics, dynamic semantics is a theory of meaning that is based on the idea that the meaning of a sentence is determined by the way it is used in context, rather than by its compositionality. Within dynamic semantics, there are a few different approaches that have been developed. Three types of dynamic semantics are Discourse representation theory, situation semantics and event semantics.
Discourse representation theory: This theory proposes that the meaning of a sentence is determined by its role in the context of a discourse (i.e., a conversation or written text). The meaning of a sentence is represented as a set of constraints on the possible interpretations of the discourse, and the interpretation of the discourse is determined by the way these constraints are resolved.
Situation semantics: This theory proposes that the meaning of a sentence is determined by the way it refers to a particular situation or state of affairs. The meaning of a sentence is represented as a set of conditions that must be satisfied for the sentence to be true in a particular situation.
Event semantics: This theory proposes that the meaning of a sentence is determined by the events or actions it describes. The meaning of a sentence is represented as a set of conditions that must be satisfied for the events or actions described in the sentence to occur.
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The sum of four consecutive integers is -10. What is the largest integer?
The largest number is -1
What is number ?
An arithmetic value known as a number is used to represent a quantity and do calculations. Numbers are represented by written symbols, such as "3," which are referred to as numerals. A number system is a method of writing that uses logically ordered digits or symbols to represent numbers.
An item in mathematics used for measurement, labeling, and counting is a number. The prime numbers 1, 2, 3, 4, and so forth are the original examples. Number words can be used to represent numbers in language.
Let the 4 consecutive integers are
x
x+1
x+2
x+3
x + (x+1) + (x+2) + (x+3) = -10
4x + 6 = -10
4x = -16
x = -4
The 4 consecutive integers are -4 , -3 , -2 , -1
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1. Evaluate each expression. Show your work. (6 points: 2 points for each correct answer with work shown)
B. (9)^1/2 + √25 - 8 ÷ 2 + 3^2
C. 1/2 x 3/5 (2^3 - 6
Please show your work for these 2 expressions.
Answer:
B.) 13
C.) 0.6
Step-by-step explanation:
The order of operations to evaluate these expressions is as follows:
Parentheses
Exponents
Multiplication/Division
Addition/Subtraction
So, for B.)
[tex]9^\frac{1}{2}+\sqrt{25}-8\div2+3^2[/tex]
This can be rewritten as
[tex]9^\frac{1}{2}+25^\frac{1}{2}-8\div2+3^2[/tex]
Since there are no parentheses, evaluate the exponents first:
[tex]3+5-8\div2+9[/tex]
Next, there are no multiplication steps, but there is one division:
[tex]3+5-4+9[/tex]
To finish, evaluate from left to right:
[tex]3+5-4+9\\8-4+9\\4+9\\13[/tex]
Follow the same pattern for C.)
[tex](\frac{1}{2})(\frac{3}{5})(2^3-6)[/tex]
This expression can be rewritten as
[tex](1\div2)(3\div5)(2^3-6)[/tex]
First, evaluate the expressions in the individual parentheses, keeping in mind the expression [tex](2^3-6)[/tex] must be evaluated following the same pattern (evaluate the exponent before subtracting six):
[tex](.5)(.6)(8-6)\\(.5)(.6)(2)[/tex]
To finish, evaluate from left to right:
[tex](.3)(2)\\.6[/tex]
Hope that helps!
Denzel must practice the piano for 210 min each week. He practices for 30 min each day. Write a linear equation represent the number of minutes denzel still has to practice after x days?.
Answer:
y = 30x - 210
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-How can I learn algebra fast?
If you're not motivated, it would take you approximately nine months; however, if you are and can dedicate an hour or two every day to studying, it would only take you about six months.
How quickly can I learn algebra?6 Unknown Methods for Quickly Mastering Algebra
Create your own memory-boosting techniques.One advantage of algebra .math in general, is that the rules never change.Learn shortcuts. familiarise yourself with the calculator. join a study group.get a tutor and encourage your child to ask their teacher for assistance.You may probably self-study Math rather simply as if you were in college with all the free materials available online, including lectures, syllabi, ebooks, and MOOCS. You can go at your own pace, which is the finest part. It's common for algebra to be challenging because we mistakenly think we're learning new material when, in reality, we're just applying language to specific concepts that we already know to be true.
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What is the nature of roots of the quadratic equation 2x² √ 5x 1 0?
The roots of the quadratic equation 2x² √5x + 1 = 0 are two complex numbers.
To solve for the roots of the quadratic equation 2x² √5x + 1 = 0, we must first use the Quadratic Formula to solve for x. The Quadratic Formula is x = (-b ± √b²-4ac)/2a. In this equation, a = 2, b = √5, and c = 1. We then simplify the equation to be x = (-√5 ± √(5²-4(2)(1))/2(2). This simplifies to x = (-√5 ± √9i)/4. The two solutions to this equation are x = (-√5 + 3i)/4 and x = (-√5 - 3i)/4. Since both solutions involve complex numbers, the roots of 2x² √5x + 1 = 0 are two complex numbers.
x = (-√5 ± √(5²-4(2)(1))/2(2)
x = (-√5 ± √9i)/4
Root 1: x = (-√5 + 3i)/4
Root 2: x = (-√5 - 3i)/4
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What is the value of x in the figure?
Enter your answer in the box.
X =
220
to
The value of x =68
We know that x+22 = 90 because the sum of the two angles is a vertical angle to the right angle and vertical angles are equal.
x+22 =90
Subtract 22 from each side
x+22-22 = 90-22
x =68
In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown.
"How do you find value of x?
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
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Answer: 68
Step-by-step explanation:
Provided the correct answer after places 34 as the answer.
the curved surface area and volume of a cylinder are 880 CM^2 and 3080 cm^3 respectively find its total surface area
The total surface area of a cylinder are 1187.35 cm sq.
What is the volume of a right circular cylinder?Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
We are given the curved surface area and volume of a cylinder are 880 CM^2 and 3080 cm^3 respectively.
A = 880
V = 3080
Curved surface area of cylinder = 2πrh
880 = 2π x r x h
rh = 880/ 2π
Volume of cylinder = πr x r x h
3080 = πr x r x h
rh = 3080 / πr
Substitue the values;
880/ 2π = 3080 / πr
440/π = 3080 / πr
r = 3080 / 440
r = 7
Now, rh = 880/ 2π
h = 20.01
The total surface area = 2πr(r + h)
= 2π x 7(7 + 20.01)
= 1187.35 cm sq.
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At which root does the graph of f x x 5 3 * x 2 2 touch the X axis?
The root of the graph of f(x) =(x - 5)3(x + 2)2 touches the x-axis at -2,5
(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.
(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.
Given: Function f(x) is (x - 5)3(x + 2)2
If a curve touches the x-axis then f(x) = 0
⇒ (x - 5)3(x + 2)2 = 0.
But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.
⇒ (x - 5)3 = 0 and (x + 2)2 = 0
⇒ (x - 5) = 0 and x + 2 = 0
⇒ x = 5 and x = - 2.
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What are the 3 ways to pass parameters in C++?
There are three parameter-passing modes in C++: by value, by pointer, and by reference.
Now, According to the question:
There are three parameter-passing modes in C++: by value, by pointer, and by reference.
What are the three main parameters?
The three main parameters assessed when calculating the Human Development Index of a place are:
A. Economic parameters.
B. Health parameters.
C. Education parameters.
D. Linguistic parameters.
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Brain Bogglers II
Solve this puzzle by finding the correct values for A and B. The
pictures are important.
A-B= 1 and
2A + 20 =B
Can a binomial have degree 3?
Yes , the given statement a binomial can have degree three is true.
As given in the question,
Binomial can have degree three is a true statement explain in a following way:
Binomial is a polynomial which is a combination of two terms combined by '+' addition or '-' subtraction mathematical operation.Binomial may have degree one , two , three , so on.Degree of the polynomial does not effect the definition of binomial.If it is of degree three it is cubic binomial or polynomial.One term represents monomial, three terms represents trinomial and so on.Therefore, binomial may have degree 3 is a true statement.
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What is nth formula?
The nth formula of any mathematical expression represents the general formula for the given sequence or series.
nth formula of the given mathematical expression is the way of representing the given sequence or series in standard form.For example nth formula of the arithmetic sequence is given by aₙ= a + ( n - 1 )d.Here aₙ represents the nth term of the sequence.'a' represents the first term of the sequence.'n' represents the number of terms.'d' represents the common difference between the consecutive terms of the sequence.nth term help us to find value of any term without calculating others terms.Therefore, the nth formula is used to represents the mathematical sequence or series in standard form.
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