Classifying an equiangular triangle as an acute equiangular triangle is unnecessary because by definition, all angles are 60°
What is an equiangular triangle?An equiangular triangle is one with three equal sides and three equal angles, all of which are measured at 60 degrees. Given that the characteristics of both triangles are the same, an equiangular triangle can also be referred to as an equilateral triangle.
This triangle is regarded as a regular polygon because its sides and angles are both equal. Equiangular refers to angles that are all equal.
All triangles have 3 angles that together total 180 degrees. Because an equilateral triangle has equal sides, its angles can only be 60 degrees. This entails that all angles must be acute. It is not required to write that it is intense because of this.
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Give an example of a number that is not a rational number. Explain why it is not rational.
Give an example of a number that is not a rational number. [tex]\pi =3.14[/tex]
Why it is not rational?
[tex]\pi[/tex] is a real number that cannot be represented by a simple fraction since it is an irrational number. [tex]\pi[/tex] is what mathematicians refer to as a infinite decimal since the digits continue indefinitely after the decimal point.What is an irrational number?
A real number that cannot be expressed as a straightforward fraction is referred to as an irrational number. It cannot be described using a ratio. When p and q are integers and q is not equal to 0, N is not equal to p/q if N is irrational.To learn more about irrational numbers, refer:
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Determine whether each set of numbers can be the measures of the sides of a triangle. If so, classify the triangle as acute, obtuse, or right. Justify your answer.
4.2,6.4,7.6
Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is obtuse.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
4.2 + 6.4 > 7.6
6.4 + 7.6 > 4.2
7.6 + 4.2 > 2.6
Hence, these set of numbers can be the measures of the sides of a triangle.
According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:
acute if [tex]a^{2} + b^{2} < c^{2}[/tex]
obtuse if [tex]a^{2} + b^{2} > c^{2}[/tex]
right if [tex]a^{2} + b^{2} = c^{2}[/tex]
∴The longest side is 7.6.
Hence, a = 4.2, b = 6.4 and c = 7.6;
Consider [tex]a^{2} + b^{2}[/tex] :
= [tex]4.2^{2} + 6.4^{2}[/tex]
= 58.6.
Now consider [tex]c^{2}[/tex] :
= [tex]7.6^{2}[/tex]
=57.76.
Thus, [tex]a^{2} + b^{2} > c^{2}[/tex]
Hence, the triangle is obtuse.
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Pre-Assessment
Test.aspx?testid=244308628¢erwin-yes
ment-
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Question 3 of 6
The limit is
Shannon McKiernan
This test: 6 point(s)
possible
This question: 1
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09/11/22 8:27 PM
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Two people pair up to create a sequence. Each of them pick five random digits from 1 to 9 (with repetitions, if they
wish). They merge their digits to make a list of ten. Now, each of them construct a different ten-digit number using
exactly the digits in the list. Let a₁ = the (positive) difference between the two numbers. Let an+1 = the sum of the
digits of an for n21. This sequence converges because it is eventually constant. What is the limit?
Answer: The nth term of the sequence whose integers are between 1 -9 such that there is the permission of repetition but no two consecutive digits must be even is 1.834 x [tex]10^{21}[/tex]
Step-by-step explanation:
Given data,
Two people pair up to create a sequence. Each of them pick five random digits from 1 to 9.
Define Consecutive numbers :
Consecutive numbers are numbers that follow each other in order. They have a difference of 1 between every two numbers. In a set of consecutive numbers, theme an and the median are Equal. If n is a number, then n, n+1, and n+2 would be consecutive numbers Examples. 1, 2, 3, 4, 5.
The numbers that are given:
1, 2, 3, 4, 5, 6, 7, 8, 9 are all consecutive.Now, suppose a (n) denotes the number of n-digit positive integers as stated in the question, thereby using:
1, 2, 3, 4, 5, 6,7, 8, 9 with the permission of repetition; no two consecutive digits are even.Then, the number of n can be computed as n!= (9!) x (8!) x (7!) × (6!) × (5!) × (4!) × (3!) × (2!) × (1!)
= 362880 x 40320 x 5040 x 720 x 120 x 24 x 6 x 2 x 1
[tex]n^{th}[/tex] = 1.834 x [tex]10^{21}[/tex]
Therefore,
The nth term of the sequence whose integers are between 1 -9 such that there is the permission of repetition but no two consecutive digits must be even is 1.834 x [tex]10^{21}[/tex].
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Determine whether the events are mutually exclusive or not mutually exclusive. Then find the probability. Round to the nearest tenth of a percent, if necessary.
selecting a number at random from integers 1 to 20 and getting an even number or a number divisible by 3
According to the question, to check whether the events are mutually exclusive or not for the even integers.
As per question, select random integer numbers from [tex]1[/tex] to [tex]20[/tex] to get either an even number or a number divisible by [tex]3[/tex].
Therefore , the probability can be written as:
[tex]P(e or d) = \frac{P(E)}{n(E)} = P(e)+P(d)-P(e and d)[/tex]
[tex]= \frac{10}{20} +\frac{6}{20} -\frac{3}{20} = \frac{13}{20} = 65%[/tex]
The event is not mutually exclusive.
Since, the calculated percentage is [tex]65%[/tex] and it is not nearest to tenth of a percent.
What are mutually exclusive events?
Mutually exclusive events are those events which cannot happen at the same time. For instance, in any event nobody can run forward or backward together at the same time.
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A grading machine can grade 96 multiple choice tests in 2 minutes. Suppose a teacher has 300 multiple choice tests to grade.
Write a proportion that could be used to predict the number of minutes it will take the machine to grade the
300
tests. Use x to represent the number of minutes.
The machine will take 6.25 minutes to grade 300 multiple choice tests.
Unitary method is a concept in which the value of a single unit is first found out and then multiplied by the necessary value to get the required answer.
Here, we are given that a grading machine can grade 96 multiple choice tests in 2 minutes.
This means that the machine will take 2/96 minutes to grade one multiple choice test
X = number of minutes taken by the machine to grade 300 multiple choice tests
Thus, we can use the proportion 2/96 to predict X in the following manner-
X = 2/96 (300)
X = 600/ 96
X = 100/ 16
X = 6.25
Thus, the machine will take 6.25 minutes to grade 300 multiple choice tests.
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What is the sine for the figure below?
The sine for the right triangle A is 3/5.
The ratio between the side opposite the angle and the triangle's hypotenuse is known as the sine (sin) of an acute angle in a right-angled triangle. A right angle in geometry and trigonometry is an angle that is exactly 90 degrees, or 2 radians, which is equivalent to a quarter turn. If a ray is positioned so that its terminal is on a line and they are equal, the neighbouring angles are right angles.
Sin(A) = opposite/hypotenuse
=BC/AB
=3/AB
Given,
BC = 3
AC = 4
Now solve for AB using Pythagorean theorem:
BC2 + AC2 = AB2
32 + 42 = AB2
9 + 16 = AB2
25 = AB2
AB = 5
Hence,
The value of AB is 5.
BC/AB = 3/5
Therefore, The sin of triangle A is 3/5.
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You have three numbers. two of the numbers are 24 and 42. what is the gcf of these two numbers? the third number is grater tan 42 and does not change the gcf. what is one possibility for the third number?
If two of the three numbers are 24 and 42, then the GCF of these two numbers is 6 and the third number is possibly 48.
Factor is a number which when a number is divided will result to another number(whole). For two or more numbers, the largest common factor that they have is called the Greatest Common Factor (GCF).
To find the GCF of 24 and 42, list all the factors of both numbers.
24 : 1, 2, 3, 4, 6, 8, 12, 24
42: 1, 2, 3, 6, 7, 14, 21, 42
Common Factors: 1, 2, 3, 6
Greatest Common Factor: 6
If the third number is grater than 42 and does not change the GCF, then the third number is possibly 48.
24 : 1, 2, 3, 4, 6, 8, 12, 24
42: 1, 2, 3, 6, 7, 14, 21, 42
48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Common Factors: 1, 2, 3, 6
Greatest Common Factor: 6
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PLEASE HELP ME ASAP RIGHT ANSWERS ONLY!
What is the slope of the line?
hi
Slope is 2 .
here is how you do the trick : by reading on the graph
if you go forward of 1 on the X axis , how much did the line goes up or down ?
Here at 0 on X- axis, we are at 0 on the Y- axis.
If you go forward of 1 on X axis, you are at 2 on Y axis.
So the slope is + 2
Other technique by calculus between two points.
Take two diffents point on the X axis. Call them A and B
Slope is : ( f(A) -f(B) ) / A-B
exemple here : we have two easy points . Take 0 as A and 1 as B
We read on the graph :
A = 0 and B = 1
f(A)= 0 and f(B) = 2
Now we apply formula :
( f(A) -f(B) ) / (A-B )
(0 -2 ) / (0-1) = -2/-1 = 2
Slope is 2
Easy, dont you think ?
9. How many 3/8 cup servings are in 1 7/8 cups of apple cider?
There are 5 cups of 3/8 servings in 1 7/8 cups of apple cider
How to calculate the number of servings ?The number of cup servings is 3/8
The number of apple cider cups is 1 7/8
Therefore the number of cup servings can be calculated as follows
15/8 ÷ 3/8
convert to multiplication
= 15/8 × 8/3
= 15/3
= 5
Hence there are 5 cups of 3/8 servings in 1 7/8 cups of apple cider
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Suppose that three customers are selected randomly, without replacement, for a survey. what is the probability that at least two selected customers use express shipping?
Answer:
3 upon 2. that's the answer ..
Solve each equation. Check each solution. 5/2x - 2/3 = 1/x + 5/6
The solution of the given equation 5/2x - 2/3 = 1/x + 5/6 is at x = 9/11.
According to the given question.
We have an equation
5/2x -2/3 = 1/x + 5/6
Since, we have to solve the above equation for x.
Thereofore, the solution of the equation 5/2x -2/3 = 1/x + 5/6 is given by
5/2x -2/3 = 1/x + 5/6
⇒ 5/2x -1/x = 5/6 + 2/3
⇒ (5 -2) /2x = 5+ 2(3)/6
⇒ 3/2x = 11/6
⇒6(3) = 11(2x)
⇒ 18 = 22x
⇒ 18/22 = x
⇒ 9/11 = x or x = 9/11
Hence, the solution of the given equation 5/2x - 2/3 = 1/x + 5/6 is at x = 9/11.
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Determine whether each sequence is arithmetic or geometric. Then identify the common difference or common ratio. 78,75,72,69,66,63,60, . . . .
The sequence 78,75,72,69,66,63,60, . . . . is arithmetic and the common difference is 3
We can determine that the sequence is arithmetic, because two consecutive terms differ by "d".
To solve this exercise we are going to apply the formula of the arithmetic sequence:
d = aₙ₊₁ - aₙ
Where:
a = first termd = common difference of the sequenceInformation about the problem:
Sequence = 78,75,72,69,66,63,60, . . . .d = ?Calculating the common difference of the sequence (d), we have:
d = aₙ₊₁ - aₙ
d =78 - 75
d = 3
What is an arithmetic sequence?It is a series of numbers that increase or decrease by a constant amount called the ratio of the progression. It is increasing when the ratio is positive and decreasing when it is negative.
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Find the values of m and n
A. m=18, n=60
B. m=35, n=60
C. m=30, n=150
D. m=120, n=18
Answer:
m = 18
n = 60
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180.
We can write the following equation to find, first value of m, then the value of n:
65 + 42 + 55 + m = 180 add like terms
162 + m = 180 subtract 162 from both sides
m = 18
Now the value of n:
65 + 55 + n = 180 add like terms
120 + n = 180 subtract 120 from both sides
n = 60
List and explain the 4 listening steps as outlined in the jade wu podcast (4 secrets therapists use to be a great listener). which step did you find the most interesting or useful?
A capable listener have find the most interesting or useful.
Here are 4 therapist secrets to help you hone this important skill -
Reflect back what you hearAsk questions instead of providing answersValidate feelings, even if you don’t agree with the logicRefrain from giving unsolicited adviceHere are 4 therapist insider tips to help you master this crucial ability.This is the first lesson in the therapy training program. It's a straightforward advice, yet it works wonders. Basically, the first action you should take as a listener is to repeat what the speaker stated back to them.Yes. I am aware that this may seem robotic, unnatural, or even unpleasant. But try it out! You won't even be aware that you're doing it, I bet the person you're listening to. Try doing it while nodding in agreement. perhaps a little bit of phrasing Begin by saying, "It sounds like..."
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How many moles of calcium atoms do you have if you have 5.03 × 10²¹ atoms of calcium. (The mass of one mole of calcium is 40.08 g.)
5.03 x 10²¹ atoms of calcium are equivalent to 8.6 × 10⁻³ moles of calcium atoms.
What is the number of moles?To convert atoms to moles we need a conversion factor: Avogadro's number. According to Avogadro's number: there are 6.02 × 10²³ calcium atoms in 1 mole of calcium atoms. The number of moles corresponding to 3.00 × 10²¹ atoms of calcium is:
Number of moles = 5.03 x 10²¹ / 6.02 × 10²³
Number of moles = 8.6 × 10⁻³ moles of calcium
5.03 x 10²¹ atoms of calcium are equivalent to 8.6 × 10⁻³ moles of calcium atoms.
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Pick the description of a geometric object that best matches the real-world object:
Box for a deck of cards
O a three-dimensional shape with two similar, parallel rectangular bases and sides that are parallelograms
O a three-dimensional shape with two similar, parallel triangular bases and sides that are parallelograms
a three-dimensional geometric shape with two parallel and circular bases and a curved side
o a three-dimensional figure in which all points on the surface are the same distance from the center
o a three-dimensional box-shaped figure, with six identical square faces
Athree dimensional shape with two similar, parallel rectangular bases and sides that are parallelogram" will be the correct option.
The box for a deck of cards will have a rectangular prism shape.
Two parallel rectangular bases, two sides that run parallel to one another along their width, and two similarly parallel rectangular sides running along their height make up a rectangular prism.
A rectangular prism has two parallel rectangular bases, 2 sides parallel to each other along width and 2 similar parallel rectangular sides along the height.
As a result, choice A, "a three-dimensional shape with two comparable, parallel rectangular bases and sides that are parallelograms," will work.
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What two nonnegative real numbers with a sum of 40 have the largest possible product?
The two non negative real numbers with a sum of 40 have the largest possible product are 20 and 20.
Steps to find Maximum of a function f(x).
Step 1 : Differentiate the function F(x)
Step 2 : Equate f'(x) to zero to find the critical points .
Step 3 : Substitute the critical points in f''(x) , if
f''(x)< 0 them maximum value will be at the critical point.
in the given function
the sum of two non negative real numbers is 40.
Let the numbers be x and y .
So , x+y=40
y=40-x ....(1)
We need to maximize the product i.e. x.y
Substituting the value of y from equation (1) we get
[tex]f(x)=x.y\\ \\ f(x)=x.(40-x)\\ \\ f(x)=40x-x^{2}[/tex]
Step (i) differentiating with respect to x we get
[tex]f'(x)=40-2x[/tex]
Step (ii) Equating f'(x) to 0
[tex]40-2x=0\\ \\ x=20[/tex]
x=20 will be the critical point .
Step (iii) Substituting the critical point in f''(x)
again differentiating with respect to x we get
[tex]f''(x)=-2\\ \\ f''(20)=-2[/tex]
Since -2<0. therefore , x=20 is the point where f(x) is maximum.
Substituting the value of x=20 in equation (1) we get
y=40-x
y=40-20
y=20.
Therefore , the two non negative real numbers with a sum of 40 have the largest possible product are 20 and 20.
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Kerim jogged 3 miles on Thursday: On Friday, he jogged of a mile
farther. How far did he jog on Friday
Answer:
4 miles
Step-by-step explanation:
3 miles plus 1 additional mile is 4 miles.
can someone help me with this? ive been trying for a while
Answer:
The value of x after simplification is 6, which when substituted in the given expression will make both the sides equal.
Step-by-step explanation:
It is given that the expression given below is to be simplified using the order of operations;
The given expression is;
=> (3×2)² + 8 = ___² + 8
Now, let us assume that the blank space is 'x' in the above-mentioned question;
Firstly,
We will solve the terms within brackets as per BODMAS rules that is multiplication of both the terms;
=> (3×2)² + 8 = x² + 8
=> 6² + 8 = x² + 8
Now, we will solve the squares of the terms given above;
=> 36 + 8 = x² + 8
Now, we will add the terms as per BODMAS rules;
=> 44 = x² + 8
=> 44 - 8 = x²
Now, we will subtract the terms as per BODMAS rules;
=> 36 = x²
Now, we will square-root both the sides given above;
=> x = √36
=> x = 6
Therefore, the value of x after simplification is 6, which when substituted in the given expression will make both the sides equal.
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Which statement is the Law of Detachment? Help asap
Answer:
d
Step-by-step explanation:
is a true statement and p is trueSolve the following equation for A. Be sure to take into account whether a letter is capitalized or not.
F = D + A
Answer:
A = f - D
Step-by-step explanation:
f = D + A ( isolate A by subtracting D from both sides )
f - D = A
Answer:
A=F-D
Step-by-step explanation:
fht7ts3yfx yi. 4hu c h 4tyfdrhuezjuf drucdtufdgyt
what is 4/3 y= 16 for math 8
What is the value of x in the equation (4x-1)-3x = -(x + 2)?
1/16
3/16
19/16
3
Answer:
Step-by-step explanation:
x − 1. _. 3. = 3 by 3 gives x − 1 = 9 and then adding 1 to both sides of x − 1 = 9 gives x = 10. Choices A, B ... written as the equation 16 + 4x = 10 + 14, which is equivalent to 16 + 4x = 24. Subtracting
The temperature was -6°F. It rose so that the temperature was 0°F
Answer:
It rose 6 degrees
Step-by-step explanation:
I hope that's what you're asking...
Owen can jog 660 yards in 3 minutes. how many yards would you expect him to jog in 10 minutes?
Answer: 2200 yards
Step-by-step explanation:
First find the unit rate, 660/3 = 220
So, Owen can jog 220 yards in one minute.
220 times 10 to find how much Owen can jog in 10 minutes.
220*10 = 2200.
Answer:
2200
Step-by-step explanation:
Determine whether y varies directly with x . If so, find the constant of variation.
y=6 x
The constant of variation in y = (6)x is (6)
y = kx (Where k is the constant)
Here,
⇒ y = (6)x
So, k = (6)
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Can someone please help me with questions 1-3? You would be a lifesaver! DUE TONIGHT!
Answer:
Step-by-step explanation:
1- 8
3 - 8+2= 10
3 3/10 dived by 1 1/4
Write and solve a system of equations for each situation. Check your answers.A store sells small notebooks for 8 and large notebooks for 10 . If you buy 6 notebooks and spend 56 , how many of each size notebook did you buy?
I bought 2 small notebooks and 4 large notebooks.
Let us represent the number of small notebooks with x and number of large notebooks with y.
Forming equation according to bought number of books -
x + y = 6 - equation 1
Rewriting the equation according to x
x = 6 - y - equation 2
Now, forming equation according to cost of notebooks -
8x + 10y = 56 - equation 3
Keep the value x from equation 2 in equation 3
8 (6 - y) + 10y = 56
Performing multiplication
48 - 8y + 10y = 56
Performing subtraction and shifting values to other side of equation
2y = 56 - 48
2y = 8
Shifting 2 to other side of equation and performing division
y = 8 ÷ 2
y = 4
Keep the value of y in equation 2
x = 6 - 4
x = 2
Hence, I bought 2 small notebooks and 4 large notebooks.
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ALGEBRA In ∠ X Y Z, m ∠ X=157, mV Y=y , and m∠Z=z . Write an inequality to describe the possible measures of V Z . Explain your reasoning.
According to the statement an inequality to describe the possible measures of ∠Z = 23.
In algebra, what is inequality?An inequality is a relationship that makes a non-equal comparison of two integers or any other mathematical expressions. It is most commonly used to compare two digits upon that number line based on their size. a statement of an order relationship—greater than, larger than the other or equal thereto, less than, or lesser than or equal to—between two integers or algebraic expressions
According to the given data:the sum of the angles' measurements
triangle is 180 and ∠ X=157.
∠ X + ∠ Y +∠ Z = 180
∠ Y +∠ Z = 23
If ∠Y was 0, then ∠Z would equal 23. But since an angle must have
a measure greater than 0, ∠Z must be less than
23, so z < 23.
an inequality to describe the possible measures of ∠Z = 23.
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