The given equation is an identity, so it is true for any value of x, and x can take infinite values, thus, the linear equation has infinite solutions.
How many solutions has the given equation?Here we have the linear equation:
x - 2 = -2 + x
And we want to see how many solutions it has, so let's solve it.
IF we add 2 in both sides we will get:
x - 2 + 2 = -2 + x + 2
x + (-2 + 2) = x + (-2 + 2)
x = x
Now, that is an identity, so it is true for any value of x, and x can take infinite values, thus, the linear equation has infinite solutions.
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PLEASEEE HELP!!!!!!!!
Answer:
108°
Step-by-step explanation:
Since angle WYT and angle UYW lie on the same line, we can use linear pair fidn the answer.
That is: 180-72= angle UYW
Therefore angle UYW=108°
-Hence proved:)
Determine whether each formula is explicit or recursive. Then find the first five terms of each sequence. a₁ = -121, a n =a n₋₁ +13
This is recursive sequence and -121,-108,-95,-82,-69,-56 these are the first five terms of sequence.
How to find the first five terms of sequence. a₁ = -121, a (n) =a (n-1)+ 13?A recursive formula is one that defines each term in a sequence by reference to the one before it. The following parameters are defined using the recursive formulas:
1. The initial term in the series.
2. The general rule for determining any term from its preceding term.
Recursive Arithmetic Sequence Formula
The following is the recursive formula to determine the nth term in an arithmetic series:
an = an-1 + d for n ≥ 2
where
The common difference is d, and an is the nth term of an A.P.
given that
a₁ = -121
a (n) =a (n-1) +13 so, d = +13
For example, we need to extend the sequence term by term in order to find the first five terms:
a(1) = -121
a(2) = a(1) + d = -121 + 13 = -108
a(3) = a(2) + d = -108 + 13 = -95
a(4) = a(3) + d = -95 + 13 = -82
a(5) = a(4) + d = -82 + 13 = -69
a(6) = a(5) + d = -69 + 13 = -56
a(7) = a(6) + d = -56 + 13 = -43
Hence,this is recursive sequence and -121,-108,-95,-82,-69,-56 these are the first five terms of sequence.
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Four friends are sitting at a table together at the prom. What is the probability that a particular one of them will sit in the chair closest to the dance floor?
The probability that a particular one of them will sit in the chair closest to the dance floor is 1/4.
Linear Permutation:
Linear permutation defines the number of ordered arrangement of objects in a line while circular permutations is an ordered arrangement of objects in a circular manner.
Given,
Four friends are sitting at a table together at the prom.
Here we need to find the probability that a particular one of them will sit in the chair closest to the dance floor.
Since the samples are arranged with a fixed reference point, this is a linear permutation.
So there are 4! or 24 ways in which the samples can be arranged.
The number of favorable outcomes is the number of permutations of the other 3 people given that a particular one of them will sit in the chair closest to the dance floor, 3! or 6.
Therefore, the probability is
=> 6/24
=> 1/4.
Therefore, the probability that a particular one of them will sit in the chair closest to the dance floor 1/4.
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Read the problem. Identify what you need to know. Then organize the data to solve the problem.
Alana has the letter tiles A, H, M , and T in a bag. If she selects a permutation of the tiles at random, what is the probability she will spell the word MATH?
A. 1/4
B. 1/12
C. 3/50
D. 1/24
The probability she will spell the word MATH P(MATH) is 1/12
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
Given ; Alana has the letter tiles A, H, M , and T in a bag. If she selects a permutation of the tiles at random.
The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.
Permutations of "MATH"
4P4 = 4! = 24
Two of the 'MATH" s we can get as a result
Then the probability she will spell the word MATH
P(MATH) = 2/24 = 1/12
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Determine whether the events are independent or dependent. Then find the probability. In a game, you roll an even number on a die and then spin a spinner numbered 1 through 5 and get an odd number.
Given events are independent events and the probability that getting an even number on die and getting odd number on a spinner numbered 1 to 5
In this question,
we have been given two events.
Let event A: rolling an even number on a die
event B: spin a spinner numbered 1 through 5 and get an odd number.
We can clearly observe that the occurrence of event A is not dependent on the other event B.
So, event A and event B are independent events.
The probability of event A is,
P(A) = n(A) / n(S)
here, sample space, n(S) = 6
n(A) = 3
So, P(A) = 3/6
P(A) = 1/2
The probability of event B is,
P(B) = n(B) / n(S)
here, sample space, n(S) = 5
n(B) = 3
So, P(B) = 3/5
Now we find the joint probability of these independent events.
⇒ P = P(A) × P(B)
⇒ P = 1/2 × 3/5
⇒ P = 3/10
Therefore, given events are independent events and the probability that getting an even number on die and getting odd number on a spinner numbered 1 to 5
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What is the common ratio in the geometric sequence 4,10,25,62.5, . . . . . ?
(A) 0.4 (B) 2.5 (C) 15 (D) 25
The common ratio of the geometric sequence 4, 10, 25, 62.5, . . . is 2.5. The answer is B.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a common ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
a = first term
r = common ratio
The common ratio must be the same for all pairs of succeeding term to be called a geometric sequence.
To find the common ratio, use the formula
a(n) = a r^(n-1)
let n = 2, a = 4, a(2) = 10
10 = 4(r^(2 - 1)
10 = 4(r)
r = 2.5
Or just simply divide each succeeding pairs of the sequence.
r = 10/4 = 2.5
r = 25/10 = 2.5
r = 62.5/25 = 2.5
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360 kilometers/ hour= m/s
Answer:
100 m/s
Step-by-step explanation:
divide by 3.6 to get km/h to m/s, multiply by 3.6 to get m/s to km/h!
The garden and a walkway around its perimeter have an area of 378. Find the width of the walkway if the garden measures 12 feet wide 15 feet long
The width of walkway is 3 feet.
What is rectangle ?
A rectangle has 2 congruent diagonals, that is the two diagonals are equal to each other. The diagonals of a rectangle bisects each other into equal segments.
We have been given that the garden and the walkway around its perimeter have an area of 378 square feet.
Let us suppose the width of the walkway is x feet.
the length of garden and the walkway will be = 15+2x
and, the breadth of garden and the walkway will be = 12+2x
Now, area of the garden and the walkway around its perimeter is given by :
A = (15+2x)(12+2x)
A = 4x^2 + 54x + 180
Now, the area is given is given as 378 square feet. Hence, we have
4x^2 + 54x + 180 = 378
4x^2 + 54x -198 = 0
Using quadratic formula to find the roots of above equation we get :
x = 3, -33/2
Taking positive value of x that is 3 as area cannot be negative.
Therefore, the width of walkway is 3 feet.
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Write an algebraic proof.
Given: Δ XYZ with medians XR , YS, ZQ
Prove: XP/PR=2
According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.
What is meant by Centroid Theorem?The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.
Consider the algebraic relationships that exist for triangle medians.
The centroid of a triangle is 2/3 the distance from one vertex to the midpoint of the opposite side, according to the Centroid Theorem.
Given: [tex]$\triangle XYZ[/tex] with medians [tex]$\overline{X R}[/tex], [tex]\overline{Y S}$[/tex], and [tex]$\overline{Z Q}$[/tex].
By using Centroid Theorem, we get
1. XP = 2/3 XR
2. XR = XP + PR( Segment Addition Postulate)
3. XP = 2/3(XR+PR) (Substitution Property)
4. XP = 2/3 XP + 2/3 PR (Distributive Property)
5. 1/3 XP = 2/3 PR(Subtraction Property)
6. XP = 2PR (Multiplication Property)
7. XP/PR = 2 (Division Property)
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1. Find a rule for the following table. Write your rule as a
sentence relating the input and the output.
Rule:
C
Input
O
Output
59
29
39
119
No output
39
Step-by-step explanation:
The attached image should be what you're looking for.
okay can someone help me with this question please! it says look at the given exponents 7 and 4 how can we easily combine them to get our result?
Choices are
[7] [4]
7/4
7-4
7+4
Answer:
7+4 (11)
Step-by-step explanation:
I think you are asking about an equation that looks like this
x^7*x^4
When multiply exponents they are added together and the sum is what the new exponent is.
7+4=11
11 is the new exponent
x^11
So I believe the answer would be 7+4? But I don't fully understand what your question is.
Find the area and perimeter of each shape.
Answer:
perimeter=4l then multiply with how many square are there
then area = l²
multiple with how many square are there
What is the solution of the system? x - 2y = 4 3x + y = 4
The given equations are
[tex]x-2y=4[/tex] …(1)
[tex]3x+y=4[/tex] …(2)
Using Substitution method,
From the equation (1) [tex]x-2y=4[/tex] , the value of x is
= [tex]x=4+2y[/tex]
Putting the value of x in equation (2), we get
= [tex]3(4+2y)+y=4[/tex]
= [tex]12+6y+y=4[/tex]
= [tex]12+7y=4[/tex]
= [tex]7y=-8[/tex]
= [tex]y=-\frac{8}{7}[/tex]
Now, putting the value of y in equation (1), we get
= [tex]x-2(-\frac{8}{7}) =4[/tex]
= [tex]x+(\frac{16}{7}) =4[/tex]
= [tex]x =4-(\frac{16}{7})[/tex]
= [tex]x =(\frac{28-16}{7})[/tex]
= [tex]x =(\frac{12}{7})[/tex]
∴ The value of x is [tex]\frac{12}{7}[/tex] and the value of y is [tex]-\frac{8}{7}[/tex]
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The value of x is (12/7) and the value of y is (-8/7) for the given equation.
The given equations are
x - 2y = 4 equation (1)
3x + y = 4 equation (2)
Using Substitution method,
From the equation (1) i.e., x - 2y = 4 , the value of x is
x = 4 + 2y
Putting the value of x in equation (2), we get
3 ( 4 + 2y ) + y = 4
⇒ 12 + 6y + y = 4
⇒ 12 + 7y = 4
⇒ 7y = (-8)
⇒ y = (-8/7)
Now, putting the value of y in equation (1), we get
x - 2 ( -8/7 ) = 4
⇒ x + ( 16/7 ) = 4
⇒ x = 4 - ( 16/7 )
⇒ x = ( 28 - 16 )/ 7
⇒ x = 12/7
∴ The value of x is (12/7) and the value of y is (-8/7).
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Determine the truth value of the given conditional statement. If true, explain your reasoning. If false, give a counterexample.
If a number is divisible by 6 , then it is divisible by 3 .
The given conditional statement is true that is If a number is divisible by 6, then it is divisible by 3".
What are conditional statement?A conditional statement involves 2 propositions, p and q. The conditional statement, is a proposition which we write as;
p⇒q, and read "if p then q"
An example of a conditional statement is : p⇒q, that is:
if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that AB^2 = BC^2 + AC^2
"If a number is divisible by 3, then it is divisible by 6." is the inverse of the conditional statement "
Thus If a number is divisible by 6, then it is divisible by 3".
Therefore, the given conditional statement is true that is If a number is divisible by 6, then it is divisible by 3".
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Is 7√56 rational or irrational? Explain.
What is Irrational Number?
An Irrational number is areal number that cannot be expressed as a ratio of integers; for example [tex]\sqrt{2}[/tex] is an irrational number. We cannot express any irrational number in the form of ratio, such as p/q, where p and q are integers, q[tex]\neq[/tex] 0. Again, the decimal expansion of an irrational number in neither terminating nor recurring.
Let us assume [tex]7\sqrt{56}[/tex] is rational.
So, we can write this number as
[tex]7\sqrt{56}[/tex] = a/b __(1)
Here, a and b are two co-prime numbers and b is not equal to zero.
Simplify the equation (1) divide by 7 both sides, we get
[tex]\sqrt{56}=\frac{a}{7b}[/tex]
Here, a and b are integers, so a/7b is a rational number, so [tex]\sqrt{56}[/tex] should be a rational number.
But [tex]\sqrt{56}[/tex] is a irrational number, so it is Contradictory.
Therefore, [tex]7\sqrt{56}[/tex] is irrational number.
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Write the estimated
thickness of a sheet of
paper using a single digit
and a power of 10.
Round 0.0013 to 0.001.
Write 0.001 as 1 x 10-³.
The estimated thickness of a sheet of paper using a single digit and a power of 10 as required in the task content is; 1 × 10-³.
What is the estimated thickness of a sheet of paper using a single digit and a power of 10 as required?It follows from the task content that the estimated thickness of paper such that it is written using a single digit and a power of 10 as required in the task content is to be determined.
Given;
Thickness of sheet = 0.0013.
By rounding to one significant digit; the digit is considered and rounded down to zero which is added to 1 so that we have;
= 0.001.
On this note, since the number, 0.001 can be written via the laws of indices as;
= (1/1000)
= 1/10³
And ultimately, we have
= 1 × 10-³.
Ultimately, the estimated thickness of a sheet of paper using a single digit and a power of 10 as required in the task content is; 1 × 10-³.
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The measure of the supplement of an angle is four times the measure of the angle. Find the measures of the angle and it's supplement.
The measures of the angle and it's supplement are144° and 36° respectively.
supplementary angles are those angles that sum up to 180°. The supplement of an angle is calculated by subtracting the value of the angle from 180°.The measure of the supplement of an angle is four times the measure of the angle. (given)
Let us consider the value of the supplement be X°.
Therefore the value of the angle is 4X°
180 - X = 4X
X = 36° (The value of supplement)
180°-X = 144°( The value of angle)
Hence the angles are 36° and 144° .
The measures of the angle and it's supplement are144° and 36° respectively.
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HELP WITH THIS PROBLEM PLS PLS
Answer:
Here,
MP=MN+NP=17+3y
or, 5y+9=17+3y
Now do equation and find the value of y.
Answer:
MP = 29
mp = mn + np
17 + 3y = 5y + 9
2y = 8
y= 4, NP = 3(4) = 12
so, MP = mn + np.... 12 + 17
MP = 29
I need help with the answer for Geometry, could someone help?
Answer:
48
Step-by-step explanation:
ABC is a right triangle so the masure of ∠A = 90°
The sum of interior angles in a triangle is equal to 180 so we will write an equation accordingly to find the
missing angle:
90 + 2x + 14 + 4x - 26 = 180 add like terms
78 + 6x = 180 subtract 78 from both sides
6x = 102 divide both sides by 6
x = 17
Now replace x with 17 to calculate the measure of m∠B
2*17 + 14 = 48
Factor the expression: 3x² - 7x + 2
Answer:
2 or 1/3
Step-by-step explanation:
by getting the product and sum,then the roots
Evaluate the equation: 6w = 180
w =
Answer: Evaluate
6w=180
Divide both sides
6
6w = 6
180
Simplify
6
6w =30
Solution
w=30
Step-by-step explanation: hope this helps
Are 1 divided by 3/4 and 1/3 divided by 4 equivalent fractions?
Answer:
No Because 1/1 : 3/4 = 4/3 and 1/3 : 4/1 = 1/12
Marc wants to qualify for the 200-meter dash at the school championship.
In order to qualify, his mean running time for 5 races must be no greater than 22.8 seconds.
A list of Marc's running times, in seconds, for his first 4 races is shown.
23.1, 23.2. 22.8, 21.9
What is the maximum running time, in seconds, Marc can have in his last race in order to qualify for the championship? Round the answer to
the nearest tenth.
______ seconds
the maximum time that he can have in his last race is 23 seconds.
What is the maximum running time, in seconds?
We know that the average can not be greater than 22.8 seconds, then if x represents the time of the last race, the maximum value that x can take is given by the equation:
(23.1 + 23.2 + 22.8 + 21.9 + x)/5 = 22.8
(That is the equation for the mean of the 5 times)
Solving that for x we will get:
(23.1 + 23.2 + 22.8 + 21.9 + x) = 5*22.8
91 + x = 114
x = 114 - 91 = 23
So the maximum time that he can have in his last race is 23 seconds.
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If P Q R S is translated along <3,-2 >, reflected in y=-1, and rotated 90° about the origin, what are the coordinates of P''' Q''' R''' S''' ?
P'''( 1 , -2 ) Q'''( 0 , 1) R'''( -1 , 3 ) S'''( -2 , 0) are the coordinates of P''' Q''' R''' S''' .
What does the term "coordinates" mean?
Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicses, scientists, and engineers frequently employ a variety of coordinate systems.( x , y) → ( x + 3 , y - 2 )
p' ( -2, -1 ) Q' ( 1 , 0) R'( 3, -3 ) S'(0, -4 )
( x , y ) → ( x , -2 - y)
p''(-2 , - 1 ) Q''( 1 , 0 ) R''( 3 , 1 ) S''( 0,2 )
( X , Y ) → ( -Y , X )
P'''( 1 , -2 ) Q'''( 0 , 1) R'''( -1 , 3 ) S'''( -2 , 0)
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The mean income of households in the US is $75,000 per year. The median household income in the US is $42,000 per year. Describe the shape of income in the US. skewed left, mean > median skewed left, mean < median skewed right, mean > median skewed right, mean < median
Answer:
skewed right, mean > median
Step-by-step explanation:
just did it
Answer:
skewed right, mean>median
Step-by-step explanation:
edge 2023
Simplify by combining like terms. 7 b-(3 a-8 b)
By combining the like terms, the simplified form of the expression 7b-(3a-8b) is -3a+15b
Given,
The algebraic expression = 7b-(3a-8b)
Expand the expression
7b-(3a-8b)= 7b-3a+8b
Rearrange the terms and combine like terms
7b-3a+8b= -3a+7b+8b
=-3a+(7+8)b
=-3a+15b
Hence, By combining the like terms, the simplified form of the expression 7b-(3a-8b) is -3a+15b
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Find the midpoint of the line segment with the given
endpoints.
(-4, 5) and (2, 5).
Answer:
Midpoint = (-1, 5)
Step-by-step explanation:
x₁ + x₂ y₁ + y₂
Midpoint = (--------------- , -----------------)
2 2
-4 + 2 5 + 5
Midpoint = (--------------- , -----------------)
2 2
-2 10
Midpoint = (--------------- , -----------------)
2 2
Midpoint = (-1, 5)
I hope this helps!
Amy hiked due east for 2 miles and then hiked due south for 3 miles.
b. How far and in what direction is Amy from her starting position?
The distance between Amy's initial and final position is 1 mile and she is facing South direction
It is given that,
Amy first moves towards East direction in reference to her initial position for 2 miles
The distance covered by Amy in East direction = 2 miles
Then,
Amy moves towards South direction in reference to her initial position(facing East side) for 3 miles
The distance covered by Amy in South direction = 3 miles
We need to find,
The distance between Amy's initial and final position which will be given by the displacement between both points
Let's say that the positive direction is East and the negative direction is south.
The distance covered by Amy in East direction = + 2 miles
The distance covered by Amy in South direction = - 3 miles
Then , +2 +(-3) = -1
Hence, the distance between Amy's initial and final position is 1 mile and she is facing South direction
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Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
P(-2,-5,8) and Q(3,-2,-1)
The midpoint is at (1/2 , -3, 7/2 )
In the given statement is
To find the midpoint of the line segment joining the pair of points
P(-2,-5,8) and Q(3,-2,-1)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =( [tex]\frac{x_{1}+x_{2} }{2}[/tex] ,[tex]\frac{y_{1}+y_{2} }{2}[/tex] , [tex]\frac{z_{1}+z_{2} }{2}[/tex])
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points P(-2,-5,8) and Q(3,-2,-1)
Solving for the midpoint , we have,
m = ([tex]\frac{-2 + 3}{2} , \frac{-5+ (-2)}{2} , \frac{8 +(-1)}{2}[/tex])
m = (1/2 , -3, 7/2 )
Therefore, the midpoint is at (1/2 , -3, 7/2 )
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Determine whether each infinite geometric series diverges or converges.
If the series converges, state the sum. 1-1+1- . . . .
Determine whether each infinite geometric series diverges or converges.The series converges.
If the series converges, state the sum. 1-1+1- . . . .
The sum of the infinite series is 1/2
What is the sum of the infinite series?
Given:
[tex]a(\text{ the first term})=1\\\\r(\text{ the common ratio})= \frac{a_2}{a_1} = \frac{-1}{1}=-1[/tex]
Since [tex]\vert r\vert < 1[/tex] , the infinite series converges.
The sum of infinite geometric series is:
[tex]S_\infty=\frac{a}{1-r} ; -1 < r < 1\\\\S_\infty=\frac{1}{1+1} =\frac{1}{2}[/tex]
The sum of the infinite series is 1/2
What is an infinite geometric series?
The result of an endless geometric sequence is an infinite geometric series.There would be no conclusion to this series.The total of all finite geometric series can be determined.However, if the common ratio of an infinite geometric series is bigger than one, the terms in the sequence will grow steadily larger, and adding the larger numbers together will not yield a solution.To learn more about infinite geometric series, refer:
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