An ordered list of terms is a Mathematical Sequences.
In mathematics, informally speaking, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements, or terms). The number of ordered elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence.
Most precisely, a sequence can be defined as a function whose domain is a countable totally ordered set, such as the natural numbers. For example, (M, A, R, Y) is a sequence of letters with the letter 'M' first and 'Y' last. This sequence differs from (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence. Sequences can be finite, as in this example, or infinite, such as the sequence of all even positive integers (2, 4, 6,...). Finite sequences are sometimes known as strings or words and infinite sequences as streams. The empty sequence ( ) is included in most notions of sequence, but may be excluded depending on the context.
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Find the area of the polygon with the given vertices (3,7), B (5,7), C (3,-7), D (5,-7)
From the given vertices, the area of the polygon is 28.
RectanglesThe rectangle is a quadrilateral. The classification for quadrilaterals is given by the length of sides and angles. For a rectangle, the opposite sides are equal and parallel and their interior angles are equal to 90°.
A rectangle is a geometric figure that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).
The area of a rectangle is given by the multiplication between the base and the height.
First, you should plot the points, then see image 1.
From the figure, it is possible to see that the bases ( AB and CD) = 5-3=2
and heights (AC and BD) =-7-(-7)=7+7=14. Thus,
A= B*H= 2*14=28
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What is the difference of the two rational expressions in simplest form? State any restrictions on the variable.
b. x-1 / x+5 - x+3 / x²+6 x+5
The simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex] is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5, x≠ -1.
As given in the question,
Given expression is [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex]
Simplify the given two rational expressions by factorizing them,
[tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{x^{2} +5x +x+5}\\\\= \frac{x-1}{x+5}-\frac{x+3}{(x+5)(x+1)}\\\\= \frac{x^{2} -1-(x+3)}{(x+5)(x+1)}\\\\= \frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]
Restriction on the variables is given by x≠ -5, x≠ -1.
Therefore, the simplification of difference of the given two rational expressions [tex]\frac{x-1}{x+5}-\frac{x+3}{x^{2} +6x+5}[/tex] is equal to [tex]\frac{x^{2}- x-4}{(x+5)(x+1)}[/tex]. Restriction on the variables is given by x≠ -5, x≠ -1.
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Last month, jennifer earned $180 for her after-school job. if she was paid $7.50 per hour, how many hours did jennifer work?
Answer: 22
Step-by-step explanation: 143 divided by 6.50 = 22, therefore our answer is 22
Simplify by combining like terms. y² / 2 + y/3 + y²/3 - y/5
On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5 the simplified value is 5y²/6 +2y/15.
In an algebraic expression Like terms are defined as those terms that have same variable and that variable has the same power .
For Example : 5a,9a are like terms .
In the given question
=y²/2 +y/3 +y²/3 -y/5
On combining the like terms , one with y² and other with y.
We get;
=y²/2 +y²/3 +y/3 -y/5
Taking LCM of like terms with y² as "6"
and LCM of like terms with y as "15".
We get ;
=(3y²+2y²)/6 +(5y-3y)/15
=5y²/6 +2y/15
Therefore , On combining the like terms of the expression y²/2 + y/3 + y²/3 - y/5, the simplified value is 5y²/6 +2y/15.
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avas sister is 9 years less than twice avas age b
Ava's age = b
Ava's sister's age = 2b -9
You and your friend are swimming against the current. You move forward 15 feet. Your friend is not a strong swimmer, so he moves back 6 feet. write each amount as the distance swam.
The amount of you swam is +15 feet and your friend swam is -6 feet.
Given that you move forward 15 feet and your friend is not a strong swimmer, so he moves back 6 feet.
The arithmetic operators means performing an addition, subtraction, multiplication, division, exponentiation, and modulus operations.
It is given that you move the forward that means you move in positive direction.
So, you move forward means you move +15 feet.
It is also given that your friend is not a strong swimmer, so he moves back that means he move in negative direction.
So, your friend moves backward means he move -6 feet.
Hence, you move forward 15 feet is +15 feet and your friend is not a strong swimmer, so he moves back 6 feet is -6 feet.
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Please help!!! I don't need a quick answer
Answer:
780 ≥ 58.53x + 566.83
Step-by-step explanation:
He has $780 that he can spend, so the total must be less than or equal to 780.
Let x = number of biking outfits.
Costs:
Bicycle: $490.50
Reflectors: 4 × $14.98 = $59.92
Gloves $16.44
Outfits: $58.53x (The cost of x outfits is 58.53x)
The total he spends is:
490.5 + 59.92 + 16.44 + 58.53x =
= 58.53x + 566.86
This total has to be less than or equal to $780.
58.53x + 566.86 ≤ 780
This can be written as
780 ≥ 58.53x + 566.83
Solve the system:
5x-6y= -44
3x + 7y = 69
Answer:
Point form:
(2, 9)
Equation form:
x = 2,y = 9
Step-by-step explanation:
!!! HELP PLEASE !!!
On Marshal’s 5th grade math test, he was asked to evaluate: 25,328.941 ÷ 104. The answer he wrote was 25.328941. Unfortunately for Marshal, his teacher marked this answer as incorrect. Explain the mistake Marshal made. What is the correct solution to 25,328.941 ÷ 104?
marshal just stoopid.. that simple
anyway marshal divided it by 100 instead of 104, the answer of it divided by 104 is 243.547509615
Solve to find x and y in the diagram.
Answer choices:
x = 3, y = 15
x = 15, y = 3
x = 15, x = 8
x = 15, y = 6
Answer:
Option 2 [tex]x[/tex] = 15, [tex]y[/tex] = 3
Step-by-step explanation:
Vertical angles are equivalent. Thus [tex]4x+10y[/tex] = 90. To solve for [tex]x[/tex], we set [tex]6x[/tex] = 90, since adjacent angles equal 180. This gives us 15 as x. Plugging 15 into the first equation we get that y is equal to 3.
Find the missing term(s) of each geometric sequence. 0.004,□,0.4, . . .
The term is 0.04
The geometric sequence given is
0.004, __, 0.4, 4....
Now let us find the value of r which is the factor between the terms, called the common ratio.
r = [tex]\frac{0.04}{0.004}[/tex] = [tex]\frac{0.4}{0.04}[/tex]
= 10
General form= [tex]a_{n}[/tex] =[tex]a_{1}[/tex]×[tex]r^{n-1}[/tex]
The geometric series
[tex]a_{n}[/tex] = 0.004× [tex]10^{n-1}[/tex]
Therefore to find the second number of the sequence is
[tex]a_{2}[/tex] = 0.004 × [tex]10^{2-1}[/tex]
= 0.004 × 10
= 0.04
Therefore the missing term of a geometric sequence is 0.04.
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SOMEBODY PLEASE: Lyle is driving from home to his friend’s house, a distance of 720 km. He plans to drive at an average speed of 80 km per hour, take an hour for lunch, and take two 15- minute breaks. He must arrive at his friend’s house by 7:00 p.m. What is the latest possible time that Lyle could leave home in order to arrive at his friend’s house on time?
Answer:
8:30 a.m.
Step-by-step explanation:
The total time it takes for Lyle to reach his friend's house is 720/80 + 1 + 0.25 * 2, which is 9 + 1.5 = 10.5 hours
The latest possible time that Lyle would be able to leave his house to reach on time is 8:30 a.m.
Determine whether each sequence is arithmetic. If so, identify the common difference and find the 32 nd term of the sequence. 3,18,33,48, . . . . .
Solving the problem with the arithmetic progression, the 32nd term of the sequence is 558.
Arithmetic progression is a sequence of numbers in which the next term is depicted by adding a fixed number 'd' to the preceding term. The series is in arithmetic progression.
We all know the formula for arithmetic progression is,
aⁿ = a + ( n-1 ) d
where d = difference between two corresponding terms, n = no. of term, a = first term
We have to find the 2nd term, and it's, a³⁸ = 3 + ( 38 - 1)( 18 - 3 ) = 3 + 37× 15 = 3 + 555 = 558.
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Determine whether the event is mutually exclusive or not mutually exclusive. Explain your reasoning.
Rolling a pair of dice and getting a sum of 7 and 6 on the face of one die
We can see that there is no element which is common Hence, they are mutually exclusive events.
Let A be the event of getting a sum of 7 on dice.
Let B be the events of getting a sum of 6 on dice.
A={ (1,6), (2,5), (3,4), (4,3), (5,2) }
B = { (1,5) , (2,4), (3,3), (4,2), (5,1), }
What are Mutaullty exclusive events?Mutaullty exclusive events are those when there is no common event between two events.
Where there is empty set of intersection.
But we can see that there is no element which is common
So, n(A∩B) = ∅
Hence, they are mutually exclusive events.
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The table represents the linear function f(x), and the equation represents the linear function g(x).
Compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
The correct option is (C) The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
Given that the following table represents the linear function f(x), and the equation represents the linear function g(x) :
x 0 2 4
f(x) 1 9 17
and g(x) = 3x + 1 .........(1)
We have to compare the y-intercepts and slopes of the linear functions f(x) and g(x) and choose the answer that best describes them.
From the graph, we note that (0, 1), (2, 9) and (4, 17) are three points on the line graph of function f(x).
We know that, the slope of any line having two points (a, b) and (c, d) on it is given by
m = d-b/c-a
So, the slope of the line of f(x) is
m = 9-1/2-0
m = 8/2
⇒ m = 4
Since the line of f(x) passes through the point (0, 1), so its equation will be
f(x) -1 = m(x-0)
⇒ f(x) -1 = 4(x-0)
⇒ f(x) -1 = 4x
⇒ f(x) = 4x+1 ........... (2)
The slope-intercept form of the equation of a line is y = mx + c, where m is the slope and c is the y-intercept of the line.
Comparing equation (2) and (1) with the slope-intercept form, we get
slope of f(x) = 4 and y-intercept of f(x) = 1 and
slope of g(x) = 3 and y-intercept of g(x) = 1.
Thus, the slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
Option (C) is CORRECT.
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For Every $100 he earns, Grayson Pays Federal income tax of $19. how much federal income tax will he pay on earnings of $500?
Find the geometric mean between pair of numbers.
5 and 20
For numbers 5 and 20 the value of the geometric mean of these numbers is
Gm (5, 20) = 10
What is the geometric mean?The definition of geometric mean is a calculation that is performed on a set of numbers which consists of calculating the square root of the product between them, the equation is as follows:
Gm (a,b) = √ab
Then in our case that we have the values 40 and 15, these are equivalent to the variables a and b
a = 5b = 20We substitute and solve for the square root
Gm (5, 20) = √5×20Gm (5, 20) = √100Gm (5, 20) = √10²Gm ( 5, 20) = 10Learn more about geometric mean in:
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PR00F Write a flow proof.
Given: XY || WZ and XW || YZ
Prove: Δ X W Z ≅ ΔZ Y X
We have proved that , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX
It is given that XY ║ WZ and XW ║ YZ.
We have to prove that ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX.
What is the SSS rule of congruency of triangles ?
SSS axiom states that if two triangles have three pairs of congruent sides, then the triangles are congruent.
As per the question ;
XY ║ WZ and XW ║ YZ
So , using this data we can conclude that ;
XY = XW and WZ = YZ
The two triangles are ΔXWZ and ΔZYX
So ,
XY = XW (from given data)
and
WZ = YZ (from given data)
and
XZ = XZ (common)
∴ Both triangles are congruent to each other ;
i.e.,
ΔXWZ ≅ ΔZYX
by using the SSS axiom.
Thus , the ΔXWZ is congruent to ΔZYX i.e., ΔXWZ ≅ ΔZYX
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HELP ASP SHOW UR WORK WILL GET BRAINILEAT AND 10 points
Answer -
1/2x + 5 = 7
1x/2 + 5 = 7
1x/2 + 5 = 7
x/2 + 5 = 7
x/2 + 5 = 7
x/2 + 2.5/2 = 7
X = 4
Which of the following systems of equations has the solution (1, 4)?
y = –3x – 1
y = –x + 5
y = 3x + 1
y = –x + 5
y = 3x + 1
y = x – 5
y = 3x + 1
y = –x – 5
Answer:
y = 3x + 1
y = -x + 5
Step-by-step explanation:
Take the system of equations and substitute (1 ,4) in any one of the equations. If both the sides are justified, then (4,1) is the solution to that pair of equations.
1) y = -3x - 1 ---------(I)
y = -x + 5
Substitute (1,4) in equation (I)
4 = -3*1 - 1
4 = -3-1
4 ≠ -4
So, (1, 4) is not a solution.
2) y = 3x + 1 ---------------(II)
y = - x + 5
Substitute (1 ,4) in equation (II)
4 = 3*1 + 1
4 = 3 + 1
4 = 4
(1 ,4) is the solution for this system of equation.
[tex]\frac{5^{7}x 125^3}{25^2 x 54}[/tex]
244140625 x^{54} value of the Algebraic functions .
What is Algebraic functions?
A function that satisfies is said to be algebraic if it has integer coefficients and is a polynomial in the variables and. Algebraic functions include inverses of those that can be created using a small number of elementary operations as well as those that can be created using only those operations.Evaluate the exponent
= [tex]\frac{5^{7} . 125^{3} }{25^{2} } . x^{54}[/tex]
Evaluate the exponent
= [tex]\frac{78125 . 125x^{3} }{25^{2} } . x^{54}[/tex]
Multiply the numbers
= [tex]\frac{78125 . 1953125 }{25^{2} } . x^{54}[/tex]
Evaluate the exponent
= [tex]\frac{152587890625}{25^{2} } . x^{54}[/tex]
Cancel terms that are in both the numerator and denominator
= [tex]\frac{152587890625}{625} . x^{54}[/tex]
= [tex]\frac{152587890625}{625} . x^{54}[/tex]
= 244140625 x^{54}
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The product of three and a number divided by six is twelve.
Answer:
24
Step-by-step explanation:
3a/6 = 12
3a = 6 * 12
3a = 72
a = 72/3
a = 24
Check:
3*24/6 = 12
72/6 = 12
9. You can buy 6 bracelets at Toy Barn for $5.40. You can buy 11 of the same
bracelets at the Dollar Deals for $10.50. (a)How much does it cost per bracelet at
each store? (b)Which store has the better buy?
Answer:
Solutions below.
Step-by-step explanation:
a) To solve this question, we can use the formula.
Average Cost per Bracelet = Total Price ÷ Number of Bracelets.
Toy Barn
Average Cost = $5.40 ÷ 6 = $0.90 per bracelet
Dollar Deals
Average Cost = $10.50 ÷ 11 = $0.95 per bracelet (rounded off to 2 decimal places)
b) The better deal comes with a lower price per bracelet, in this case, Toy Barn has a better deal.
"a
4. Mr. Jensen's class was tracking the average
temperature each month. Given the data below,
calculate the slope and explain what it means in
context.
Month
Avg. Temp (°F)
Jan Feb
42 56
Mar
70
Apr
84
The slope of the given problem is 14
It is a problem of linear regression Line
y = a +by
where a = ∑Y - b ∑X / N
and b = N ∑XY - (∑X×∑Y)/ ( N∑x²- (∑X)
Month(X) Temperature (y) X² XY
1 42 1 42
2 56 4 112
3 70 9 210
4 84 16 336
Total 10 252 30 700
Number of observation (n) = 4
So, b = 4(700) - (10)(252) / ( 120 - 10²)
= 2800-2520/20
= 280/20
= 14
b = 14
Now a= 252 - (14)10/ 4
=112 /4
= 28
So, The linear regression line is
y= 28 + 14x
Slope = 14
The slope here is positive which means increase in period or moving forward in month is increasing the average temperature of the month.
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PLEASEEE HELP!
6 Chasing Angles: Find the measure of all the missing interior and exterior angles in this figure using linear pairs, vertical angles, and triangle angle sum. Label the diagram
Answer:
Needs alot of steps which you can try
Step-by-step explanation:
Sum of interior angles=exterior angle
Eg, left side 60°+90° = the exterior (big angle outside triangle)
All of the lines are straight so you can find angles using (angles on a straight line) so 180°- the angle known when your solving
There is also opposites angles which are equal, you can search it up
Simplify by combining like terms. 1/2 / ( x² - y²) - 5/2(x² - y²)
The simplified value of the expression 1/2 / ( x² - y²) - 5/2(x² - y²) is -2/x² + 2/y² .
Like terms in an algebraic expression is defined as those terms that have same variable and that variable has the same power .
For Example : 5y,2y are like terms .
In the given question 1/2 / ( x² - y²) - 5/2(x² - y²) the first term is a complex fraction,
[tex]=\frac{\frac{1}{2} }{(x^{2}-y^{2} ) } -\frac{5}{2(x^{2} -y^{2}) }[/tex]
Simplifying the complex fraction we get ,
= 1/2(x² -y²) -5/2(x² -y²)
= 1/(2x² - 2y²) -5/(2x² -2y²)
On further simplifying
= 1/2x² -1/2y²- 5/2x² +5/2y²
On combining the like terms of x² and y².
= 1/2x² - 5/2x² -1/2y² +5/2y²
taking LCM of like terms as 2x² and 2y².
=(1-5)/2x²+(-1+5)/2y²
= (-4)/2x² + 4/2y²
=-2/x² + 2/y²
Therefore , the simplified value of the expression 1/2 / ( x² - y²) - 5/2(x² - y²) is -2/x² + 2/y² .
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Solve each system by elimination.
y = 4 - x , 3x + y = 6
The solution of the given system of equations is (1, 3)
We can solve a system of equations using:
- graphical method
- elimination method
- substitution method
The given system of equations:
y = 4 - x ....... (1)
3x + y = 6 ....... (2)
To use elimination method, add x to both sides of equation (1)
x + y = 4 ....... (3)
Substract equation (3) from equation (2)
3x + y = 6
x + y = 4 –
2x = 2
x = 1
Substitute x = 1 into equation (1)
y = 4 - x
= 4 - 1 = 3
Thus the solution is (1,3)
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Sam has a car that is worth $8,500. However,
he still owes $4,750 on the car. He also has
$1,500 in his savings account, a comic book
collection worth $900 and owes $475 on his
credit card. What is the total of Sam's
liabilities?
The total of Sam's liabilities are $5225.
What is a liability?A liability is an obligation of an individual towards his creditors arising out of some transactions. Bank loans, credit card bills, accounts payable , accrued expenses are examples of liabilities.
Given that Sam has a car that is worth $8,500. However, he still owes $4,750 on the car. He also has $1,500 in his savings account, a comic book collection worth $900 and owes $475 on his credit card.
Irrespective of his assets and savings Sam still owes $4750 on the car and $475 in his card card , therefore these are his liabilities.
Total liabilities of Sam = $4750+$475 = $5225
Therefore, total of Sam's liabilities are $5225
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solve for x and y
6x+5y=-10
3x+5y=20
Answer: x = -10
Step-by-step explanation:
Answer:
(- 10, 10 )
Step-by-step explanation:
6x + 5y = - 10 ( subtract 6x from both sides )
5y = - 10 - 6x → (1)
3x + 5y = 20 → (2)
substitute 5y = - 10 - 6x into (2)
3x - 10 - 6x = 20
- 3x - 10 = 20 ( add 10 to both sides )
- 3x = 30 ( divide both sides by - 3 )
x = - 10
substitute x = - 10 into (2) and solve for y
3(- 10) + 5y = 20
- 30 + 5y = 20 ( add 30 to both sides )
5y = 50 ( divide both sides by 5 )
y = 10
solution is (- 10, 10 )
On his first 2 tests Nate's average score was 80 percent.
On his next 3 tests Nate's average score was 90 percent.
What was his average score for all 5 tests? (Hint: Find the
total number of points scored on all tests, then divide by 5.)
Answer:
i think the answer may be possibly 86%
