The sequence 1,1,2,3,5,8, ........... doesn't form an AP as they have the varying common difference.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between these two numerical orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come across a few specific keywords in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be explained in expressed in the form of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' : d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the sequence given is; 1,1,2,3,5,8, ...........
The series contains of given 6 terms.
Let the initial term be 'a₁' = 1.
The second term be 'a₂' = 1.
The third term be 'a₃' = 2.
And, the fourth term is 'a₄' = 3.
For the sequence to form the AP, they must have the equal common difference. So,
d = a₃ - a₂
Substitute the values.
d₁ = 2 - 1
d₁ = 1
Thus, the calculated common difference is 1.
or d = a₅ - a₄ (Put the values)
d₂ = 5 - 3
d₂ = 2
Since, d₁ ≠ d₂
Thus, we can say that the given sequence is not forming an AP.
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help me understand the linear equation
Answer:
y = 4x - 4
Step-by-step explanation:
Slope intercept follows the form y = mx + b
m represents the slope
b represents the y intercept
To find the slope of a table you can find the constant change in y over the constant change in x. The y values 0, 4, 8, 12 are increasing by 4 every point meaning the change in y is 4. The x values 1, 2, 3, 4 are increasing by 1 every point meaning the change in x is 1. Making the slope 4/1 or just 4.
Now use what you know: y = 4x + b to find b, we can use any of the coordinate points to substitute. I'm going to use point (1,0) where 1 is the x value and 0 is the y value.
y = 4x + b
0 = 4(1) + b
Solve for b
b = -4
:)
can you please help me? i also need to know how you got the answer pls and thabk u
Answer:
7 degrees
Step-by-step explanation:
Start with the temperature of -7 deg at 6:00 a.m.
The temperature increases 14 degrees in the next 6 hours.
6 hours after 6:00 a.m. is noon.
We are asked the temperature at noon.
At noon, the temperature is 14 degrees higher than -7 deg.
We add the increase, 14 deg, to the starting temperature, -7 deg.
-7 deg + 14 deg = 7 deg
Answer: 7 degrees
Identify what you need to know. Then use the information in the problem to solve.
Which triangles are not necessarily similar?
F. two right triangles with one angle measuring 30°
G. two right triangles with one angle measuring 45°
H. two isosceles triangles
J. two equilateral triangles
Two isosceles triangles are not necessarily similar triangles.
Similar triangles are triangles that have congruent corresponding angles and proportional corresponding sides.
Analyzing each statements:
F. two right triangles with one angle measuring 30°
- these two triangles have angles measuring 90°, 30°, and 60°
- they both have equal angle measurements
∴ they are similar triangles
G. two right triangles with one angle measuring 45°
- these two triangles have angles measuring 90°, 45°, and 45°
- they both have equal angle measurements
∴ they are similar triangles
H. two isosceles triangles
- isosceles triangles are triangles that have two sides of equal lengths
- two isosceles triangles are similar if the angle of one is congruent to the corresponding angle of the other
∴ they are not necessarily similar, unless stated that their corresponding angles are equal
J. two equilateral triangles
- all equilateral triangles of any side lengths are considered similar triangles as each of its corresponding sides are proportional
∴ they are similar triangles
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Below are two parallel lines with a third line
intersecting them.
46°
What is x equal to?
Answer:
x = 134°
Step-by-step explanation:
The angle labelled [tex]x^{\circ}[/tex] and the 46° add up to 180° as they are co-interior angles.
∴ [tex]x^{\circ} + 46^{\circ} = 180^{\circ}[/tex]
⇒ [tex]x^{\circ} = 180^{\circ} - 46^{\circ}[/tex] [Subtracting 46° from both sides]
⇒ [tex]x = 134^{\circ}[/tex]
Therefore [tex]x[/tex] is equal to 134°.
The coordinates of the vertices of quadrilateral are A(-6,-1),B(-5,2),C(-1,-5), and D(0,-2). Parker states that quadrilateral is a parallelogram. Prove or disprove Parker’s statement.
=======================================================
Explanation:
Use the slope formula to find the slope of the line through A(-6,-1) and B(-5,2)
[tex](x_1,y_1) = (-6,-1) \text{ and } (x_2,y_2) = (-5,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - (-1)}{-5 - (-6)}\\\\m = \frac{2 + 1}{-5 + 6}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]
The slope of segment AB is 3.
-------------
Repeat these set of steps for segment CD
C = (-1,-5)
D = (0,-2)
[tex](x_1,y_1) = (-1,-5) \text{ and } (x_2,y_2) = (0,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - (-5)}{0 - (-1)}\\\\m = \frac{-2 + 5}{0 + 1}\\\\m = \frac{3}{1}\\\\m = 3\\\\[/tex]
The slope of segment CD is also 3
Parallel lines have equal slopes, but different y intercepts.
Since AB and CD have the same slope of 3, this shows AB is parallel to CD.
--------------
Now find the slope of segment BD
B = (-5,2)
D = (0,-2)
[tex](x_1,y_1) = (-5,2) \text{ and } (x_2,y_2) = (0,-2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-2 - 2}{0 - (-5)}\\\\m = \frac{-2 - 2}{0 + 5}\\\\m = -\frac{4}{5}\\\\[/tex]
Segment BD has a slope of -4/5
--------------
Lastly, compute the slope of segment AC
A = (-6,-1)
C = (-1,-5)
[tex](x_1,y_1) = (-6,-1) \text{ and } (x_2,y_2) = (-1,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - (-1)}{-1 - (-6)}\\\\m = \frac{-5 + 1}{-1 + 6}\\\\m = -\frac{4}{5}\\\\[/tex]
Segment AC has a slope of -4/5
Both segments BD and AC have the same slope of -4/5.
Therefore, segments BD and AC are parallel
----------------
We have two pairs of opposite parallel sides. Ultimately figure ABDC is a parallelogram
See the diagram below.
Pleaseeee Helppp
mx=n+p for x
Answer:
n – p
x= –––––
m
Hope that helps! Have a good day :)
Fireworks are shot from a barge in a river There is an explosion circle inside which all n the fireworks will explode. Spectators sit outside â safety circle 800 feet from the center of the fireworks display.
a. Find the approximate circumference of the safety circle.
The approximate circumference of the safety circle is 5026.54825 meters.
What do we mean by a circle?A circle is a shape formed by all points in a plane that are at a given distance from the center. It is the curve traced out by a point moving in a plane so that its distance from a given point remains constant. The radius is the distance between any two points on a circle and the center. Typically, the radius must be a positive number. A degenerate case is a circle with r = 0. Except where otherwise noted, this article is about circles in Euclidean geometry, specifically the Euclidean plane.To find the circumference:
Formula: 2πrRadius = 800 metersSo,
C = 2πrC = 2π800C = 5026.54825Therefore, the approximate circumference of the safety circle is 5026.54825 meters.
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3m / 6 > 3; m = 8 I know the answer is no but can someone explain why???
Answer:
Statement is true
Step-by-step explanation:
3m
---------- > 3; m = 8
6
3(8)
---------- > 3
6
24
---------- > 3
6
24 ÷ 6 = 4
4 > 3
or
3m
---------- > 3; m = 8
6
3m
---------- > 3 (6)
6 (6)
3m > 18
÷3 ÷3
m > 6
8 > 6
Either way, the statement is true. I have no idea why it would be no. I'm sorry if I wasn't of any help.
Determine whether each sequence is geometric. If so, find the common ratio. 1/2, 1/4, 1/6, 1/8, . . . . .
The given sequence is not geometric.
What is a geometric progression?A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.
Given: [tex]\frac{1}{2}, \frac{1}{4},\frac{1}{6},\frac{1}{8},...[/tex]
Here, [tex]\frac{\frac{1}{4}}{\frac{1}{2}}\neq \frac{\frac{1}{6}}{\frac{1}{4}}\neq \frac{\frac{1}{8}}{\frac{1}{6}}[/tex]
That is, the given sequence doesn't follow the only required condition for a sequence to be geometric.
Hence, The given sequence is not geometric.
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Half of the smaller of two consecutive even integers is equal to two more than the larger integer
By solving a linear equation we can see that:
The smaller number is -8The larger number is -6How to find the two numbers?
Here we have two consecutive even integers, we can write these as x and x + 2
We know that half of the smaller of the two is equal to 2 more than the larger one, this can be writen as:
x/2 = (x + 2) + 2
Now we can solve that linear equation for x:
x/2 = x + 2 + 2
x/2 = x + 4
-4 = x - x/2
-4 = x/2
-4*2 = x = -8
The smaller number is -8
The larger number is -8 + 2 = -6
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Find the sum of each finite series. Σ⁹ n=1 (-1)ⁿ . . . . 2
The sum of the given finite series is -1
The given series is:
[tex]\sum\limits^9_{n=1} {(-1)^{n}}[/tex]
The summation notation tell us that we need to add each term (-1)ⁿ as n moves from 1 to 9.
Let us expand this summation notation:
n = 1 ⇒ a(1) = (-1)¹ = -1
n = 2 ⇒ a(2) = (-1)² = 1
n = 3 ⇒ a(3) = (-1)³ = -1
We can continue to expand until n = 9, but we can see the pattern. The series can be written as:
[tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1[/tex]
We can see that a(1) and a(2) are cancelled out to each other. This applies to each pair of consecutive odd and even terms. Each term is cancelled out except a(9). Therefore:
[tex]\sum\limits^9_{n=1} {(-1)^{n}}=-1+1-1+1...-1=-1[/tex]
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Determine the slope of the line that contains the given points.
T(-6,-11), V(-12,-10)
The slope of the line containing (-6,-11) and (-12,-10) is (-1/6).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = -10 , [tex]y_{1}[/tex] = -11 , [tex]x_{2}[/tex] = -12 , and [tex]x_{1}[/tex] = -6 .
On substituting the values of variables in equation1, we will get
m = ( (-10)-(-11) ) / ( (-12)-(-6) ) = (1/(-6)) = (-1/6).
As the slope of a line is (-1/6), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (-6,-11) and (-12,-10) is (-1/6).
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What’s the answers to b,c and d for 20 points.
The expression can be simplified as follows:
a. (-4)(-2) -6(2 - 5) = 26
b. 12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = 43
c. 23 - (17 - 3.4)² + 6 = -155.96
How to solve an expression using PEMDAS rule?The expressions can be solved using PEMDAS rule,
P = Parenthesis
E = Exponential
M = Multiplication
D = division
A = addition
S = Subtraction
Hence,
a.
(-4)(-2) -6(2 - 5) = (-4)(-2) - 6(-3) = 8 + 18 = 26
b.
12.7 - 18.5 + 15 + 6.3 - 1 + 28.5 = -5.8 + 15 + 6.3 - 1 + 28.5 = 9.2 + 6.3 - 1 + 28.5 = 15.5 - 1 + 28.5 = 14.5 + 28.5 = 43
c.
23 - (17 - 3.4)² + 6 = 23 - (13.6)² + 6 = 23 - 184.96 + 6 = -161.96 + 6 = -155.96
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Each of these sequence or series formulas involves four quantities that are represented by a variable. For each fomula, describe the four quantities.
c. a n = a₁ rⁿ⁻¹
The four Quantities are a1 , r, n , [tex]S_{n}[/tex]
What is a Series:
A series can be highly generalized as the sum of all the terms in a sequence. However, there has to be a definite relationship between all the terms of the sequence.
Arithmetic progression
an = a1 + ( n-1) d
a1 is the first term
d =common difference
an is the nth term
an can be found out if we know the a1 , d and n
b) Arithmetic progression
a1 is the first term
an is the nth term
sn is the sum of the n terms of the series
Sn = n/2 ( a1 + an)
we can calculate sn if we know a1 , an and n
c)Geometric progression
an = a1rn-1
a1 is the first term
an is the nth term
r is the common ratio
we can calculate an if we know a1 , r and n
d)Geometric progression
Sn = a1( 1- rn) / 1 - r
a1 is the first term
r is the common ratio
sn is the sum of the n terms of the series
If we know a1 , r and n we can calculate [tex]S_{n}[/tex].
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HELP How do i calculate the surface area
Answer:
384, 576
Step-by-step explanation:
The surface area is
[tex]2(12 \cdot 6+12 \cdot 6+6\cdot 8)=384[/tex]
The volume is
[tex](12)(8)(6)=576[/tex]
Simplify by combining like terms. 0.5 g+g
The simplification by combining like terms of 0.5g + g is 1.5g.
According to the given question.
We have an expression 0.5g + g .
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression 0.5g + g.
Here 0.5g, and g both are the like terms.
So, we add coeffcients of g to simplify the given expression.
Therefore, the simplification of 0.5g + g is given by
0.5g + g
= 1.5g
Hence, the simplification by combining like terms of 0.5g + g is 1.5g.
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help please i’ll name you brainliest
Answer: 6 and 27
Step-by-step explanation:
Answer:
Step-by-step explanation:
4x+8= 4(x+2) and that should be the answer if not then i don't know what to do
Determine whether each infinite geometric series converges or diverges. If the series converges, state the sum. 150+30+6+ . . .
The given infinite geometric series 150+30+6+ . . . is convergent and the sum is 187.5
The given geometric series is:
150 + 30 + 6 + . . .
The common ratio (r) of a geometric series is given by:
r = a(n) / a(n - 1)
Notice that in the given series:
a(1) = 150
a(2) = 30
a(3) = 6
Hence, the common ratio is
r = a(2) / a(1) = 30/150 = 1/5
An infinite geometric series is convergent if 0 < | r | < 1.
Since r = 1/5, then the series is convergent and the sum exists.
Use the sum formula:
S = a(1) / (1 - r)
Substitute a(1) = 150 and r = 1/5 into the formula:
S = 150 / (1 - 1/5)
= 150 / (4/5)
= 187.5
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Suppose a is a 57 matrix. How many pivot columns must a have if its columns span ? why?.
There must be pivot columns in the matrix. "A has a pivot place in every row" and "A's columns span an R5" seem to be logically equivalent.
What is defined as pivot columns?When a matrix has been in row-echelon form, the first nonzero entry in each row is referred to as a pivot, as well as the columns wherein pivots appear are referred to as pivot columns.
If two matrices in row-echelon form seem to be row-equivalent, their pivots are in the exact same locations.In the question asked, if the column of the 5x7 matrix is equal to R5, and the A span is equal to R5, and the value of A has a pivot for each row, then the position of each pivot in the separate columns of A has the 5 pivot columns.The matrix must contain pivot columns. "A has a pivot position in each row" & "A's columns span an R5" appear rationally equivalent.
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The correct question is-
Suppose A is a 5x7 matrix. How many pivot columns must A have if its columns span R⁵? Why?
if p=the mounttain bike's orginal price in dollars, which algebraic expression represents the reduced price ?
Algebraic expression (C) p - 125 represents the reduced price.
What do we mean by algebraic expressions?In mathematics, an algebraic expression is an expression made up of variables and constants as well as algebraic operations (addition, subtraction, etc.). Expressions are made up of terms. Algebraic expressions have at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression.So, if p is the mountain bike's original price.
Then, the reduced price will be p - 125.Therefore, algebraic expression (C) p - 125 represents the reduced price.
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osslyn is thinking of a number, n and she wants her sister to guess the number. Her first clue is that eight less than two times her number is between two and six (inclusive). Write a compound inequality that shows the range of numbers that Josslyn might be thinking of.
The required number that is guessed is 2x - 8 where inequality 2 < x < 6.
Given that,
Osslyn is thinking of a number, n.
Her first clue is that eight less than two times her number is between two and six (inclusive).
To write a compound inequality that shows the range of numbers that Josslyn might be thinking of.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let the number be x,
According to the question,
Gusset number = 2x - 8, where x is between 2 and 8 implies
2 < x < 6
Thus, the required number that is guessed is 2x - 8 where inequality 2 < x < 6.
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how do you do factors of 5 grade
Answer:
If we divide 5 by any other integer, then the remainder will be a non-zero positive integer.
Step-by-step explanation:
Solve: 212x +41 = 32
I need help plssss
Simplify 8x + 9 - 4x - 2.
Answer:
4x + 7
Step-by-step explanation:
8x + 9 - 4x - 2 ← collect like terms
= (8x - 4x) + (9 - 2)
= 4x + 7
Supergym is a natural chain of gyms. it's employees sold 5,190 gym memberships last year. this year, they sold 70% more memberships than that. how many memberships did they sell this year?
Super Gym employees sold 8,823 gym memberships this year, 70% more than the 5,190 gym memberships last year.
In mathematics, a percentage, usually denoted by %, is a number or ratio that represents a fraction of 100.
If the problem states that the gym's employees sold 70% (70 percent) more memberships than last year, and it's employees sold 5,190 gym memberships last year, then
memberships this year = 70% more than last year
memberships this year = 70%(5,190) + 5,190
memberships this year = 3,633 + 5,190
memberships this year = 8,823
Hence, the gym's employees sold 8,823 memberships this year.
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the number in this sequence increase by 40 each time
the sequence is continued with the same rule.
which number in the sequence will be closest to 300
The 8th term of the sequence 310 is closest to the term 300.
What is referred as the arithmetic progression?An arithmetic progression is a series of numbers that have a set common difference in between two consecutive numbers (A.P.).
Each term in an arithmetic sequence increases or decreases by adding or subtracting a constant term.
a = 30 for the first term
d = 40, common difference
We solve in what term is closest to 300 in this manner;
300 / 40 = 7.5
Thus, find the 7th and 8th term.
7th is solved by verifying for;
a₇ = a + ( n - 1 ) d
a₇ = 30 + ( 7 - 1 ) 40
a₇ = 30 + 240
a₇ = 270
The 8th term to certify the closest;
a₈ = T7 + d
a₈ = T7 + 40
a₈ = 270 + 40
a₈ = 310
As a result, the 8th term is the closest, with a value of 310.
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The complete question is-
The numbers in this sequence increase by 40 each time 30, 70, 110,The sequence is continued with the same rule. Which number in the sequence will be closest to 300?
< Exit
1-4: MathXL for School: Additional Practice
Assignment is past due (09/13/22 11:59pm)
A 150-pound person uses 5.6 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 180 calories?
CH
Answer:
32,14 minutes
Step-by-step explanation:
5.6 calories per hour = 5.6 x 60 = 336 calories per hour
So in 1 hour, that person will lose 336 calories
To lose only 180 calories time he should walk = 180/336 hour = 180/336 x 60 = 32,14 minutes
We can figure out our answer is in the ballpark by noting that 336/2 = 168
So to lose 168 calories, the person should walk for 1/2 hour so since 180 is slightly greater than 168, the person should walk for slightly more than half-hour
x+3y-z=2
x+y-z=0
3x+2y-3z=-1
Answer:
add the like terms if there's no like the answer will be 3x+2y-3z=-1
find the volume of the cylinder
Area of base:
3 * 9 = 27
27*9 = 243So, 243 is the answer.
You are driving to a vacation spot with your family that is 1500 miles away. Including rest stops, you take 42 hours to get the the vacation spot. You drove on an average speed of 42 miles per hour. How many hours were you NOT driving? Please include an algebraic equation.
Answer:
Below in bold.
Step-by-step explanation:
The time you were driving = distance / average speed
= 1500/42
= 35.714 hours.
Required equation is
t = 42 - d/s where t = time not driving, d = distance and s = average speed
Time not driving :
t = 42 - 35.714
= 6.286 hours
That is about 6 hours 17 minutes.
