An arithmetic progression (AP) is a sequence of numbers ordered such that the difference between any two consecutive numbers is a constant value. Also called arithmetic sequence. For example, the sequence of natural numbers: 1, 2, 3, 4, 5, 6, … is an arithmetic sequence in which the common difference between two consecutive terms (e.g., 1 and 2) is 1 (2 - 1) ... It can be seen that the tolerance of two consecutive terms is equal to 2, even for odd and even numbers.
First term a=-3.5,
Common difference d=2.25,
Number of terms n=8
Solution:
Here first term a=-3.5,
Common difference d=2.25
We know that,
f(n)=a+(n-1) d
f (8)=-3.5+(8-1)(2.25)
=-3.5+(15.75)
=12.25
We know that,
Sn=n2[2a+(n-1)d]
∴S8=82⋅[2(-3.5)+(8-1)(2.25)]
=4⋅[-7+(15.75)]
=4⋅[8.75]
=35
Hence, 8th term of the given series is 12.25 and sum of first 8th term is 35.
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Do 300 MM, 190 MM make a triangle?
The side lengths 300 mm and 190 mm make a valid triangle because of the triangle inequality theorem
How to determine if the side lengths make a triangle?The side lengths are given as
300 mm and 190 mm
To solve this question, we make use of the triangle inequality theorem
The triangle inequality theorem states that
Given that the sides of a triangle are x, y and z.
The sum of any two sides of a triangle is greater than or equal to the third side;
This means that
x + y ≥ z
Using the above as a guide, we have the following inequality expressions
300 + 190 ≥ z
300 + z ≥ 190
z + 190 ≥ 300
Evaluate the inequality expressions
490 ≥ z
z ≥ -110
z ≥ 110
Remove the negative value
490 ≥ z
z ≥ 110
Combine the inequalities
110 ≤ z ≤ 490
The above inequality is a valid inequality expression
Hence, the side lengths 300 mm and 190 mm make a valid triangle
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Please i need help, can someone help me pls :<
Answer:
3-2.253.03964-10197Step-by-step explanation:
You want the quadratic expression evaluated for several different values of x.
SolutionEvaluating a polynomial is often easier when it is written in Horner form.
f(x) = -x² -2x +3
f(x) = (-x -2)x +3 = -(x +2)x +3
Repetitive evaluations are often easier to do by programming a spreadsheet or calculator to do them. The basic idea is to put the value where x is, then do the arithmetic.
1. f(0)f(0) = -(0 +2)(0) +3 = 3
2. f(1.5)f(1.5) = -(1.5 +2)(1.5) +3 = -(3.5)(1.5) +3 = -5.25 -3 = -2.25
3. f(-0.02)f(-0.02) = -(-0.02 +2)(-0.02) +3 = (1.98)(0.02) +3 = 3.0396
4. f(-1)f(-1) = -(-1 +2)(-1) +3 = 1 +3 = 4
5. f(100)f(100) = -(100 +2)(100) +3 = -10200 +3 = -10197
__
Additional comment
Horner form rewrites the polynomial to minimize the number of arithmetic operations required to evaluate it.
ax^5 +bx^4 +cx^3 +dx^2 +ex +f = ((((ax +b)x +c)x +d)x +e)x +f
What else is needed to prove these triangles congruent using the SAA postulate?
The additional information needed to prove that both triangles are congruent by SAA postulate is:
A. <B ≅ <D and <A ≅ <E
What is the SAA Postulate?The SAA postulate is a condition that is used to prove that two triangles are congruent if they have two pairs of corresponding congruent angles and a pair of non-included congruent sides.
From the information we have in the diagram, we can deduce that:
AC ≅ EC (one pair of congruent sides)
ACB ≅ ECB (one pair corresponding congruent angles)
Therefore, the additional information needed to prove that both triangles are congruent by SAA postulate is:
A. <B ≅ <D and <A ≅ <E
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Given point M is between L and N, where LM = 10 and NM = 8, What is LN?
Answer:LN=18
Since point M is between the two other points, you add each number, giving you the answer
3(10-8)^2+4
STEP BY STEP PLEASE IT NEED TO BE EVALUATE AND EXPLAIN <33
Answer:
16
Step-by-step explanation:
We use PEMDAS
Parenthesis
Exponents
Multiplication
Division
Addition
Subtracting
1. 3 (10 - 8)^2 + 4: 3 (2)^2 + 4
2. 3 (2)^2 + 4: 3 (4) + 4
3. 3 (4) + 4: 12 + 4
4.12 + 4 = 16
So, our answer is 16.
mrs. joshi purchase dance shoes for her students to wear to and upcoming festival. The smallest size was 4 1/2 and the largest was 8. Let s respresent the various sizes of shoes the dancers needed. what the answer plssssss
Answer:
C is the correct answer
Step-by-step explanation:
hope you get it right :))
Identify a pattern and find the next three numbers in the pattern. 30,45,60,75,. . .
The next three numbers in the pattern are 80, 85, 90....
These are the multiples of 5.
The complete pattern is 30,45,60,75,80, 85, 90....
What does pattern completion entail?Look at the first three or four numbers in the pattern. You might wonder what link there is between these figures. In this mathematical pattern, for instance, the first three to four numbers are 1, 3, 6, and 10. It seems like you must add to get the higher numbers as you go up the scale. Start with adding 2, then follow with 2, 3, and finally 4. So, if you write this down, you probably see a pattern starting to emerge.
Try the remaining elements of the supplied pattern to see whether your solution works.
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Complete the following statement.
According to the Angle Bisector Theorem, if a point is on the bisector of an angle, then it is
The point bisector hypothesis expresses that on the off chance that a point is on the bisector of a point, the point is equidistant from the sides of the point.
What is the Angle Bisector Theorem?
In math, the point bisector hypothesis is worried about the overall lengths of the two fragments that a triangle's side is separated into by a line that cuts up the contrary point.
The point bisector hypothesis talk expresses that on the off chance that a point is in the inside of a point and equidistant from the sides, then it lies on the bisector of that point.
According to the angle bisector theorem, PQ/PR = QS/RS or a/b = x/y. A point bisector is a line or beam that separates a point in a triangle into two equivalent measures.
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3/2(2c+7) -3c =6(c+5)
Answer:
c = -3 1/4
Step-by-step explanation:
You want the solution to 3/2(2c+7) -3c =6(c+5).
SolutionSimplifying the equation gives ....
3c +21/2 -3c = 6c +30
21/2 -60/2 = 6c . . . . . . . . . subtract 30
-39/2 = 6c . . . . . . . . . . combine terms
-13/4 = c . . . . . . . . . . divide by 6
The value of c is -3 1/4.
Solve for x.
2x-17=51+61
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: 2x - 17 = 51 + 61[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x - 17 = 112[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 112 + 17[/tex]
[tex]\qquad \sf \dashrightarrow \: 2x = 129[/tex]
[tex]\qquad \sf \dashrightarrow \: x = \dfrac{129}{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 64.5[/tex]
Which quadrilateral is trapezoid?
Answer:
A.
Step-by-step explanation:
A quadrilateral is a trapezoid if two opposite sides are parallel, and the other 2 opposite sides are not parallel.
Answer: A.
Answer:
it's a
Step-by-step explanation:
find the midpoint of the segment that has endpoints (-3,4) and (-6,0)
Answer:
the mid point of (-3,4) and (-6,0) is (4.5,2)
Answer:
[tex]=(-4.5, 2)[/tex]
Step-by-step explanation:
Midpoint formula is:
[tex](x_m, y_m) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
where
x1=-3, x2=-6
y1=4, y2=0
Now just plug into formula
[tex]=( \frac{-3+-6}{2}, \frac{4+0}{2})[/tex]
[tex]= ( \frac{-9}{2}, \frac{4}{2})[/tex]
[tex]=(-4.5, 2)[/tex]
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 21 to 49
At your job, you get paid 1.5 times your hourly wage for any hours worked over 40 hours. You work 52 hours during a week in the summer. Your total paycheck was for $982.50. What is your hourly wage?
At the job, the hourly Wage was solved to be $16.94.
How to find the hourly wage
Given data
rate of hours worked over 40 hours = 1.5
hours worked in a week = 52
total paycheck = $982.50
let the pay hourly rate be x, and over 40 hours pay is 1.5x
finding the hours worked over 40
52 - 40 = 12
total paycheck $982.50 is gotten as follows:
$982.50 = 40 * x + 12 * 1.5x
982.50 = 40x + 18x
982.50 = 58x
x = 982.50 / 58
x = 16.9397
x = 16.94
Since x which is the hourly wage is found to be 16.94m, we can therefore say that the hourly wage is $16.94.
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which inequality matches this graph?
Answer:
x>4
Step-by-step explanation:
Since it is pointing right, it must be either
x>4
x≥4
Since it is not a filled circle the answer can't be greater than or equal to. So it must be x>4.
Each Sophomore and Junior at a high school collected aluminum cans and plastic bottles. The table shows the average number of cans and bottles collected per student by grade level during a 2-week recycling drive.
a. Write a system of equations to represent the situation. Let x represent the number of sophomores, and let y represent the number of juniors. The equation for week 1 is (Type an equation.)
The equation for week 1 at a high school showing collected aluminum cans and plastic bottles is; x + 4y = 2319
How to create Simultaneous Linear Equations?From the given table, we are told that;
Average number of cans and bottles collected by Sophomores in week 1 = 1
Average number of cans and bottles collected by Sophomores in week 2 = 4
Average number of cans and bottles collected by Juniors in week 1 = 4
Average number of cans and bottles collected by Juniors in week 2 = 2
Total number of cans and bottles collected by all in week 1 = 2319
Total number of cans and bottles collected by all in week 2 = 2290
Let x represent the number of sophomores, and let y represent the number of juniors. Thus, the equation for week 1 is;
x + 4y = 2319
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Mr. Sanchez’s class sold fruit pies for $1.89 each and Mr. Kelly’s class sold bottles of fruit juice for $1.56 each. Together, the classes sold 82 items and earned $140.13 for their school. Write and solve a system of equations that models this problem. Show all your work!
Mr. Sanchez's class sold fruit pies, and Mr. Kelly's class sold bottles of fruit juice.
Mr. Sanchez's class sold 45 fruit pies, and Mr. Kelly's class sold 37 bottles of fruit juice.
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to write and solve a system of equations that models this problem.To solve this question, we use the following representations:
x represents the fruit pies
y represents the fruit juice
A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
1.89x + 1.56y = 140.13 ---- the total cost
x + y = 82 --- the number of sales
Make x the subject in x + y = 82
So, we have
x = 82 - y
Substitute x = 82 - y in 1.89x + 1.56y = 140.13
1.89(82 - y) + 1.56y = 140.13
Expand
154.98 - 1.89y + 1.56y = 140.13
Evaluate the like terms
-0.33y = -14.85
Divide by -0.33
y = 45
So, we have
x = 82 - y
x = 82 - 45
Evaluate
x = 37
Hence, Mr. Sanchez's class sold 45 fruit pies, and Mr. Kelly's class sold 37 bottles of fruit juice.
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If quadrilateral WXYZ is reflected across the y -axis to become quadrilateral W' X' Y' Z' , what are the coordinates of X' ?
When the quadrilateral WXYZ is mirrored across the y axis to form the quadrilateral W' X' Y' Z', the coordinates of X' are (-1,6).
Briefing:When the x value is reflected across the y-axis, it takes on the opposite sign.
What exactly is a coordinate system?A coordinate system is a method of determining the position of points or other geometric components on a manifold, such as Euclidean space, by using one or even more numbers, or coordinates.
Why do we employ a coordinate system?A coordinate system is a framework for specifying the relative locations of objects in a specific area, such as an area here on earth's surface or the entire earth's surface. A geographic coordinate system determines locations on the world by using a three-dimensional spherical surface.
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Brandon wants to find the width of his rectangular neighborhood park. How can he
rearrange the formula for perimeter of a rectangle, p = 2( +w), to solve for w?
A. W=(2l+p)/2
B. W=(p-2l)/2
C. W=p-2l
D. W=2l-p
Evaluate each expression for a=3 and b=-5 . -4+2 a b
Evaluating the expression -4 + 2ab for a = 3 and b = -5 is equal to -34.
An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".
To evaluate an expression or an equation means to substitute a value to the variable and perform the arithmetic operations included.
Given the expression -4 + 2ab, substitute the value of the variable a and the value of variable b.
-4 + 2ab
-4 + 2(3)(-5)
Performing the arithmetic operations, we can have the value of the expression.
-4 + 2(3)(-5)
= -4 + (-30)
= -34
Hence, the expression -4 + 2ab when a = 3 and b = -5 is equal to -34.
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HELP WITH THIS MATH PROBLEM PLS PLS
Answer:
MP = 29
Step-by-step explanation:
Given:
The entire line (MP) is equal to 5y + 9MN = 17NP = 3yMN + NP = MP
17 + 3y = 5y + 9
Find what y =____
17 + 3y = 5y + 9
subtract 9 from both sides
17 - 9 + 3y = 5y + 9 - 9
8 + 3y = 5y
subtract 3y from both sides
8 + 3y - 3y = 5y - 3y
8 = 2y
divided both sides by 2 to get y alone
8/2 = 2y/2
4 = y
Now plug in y to MP to find its length
5(4) + 9 = 20 + 9 = 29
MP = 29
To find NP, plug in y as well
3y = 3(4) = 12
NP = 12
Check:
MN + NP = MP
17 + 12 = 29 yes!!!!
determine the length of XY. Round to the nearest hundredth.
X(-9,2)X(−9,2) and Y(5,-4)Y(5,−4)
Answer:
Step-by-step explanation:
15.23 units
A die is rolled twice. What is the probability that the first number rolled is a 3 and the second number rolled is a 5 ?
When a die is rolled twice, the probability of getting a 3 and then a 5 is 1/36.
When a die is rolled twice, the following combinations are possible:
1, 1 - 1, 2 - 1, 3 - 1, 4 - 1, 5 - 1, 6
2, 1 - 2, 2 - 2, 3 - 2, 4 - 2, 5 - 2, 6
3, 1 - 3, 2 - 3, 3 - 3, 4 - 3, 5 - 3, 6
4, 1 - 4, 2 - 4, 3 - 4, 4 - 4, 5 - 4, 6
5, 1 - 5, 2 - 5, 3 - 5, 4 - 5, 5 - 5, 6
6, 1 - 6, 2 - 6, 3 - 6, 4 - 6, 5 - 6, 6
Thus, the sample space is 36.
3, 5 only occurs once in the sample space.
∴ P (3 and 5) = 1/36.
Hence, the probability of rolling a 3 and then a 5 is 1/36.
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HELPPPPPP! How many groups of 9/2 are in 1?!?
Task #6
How many buckets do we need?
Abinash wants to fill his pool but his hose is busted! His
friends decided to help him fill the pool with water buckets.
The base of the pool has dimensions 4 m by 2 m and the
height is 1 m, but they decided to fill the pool only
two-thirds way.
Each water bucket has radius
0.13 m and height 0.55 m.
a) How many buckets of water would they need to fill the pool two-thirds way?
b) What assumption did you make to arrive at your answer?
Find the 32 nd term of each sequence. 34,37,40,43, ...........
The arithmetic sequence AP's 32nd term is estimated to be 127.
What exactly is an arithmetic sequence AP?An arithmetic progression (AP) in mathematics is a list or sequence of numbers within which each term is acquired by adding a sequence to the term before it.
The fixed number is denoted by the letter 'd' in the arithmetic progression's common difference.nth term of an AP: an = a + (n - 1) dThe common difference => d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.The sum of n terms of an AP's => Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the last term of the AP.Finally, the response to the question;
The numbers in the provided sequence are as follows:
34,37,40,43, ...........
There are 32 terms in the series, so we must obtain the 32nd number.
Suppose the first term is 'a₁' = 34.
Suppose 'a₂' = 37 be the second term.
Suppose 'a₃' = 40 be the third term.
The common difference between the two consecutive terms of an AP that are equal is 'd.'
d = a₂ - a₁
Put the values in the preceding formula; the 32nd term is
d = 37 - 34
d = 3
The nth term equation is now used to calculate.
nth term of an AP: an = a + (n - 1) dTotal number of terms is; n = 32First term is a = 34common difference d = 3Substitute all of the values in the formula now.
a₃₂ = a + (n - 1) d
a₃₂ = 34 + (32 - 1)(3)
a₃₂ = 34 + 96 - 3
a₃₂ = 127
Thus, the arithmetic sequence's 32nd term is evaluated to be 127.
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Find the 32 nd term of each sequence. 0.1,0.5,0.9,1.3, ...........
The 32nd term of the arithmetic sequence AP is computed to be 12.5.
What is an AP arithmetic sequence?In mathematics, an arithmetic progression (AP) is a list or sequence of numbers in which each term is attained by adding a pattern to the term before it.
With in arithmetic progression's common difference, the fixed number is marked by the letter 'd.'The common difference => d = a2 - a1 = a3 - a2 = a4 - a3 =...... = a - an-1.nth term of an AP: an = a + (n - 1) dThe sum of n terms of an AP's => Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the last term of the AP.Finally, here is the answer to the question;
The following are the numbers in the presented sequence:
0.1,0.5,0.9,1.3, ...........
Because the series contains 32 terms, we must find the 32nd number.
Assume the first term is'a₁' = 0.1.
Assume 'a₂' = 0.5 is the second term.
Assume the third term is 'a₃' = 0.9
'd' is the common difference between two consecutive terms of an AP that are equal.
d = a₂ - a₁
Put the values in the preceding formula; the 32nd term is
d = 0.5 - 0.1
d = 0.4
The nth term equation is found by the formula;
nth term of an AP: an = a + (n - 1) dTotal number of terms is; n = 32Initial term is a = 0.1Common difference d = 0.4Substitute the given values in the formula;
a₃₂ = a + (n - 1) d
a₃₂ = 0.1 + (32 - 1)(0.4)
a₃₂ = 0.1 + 12.8 - 0.4
a₃₂ = 12.5
Therefore, the arithmetic sequence's 32nd term value is estimated to be 12.5.
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168>=7x+4y
i need help solving for y
btw this is an inequality
For solving y, we can use this inequality: y≤(168-7x)/4
What is an inequality and steps to solve an inequality ?An inequality is an equation which compares two non equal expressions using operators ≤,≥,<,> .
Steps for solving inequalities:
if we add same number to both sides the inequality remains same.If we divide both sides by a positive number the inequality remains same .if we divide both sides by a negative number the inequality , the inequality reverses.For given inequality, 168≥ 7x + 4y
Adding -7x both sides,
168-7x ≥ 7x+4y-7x
168 - 7x ≥ 4y
Dividing both sides by a positive number 4,
(168-7x)/4 ≥ y
we can solve for y using above expression that y will be less than or equal to (168-7x)/4
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16. The denominator of a fraction is 4 more than the numerator. If 1 is added to numerator and 2 is subtracted from denominator fraction becomes 24 upon 25 find the fraction
The fraction is 23/27.
Let the numerator and denominator of the given fraction be x and y respectively.
According to the question,
Case 1 :-
Denominator of the fraction is 4 more than the numerator.
⇒ Numerator = Denominator - 4
⇒ x = y - 4 ...(1)
Case 2 :-
If 1 is added to numerator and 2 is subtracted from denominator fraction becomes 24/25
⇒ (Numerator + 1) / (Denominator + 2) = 4/5
⇒ (x + 1) / (y - 2) = 24/25
⇒ 25(x + 1) = 24(y - 2)
⇒ 25x + 25 = 24y - 48
⇒ 25x - 24y = -73 ...(2)
Substituting the value of x from (1) in (2), we have
⇒ 25(y - 4) - 24y = -73
⇒ 25y - 100 - 24y = -73
⇒ y = -73 + 100
y = 27
substitute the value of y in equation 1.
x = 27 - 4
x = 23
Now, At the beginning of our solution we took the numerator & denominator to be x & y respectively. So the fraction is:
⇒ x / y
⇒ 23/27
Hence the fraction is 23/27.
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How many binary strings of length 10 are there in which the number of 0's in the string is not equal to the number of 1's in the string?
The binary strings of length 10 are there in which the number of 0's in the string is not equal to the number of 1's in the string is 2¹⁰ - 2⁹.
Binary number:
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" and "1".
Given,
Here we need to find How many binary strings of length 10 are there in which the number of 0's in the string is not equal to the number of 1's in the string.
Here the length of the binary string is 10.
So, it can be written in the power form as 2¹⁰.
Now we need to find the number of 0's in the string is not equal to the number of 1's in the string.
For that, we have to consider,
There are 2⁹ number of binary strings are not have same number of 0's in the string is not equal to the number of 1's in the string.
So, it can be written as,
=> 2¹⁰ - 2⁹
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