Computing the sum of the first term in the arithmetic series is relatively straightforward. Just add these values together. However, adding, say, the first 100 words creates more problems. Instead of manually summing all these terms, mathematicians devised an arithmetic progression formula that efficiently computes the sum of the arithmetic progression.
a1 =-6
S50 = -5150
an=?
Sn=n(a1+an)/2
So, to find an
((2*sn) /n)-a1=an
((2*-5150) /50) -(-6)=an
An=200
D=-194/49
Here the first term a=-6,
Common difference d=-3.96
We know that,
f(n)=a+(n-1)d
f(50)=-6+(50-1)(-3.96)
=-6+(-193.99)
=-199.99
We know that,
Sn=n2[2a+(n-1)d]
∴S50=502⋅[2(-6)+(50-1)(-3.96)]
=25⋅[-12+(-193.99)]
=25⋅[-205.99]
=-5149.78
More similar question are solved in the link below.
https://brainly.com/question/21961097?referrer=searchResults
#SPJ4
How much money will you have if you invest $2200 at 2%/a compounding annually for 30 years?
Answer:
$3,985.00
Step-by-step explanation:
The formula for the amount accrued, A if you invest an amount P at r% compounded annually for n years is given by the formula
[tex]A = P\left(1 + \dfrac{r}{100}\right)^n[/tex][tex]A = P\left(1 + \dfrac{2}{100}\right)^{30} \\\\= P\left(1 + 0.02\right)^{30} \\\\= P\left(1 .02\right)^{30} \\\\= \; \$3,985.00[/tex]
The division by 100 is necessary to allow r% to be reduced to a decimal
So using this formula directly by substituting values gives
in 2008, the world record for swimming the 50 m style event was 21.3 four seconds supposing the athlete swim at a con stamp rate what was his speed round your answer to the nearest hundredth.
Athlete swam at a constant rate, his speed in m/s is 2.343 m/s
What is Speed?The pace at which a distance changes over time is referred to as speed. It has a dimension of time-distance. As a result, the fundamental unit of time and the basic unit of distance are combined to form the SI unit of speed. Thus, the metre per second (m/s) is the SI unit of speed.
The formula for speed is as straightforward as dividing a distance by a time. We may define speed as the rate of change of position of an item in any direction by taking the distance traveled and dividing it by the time.
Given,
the distance covered = 50m
total time taken = 21.34s
Speed = distance / Time
speed = 50/ 21.34
speed = 2.343 m/s
To learn more about speed from given link
https://brainly.com/question/26046491
#SPJ9
Multiply the numbers.
The result of multiplying the numbers 234 x 0.35 is 81.9
How to multiply the numbers?The numbers are given as:
234 and 0.35
Express the numbers in a product expression
So, we have
234 x 0.35
Express 234 as 200 + 34
So, we have
234 x 0.35 = (200 + 34) x 0.35
Expand the bracket
So, we have
234 x 0.35 = 200 x 0.35 + 34 x 0.35
Evaluate the product
So, we have
234 x 0.35 = 70 + 11.9
Evaluate the sum
So, we have
234 x 0.35 = 81.9
Hence, the result of multiplying the numbers 234 x 0.35 is 81.9
Read more about expressions at
https://brainly.com/question/723406
#SPJ1
with the steps as well please
Answer:
Step-by-step explanation:
(i)
[tex]2.014^2-2.012^2=\\(2.014+2.012)(2.014-2.012)=\\4.026*0.002=\\0.008052=\\8.052*10^{-3}[/tex]
(ii)
[tex]12^3+8^3=\\(12+8)(12^2-(12)(8)+8^2)=\\20*(144-96+64)=\\20*112=\\2240[/tex]
(iii)
[tex]9^3-5^3=\\(9-5)(9^2+(9)(5)+5^2)=\\4*(81+45+25)=\\4*151=\\604[/tex]
Determine whether the quadrilateral can always, sometimes, or never be inscribed in a circle. Explain your reasoning.
square
A quadrilateral (square) may always be used to create a square in a circle. Because squares have right angles at each vertex, every pair of opposing angles in a square is complementary and inscribed in a circle. This is an unavoidable characteristic of squares.
If the form in question is a square, each pair of adjoining angles is supplementary and inscribed in a circle. This is owing to the presence of right angles at each vertex of the square. This means that the assertion can never be proven false.
Learn more about quadrilaterals and squares - https://brainly.com/question/23935806
the sum of 12 and twice y
Answer:12+2y
Step-by-step explanation:
Answer:
12 + 2y
Hope this helps :)
Step-by-step explanation:
When it says "sum," this means the answer to 2 numbers you add. The first number would be 12, and the other number will be y 2 times. So y plus y equals 2y. The final equation is 12 + 2y.
4,000 is blank times much as 4
Answer: 1000
Step-by-step explanation:
4000/4
Answer:
1000
Step-by-step explanation:
blank can be written as x. since this is a multiplication problem we need to the opposite of multiplying, which is dividing. rewrite the problem as 4000/4=x
solve by dividing 4000 by 4 to get 1000
Use distributive property to rewrite (3+8)15
By using distributive property 15(3 + 8) 15 11 = 165 both approaches yield the same conclusion.
Distrubutive Property Formula : a(b+c)=a b+a c
The distributive property is also known as the distributive law of multiplication over addition and subtraction. By its very name, the procedure implies that something will be divided or distributed. According to the distributive property, an expression of the form A (B + C) can be resolved as A (B + C) = AB + AC. Subtraction also belongs to the scope of this distributive law, which is expressed as A (B - C) = AB - AC. The distribution of operand A among the other two operands is seen from this.
A (B + C) = AB + AC represents the distributive property of multiplication over addition.
15(3+8) = (15.3) + (15.8)
15.11 = 45 + 120
165 = 165
Using the law of BODMAS, we can now attempt to solve the expression. The solution is as follows. We will first add the figures in brackets, and then we will multiply this total by the figure outside of the brackets.
Hence, using distributive property, it follows that 15(3 + 8) x 15 = 165. As a result, both approaches yield the same conclusion.
To learn more about BODMAS visit:
https://brainly.com/question/16738857
#SPJ1
y^2/3 - 5y^1/3 +6=0
Answer:
Solution on Screen
Step-by-step explanation:
It's okay don't worry
Determine whether each infinite geometric series diverges or converges. 1/64 + 1/32 +1/16 + . . . .
A geometric series exist as the totality of an infinite number of terms that contain a constant ratio between consecutive terms.
The infinite geometric series 1/64 + 1/32 +1/16 + . . . . diverges.
What is an infinite geometric series?The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³+…, where r is the common ratio and a1 is the first term.
The equation be S = a1/(1-r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.
Let the sequence be 1/64 + 1/32 + 1/16 + . . . .
a(first term) = 1/6
r(common ratio) = a2/a1 = (1/32) / (1/64)
= (64/32) = 2
Since, | r | > 1, the infinite geometric series diverges.
To learn more about infinite geometric series, refer to:
brainly.com/question/27350852
#SPJ4
The measures of two vertical angles are 5y + 10 and 2y + 16. Find the measure of both angles.
Answer:
20
Step-by-step explanation:
We know that two vertical angles are equal to each other.
Then
First, We have to solve the equation 5y + 10 = 2y + 16 for y.
After that ,we can easily find the measure of the angles by substituting y by its value in their expression.
SOLVING THE EQUATION :
5y + 10 = 2y + 16
⇔ 5y - 2y = 16 - 10
⇔ 3y = 6
⇔ y = 2
Determining the measure of the angles :
angle 1 → 5(2) + 10 = 20
angle 2 → 2(2) + 16 = 20
opy the vectors. Then find each sum or difference.
→w + →z
The components of the two vectors are added and subtracted to produce the addition and subtraction vector PQ. i.e. →PQ = →Q + →P and →PQ = →Q - →P
A vector, which denotes the mathematical and geometrical direction of the provided quantity, is a quantity with both magnitude and direction.
For example : Velocity, Displacement etc.
Let's start by assuming that,
P(x,y,z) and Q(u,v,w)
Now, we need to find the vector addition and subtraction
Addition of vectors to give →PQ
→PQ = →Q + →P
= (ui + vj + wk ) + (xi + yj + zk)
= (ui + xi ) +(vj + yj) + (wk +zk)
= (u+x) i + (v + y) j + (w + z)k
= →PQ
Similarly, Subtraction of vectors to give →PQ
→PQ = →Q - →P
= (ui + vj + wk ) - (xi + yj + zk)
= (ui + vj + wk - xi - yj - zk)
= (ui - xi ) +(vj - yj) + (wk -zk)
= (u-x) i + (v - y) j + (w - z)k
= →PQ
For example : Let P(1,2,1) and Q ( -1, -2,4)
Then, Addition →PQ = →Q + →P
= (1i + 2j + 1k ) + (-1i + (-2)j + 4k)
= (1-1) i + (2 -2) j + (1 + 4)k
= oi+0j +5j
= 5j
Subtraction →PQ = →Q - →P
= (1i + 2j + 1k ) - (-1i + (-2)j + 4k)
= (1+1) i + (2 +2) j + (1 - 4)k
= 2i+4j -3j
Hence, the vector PQ addition and subtraction is given by the addition & subtraction of the components of the two vectors.
To learn more about Vectors, here
brainly.com/question/24256726
#SPJ4
Given f(x)= 3(2−x), what is the value of f(−4)?
The value of f(-4) is 18 because
3(2+4)
6+12=18
2(3+6)+6-2=?
Solve the problem step by step
Answer:
13
Step-by-step explanation:
first use PEMDAS= P= Parentheses E= Exponents M= Multiplication D= Division A= Addiction S= Subtraction.
(3+6)+6-2=
9+6-2=
15-2=
13
Add 3+6 which is 9
Add 3+6 which is 9then add 9+6 equal to 15
Add 3+6 which is 9then add 9+6 equal to 15finally subtract 2 from 15
Add 3+6 which is 9then add 9+6 equal to 15finally subtract 2 from 15boom that's how you do it
Answer:
22
Step-by-step explanation:
Use Pemdas
P means parenthesis so add the numbers in the parenthesis
3 + 6 = 9
2(9) + 6 - 2 =
Next is E, but there are no exponents so now there is M
multiply 2 times 9, you will get 18.
18 + 6 - 2 =
So next is A which is addition, add 18 + 6
18 + 6 = 24.
24 - 2
And lastly, S which is subtraction.
24 - 2 = 22
So the answer is 22
Solve each equation. Check each solution. 2a + 1 / 6 + a/2= a-1/3
The solution of the given equation 2a + 1 / 6 + a/2 = a-1/3 is a = -1
In this question, we have been given an equation.
[tex]\frac{2a+1}{6}+\frac{a}{2} = \frac{a-1}{3}[/tex]
We need to find the solution of given equation.
[tex]\Rightarrow \frac{2a+1}{6}+\frac{a}{2} = \frac{a-1}{3}\\\\\Rightarrow \frac{2(2a+1)+6a}{12}=\frac{a-1}{3}\\\\\Rightarrow \frac{4a+2+6a}{12}=\frac{a-1}{3}\\\\ \Rightarrow \frac{10a+2}{4}=a-1\\\\\Rightarrow 10a+2=4a-4\\\\\Rightarrow 6a=-6\\\\\Rightarrow a=-1[/tex]
We need to check above solution.
Substitute a = -1 in LHS of given equation.
2a + 1 / 6 + a/2
= [2(-1) + 1 / 6] + [-1/2]
= (-1/6 - 1/2)
= -(4/6)
= -2/3
Substitute a = -1 in RHS of given equation.
a-1/3
= (-1 - 1)/3
= - 2/3
So, LHS = RHS
Therefore, the solution of the given equation 2a + 1 / 6 + a/2 = a-1/3 is a = -1
Learn more about an equation here:
brainly.com/question/649785
#SPJ4
how to solve 4x² -12x
Answer:
[tex]4x\left(x-3\right)[/tex]
Step-by-step explanation:
[tex]x^{y+z}=x^yx^z\\x^2=xx\\=4xx-12x\\=4xx-4\cdot \:3x\\=4x\left(x-3\right)[/tex]
(12+6) divided by 3 squared simplified :p
Answer:
The answer is 36
Step-by-step explanation:
12+6=18
18/3=6
6 squared is 36
36 simplified is still 36
1 Use the number line to find the coordinate of the midpoint of JP. K L M + -7-6-5-4-3-2-1 0 1 2 3 4 5 6 N P
The coordinate of the midpoint of JP is -1
How to find the coordinate of the midpoint of JP?On the number line, we have the following coordinates
J = -7
P = 5
The coordinate of the midpoint of JP is calculated using
Midpoint = 1/2 * (J + P)
This gives
Midpoint = 1/2 * (-7 + 5)
Evaluate the sum
Midpoint = 1/2 * -2
Evaluate the product
Midpoint = -1
Hence, the coordinate of the midpoint of JP is -1
Read more about coordinate at
https://brainly.com/question/17206319
#SPJ1
Find the distance between each pair of parallel lines with the given equations.
y=-2 x+1 y=-2 x+16
The distance between each pair of parallel lines with the given equations y = -2x+1 and y = -2x+16 is 15 units.
We can find the points passing through the lines.
Hence,
The points passing through the line y = x - 11 are:-
Let x = 0
y = -2(0) +1
(0,1)
and;
Let x = 1/2
y = -2(1/2) + 1 = -1 +1
(-1/2,0)
The points passing through the line y = -2x + 16 are:-
Let x = 0
y = -2(0) + 16 =16
(0,16)
and;
Let x = 8
y = -2(8) + 16 = -16 + 16
(8,0)
Hence, using distance formula, the distance between the parallel lines will be:-
[tex]\sqrt{(16-1)^2+(0-0)^2} = \sqrt{15^2+0}=\sqrt{225} = 15[/tex] units.
To learn more about distance formula, here:-
brainly.com/question/8283882
#SPJ4
State the property that justifies each statement.
If x/2=7 , then x=14 .
According to the given data the property justifies statement is: Multiplication Property of Equality.
What is the Equality Multiplication Property?According to the Multiplication Property for Equations, an equation can be multiplied as well as divided by the exact number upon every of the equation's sides without changing the solution.
How do you demonstrate equality's multiplication property?If a = b, then a/c = b/c where c is greater than zero. In other words, if two expressions are equal and subsequently multiply or divide (except for 0) the same constant by both, the two sides will remain equal.
According to the data:x/2=7
x = 14
Multiplication Property of Equality is :
If a = b,
Multiply constant on both sides.
a * c = b * c
so ,
in the given sum x/2 = 7
multiplying this equation by 2 * x/2 = 7 * 2
= x = 14
According to the given data the property justifies statement is: Multiplication Property of Equality.
To know more about Multiplication Property of Equality visit:
https://brainly.com/question/9070018
#SPJ4
14. In science class, students weighed different
amounts of clay. Miguel's weighed
4.361 ounces, Kim's weighed 2.704 ounces,
Simon's weighed 5.295 ounces, and
Victoria's weighed 8.537 ounces.
A. How many ounces of clay did Miguel
and Victoria have in all?
B. How many ounces of clay did Kim and
Simon have in all?
Answer:
A:12.898
B:7.999
Step-by-step explanation:
A: 4.361+8.537
B:2.704+5.295
Given: ∠1 and ∠2 form a linear pair; m∠2 + m∠3 = 180 prove: ∠1 is congruent to ∠3
Based on the linear pair postulate, the statements and the reasons for the proof are explained below.
What is the Linear Pair Postulate?The linear pair postulate states that if two angles form a linear pair, then both angles are supplementary, and therefore have a sum of 180 degrees.
The proof that states that angle 1 and angle 3 are congruent angles is shown below:
Statement 1. ∠1 and ∠2 are a linear pair
Reason: Given
Statement 2: ∠1 and ∠2 are supplementary
Reason: Linear Pair Postulate
Statement 3: m∠1 + m∠2 = 180°
Reason: Definition of Supplementary Angles
Statement 4: ∠2 = ∠4
Reason: Given
Statement 5: ∠3 = ∠4
Reason: Vertical Angles Theorem
Statement 6: ∠2 = ∠3
Reason: Corresponding angles theorem
Statement 7: m∠2 = m∠3
Reason: Corresponding angles are congruent
Statement 8: m∠1 + m∠3 = 180
Reason: Supplementary angle theorem
Statement 9: <1 and <3 are supplementary
Reason: Definition of supplementary angles
Learn more about linear pair on:
https://brainly.com/question/13218054
#SPJ1
-1/6 + (-3/7) = please help
Answer:
-0.595
Step-by-step explanation:
..
If h(x)=|1-7x|, find each value… 23-h(9)
Answer:
-41
Step-by-step explanation:
h(x) = | 1-7x
First, calculate the value for the function for x = -9
h(-9) = |1--7x|
h(-9) = |1+63|
h(-9) = |64|
h(-9) = 64
23-h(-9) = 23-64 = -41
Hope this helps ;0
What is the sum of the finite geometric series?
a. -15+30-60+120-240+480
What is the sum of the finite geometric series?
a. -15+30-60+120-240+480= 315
Given:
a=-15
r= -2
n=6
[tex]S_n=\frac{a(1-r^{n})}{1-r} \\\\S_6=\frac{-15(1-(-2)^{6})}{1+2}\\\\S_6=\frac{-15(1-64)}{3}\\\\S_6=\frac{-15(-63)}{3}\\\\S_6=5*63=315[/tex]
What is a finite geometric series?
A geometric series is a series with a geometrically connected progression.A geometric series is a list of numbers where each number, or term, is found by multiplying the preceding term by a common ratio r.Because there are only a finite number of terms, we refer to this geometric series as a finite geometric series (an infinite geometric series continues on forever.)To learn more about finite geometric series, refer:
brainly.com/question/4520322
#SPJ4
Find the next term of the following sequence.
9, 6, 4,
Answer:
Step-by-step explanation:
Differences are 3 less then 2 less.
So, the next term would be 4-1 = 3.
what is multiples of 30 and 45?
Solve for y in terms of x
5x+y=31
Solving for y in terms of x gives y = 31 - 5x
What is the subject of formula?The subject of a formula is defined as the variable that is expressed in terms of the other variables in an equation or given expression.
It is also described as the variable that is being worked out in a given equation.
Given the equation;
5x +y = 31
Let's make 'y' the subject
We have to make 'y' stand alone by taking the other variables or terms over the equality sign, we have
y = 31 - 5x
Thus, solving for y in terms of x gives y = 31 - 5x
Learn more about subject of formula here:
https://brainly.com/question/10643782
#SPJ1
Determine whether the given measures define 0,1,2 , or infinitely many triangles. Justify your answers.
a=5, b=9, c=6
When only three sides are provided without any information regarding the angle, such as a = 5 m and b = 9 m, c = 6m we can either create no triangle or create an unique triangle. Hence, either 0 or 1 Triangle.
For example :
How many different triangles may be formed with side lengths of 5m,9m and 6 m ?
Create a triangle with the following measurements: 5 meters, 9 meters , and 6meters, by protractor-adjusted to the given length of sides. You have constructed a triangle.
We can only create one triangle here, as no choice can be made in the given length of side as they are prefixed.
This implies that you cannot chose the side length independently. So, only one triangle which is unique will be formed. Hence, 0 or 1 triangle is formed
To learn more about, Triangles here
brainly.com/question/2773823
#SPJ4
Solve $2+\frac{1}{6}y=3x+4$
Answer:
[tex]y=18x+ 12[/tex]
Step-by-step explanation:
Given equation:
[tex]2+\dfrac{1}{6}y=3x+4[/tex]
Solve for ySubtract 2 from both sides:
[tex]\implies 2+\dfrac{1}{6}y-2=3x+4-2[/tex]
[tex]\implies \dfrac{1}{6}y=3x+2[/tex]
Multiply both sides by 6:
[tex]\implies 6 \cdot \dfrac{1}{6}y= 6 \cdot3x+ 6 \cdot2[/tex]
[tex]\implies y=18x+ 12[/tex]
