The first five terms of a geometric sequence with first term 2 and common ratio (-2) are 2, -4, 8, -16, 32
The given parameters:
a₁ = 2, r = -2
r is the common ratio, hence, the given sequence is a geometric sequence.
In a geometric sequence, the formula for the nth term is given by:
a(n) = a(1) . rⁿ⁻¹
We can also find the terms using recursive formula. The nth term of a geometric sequence is equal to the (n-1)th term times the common ratio, r. Mathematically,
a(n) = a(n -1) . r
Let us start from n = 1
a(1) = 2 (given)
a(2) = a(1) . r = 2 . (-2) = -4
a(3) = a(2) . r = -4 . (-2) = 8
a(4) = a(3) . r = 8 . (-2) = -16
a(5) = a(4) . r = -16 . (-2) = 32
Thus, the first five terms are 2, -4, 8, -16, 32
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on february 26 berkshire hathaway closed at 185,690 per share. one year earlier one share closed at 215,970. what was an approximate one year percent change?
One year percent change is 14 percent.
What is percentage?A portion of a whole expressed in hundredths the number of students present was high. B: The outcome of dividing a number by a percentage is that the percentage equals the rate divided by the base. A portion of victories or profits (2a).
Given that,
Berkshire Hathaway closed at 185,690 per share on February 26.
One share's closing price from one year ago was 215,970.
So,the percentage of one year is 215970 × 185690/185690 × 100
So, the percent of one year is 14 percent.
Therefore, One year percent change is 14 percent.
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PLEASE HELP!!!
In the figure below, mWXZ=108*, and m1 is two times m2 Find m2.
Here mWXZ=108*and m1 is two times m2 so, The value of m2 is [tex]36[/tex]°.
The fundamental geometric shapes are lines and angles. Infinite points that stretch infinity in both directions make up lines, which are geometric objects. Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point. In this area, you could also encounter contrasting and related viewpoints. The most useful area of mathematics is the study of geometric shapes and their characteristics. As we've already mentioned, the foundation of any geometric shape is made up of lines and angles. Without employing lines and angles, it is impossible to draw a two-dimensional to three-dimensional shape. Consequently, it is imperative to discover the meanings of the two terminologies. Here, the fundamental definitions and characteristics of lines as well as angles are provided. A line is a simple, one-dimensional shape that can go on forever in opposing directions. A line may be vertical or horizontal. It can be drawn either top to bottom or left to right. When the ends of two rays collide at a single location, an angle is a geometry that results. They are expressed as radians or degrees (°). A 360-degree angle is the same as a whole rotation.
Let the angle m2 be x
so, according to the question m1= 2m2=2x
so, m1+m2=[tex]108[/tex]°
⇒2x+x=[tex]108[/tex]°
⇒3x=[tex]108[/tex]°
⇒x=[tex]36[/tex]°
means angle m2=[tex]36[/tex]°
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what fraction pieces when used twice will cover up 4/6 of a circle
hewppp just write the answers below...
Answer:
c) 0.67
c) 0.67 d) 2.4
c) 0.67 d) 2.4 e) 0.046
c) 0.67 d) 2.4 e) 0.046f) 0.26
c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537
c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537h) 3.863
c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537h) 3.863i) 0.043
c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537h) 3.863i) 0.043j) 0.2535
c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537h) 3.863i) 0.043j) 0.2535k) 0.074
c) 0.67 d) 2.4 e) 0.046f) 0.26 g) 0.537h) 3.863i) 0.043j) 0.2535k) 0.074 l) 0.4305
Step-by-step explanation:
Method 1: Without a calculator
To divide just move the decimal point to the right to how many zeros there are (for example 10 is one zero so you move the decimal point to the right one time).
Method 2: With a calculator
Type the equation press enter or "=" and you get your answer.
State whether the sentence is true or false. If false, replace the underlined term to make a true sentence.
The slant height is the height of each lateral face of a pyramid or cone.
The given statement is completely true.
This is because the definition of slant height is the altitude of the lateral face of a pyramid or cone which is true.
There are three dimensions of a cone.
The vertical height (or altitude) is the perpendicular distance from the top down to the base.
The radius of the circular base slant height is the distance from the top, down the side, to a point on the base circumference.
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The exchange rate of Japanese Yen on a certain day was Rs 10.25 . On the same day, if $3 was exchanged for Rs 345, how many Yens could be exchanged for $123?
The amount of $123 will be equal to 1380 yens.
What is currency exchange?The rate at which one currency will be exchanged for another is known as the exchange rate in the world of finance. The most frequent types of currencies are national currencies.
Given that the exchange rate of the Japanese Yen on a certain day was Rs 10.25. On the same day, if $3 was exchanged for Rs 345.
The amount of $123 in the yens will be calculated by forming the equations below:-
1 yen = 10.25 rs
1 rs = ( 1 / 10.25 ) yens ........................(1)
$3 = 345 rs
1 rs = $3 / 345 .........................(2)
From both the equations:-
( 1 / 10.25 ) yens = $ ( 3 / 345 )
$ 1 = ( 345 / ( 10.25 x 3 ) yen
$ 123 = ( 345 x 123 / ( 10.25 x 3 ) yen
$ 123 = 1380 yen
Therefore, the amount of $123 will be equal to 1380 yens.
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When designing a simulation where darts are thrown at targets, what assumptions need to be made and why are they needed?
The assumptions need to be made in the dart simulation is that the object lands within the target area, and that it is equally likely that the object will land anywhere in the region. These are needed because in the real world it will not be equally likely to land anywhere in the region.
Dart game:
Basically, the dart game board consists of sisal fibers or boar bristles and cork. An 18 inch diameter board is divided into 20 sections.
Thin metal structures are used to design the dividing lines and with the same materials the numbers are designed.
Sometimes the manufactures opt for printing number formats. The board should be positioned on the wall in such a manner that the bull’s eye should be 5ft 8 inch above the floor.
Given,
Here we need to find When designing a simulation where darts are thrown at targets, what assumptions need to be made and why are they needed.
While looking at the definition of the dart game board,
We know that, we have to do the following,
We assume that the object lands within the target area, and that it is equally likely that the object will land anywhere in the region. These are needed because in the real world it will not be equally likely to land anywhere in the region.
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What is ±/324 ?
Nesecito ayar la respuesta
Answer:
+18 or -18
Step-by-step explanation:
in subscript 4 200 = what
Answer:
8
Step-by-step explanation:
200 ×4=800
OR
200+200+200+200=800
Log x + log 6= log(2x+1)
In logarithm , value of function is 1/4.
How should log be defined?
The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, the logarithm of 100 in base ten is 2, since ten multiplied by two equals 100: log 100 = 2, since 102 = 100.The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e.Log x + log 6= log(2x+1)
use log property log m + log n = log ( mn)
log ( 6x) = log (2x + 1)
6x = 2x + 1
4x = 1
x = 1/4
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Back in 1997, Sally paid $11,448 for a new automobile. This amount included
the 6% sales tax. What was the price of the automobile without the tax? (Please show step by step)
Answer:
$10800
Step-by-step explanation:
$11,448 = 100% + 6%
= 100%
$11,448 = 106%
= 100%
Cross-multiply it :
$11,448 × 100% = × 106%
$11,448 × 100/100 = 106/100
$11,448 × 100/106 =
= $10800
Hope this helps. Pls mark me as the brainliest as it would help me too.
T
15
the
2
-2
y
0
(4.3)
2
(4.-2),
**
Which is the equation of the given line?
Evaluate the given expression when x = 3.
2
x + x² +2:
Answer:
3.2 + 3.2squared + 2 = 15.44
Step-by-step explanation:
Answer:
Step-by-step explanation:
x + x^2 + 2
3.2 + 3.2^2 + 2
3.2 + 10.24 + 2 = 15.44
30% squares units percent of increase 70%
133.3333333333% (increase) is percent of increase 70%.
What is the percentage formula?
By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.The word percentage comes from the Latin term per centum, which means "by the hundred." In the 16th century, the Latin phrase made its way into English. Later, it was shortened to percent and ended with a period.Use the formula percent change
Percent change = [tex]\frac{New - old}{old} * 100[/tex]
= 70- 30/30 * 100
= 40/30 * 100
= 133.3333333333% (increase)
Where: 30 is the old value and 70 is the new value.
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If f(x)=x² + x + 2 and g(x) = 2x² - 7 then prove that: 2 fg(2) = f(2) g(2).
Answer:
See explanation
Step-by-step explanation:
f(x)=x² + x + 2 and g(x) = 2x² - 7
f(2) g(2)=
((2)² + (2) + 2)(2(2)² - 7)=
(4 + 2+ 2)(2(4) - 7)=
(8)(8 - 7)=
8*1=8
2 fg(2)=
2 f(g(2))=
2 f(2(2)² - 7)=
2 f(2(4)-7)=
2 f(8-7)=
2 f(1)=
2(1² + 1 + 2)=
2(1+3)=
2(4)=8
8=8
2 fg(2)=f(2) g(2) √
2 points
Donna Preski works 8 hours a day, 5 days a week. So far this year she
has worked 680 hours. How many weeks has she worked?
17 weeks
Step-by-step explanation:
you multiply the number of hours by the number of weeks, giving you 40, then divide the amount of total hours worked by 40, giving you 17
5 x 8 = 40
680/40 = 17
17 weeks.
Take figure Q to figure R
1 unit left,2 units down and 90° clockwise rotation is the transformation of figure Q to make figure R.
What is the transformation of a graph?Transformation is rearranging a graph by a given rule it could be either increment,decrement, reflection, or rotation.
Reflection is a mirror image of a graph about any axis.
It seems that figure R is the rotation of Q clockwise by 90°.
In figure Q,
The Coordinate of the bottom left point of it is (3,1) if we rotate by 90° then it will remain at (3,1).
The coordinate of the same point in figure R is (2,-1)
So,
3 + x = 2 → x = -1 (1 unit left)
1 + y = -1 → y = -2 (2 units down)
Hence "1 unit left,2 units down and 90° clockwise rotation is the transformation of figure Q to make figure R".
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I need help please solving …
It takes the object about 26/49 minutes to travel 5 1/5 miles.
How long would it take the object to travel 5 1/5 miles?A mixed fraction is a non-integer that consists of a whole number and a proper fraction. An example of a mixed fraction is 1 1/2.
Speed measures how fast an object is moving with respect to time. Speed is the total distance travelled per time.
Speed = total distance / total time
In order to determine the total time it would take the object to travel the distance, divide the distance travelled by the speed.
Time = distance / speed
5 1/5 ÷ 9 4/5
26/5 ÷ 49 / 5
26/5 x 5/49 = 26 / 49 minutes
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ASSIGN #1: Object A is moving 12 feet per second (ft/sec). Object B is moving 5 miles per
R.A. hour (mila/hr). Which object is moving faster
According to the given statement;
object A is moving faster by 8.184-5= 3.184
3.184 mph faster.
What is speed?The distance traveled in relation to the time it took to travel that distance is how speed is defined. Since speed only has a direction and no magnitude, it is a scalar quantity.
The most crucial scientific concept is measurement. Base or physical fundamental units are used to measure a wide range of measurable quantities. One such measurable quantity is speed, which calculates the ratio between the distance an object travels and the time needed to cover that distance. Let's explore speed in-depth in this session.
According to the given valus;
Speed of object A = 12 ft per sec
I foot per second = 0.682 mph
12 ft per sec = 0.682x 12
= 8.184 mph
object В speed = 5 mph
object A is moving faster than B.
object A is moving faster by 8.184-5= 3.184
3.184 mph faster.
Hence,object A is moving faster than B by 3.184 mph.
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If p( a,2a) Q(4,3) and distance between them is 10 units find the coordinates of p
The distance between the coordinates is 2+√19.
According to the question, the given problem can be solved by using the standard distance formula.
Now, the coordinate values are:
p(a, 2a); q(4, 3) and Distance = 10 units
Therefore, from the given parameters we can write:
x1 = a; y1 = 2a; x2 = 4; y2 = 3
Now,
Distance^2 = (x1 - x2)^2 + (y1 - y2)^2
Substituting the given values, we get:
Distance^2 = (4 - a)^2 + (3 - 2a)^2 = 16 +a^2 - 8a + 9 +4a^2 - 12a
100 = 25 + 5a^2 - 20a
5a^2 - 20a - 75 = 0
a^2 - 4a - 15 = 0
a = 2+√19
Hence, the distance between the coordinates is 2+√19.
What is distance?
Distance can be defined as the resultant displacement between the two endpoints. It can measured in different units like meters, centimeters, kilometers, etc. And the respective values can be calculated by using the standard formula.
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bir basamaklı en küçük pozitif tam sayı
Answer:
Step-by-step explanation:
jjjjjjjj
Use the values of a₁ and Sn to find the value of a n a₁=4 and S₄₀=6080 ; a₄₀
Using the values of the first term and the sum of the first 40 terms of the given series, a(40) = 300
Suppose we are given a series:
a(1) + a(2) + a(3) + ....+ a(n)
Then, the sum of the first n terms is given by:
S(n) = n/2 [a(1) + a(n)]
Parameters given in the problem:
a(1) = 4
S(40) = 6080
To find a(40), substitute n = 40, a(1) = 4, and S(40) = 6080 into the formula:
S(n) = n/2 [a(1) + a(n)]
S(40) = 40/2 [4 + a(40)]
6080 = 20 . [4 + a(40)]
Divide both sides by 20
304 = 4 + a(40)
Subtract 4 from both sides:
304 - 4 = 4 + a(40) - 4
a(40) = 300
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You can find many different proofs to prove that (0.999 . . . =1 . How can you use the formula for the sum of a geometric series to show that 0.999 . . . . . =1 ?
We can use the formula for the sum of a geometric series as Summation.
What is Geometric Series:
A geometric series is the sum of finite or infinite terms of a geometric sequence. For the geometric sequence a, ar, ar2, ..., arn-1, ..., the corresponding geometric series is a + ar + ar2 + ..., arn-1 + .... We know that "series" means "sum". In particular, the geometric series means the sum of the terms that have a common ratio between every adjacent two of them. There can be two types of geometric series: finite and infinite.
Now, Solution of the given problem
We can write
0.999...=9/10+9/100+9/1000+⋯
=9/10+9/10(1/10)+9/10(1/10)2+⋯
=∞∑n=0 9/10(1/10)n,
which is a geometric series
with a=9/10and r=1/10
.So, the sum is a/1−r=9/10 / 1−1/10 = 1.
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At a banquet, 6 people sit at each of 8 tables. The server receives $96 in tips. How much did the server receive per person?100 points if u hurry up and give me the answer
Answer:
$2 per person
Step-by-step explanation:
6*8=48
96/48=$2
Answer:
$2Step-by-step explanation:
6 x 8 = 48
96 / 48 = 2
State whether each sentence is true or false. If false, replace the underlined word or phrase to make a true sentence.
To find the length of the hypotenuse of a right triangle, take the square root of the difference of the squares of the legs.
Given statement 'To find the length of the hypotenuse of a right triangle, take the square root of the difference of the squares of the legs.' is False.
In given question,
We have been given a statement 'To find the length of the hypotenuse of a right triangle, take the square root of the difference of the squares of the legs.'
We know that a hypotenuse is the largest side of a right triangle.
According to Pythagoras theorem,
in a right triangle c² = a² + b²
where c is the hypotenuse of a right triangle
a, b are perpendicular sides of the right triangle
This means, to find the length of the hypotenuse of a right triangle, take the square root of the sum of the squares of the legs.
Therefore, given statement 'To find the length of the hypotenuse of a right triangle, take the square root of the difference of the squares of the legs.' is False.
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hello people! if you have trouble in math in 8th grade pls dm me ill help
Step-by-step explanation:
Tell me the problem and I may help u
A= 7x^2-3x+10 B=-4x^2+6x-4
A-B=
Hello,
A - B = 7x² - 3x + 10 - (-4x² + 6x - 4)
A - B = 7x² -3x + 10 + 4x² -6x + 4
A - B = 11x² - 9x + 14
which function is increasing? a. f(x) = (0.5)^x b. f(x) = (1/5)^x c. f(x) = 5^x d. f(x) = (1/15)^x
The function is increasing is f(x) = [tex]5^x[/tex]
For exponential functions: f(x) = [tex]a^{x}[/tex] (a>0 and a[tex]\neq 0[/tex] ), when A is greater than the function is increased.
0.5 <1, [tex]\frac{1}{15}[/tex]<1 , [tex]\frac{1}{5}[/tex]<1 , 5>1
so C is correct.
The exponential is a mathematical function denoted by the argument x is written as an exponent. Unless otherwise specified, the term generally refers to the positive-valued function of a true variable, although it are often extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all or any real arguments, including irrational numbers. Its ubiquitous occurrence in pure and applied math led mathematician Walter to opine that the exponential function is "the most important function in mathematics".
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The tape diagram shows that Elizabeth spent 919191 minutes, which was 70\%70%70, percent of her study time for her language exam, on conversation practice.
The total time needed for Elizabeth on the practice is 130 minutes.
What will the time be?It should be noted that Elizabeth spent 91 minutes, which was 70 percent of her study time for her language exam,
Let the total time be represented by x.
Therefore, 70% × x = 91
0.7 × x = 91
0.7x = 91
Divide
x = 91/0.7
x = 130
The total time needed is 130 minutes.
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The tape diagram shows that Elizabeth spent 91 minutes, which was 70 percent of her study time for her language exam, on conversation practice. What was the total time needed?
Simplify by combining like terms. b-2(1+c-b)
The simplification by combining like terms of b -2(1 + c - b) is 3b -2c - 2.
According to the given question.
We have an expression b -2(1 + c - b).
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 b -2(1 + c - b).
Here b and 2b both are the like terms.
So, we add and subtract coeffcients of b to simplify the given expression.
Therefore, the simplification of the expression b -2( 1 + c - b) is given by
b - 2( 1+ c - b)
= b - 2 -2c + 2b
= 3b -2c - 2
Hence, the simplification by combining like terms of b -2(1 + c -b) is 3b -2c - 2.
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