The eighth term of the given geometric sequence is: 384.
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.Now, given: -3, 6, -12, ....
Here, [tex]\frac{6}{-3}=\frac{-12}{6} = -2[/tex]
Thus this geometric progression has the common ratio = -2.
The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 8, a₈ = a₁ ( r⁸⁻¹)
=> a₈ = (-3)(-2)⁷
=> a₈ = 3 ( 128) = 384.
Hence, The eighth term of the given geometric sequence is: 384.
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Simplest radical form
(-2,3) and (6,-4).
The simplest radical form of (-2,3) and (6,-4). is √113
How to determine the simplest radical form?The points are given as:
(-2,3) and (6,-4).
The distance is calculated using
d = √(x2 - x1)^2 + (y2 - y1)^2
This gives
d = √(-2 - 6)^2 + (3 + 4)^2
Evaluate
d = √113
Hence, the simplest radical form of (-2,3) and (6,-4). is d = √113
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Alejandro buys 4 bottles of pineapple juice at the corner store for a total cost of
$2.64. If each bottle costs the same amount, how much is 15 bottles of juice?
Answer:
$9.9
Step-by-step explanation:
4 = $2.64
15= ?
15 × $2.64 = 39.6
39.6 ÷ 4 = $9.9
Helen Mountain Tubing charges $25 for tube rental and $5 an hour to float down the river. Alpine Tubing charges $30 for tube rental and $2 an hour to float down the river. Create an equation to determine at what point the cost of both tubing companies is the same.
25x - 5 = 30x - 2
25x + 5 = 30x + 2
25 + 5x = 30 + 2x
25 - 5x = 30 + 2x
hi
As rental charges is contant and then price vary with time of location, then it's answer C
25 + 5x = 30 + 2x
Give an example of a function that represents a direct variation.
If y varies in direct proportion to x and y = 6 when x = 2, the variational constant is k = = 3. Consequently, y = 3x is the equation that describes this direct variation.
What is direct variation?Direct variation is the change in one quantity as a result of the change in another. This suggests that if one quantity rises or falls, the other must rise or fall correspondingly as well.
The formula y = kx is used to answer direct variation questions. If finding the proportionality constant is necessary, the answer is obtained by dividing y by x.
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Solve for the value of w
Answer:
[tex]w=9[/tex]
Step-by-step explanation:
[tex](4w-7)+(7w-2) = 90\\11w-9=90\\11w=99\\w=9[/tex]
What is the domain and use properties of continuity to support your answer
The domain of the function is x < 2 and it is discontinuous at x = 2
What is the domain of a function?The domain of a function is the range of input values to the function.
How to find the domain of the given function?Given that the above function f(x) = √[(x² + 1)/(2 - x)]
The domain of the function is the range of values of x that make the denominator greater than zero
So, the domain is √(2 - x) ≥ 0
2 - x ≥ 0
2 ≥ x
x ≤ 2
So, the function is valid for x < 2 and discontinuous at x = 2 since at x = 2, √(2 - x) = √(2 - 2) = 0
So, we see that the function is valid for x < 2 and discontinuous at x = 2
So, the domain of the function is x < 2 and it is discontinuous at x = 2
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Solve the math problem
Answer/Step-by-step explanation:
5.)
Square = 2
Triangle = 3
Circle = 3
Star = 4
2(circle) + 2(triangle) = 12
12 ÷ 4 = 3
2(3) + 2(3) = 12
2(triangle) + 2(square) = 10
2(3) + 2(square) = 10
6 + 2(square) = 10
-6 -6
2(square) = 4
÷2 ÷2
Square = 2
(circle) + (star) + 2(square) = 11
(3) + (star) + 2(2) = 11
3 + (star) + 4 = 11
7 + (star) = 11
-7 -7
Star = 4
6.)
Circle = 3
Star = 5
Triangle = 4
4(star) = 20
÷4 ÷4
(star) = 5
(star) + 3(circle) = 14
5 + 3(circle) = 14
-5 -5
3(circle) = 9
÷3 ÷3
circle = 3
2(triangle) + (circle) + (star) = 16
2(triangle) + 3 + 5 = 16
2(triangle) + 8 = 16
-8 -8
2(triangle) = 8
÷2 ÷2
triangle = 4
I hope this helps!
Dominic rented a car for the weekend. When he started driving on the highway he noticed the odometer had already logged 18,115 miles. After 45 minutes of highway driving, the odometer read 18,169 miles.
If he drove on the highway a total of four hours and traveled at a constant speed that entire time, what did the odometer read when he exited the highway?
The reading in the odometer will be 18,403 miles after travelling for 4 hours on the highway as Dominic covered a distance of 288 miles on the highway.
Distance on the odometer that was already logged = 18,115 miles.
Distance on the odometer after 45 minutes = 18,169 miles.
Distance covered in 45 mins = 18169 - 18115 = 54 miles.
Speed = 54 miles / 45 min
Speed = 6 miles / 5 minutes = 72 miles / hour
Now, he drove on the highway for 4 hours.
Time = 4 h
Distance = speed × time
D = 72 × 4 miles
D = 288 miles
Reading on the odometer when he exited the highway will be:
R = 18115 + 288 miles
R = 18403 miles.
Therefore, we get that, the reading in the odometer will be 18,403 miles after travelling for 4 hours on the highway as Dominic covered a distance of 288 miles on the highway.
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A rectangle on a coordinate plane is translated 5 units up and 3 units to the left. Which rule describes the translation?
O(x, y)
(x + 5, y-3)
O(x, y)
(x + 5, y + 3)
O(x, y) -
(x-3, y + 5)
O(x, y)
(x + 3, y + 5)
Sep 9
According to the translation rule, The translation of the rectangle is (x, y) → (x – 3, y + 5). Thus option C is correct.
According to the statement
We have to find that the translation rule.
So, For this purpose, we know that the
Translation is refers to the movement of a shape from one point to a different, without altering its appearance.
From the given information:
A rectangle on a coordinate plane is translated 5 units up and 3 units to the left.
With this in mind,
Once there's an upwards or downwards movement, there's a shift within the y coordinate
A move to the left or right movement, the x- coordinate is affected and moving left is negative
Hence,
y-coordinate is positive
x-coordinate is negative
Therefore, the rectangle translating 5 units up and three units to the left would be: (x, y) → (x – 3, y + 5)
So, According to the translation rule, The translation of the rectangle is (x, y) → (x – 3, y + 5). Thus option C is correct.
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Find the first five terms of each sequence. aₙ=a n₋₁ +2 n , where a₁ = 1
The first five terms of the sequence are 1,4,7,9,11.
What is a sequence?A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.
Given,
aₙ=a n₋₁ +2 n
For a1 = 1
a2 = 1 + 2.2 = 1 + 4 = 5
a3 = 1 + 2.3 = 1 + 6 = 7
a4 = 1 + 2.4 = 1 + 8 = 9
a5 = 1 + 2.5 = 1 + 10 = 11
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Find the perimeter of the figure write your answer in simplest form
Answer:
7 1/8
Step-by-step explanation:
Convert 2 3/8 to improper fraction 19/8 and multiply by 3/1. Reduce to lowest terms.
What are the assumptions for a chi square test for homogeneity? mark all that apply.
The assumptions for a chi square test for homogeneity are
The variables are assumed to be categorical variablesThe observations are assumed to be independentThe cells in the contingency table are assumed to be mutually exclusive.How to determine the assumptions for a chi square test?In statistics, the chi square test is used to determine where there exists a relationship or association between two variables
Amongst other assumptions, the variables are assumed to be categorical variables.
This means that variables can be used as labels
The other assumptions are:
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a₁ is the first term of a sequence, r is a common ratio, and d is a common difference. Write the first five terms. a₁=-100, r=1/5
The first five terms of a geometric sequence with first term -100 and common ratio 1/5 are -100, -20, -4, -4/5, -4/25
The given parameters:
a₁ = -100, r = 1/5
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) = -100 (given)
a(2) = a(1) . r = (-100) . 1/5 = -20
a(3) = a(2) . r = (-20) . 1/5 = -4
a(4) = a(3) . r = (-4) . 1/5 = -4/5
a(5) = a(4) . r = (-4/5) . 1/5 = -4/25
Therefore, the first five terms are -100, -20, -4, -4/5, -4/25
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Write the equation of the line through each point. Use slope-intercept form. (1,-1) ; parallel to y = (2/{5)x - 3
The equation of the line in slope-intercept form passing through the point (1 , -1) and parallel to y = (2/5)x - 3 is y = (2/5)x - 7/5.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The slope-intercept form of the equation of a line is given by the formula:
y = mx + b
where m is the slope of the line
b is the y- intercept
If the line is parallel to y = (2/5)x - 3, then their slopes are equal.
y = (2/5)x - 3 : m = 2/5
m = 2/5
Substitute the values of the slope and the point to solve for the y-intercept, b.
y = mx + b
-1 = 2/5(1) + b
b = -7/5
Write the equation of the line by plugging in the value of the slope and y-intercept.
y = mx + b
y = (2/5)x - 7/5
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pls who ever answers this question correctly i will give that person brainiest
1. what must be added to 649254 to make it equal to 97485
Answer:
-551,769
Step-by-step explanation:
We could just simply use subtraction:
97,485 - 649,254 = -551,769
Hope this helps!
Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x)=-9 x-2 for x=
f (7) = -65 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= -9 x-2
Put x = 7 ⇒ - 9 * 7 - 2
⇒ -63 - 2
⇒ -65
Therefore f (7) = -65
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The complete question is -
Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x)=-9 x-2 for x= 7
Kia deposits $2650 into an account the internet rate on the account is 6% compounded annually annually what is the balance in Kia’s account after 2 years? After 3 years
The balance in Kia’s account after 2 years is $2,977.54
The balance in Kia’s account after 3 years is $3,156.19
What is future value of the deposit?
The future value of the deposit, is the equivalent future worth of the deposit after having earned interest over the 2-year and 3-year periods using the future value formula of a single cash flow as shown below:
FV=PV*(1+r)^N
FV=balance after 2 and 3 years
PV=initial deposit=$2,650
r=interest rate=6%
N=number of years 2 and 3 years respectively
FV(2 years)=$2,650*(1+6%)^2
FV(2 years)=$2,977.54
FV(3 years)=$2,650*(1+6%)^3
FV(3 years)=$3,156.19
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How many pints are in 3.5 gallons
b ˜µ /ndf gn df/ng df/ng /dnf gn fdng
Answer:
28 pints
Step-by-step explanation:
1 gal= 8 pints
for reference: pint = gallon × 8
so,
3.5 gallons × 8 gives you 28.
A die is rolled. Find the probability of the outcome. P(odd)
The probability of the outcome P(odd) is 1/2.
Probability is a measure of the likelihood of an event to occur. It can range in from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.
We know that,
All outcomes in a die are 1,2,3,4,5, and 6.
Even outcomes = 2,4, and 6
Odd outcomes = 1,3, and 5
Hence,
Total number of odd outcomes = 3
Total number of outcomes = 6
We know that,
Probability of an event = Number of possible outcomes of the event/ Total number of outcomes
Therefore, we can write:-
Probability of the odd outcomes = 3/6 = 1/2
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[ Brainliest ]
Apply it! The measure of each central angle of a regular 10-sided polygon is ____ degrees.
Work Shown:
n = number of sides
c = central angle
c = 360/n
c = 360/10
c = 36
This formula applies to regular polygons only (all sides must be the same length; all angles must be the same).
Fran's account balance is -$22.91, and Zach's account balance is -$26.45. Which of the following is true?
A.
Fran's account balance = Zach's account balance
B.
Fran's account balance > Zach's account balance
C.
Fran's account balance < Zach's account balance
Answer:
B.
Fran's account balance > Zach's account balance
Step-by-step explanation:
help please
15 points
Answer: three and two.
If you add the digits of the number you have, for example, 36 (3+6 = 9), and the result is in the on the table of multiplication of 9; then is divisible by 9.
the difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0
Step-by-step explanation:
Rashid asked the genie, "How many wishes have you granted?"
Is this a statistical question?
The question asked by Rashid to genie, “ How many wishes have you granted ?” is not a statistical question.
Statistical question is a question that can be answered by collecting the data that vary and for which there will be variability in that data.
According to question, the question asked by Rashid has a direct answer for which there is no need to collect any data that is it has single data point which does not have any variability.
Thus the question asked by Rashid to genie is not a statistical question.
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Sandi and Felipe are participating in a Walk for Life to raise money for charity. Sandi will raise $30, plus $2.50 for each mile she walks. Felipe will raise $20, plus $5 for each mile he walks. The total amount that each will raise can be calculated using the following expressions, where n stands for the number of miles walked: Sandi: 30 + 2.5n Felipe: 20 + 5n After how many miles will Sandi and Felipe have raised the same amount of money?
Using linear equations, Sandi and Felipe have raised the same amount of money after 4 miles.
We can calculate using linear equations
Formulate based on the criteria stated: 30 +2.5 x x = 20 + 5 × x
Unknown terms should be moved to the left side of the equation:
2.5x-5x= 20-30
combining similar terms
-2.5x = 20 - 30
Determine the total or difference: 2.5x = -10
Subtract the coefficient of the variable from both sides of the equation: = -10 ÷ (−2.5)
Take the parenthesis out: 10 ÷ 2.5 =
Determine the quotient or product:
x = 4
find the outcome: = 4
Response: x = 4.
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Work out the next three terms in the sequence shown below. Give your
answers as simply as possible, without any brackets.
2.x
The term-to-term rule is
multiply by 2 then add x + 2 each time
→5x+2 →
D
7
The next three terms are 11x+6 , 23x+14 , 47x+30
The term-to-term rule is multiply by 2 then add x + 2 each time
First term is 2x
second term is 5x +2
next terms we can find by multiply by 2 then add x + 2 each time
third term 2(5x+2)+x+2
= 10x+4+x+2
= 11x+6
fourth term 2(11x+6)+x+2
= 22x+12+x+2
= 23x+14
fifth term = 2(23x+14)+x+2
= 46x+28+x+2
= 47x+30
The phrase equation and its cognates in other languages can also have subtly extraordinary meanings; as an example, in French an équation is described as containing one or more terms , even as in English, any well-shaped components together with two expressions related with an equals sign is an equation.
There are two kinds of equations: identities and conditional equations. An identity is authentic for all values of the variables. A conditional equation is simplest genuine for particular values of the variables
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y=2
How do I graph this
A horizontal line passing through A ( 0 , 2 )
WILL CHOOSE BRAINLIEST!!!!
7/8 add 1/2 in fractions
Answer:
so first we should find LCM of the denominator.and then find the answer
[tex] \frac{7}{8} + (\frac{1}{2} \times 4) = \: \: \: \frac{7}{8 } + \frac{4}{8 } = \frac{11}{8} or1 \frac{3}{8} [/tex]
The common sparrow has a wingspan of 9 to 15 centimeters. Which inequality matches the wingspan of the common sparrow?
The inequality which matches the wingspan of the common sparrow is :
9 ≤ x ≤ 15.
What is inequality and how can we frame one?
Inequalities are the equations in which two non equal expressions are compared using the mathematical relations such as ≤(less than or equal to ), ≥ (more than or equal to ), < (less than ) , >( more than).
Given that the common sparrow has a wingspan of 9 to 15 centimeters.
Let the wingspan of sparrow be x then given that x is more than or equal to 9 which gives an inequality : x ≥ 9 ....(1)
Also it is given that wingspan, x is not more than 15 centimeters which means x is less than or equal to 15 and this gives an inequality: x ≤ 15 ....(2)
Combining (1) and (2), we get:
9≤ x ≤ 15
Therefore wingspan (x) of common sparrow is shown by the inequality : 9≤ x ≤ 15
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Determine whether the regular polygon will tessellate in the plane. Write yes or no. Explain.
16 -gon
No, he regular polygon 16 -gon will not tessellate in the plane.
What is tessellation?A tessellation or tiling is the seamless application of one or more geometric shapes, known as tiles, to a surface, frequently a plane. Tessellation in mathematics can be expanded to include other geometries and higher dimensions.
A tiling constructed of materials like cemented ceramic hexagons or squares is referred to as a real-world tessellation. Such tilings may be ornamental designs or serve practical purposes such providing long-lasting and water-resistant pavement, floor, or wall coverings.
Tessellations were historically employed in Islamic art, such as the Moroccan architecture and the ornamental geometric tiling of the Alhambra palace. They were also used in Ancient Rome.
Regular polygons tessellate if their interior angles divide by 360° evenly or if the total of their interior angles is a factor of 360°. A tessellation is a pattern made of identical forms that fit together seamlessly.
So lets find out how pentagon won't tessellate.
First we find the measure of the interior angles of 16 -gon,
[tex]\frac{2520\°}{16} = 157.5\°[/tex]
Now divide the interior angle by 360°
[tex]\frac{360\°}{157.5\°} = 2.28[/tex]
Hence, the measure of the interior angle does not divide by 360°.
Therefore, we conclude that the regular polygon 16- gon will not tessellate in the plane.
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