Common ratio= 1/2, Next two term= 1/16, 1/32
This is a geometric sequence since there is a common ratio between each term.
i.e.,
the common ratio (r) = [tex]\frac{1/2}{1}[/tex] = [tex]\frac{1/4}{1/2}[/tex]
= 1/2
We can write the formula for general term of the series as
[tex]a_{n}[/tex] = a[tex](\frac{1}{2})^{n-1}[/tex]
If the further sequence does continue in the same way then the whole infinite sequence indicated is a geometric series.
So we have
[tex]a_{2}[/tex] =(1) [tex](\frac{1}{2} )^{2-1}[/tex]= 1/2
[tex]a_{3}[/tex] = 1× [tex](\frac{1}{2} )^{3-1}[/tex]= 1/4
[tex]a_{4}[/tex] = 1× [tex](\frac{1}{2} )^{4-1}[/tex]= 1/8
[tex]a_{5}[/tex] = 1× [tex](\frac{1}{2} )^{5-1}[/tex]= 1/16
[tex]a_{6}[/tex] = 1× [tex](\frac{1}{2} )^{6-1}[/tex]= 1/32
......
Therefore the sequence is in the same series, and we get the next two terms of the sequence which are 1/16, 1/32
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⠀I
R={(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Select all numbers that are in the domain.
-3
-2
-1
0
1
2
Answer:
-3, -1, 1
Step-by-step explanation:
Answer: -3,-1, and 1.
Step-by-step explanation: You are given the relation R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)} The domain of the relation are all possible inputs and the range of the relation are all possible outputs. So, the inputs are : -3,-1,1; and the outputs are : -2,0,2. As a result, the domain is : -3,-1,1; and the range is : -2,0,2.
Question down below, answer if you know :)
Answer:
Yes, they are similar as the difference between the smaller rectangle and the larger one is a scale factor of 2.
answer:
yes
explanation:
you can tell if figures are similar (proportional side lengths with points of the same orientation), if you can divide the respective side lengths of the image and preimage together.
write an equation for the nth term of the arithmetic sequence
5,11,17,23
The equation for the nth term of the arithmetic sequence is (6n – 1)
The given arithmetic progression is 5,11,17,23
Here we have been given
a = 5
d = a2 – a1
= 11 – 5
d = 6
The formula for the nth term is given as follows:
an = a + (n-1)d (1)
where, a = first term
d = common difference
putting the required values of ‘a’ and ‘d’ in equation (1) we get
an = 5 + (n-1)6
an = 5 + 6n – 6
an = 6n – 1
which is the required equation for the nth term of the arithmetic sequence
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At Central High School, there are 60 football players and 25 cheerleaders. What is the ratio of cheerleaders to football players?
Answer: 5:12
Step-by-step explanation:
25:60
But we can simplify this down too.
25:60
5:12
The expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped. What is the distance the object falls during each time?
2 seconds
If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance of the object falls during the time 2 seconds is 64 foot
Given,
The algebraic expression off the distance in feet that an object fall= [tex]16t^{2}[/tex]
Where t is time in seconds
Here,
Time t= 2 seconds
Substitute the values in the expression
[tex]16t^{2}=16(2)^{2}[/tex]
=64 foot
Hence, if the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped, then the distance of the object falls during the time 2 seconds is 64 foot.
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Part A
BOOKLETS A digital media company is ordering booklets to promote their business. The manufacturer charges $0.50 for each booklet when 50
or fewer are ordered, $0.45 for each booklet when 51 to 100 booklets are ordered, $0.40 for each booklet when 101 to 250 booklets are ordered,
and $0.35 for each booklet when 251 or more booklets are ordered. Each order consists of a $10 shipping charge, no matter the size of the order.
Answer:
Step-by-step explanation:
Paisley took a taxi from her house to the airport. The taxi company charged a pick-up fee of $1.70 plus $1.75 per mile. The total fare was $17.45, not including the tip. Which equation or tape diagram could be used to represent the context if a represents the number of miles in the taxi ride?
An equation that could be used to represent the context if a represents the number of miles in the taxi ride is 1.70 + 1.75a = 17.45
How to solve equation word problems?
We are given;
Base pick up fee = $1.70
Additional taxi fee per mile covered = $1.75
Total taxi fare = $17.45
Now, if we assume that a represents the number of miles in the taxi ride, then we can form the equation to represent the given scenario above as;
1.70 + 1.75a = 17.45
We conclude that an equation that could be used to represent the context if a represents the number of miles in the taxi ride is 1.70 + 1.75a = 17.45
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117 divided by 9 step by step
The quotient of 117 divided by 9 is 13.
What is Division?Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.
The answer thus got is called the quotient.
We have to divide 117 by 9.
Division algorithm states that,
Dividend = (Divisor × quotient) + Remainder
Remainder will be 0 if divisor is a factor of dividend.
Here dividend = 117 and divisor = 9
We know that 90 is a multiple of 9, where 90 = 9 × 10.
Remainder is 117 - 90 = 27
27 = 9 × 3
Hence 117 = 90 + 27 = (9 × 10 ) + (9 × 3) = 9 (10 + 3) = 9 × 13
So 117 / 9 = 13
Hence the quotient is 13.
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Darren teaches a class of 25 students. He assigns homework 3 times a week, and each assignment consists of 12 problems. How many problems must Darren correct each week?
The number of problems which Darren must correct each week according to the task content is; 900 corrections.
How many corrections must Darren provide?Since it follows from the task content that; the class contains 25 students, each who are each given 3 assignments per week consistent of 12 problems.
On this note, the number of problems he must correct since the homework is assigned distinctly to each student, the number of problems which he must correct is;
= 25 × 12 × 3
= 900 corrections.
However, if the assignment is same for all students; the number of corrections is;
= 12 × 3 = 36 corrections.
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In which one of the following numbers are none of the zeros significant?
a) 298.010
b) 3100
c) 0.00001470
d) 2.70400
Significant digits are all non-zero numbers. The numbers are none of the zeros significant is 3100.
What are significant figures?Significant figures in positional notation are the digits in a number that may be trusted to accurately represent how much of something there is.
Only the digits allowed by the measurement resolution are reliable, and only these can be significant figures if a measurement result is reported as a number with more digits than those allowed by the measurement resolution.
What are the rules for significant zeroes?Significant digits are all non-zero numbers. Any pair of non-zero digits that is not divided by zero is significant. Every zero that is both right and left of a non-zero digit and the decimal point has no significance. Any zeros to the right of a decimal point are only important if a non-zero digit comes after them. All the zeros to the right of the last non-zero digit after the decimal point are significant. If a measurement includes the zeros to the right of the final non-zero digit, they are all meaningful.To learn more about significant zeroes, refer to:
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(Laws of Exponents with Whole Number Exponents MC)
Evaluate one third raised to the seventh power divided by one third raised to the sixth power comma all raised to the second power.
one eighteenth
one ninth
1
one and one ninth
The simplified form of the given expression is 1/9. Therefore, option B is the correct answer.
The given expression is [tex](\frac{(\frac{1}{3})^{7}}{(\frac{1}{3})^{6} } )^{2}[/tex].
We need to evaluate the given expression.
What are the laws of exponents?Laws of exponents:
When multiplying like bases, keep the base the same and add the exponents. When raising a base with power to another power, keep the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.Now, [tex](\frac{(\frac{1}{3})^{7}}{(\frac{1}{3})^{6} } )^{2}=((\frac{1}{3})^{7-6})^{2}[/tex] (Because [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex])
[tex]=(\frac{1}{3})^{2}[/tex]
=1/9
The simplified form of the given expression is 1/9. Therefore, option B is the correct answer.
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Pls pls help whoever gets it right gets a crown
Answer:
Step-by-step explanation:
A. The common factor of the expression is 5[tex]x^{3}[/tex]y
B. In order to find a common factor, you find the prime factor. In this case, the biggest number that goes evenly into 40 and 25 is 5.
C. Divide the original problem by the common factor 5[tex]x^{3}[/tex]y
that gives you 5[tex]x^{3}[/tex]y(8x[tex]y^{2}[/tex]-5)
Hope this helps!
Determine whether each sequence is geometric. If so, find the common ratio. 18,-6,2,-2/3, . . . . .
Th given sequence is geometric with the common ratio being [tex]\frac{-1}{3}[/tex].
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: 18, -6, 2, -2/3, ....
Here, [tex]\frac{-6}{18}=\frac{2}{-6}=\frac{\frac{-2}{3}}{2}=\frac{-1}{3}[/tex]
Since, it follows the definition of a geometric progression, the sequence is geometric.
Thus, the given sequence is geometric, having common ratio = [tex]\frac{-1}{3}[/tex].
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Determine whether the events are independent or dependent. Then find the probability. In a bag of 3 green and 4 blue marbles, a blue marble is drawn and not replaced. Then, a second blue marble is drawn.
The probability. In a bag of 3 green and 4 blue marbles, a blue marble is drawn and not replaced. Then, a second blue marble is drawn is 3/7.
What is probability?Total number of marbles is 7.
Number of blue marbles are 4.
the probability that a second blue marble is drawn is 3/7.
Probabilities are mathematical explanations of the likelihood that an event will occur or that a proposition is true. The likelihood of an event is represented by a number between 0 and 1, with 0 typically signifying impossibility and 1 typically signifying certainty.
Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated. To forecast the likelihood of events, probability has been introduced in mathematics.
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hi i need help the question says
the length of a rectangle is one less than double the width . if the perimeter is 70 find the width
15 points please help
Step-by-step explanation:
let's just write it down in mathematical notation :
length = 2×width - 1
the perimeter is the way all around an object.
so, for a rectangle that is
2×length + 2×width
for our rectangle here
2×length + 2×width = 70
now we use the original identity of length via width and get
2×(2×width - 1) + 2×width = 70
4×width - 2 + 2×width = 70
6×width - 2 = 70
6×width = 72
width = 12
FYI
length = 2×width - 1 = 2×12 - 1 = 24 - 1 = 23
Write the equation of the line that passes through the points (6,-4) and (6,-1) Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The line that passes through the points (6,-4) and (6,-1) is:
x = 6
How to find the equation of the line?We want to find the equation of the line that passes through the points (6, -4) and (6, -1)
Now, this is really trivial, as you can see that both points have the same x-value (the x-value is the first value of each coordinate pair), which means that our line is x = constant = 6
Then we have a vertical line:
x = 6
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3b+2≤8
Help me please
Work Shown:
3b+2 ≤ 8
3b+2-2 ≤ 8-2
3b ≤ 6
3b/3 ≤ 6/3
b ≤ 2
Explanation: In the 2nd step, I subtracted 2 from both sides. In step 4, I divided both sides by 3. The inequality sign stays the same. It would flip if we multiplied or divided both sides by a negative number.
If you want to graph this on a number line, then plot a closed filled in circle at 2. Then shade to the left. This visually represents numbers that are 2 or smaller.
A seamstress is designing a triangular scarf so that the length of the base is 7 less than twice the height h, express the height of the scarf as a function of the height
Using algebraic expression, For the given expression, the height of the scarf will be 2h - 7
What is an Algebraic expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given the height = h
length of the base = 2h - 7
The area will be - 1/2 . B . H
= 1/2 . (2h - 7) . (h)
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-4(x + 7) + 2(2 + x) = -20
Answer:
x = -2
Step-by-step explanation:
Step 1: Distribute
-4(x + 7) + 2(2 + x) = -20 ----> -4x-28 + 4+2x=-20
Step 2: Combine Like Terms
-4x-28+4+2x=-20 ----> -2x-24=-20 ----> -2x=4
Step 3: Divide both sides by -2, solving for x.
-2x=4 ----> -2/-2x = 4/-2 ----> x = -2
Oabc is a square o is 0,0 a is -2,2 b is 0,4 c is 2,2 A single transformation of oabc is such that A is mapped to c. C is mapped to a O and b are invariant points Describe fully transformation
Using translation concepts, it is found that the transformation is a reflection over the y-axis.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For this problem, we have that A is mapped to C and vice-versa. Since they are equidistant to the y-axis, we have that the rule is given by:
(x,y) -> (-x,y).
Meaning that the transformation is a reflection over the y-axis.
For O and B, the rules are given as follows:
O: (0,0) -> (-0,0) = (0,0).B: (0,4) -> (-0, 4) = (0,4).Showing that points O and B are invariant, keeping the same coordinates and confirming that the transformation is a reflection over the y-axis.
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How do you say someone that cries guiltily, but the person is angry and sad with him/herself?
(NEEDS TO BE AN ADVERB)
When someone cries guiltily, but the person is angry and sad with him/herself is reflex crying.
What is an adverb?Verb, adjective, another adverb, determiner, clause, preposition, or sentence is typically modified by an adverb. Adverbs often answer questions like "how," "in what way," "when," "where," and "to what extent" by expressing things like method, place, time, frequency, degree, level of certainty, etc.
Many adverbs have -ly endings, and they frequently follow the word they modify. Adverbs typically give information about an action's when, where, how, and how much it happened.
It should be noted that in literature, an adverb simply means the part of speech that can be used to qualify a verb.
It should be noted that when someone cries guiltily, but the person is angry and sad with him or herself is reflex crying.
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A shipping box is in the shape of a cube. What is the volume of the shipping box if the length of one side of the box is 4m24n4
Answer:
A shipping box is in the shape of a cube. What is the volume of the shipping box if the length of one side of the box is 4m24n4
You are choosing between two different cell phone plans. The first plan charges a rate of 23 cents per
minute. The second plan charges a monthly fee of $44.95 plus 8 cents per minute.
Lett be the number of minutes you talk and C₁ and C₂ be the costs (in dollars) of the first and second
plans. Give an equation for each in terms of t, and then find the number of talk minutes that would
produce the same cost for both plans (Round your answer to one decimal place).
Answer:
257757
Step-by-step explanation:
Answer:
300 minutes 0.23c1=44.95+0.08c2
Step-by-step explanation:
how many positive integers are bigger than -3 and smaller than 5?
Answer:
4
Step-by-step explanation:
1,2,3,4
Please help I dont get this its due soon
the temperature in stratford starts at -5ºc, rises at -18ºc then falls at -8ºc what is the final temperature
Cameron works at an electronics store as a salesperson. Cameron earns a 4% commission on the total dollar amount of all phone sales he makes, and earns a 6% commission on all computer sales. Cameron made a total of $3600 in sales and earned $178 in commission. Write a system of equations that could be used to determine the dollar amount of phone sales Cameron made and the dollar amount of computer sales he made. Define the variables that you use to write the system.
Step-by-step explanation:(4/100x)+(6/100y)=178---------(i)
2х+3y=8900-----------(i)
x+y=3600---------(ii)
where x is phone
y is pen
The system of equations that describes the situation are 4x + 6y = 17800 and x + y = 3600.
What is a linear equation?A linear equation is an algebraic equation of degree one. In general, the variable or the variables(in the case of a linear equation in two variables) the variables are x and y.
Let the cost of 1 phone is x dollars and cost of 1 computer is y dollars.
Cameron earns a 4% commission on the total dollar amount of all phone sales he makes and earns a 6% commission on all computer sales.
∴ (4/100)x + (6/100)y = 178
4x + 6y = 17800...(i)
Cameron made a total of $3600 in sales.
∴ x + y = 3600...(ii)
Now to solve the equations we'll multiply eqn(ii) by 4 or 6 to cancel out x or y, and then we'll substitute the numerical value of x or y in any of these equations.
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Simplify by combining like terms. 3 a+b+a
The simplification by combining like terms of 3a + b + a is 4a + b.
According to the given question.
We have an expression 3a + b + a.
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 3a + b + a.
Here 3a and a both are the like terms.
So, we add coeffcients of a to simplify the given expression.
Therefore, the simplification of 3a + b + a is given by
3a + b + a
= 3a + a + b
= 4a + b
Hence, the simplification by combining like terms of 3a + b + a is 4a + b.
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Find the approximate circumference of a circle with a diameter of 6 inches. Use 3.14
as an estimate of 77 that is correct to two decimal places.
O A. C = 18.84 in
OB. C≈ 20.46 in
C. C 18.84 in
OD. C≈ 18.84954 in
The correct option is (C) 18.84 in. The circumference of the circle with a diameter 6 in is 18.84 in.
What is the circumference of a circle?A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.
Given, the diameter of the circle = 6 in.
The radius of a circle is calculated as
r = d / 2
r = 6 / 2
r = 3 in
The circumference of a circle is calculated as
C = 2πr
Substitute r = 3 in the circumference formula
=2 × 3.14 × 3
= 6 × 3.14
= 18.84 in
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The circumference of the given circle with a diameter of 6in is 18.84in.
What do we mean by the circumference of the circle?The circumference of a circle is known as its perimeter. It is the circumference of the entire circle. The circumference of a circle is calculated by multiplying its diameter by the constant. This diameter measurement is required for anyone crossing a circular park or enclosing a circle. Circumference, which is a linear variable, is measured in the same units as length.So, the diameter is 6in.
Then, the radius is:
r = d / 2r = 6 / 2r = 3 inThe formula for the circumference of the circle: 2πr
Now, substitute 'r = 3' in the formula of circumference as follows:
= 2 × 3.14 × 3= 6 × 3.14= 18.84 inTherefore, (C) 18.84 is the circumference of the given circle.
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Find the slope of the line that contains the points (7,2) and (3,4)
According to the given statement the slop of the given points are: -(1/2).
The line's slope is described as:The slope of the line is the mathematical ratio of overall rise to the run, or rise divided by the run. It expresses the slope of a line in the coordinate plane. Calculating the slope of a line is comparable to finding the slope between two separate places.
How do I calculate the slope of an equation?The procedure for calculating the slope from such an equation will vary based on the form of the equation presented to you. If the equation is written as y=mx+c, the slope (or gradient) is simply m. If the formula does not exist in this form, try rearrangement.
According to the given information:The slope of a line is easily calculated by hand using small, whole number coordinates.
so,
X1 = 7
X2 = 3
Y1 = 2
Y2 = 4
Applying the formula for slope:
slope = (y₂ - y₁) / (x₂ - x₁)
= (4 - 2) / (3 - 7)
= 2/(-4)
= - (1/2)
The slop of the given points are: -(1/2)
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Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. -1,1,-1,1,-1,1, ......
The formula for finding any term of the given sequence is [tex]a_{n}[/tex] = [tex]n^3[/tex].
According to the given question.
We have a sequence
-1,1,-1,1,-1,1....
As we know that, a sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.
The above of given sequence -1,1,-1,1,-1,1,..... is following a rule i.e. each term is the cube of its number of term.
Here,
The first term is -1, so the cube of -1 is -1.
The second term is 1, so the cube of 1 is 1.
So, the nth term of the given sequence is [tex]n^{3}[/tex].
Therefore, the formula for finding any term of the given sequence is given by
= [tex]n^3[/tex]
Where, n = Therefore, the formula for finding any term of the given sequence is given by
= [tex]n^3[/tex]
Where, n = -1,1,-1,1,-1,1, .......
So, for n = -1
The first term will be -1.
for n =1
The second term will be 1
for n= 1
The fourth term will be 1 and so on .
Hence, the formula for finding any term of the given sequence is [tex]n^3[/tex].
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