Answers
The common difference of the given arithmetic sequence is 8.
What is an arithmetic sequence?An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.
The given arithmetic sequence is -1, 7, 15,....
Common difference = Second term - First term
= 7-(-1)
= 7+1=8
Common difference = Third term - Second term
= 15-7
= 8
Therefore, the common difference is 8.
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The solution is, the common differences are -3, -20, -10, -2, 5.
What is common difference?In an arithmetic sequence, the difference between any two consecutive terms must always be the same number, which is known as the common difference.
here, we have,
So we just need to take different pairs of consecutive terms and see if their difference is always the same:
1) The differences are:
32 - 35 = -3
29 - 32 = -3
26 - 29 = -3
So yes, this is an arithmetic sequence and the common difference is -3
2) The differences are:
-23 - (-3) = -20
-43 - (-23) = -20
-63 - (-43) = -20
This is an arithmetic sequence, and the common difference is -20
3) The differences are:
-64 -(-34) = -30
-94 -(-64) = -30
-124 -(-94) = -30
This is an arithmetic sequence and the common difference is -30
4) The differences are:
-40 -(-30) = -10
-50 - (-40) = -10
-60 - (-50) = -10
This is an arithmetic sequence and the common difference is -10
5) The differences are:
-9 - (-7) = -2
-11 - (-9) = -2
-13 - (-11) = -2
This is an arithmetic sequence, and the common difference is -2
6) The differences are:
14 - 9 = 5
19 - 14 = 5
24 - 19 = 5
This is an arithmetic sequence, and the common difference is 5.
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Related Questions
Write the equation of the graph shown below in factored form
Answers
The equation of the polynomial is P(x) = -4(x + 1)(x - 1)(x - 2)^2
How to determine the equation of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -1A root of multiplicity 1 at x = 1A root of multiplicity 2 at x = 2y-intercept = -12A polynomial is represented as
P(x) = a * (x - zero)^multiplicity
Using the above as a guide, we have the following:
P(x) = a * (x + 1)(x - 1)(x - 2)^2
The y-intercept is -12
So, we have
a * (0 + 1)(0 - 1)(0 - 2)^2 = -12
This gives
a = -4
Hence, the expression is P(x) = -4(x + 1)(x - 1)(x - 2)^2
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Suppose you have $200 with which you can buy shares of stock from two companies:
ABC Hot Chocolate Company and XYZ Lemonade. Each company's stock currently sells for $100 per share. If the temperature next year is lower than average, the stock price for ABC will increase by $20, and the stock price for XYZ will not change.
If the temperature next year is higher than average, the stock price for XYZ will increase by $20, and the stock price for ABC will not change. There is a 50% chance that it will be colder than average next year, and a 25% chance that it will be warmer than average.
If you purchase two shares of ABC stock and no shares of XYZ stock, there is a _____ chance that your gain will be $40. Otherwise, your gain will be _____.
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
Answers
The chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and if it is not $40 the gain is:
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
So, the option (4) 50%, $20 is the correct option.
The given question is asking what the chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and what the gain will be if it is not $40.
Mathematically, this can be broken down as follows:
There is a 50% chance that the temperature will be lower than average, in which case the stock price for ABC will increase by $20. Thus, the expected gain from investing in ABC is 50% x $20 = $10.
There is a 25% chance that the temperature will be higher than average, in which case the stock price for XYZ will increase by $20. Since you are not investing in XYZ, your expected gain from this is 0.
Therefore, the expected gain from investing in ABC and not investing in XYZ is 50% x $10 + 25% x $0 = $10 + $0 = $10.
Since you are investing in two shares of ABC stock, your expected gain is 2 x $10 = $20. Thus, there is a 50% chance that your gain will be $40, and otherwise your gain will be $20.
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please help me solve this quick!
Answers
On solving the provided question we can say that the quadratic equation is 3x²+15x+9=0
What is quadratic equation ?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation is 3x²+15x+9=0
by Shridhara Charya formula method, we have
x=−0.697224
x=−4.30278
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The polynomial of degree 4,
P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at x=0 and x = - 4. It goes through the point (5,144). Find a formula for P(x).
Answers
Answer:
Step-by-step explanation:
Since the polynomial has a root of multiplicity 2 at x = 3, it can be written as (x - 3)^2 times another polynomial Q(x). Also, since it has roots of multiplicity 1 at x = 0 and x = -4, it can be written as (x - 3)^2 * (x - 0) * (x + 4) * Q(x).
Next, we can use the fact that the polynomial goes through the point (5, 144) to find the formula for Q(x). The polynomial P(x) must satisfy P(5) = 144, so we can write:
(5 - 3)^2 * (5 - 0) * (5 + 4) * Q(5) = 144
4 * 9 * 9 * Q(5) = 144
36 * Q(5) = 144
Q(5) = 4
So, the polynomial P(x) can be written as:
P(x) = (x - 3)^2 * (x - 0) * (x + 4) * 4
= 4 * (x - 3)^2 * (x - 0) * (x + 4)
= 4 * (x^2 - 6x + 9) * x * (x + 4)
= 4x^4 - 84x^3 + 378x^2 - 648x + 576
This is the formula for P(x).
What are the domain and range of the real-valued function f(x) = -3-√√4x - 12?
Answers
The domain of the real valued function as required is; [3, infinity).
The range of the function as required is; (-infinity, -3].
What is the domain of the function?By observation of the given function; the domain is the set of all real numbers except those for which;
4x - 12 < 0
4x < 12
x < 3.
Hence, the domain of the function is; [3, infinity).
The range as observed in the task content has a maximum value of; -3. Hence, the range of the function as required is; (-infinity, -3].
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Which shows the expression x^2-1/x^2-x
in simplest form?
Answers
Answer:
x+1/x
Step-by-step explanation:
One loaf of bread weighs 0.68 kilogram. Six muffins weigh 1.12 kilograms. How much more do two loaves of bread weigh than the muffins? 0.08 0.12 0.24 1.30
Answers
Answer:
C) 0.24 kg
----------------------------
Find the weight of two loaves of bread:
0.68*2 = 1.36 kgFind the difference of weights of 2 loaves of bread and 6 muffins:
1.36 - 1.12 = 0.24 kgThe matching choice is C.
The difference of weights of 2 loaves of bread and 6 muffins:
= 0.24 kg
We have to given that,
One loaf of bread weighs 0.68 kilogram.
And, Six muffins weigh 1.12 kilograms.
Now, We can Find the weight of two loaves of bread:
Here, One loaf of bread weighs 0.68 kilogram.
Hence, the weight of two loaves of bread:
0.68 x 2 = 1.36 kg
Hence, the difference of weights of 2 loaves of bread and 6 muffins:
= 1.36 kg - 1.12 kg
= 0.24 kg
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HELPPP PLEASE I NEED HELP
Answers
The rule A(x,y) ⇒ (-y,x) describes a transformation. The correct option is D.
What is a transformation of rotation?The concept of rotation in mathematics has its roots in geometry. Any rotation is a movement of a certain area while maintaining at least one point. It may be used to describe, for instance, how a rigid body moves around a fixed point.
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x). To put it another way, flip x, and y, making y negative.
The transformation is described by the rule A(x,y) (-y,x). The right answer is D.
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Claudia is interested in knowing which figure skater competing in the
Olympic Games is most favored to win a gold medal. To sample the
students in her school, she prepares a list of all of the boys and girls in the
school and randomly chooses a sample from each group so that the size of
each group is proportional to the number of boys and girls in the school.
Which sampling method did Claudia use?
OA) simple random sampling
OB) stratified random sampling
OC) systematic random sampling
OD) simple non-random sampling
Answers
In stratified random sampling, the population is divided into subgroups (strata) based on a certain characteristic, and a random sample is taken from each stratum. In Claudia's case, she divided the population into two subgroups based on gender (boys and girls), and took a random sample from each group proportional to the number of boys and girls in the school. This method is used when the researcher wants to ensure that the sample is representative of different subgroups in the population.
OD) Is simple non-randon sampling
Step-by-step explanation:
because Claudia randomly choose a sample from each group.
100 points!!!!!!!!
Martina is playing a carnival game. She is blindfolded while she throws a dart at a board of 12 balloons, as shown below. Each balloon is labeled "S" for small,
"M" for medium, "L" for large, or "XL" for extra-large. The board has 5 small balloons, 1 medium balloon, 4 large balloons, and 2 extra-large balloons. She hits one of the balloons at random and wins a stuffed animal of that size.
(a)Find the odds in favor of Martina winning a medium stuffed animal.
(b) Find the odds against Martina winning a medium stuffed animal.
Answers
Answer:
(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.
(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.
Answer:
(a) The odds in favor of Martina winning a medium stuffed animal is 1/12, as there is only 1 medium balloon on the board out of the total of 12 balloons.
(b) The odds against Martina winning a medium stuffed animal is 11/12, as there are 11 balloons on the board that are not medium out of the total of 12 balloons.
Consider the line 8x-5y=1.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line ?
Answers
Brainliest pls.
Simplify the following expression using rational exponents. Assume all variables are positive.
a3/5⋅a3/4
Answers
Answer:
The simplified expression is a^(21/20).
Step-by-step explanation:
To simplify the expression, we can use the rule for multiplying two powers with the same base, which is to add the exponents.
a^(3/5) * a^(3/4) = a^(3/5 + 3/4) = a^(6/5 + 3/4)
We can then simplify the fractional exponent by finding a common denominator for the numerators, which is 20 in this case:
a^(6/5 + 3/4) = a^(6/20 + 15/20) = a^(21/20)
The simplified expression is a^(21/20).
In the diagram, ACDF∼VWYZ
. Find the value of y.
Answers
The value of the variable y is 3
How to determine the valueFrom the information given, we have that;
ACDF∼VWYZ
Given that the lengths are;
A= 12CD = 9YW = 6VZ = 3y -1Since the diagrams are equivalent, then,
A/VZ = CD/YW
substitute the values, we have;
12/3y - 1 = 9/6
cross multiply
3y - 1 = 12(6)/9
divide the values
3y - 1 = 8
collect like terms
3y = 9
Make 'y' the subject
y =3
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Jade and Juliette are riding their bikes across the country to promote autism awareness. They rode their bikes 45.4 miles on the first day and 56.3 miles on the second day. From now on, Jade and Juliette plan to ride their bikes 62 miles per day. If the entire trip is 2,878 miles, how many more days do they need to ride?
Write a short script that could be used to make a video about this cross-country bike trip. Provide a short character description, dialogue (conversation between characters), and directions for the actors, but keep the script simple
Answers
Jade and Juliette 44.7days more days to complete their trip.
How to calculate the number of days to complete the tripTo calculate how many more days Jade and Juliette need to ride, we can use the equation:
Total distance = Distance on first day + Distance on second day + Distance on remaining days
We know the first and second day distances, and the daily distance for the remaining days, so we can substitute those values in the equation:
2878 = 45.4 + 56.3 + 62x
where x is the number of remaining days they need to ride.
Simplifying the equation:
2878 - 101.7 = 62x
2776.3 = 62x
Dividing both sides of the equation by 62
x = 44.7
hence, Jade and Juliette need to ride for 44.7 more days to complete their trip.
Please help me answer this
Answers
The given expression can be written in a single radical as q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]. The solution has been obtained by solving the radical expressions.
What are radical expressions?
An expression which contains a square root is referred to as a radical expression. The 'V'-shaped portion of the radical sign will have a superscript number when it is used to represent any root other than a square root.
We are given √q³ [tex]\sqrt[3]{q^{8} }[/tex].
On simplifying the expression, we get
⇒√q² . q [tex]\sqrt[3]{q^{3} . q^{3} . q^{2} }[/tex]
⇒q . √q . q² . [tex]\sqrt[3]{ q^{2} }[/tex]
⇒q³ . √q [tex]\sqrt[3]{ q^{2} }[/tex]
⇒q³ . [tex]\sqrt[]{ q^{\frac{1}{2} + \frac{2}{3} } }[/tex]
⇒q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex]
Hence, the given expression can be written in a single radical as q³ . [tex]\sqrt[]{ q^{\frac{7}{6} } }[/tex].
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Hasten plans to choose a book from the section of the store where everything is 25% off he likes expression D -0.25 days to find the sale price of the book it if there is a YZ dollars below correctly write another expression 0.7 5D that will also find the surprise of the book if the original price is de dollars
Answers
Another form of representing the cost of the book is (75/100)×D.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
We know, Percentages and decimals are related.
10% in decimal form is equivalent to (10/100) - 0.1 in decimal.
An expression that represents the sale day book price is 0.75D.
Another expression that would represent the cost of the book priced 'D' would be,
= (75/100)×D.
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The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6. Terrence owns 36 models cars. How many model cars does Jim own? How will the ratio change if Jim and Terrence each sell ten of their model cars?
Answers
As said, 48 model automobiles are driven by Jim at the moment, and the ratio might alter to 19:13.
What does a mathematical ratio mean?An organisation of the integers a and b stated as a/b is still a ratio if b is truly not comparable to 0. Two ratio with the same value are established by the percent formula. As an illustration, you might write your ration as follows: 1:3 when there is 1 man and 3 females.
You know there's an 8:6 ratio between the grand total of model cars Jim and Terrence possess.
As a result, you can respond to the assignment as follows: Assume Jim owns x different car models.
8/6 = x/36
x = 36*8/6
x = 288/6
x = 48
The new percentage of Jim's against Terrence's model vehicles will be as follows because both Jim & Terrence sell ten of their model cars:
(48-10)/(36-10) = 38/26 = 19/13
Jim's to Terrence's miniature automobiles will now be in a 19:13 ratio.
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LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN = 4x+10 and MP = 9x-5
X =
Answers
Answer:
x=5 and LN= 30, MP= 40
Step-by-step explanation:
Add like terms to both sides of the equation and you will get your answer
Can the following fraction be simplified or expressed in a different form -
(5x-1)/x+4
Answers
Answer:
= 9x - 1
Step-by-step explanation:
[tex] \frac{(5x - 1)}{x} + 4 \\ = x \times \frac{5x - 1}{x} + 4(x) \\ = 5x - 1 + 4x \\ = 5x + 4x - 1 \\ = 9x - 1[/tex]
In simple terms, please explain to me what is the difference between horizontal shrink and vertical stretch.
Answers
Answer:
see attached
Step-by-step explanation:
You want the difference between horizontal shrink and vertical stretch.
Horizontal shrinkA horizontal shrink compresses a graph horizontally. In the attached figure, the original graph is the red circle. The blue ellipse is that circle shrunk horizontally by a factor of 3. It retains the same height, but is compressed sideways.
Vertical stretchA vertical stretch expands the graph vertically. The green ellipse in the attached figure is the original circle stretched vertically by a factor of 3. The horizontal dimension remains unchanged.
InterchangeableYou will notice that replacing a variable x by x/k effectively accomplishes a stretch by a factor of k in that variable's direction. Similarly, replacing a variable x by kx accomplishes a compression by a factor of k.
Your question suggests that you have noticed the similarities between vertical stretch and horizontal compression. For some figures, there is basically no difference.
Here are a couple of examples of that:
line y = x. Vertical stretch by 2: y/2 = x, or y = 2x. Horizontal compression by 2: y = 2x. These equations are identical.
parabola y = x². Vertical stretch by 4: y/4 = x² or y = 4x². Horizontal compression by 2: y = (2x)² = 4x². These equations are identical.
DifferencesThe differences between stretch in one direction and compression in the other direction are more apparent for figures with multiple reversals of direction. The second attachment shows the sine function (red) vertically stretched (blue) and horizontally compressed (green).
The area of a rectangular red sticker is 33 millimeters.The perimeter is 28 millimeters. what are the dimensions of the sticker?
Answers
The dimensions of the sticker are 11 millimeters and 3 millimeters.
What is Area and Perimeter?Area of a two dimensional shape is the total region which is bounded by the object's shape.
Perimeter of a straight sided figures or objects is the total length of it's boundary.
Given is a sticker which is rectangular in shape.
Area of the sticker = 33 millimeters²
Perimeter of the sticker = 28 millimeters
Area of a rectangle = Length × Width
Perimeter of a rectangle = 2(Length + Width)
Let x be the length and y be the width of the rectangle.
x y = 33
2(x + y) = 28 ⇒ 2x + 2y = 28 ⇒ 2y = 28 - 2x ⇒ y = 14 - x
Substituting y = 14 - x in x y = 33,
x(14 - x) = 33
14x - x² = 33
-x² + 14x - 33 = 0
x² - 14x + 33 = 0
Factorizing the quadratic equation,
(x - 11) (x - 3) = 0
x - 11 = 0 or x - 3 = 0
x = 11 or x = 3
If x = 11, then y = 33/11 = 3
If x = 3, y = 33/3 = 11
Hence the dimensions are 11 millimeters and 3 millimeters.
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13. Landon is 6 ft. tall and measures his shadow to
be 8.3 ft. long. At the same time of day, he
measures a tree's shadow to be 17.6 ft. long. How
tall is the tree?
Answers
Answer: 12.72 ft.
Step-by-step explanation:
[tex]\frac{6}{8.3} = \frac{x}{17.6} \\\\ 8.3x= 105.6\\\\x= 12.72[/tex]
Reactive Power VARS Apparent Power VA CD True Power W
Answers
a. Reactive power is the power lost in the inductive or capacitive load in an AC electrical circuit.
b. Apparent power is the power is the total power delivered to an AC electrical circuit
c. True power is the power lost in a resistive load in an AC electrical circuit.
What is power?Power is the rate at which work is done.
a. What is reactive power VARS?Reactive power is the power lost in the inductive or capacitive load in an AC electrical circuit. The reactive power is given by
P' = IVsinФ where
I = current in circuit, V = voltage in circuit and Ф = load angleb. What is apparent power VA?Apparent power is the power is the total power delivered to an AC electrical circuit. The apparent power is given by
S = IV where
I = current in circuit, V = voltage in circuit c. What is true power W?True power is the power lost in a resistive load in an AC electrical circuit. The true power is given by
P' = IVcosФ where
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wer:
My number is a 2-digit multiple of 9. The ratio of its units digit to its tens digit is 1:2.
What is my number?
Answers
Let's call the tens digit "x" and the units digit "y". We know that the number is a multiple of 9, so:
x + y = 9
and the ratio of the units digit to the tens digit is 1:2, so:
y = 2x
Substituting the second equation into the first, we get:
x + 2x = 9
3x = 9
x = 3
So the tens digit is 3 and the units digit is 2 times that, or 6. The number is 36.
Answer:
63
Step-by-step explanation:
___________________
First, let's list all the 2-digit multiples of "9":
______________________________________________________
18, 27, 36, 45, 54, 63, 72, 81, 90, 99.
______________________________________________________
From this list, the only answer that has a ratio in which its "units digits to its tens digits" is "1:2" is: "63" . "3:6" = "1:2" .
Is 2/3 equal or bigger than 1/2
Answers
Answer: 1/2 is
Step-by-step explanation:
See attached image and answer questions.
Answers
The properties of the polynomial are
Degree = oddLeading coefficient = NegativeOdd multiplicity = 3Even multiplicity = 1How to determine the properties of the polynomialFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we have the following readings:
A root of multiplicity 1 at x = -5A root of multiplicity 1 at x = -2A root of multiplicity 2 at x = 1A root of multiplicity 1 at x = 4y-intercept = 2Using the above as a guide, we have the following:
Degree = sum of multiplicities
Degree = 1 + 1 + 2 + 1
Degree = 5
The leading coefficient is negative
This is so because the graph opens down
There are 3 zeros with odd multiplicities and 1 zero with even multiplicity
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2/3 of the students in Mrs. Gracie’s class are boys . If there are 27 students in the class, how many of them are girls?
Answers
Answer:
9
Step-by-step explanation:
divide 27 by 3
It equals 9
9 x 2 = 18 boys
27-18= 9 girls
please, help with this one
r log a + y log c
Answers
The required r log a + y log c is equivalent to the expression as [tex]r log a + y log c = log (a^r c^y)[/tex].
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The expression r log a + y log c can be simplified using logarithmic properties. Specifically, we can use the rule that says:
[tex]log a^b = blog a[/tex]
Using this rule, we can write the expression as:
[tex]r log a + y log c = log a^r + log c^y[/tex]
Now we can use the rule that says:
log a + log b = log ab
to combine the two logarithms:
[tex]log a^r + log c^y = log (a^r c^y)[/tex]
Therefore, the expression r log a + y log c simplifies to:
[tex]r log a + y log c = log (a^r c^y)[/tex]
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Please help me I’m confused
Answers
Answer:
Below
Step-by-step explanation:
Here is what the graph should look like ...you can see that he will have 0 fence left to paint ( 0 = y ) when time = 3 hrs
Help please I don’t understand it at all
Answers
Answer:
Both of them are correct.
Step-by-step explanation:
Let's review both of their methods and check their validity.
Kaylee's Method:This method is the most straight forward and seems to be correct as we're simply calculating the total value of each, and then subtracting the difference. We can write the expression as: [tex]2.25(4.25)-2.25(2.85)[/tex] and this should give us the difference assuming the prices and math is done correctly.
Ariel's Method:While this method is a bit difference, it actually does work! Think of this way, we first calculate the difference in the prices and then for each pound we increase it by, the difference also increases by this amount. It also helps to look at our original expression: [tex]2.25(4.25)-2.25(2.85)[/tex], notice how we have a factor of 2.25 on both sides? Well we can just factor that out to get: [tex]2.25(4.25 - 2.85)[/tex] and this is essentially what Ariel's method is. This should give us the difference in prices and is likely easier than Kaylee's method as we do less multiplication and with smaller numbers.
