The first four terms of the sequence are 7, 17, 37 and 77, respectively.
How to determine the first four terms of a sequence by a recursive formula
Sequences can be generated by using recursive formulas, that is, formulas that are in terms of the previous elements of a sequence. Herein we find a case of sequences by using recurrence formulas, whose procedure is shown below:
n = 1
f(1) = 7
n = 2
f(2) = 2 · f(1) + 3
f(2) = 17
n = 3
f(3) = 2 · f(2) + 3
f(3) = 37
n = 4
f(4) = 2 · f(3) + 3
f(4) = 77
The first four terms of the sequence are 7, 17, 37 and 77, respectively.
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I NEED HELP ASAP
Which expressions are polynomials?
Select each correct answer.
(to make it easier j put A,B,C,D. u also have to picc more thn one.)
You can find the area A of a square whose side is s units with the formula A=s². What. is the best estimate for the side of a square with an area of 32m² ?
(A) 4.2m C) 8.0m (B) 5.7m(D) 16m
The side of square is (B) 5.7m
We are given the formula relating side and area of square. Using the mentioned formula to find the value of side of square.
Side² = Area
Rewriting the equation according to side of the square -
Side = √Area
Keep the values in formula to find the value of side of square
Side = √32
Finding square root of the number to find the value of side of square
Side = √(8×4)
Side = √(4×2×4)
Side = 4√2
Side = 4×1.414
Performing multiplication to find the value of side of square
Side = 5.66
Side = 5.7 meters
Hence, the side of square is (B) 5.7m
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What is the least common denominator (LCD) of 1/10 and 1/6?
Answer:
LCD = 30
Equivalent Fractions with the LCD
1/10 = 3/30
1/6 = 5/30
Step-by-step explanation:
Rewriting input as fractions if necessary:
1/10, 1/6
For the denominators (10, 6) the least common multiple (LCM) is 30.
LCM(10, 6)
Therefore, the least common denominator (LCD) is 30.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
1/10 = 1/10 × 3/3 = 3/30
1/6 = 1/6 × 5/5 = 5/30
A speedboat travels 18 Miles in 12 minutes. At this rate, how far will the boat go in 1 hour? (12 minutes = 1/5 hour)
Answer: 90 miles.
Step-by-step explanation:
Since 12 is 1/5 of an hour, you can simply multiply 18 by 5 to get 90.
If Terrence jogged 4380 km how many meters did he jog
I need to write the place value of a number. I know how to do that but I don't know how to write it as a fraction. Like "state the place value of 4 in the number 23.45. Write you answer as a fraction"
Answer:
the answer is 4 hundreds because starting from the decimal point is hundreds
Use natural logarithms to solve each equation.
e ²x=10
In [tex]e^{2x} =10[/tex] , x = 1., by the properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
In [tex]e^{2x} =10[/tex] , taking natural logarithm on both side.
=> [tex]log_e(e^{2x})=log_e(10)[/tex]
By properties of logarithm, we know that: [tex]log_b(a)^m = m(log_b(a))[/tex]
=> [tex]2x(log_e(e))=ln(10)[/tex]
Also, as [tex]log_e(e)[/tex] = 1,
=> 2x (1) = ln(10)
=> 2x = 2.302 (approx)
=> x = 1.151
Hence, In [tex]e^{2x} =10[/tex] , x = 1.151, by the properties of logarithm.
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you and a friend are making jewelry for your friends. Bracelets cost $2.25 to make and
you spent $21.50 on supplies for necklaces. You only have $45 total to spend on supplies. Can you make bracelets for at least 10 friends? Explain your reasoning and show your work.
The fact that $45 is enough to make bracelets for 10.44 persons means that the we can make bracelets for 10 friends
What is the total necklace cost function?
The total cost of necklaces that can be made within the total budget of $45 can be modeled using a straight-line equation, which considers the fixed cost of necklace supplies of $21.50 and the total variable cost of supplies, the cost per necklace multiplied by the total number of necklaces possible, defined as x
45=21.50+2.25x
let solve for x to determine whether we can make bracelets for 10 friends
45-21.50=2.25x
23.50=2.25x
x=23.50/2.25
x=10.44
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Mary is going to sell her cakes at a bake sale. She spent $52 on supplies, and she is going to sell her cakes for $12 each. How many cakes does she need to sell to make a profit. Solve the inequality, and answer in a complete sentence. Let x= the number of cakes.
Add one pair of parentheses or square
brackets to the left side of each equation to
make a true statement.
a) 3.5 x 4.1 3.5 2.8 = -0.7
b) 2.5+ (-4.1) + (−2.3) × (-1.1) = 4.29
c) -5.5 (-6.5) ÷ 2.4+ (-1.1) = -0.5
a. 3.5 x 4.1 (3.5 ×2.8) = -0.7
b. 2.5+ (-4.1) + [(−2.3) × (-1.1)] = 4.29
c. [-5.5 (-6.5) ÷ 2.4]+ (-1.1) = -0.5
Hence the required parentheses are added to make the statement true.
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The probability that Gordon wins a raffle is given by the expression
n/n+4
Write down an expression, in the form of a combined single fraction, for the probability that
Gordon does not win.
An equation for the likelihood that Gordon does not win, in the form of such a combined single fraction:
= [tex]$\frac{4}{n+4}$[/tex]
Probability can be defined as:Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 as well as 1, where 0 denotes the event's impossibility and 1 represents certainty.
What are the three probability laws?The addition rule, the multiplication rule, and indeed the complement rule are the three main rules related with basic probability.
According to the given data:Formulate based on the provided conditions:
[tex]$1-\frac{n}{n+4}$[/tex]
Look for the common denominator as well as write additional numerators above it denominator:
[tex]$\frac{n+4-n}{n+4}$[/tex]
Rearrange and collect related terms:
[tex]$\frac{(n-n)+4}{n+4}$[/tex]
Gather coefficients for similar terms:
[tex]$: \frac{(1-1) \times n+4}{n+4}$[/tex]
The product of two polar opposites is 0:
[tex]$: \frac{0 n+4}{n+4}$[/tex]
Use the Multiplication Zero Property:
[tex]$\frac{4}{n+4}$[/tex]
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Simplify the expression 34 ÷ 39.
Answer:
1/243
Step-by-step explanation:
Solve each equation.
log₇343=x
The value of x for the equation log₇343=x will be 3.
What are the basic properties of logarithmic function?Logarithmic function properties. You have encountered several characteristics during your study of algebra, including the commutative, associative, and distributive properties.
These characteristics make it easier to simplify a complex statement or equation. With logarithms, the same holds true.
For log₇343=x
It can be expressed in the form of -
343 = 7ˣ
It can be further expressed as -
7³ = 7ˣ
As base is same,
x = 3
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8. If mZABC is one degree less than three times mZABD and m2DBC = 47°, find each measure.
The measured angle ABD=24° and ABC=71°
The figure in the question is either a triangle or a quadrilateral, but this has not been stated. It is possible to solve this regardless of shape. The accompanying graphic shows the two potential shapes and angles.
Now, based on the information provided, we may deduce that line BD divides angle ABC into two parts: Angle ABC is equal to angle ABD plus angle DBC.
Additionally, we know that angle DBC is 47 degrees and angle ABC is 1 degree less than 3 times angle ABD.
Angle ABC Equals 3x-1 if angle ABD is x.
Angle ABC also equals Angle ABD plus Angle DBC.
Changing the values in the equations above 3x-1 = x+47 ⇒ 2x = 48⇒ x = 24
Angle ABD thus equals 24 degree, and angle ABC = 3(24)-1 = 71-1 = 71 degree
∴∠ABD=24° and ∠ABC=71°
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Find each value without using a calculator. If the expression is undefined, write undefined.
sec (-π)
The value of the expression sec (-π) is equal to -1 if the given expression is undefined.
As given in the question,
Given expression: sec (-π)
Standard position of unit circle: -π is representing semicircle with terminal point on negative x-axis with coordinates (-1, 0)
Hypotenuse = √ (-1)² + 0²
= 1
Value of the expression is given by
sec α = Hypotenuse / Base (x-coordinate)
⇒sec(-π) = 1 / -1
⇒sec(-π) = -1
Therefore, the value of the expression sec (-π) is equal to -1.
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Please help im stuck
The slope of the line is 1 / 3
How to find the slope of a line?The slope of a line is a measure of its steepness.
The slope of the line is the ratio of the rise to the run, or rise divided by the run.
Mathematically, the slope of a line can be described as follows;
slope = change in y / change in x
Therefore,
slope = y₂ - y₁ / x₂ - x₁
Let's take two points from the graph
(0, 2)(3, 3)
where
x₁ = 0
x₂ = 3
y₁ = 2
y₂ = 3
Hence,
slope = 3 - 2 / 3 - 0
slope = 1 / 3
Therefore, the slope of the line is 1 / 3
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A nursery owner buys 9 panes of glass to fix some damage to hes greenhouse. The 9 panes cost 25.65 $. Unfortunately, he breaks 2 more panes while repairing the damage. What is the cost of another panes of glass?
Question content area bottom
Part 1
Another 2 panes of glass cost x $
enter your response here.
Answer:
For 2 more panes of glass it will cost $5.70.
Step-by-step explanation:
To find the price of each pane of glass you take the total price/ total panes of glass.
25.65/ 9 = $2.85.
If he wanted one more pane of glass it would be $2.85 but since you asked for two you multiply by 2 and get $5.70. Hope this helps!
PLEASE ANSWER QUESTION IN THE SCREEN SHOT!<3
Based on the information, it should be noted that there's an increase in percentage of 30%.
How to illustrate the information?Based on the information, it should be noted that the following can be illustrated:
Original amount = 30
New amount = 39
Therefore, it should be noted that the change in percentage will be:
= Change in amount / Old amount × 100
= (39 - 30) / 30 × 100
= 9/30 × 100
= 30%
Therefore, there's a increase in percentage of 30%.
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A scientist analyzed numerous samples of drinking water for the presence of lead and nickel. One sample is chosen at random. Let L be the event that the sample contains lead. Let N be the event that the sample contains nickel. Which Venn diagram is shaded to represent the event ? a. c, B. D.
Answer:
A
Step-by-step explanation:
if it is meant literally as stated (lead AND nickel), then the check was only for both to be present.
and then A is the correct answer (L n N : intersection of both sets).
if it would have the typical meaning (we say we check for L and A, but mean inclusive "or" : either L or N or both), then B would be correct.
If mWVY = 70, find mYVX.
Two or more expressions with equal sign is called as Equation. If mWVY = 70 is an angle then mYVX =165 we get by solving the equation x-13=70.
What is equation?Two or more expressions with equal sign is called as Equation.
mWVY = 70
From the figure we can observe that mWVY =x-13
By this we form an equation
x-13=70
x-13=70
x=70+13
x=83.
So value of x is 83.
Now mYVX=2x-1
2(83)-1
166-1
=165
Therefore mYVX is 165 degree when mWVY = 70.
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4.
Which inequality describes all the solutions to 11(3 - x) < -2x + 6?
x < -27
x > 3
x < -3
x > 4 1/3
Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions. x<3 is the inequality describes all the solutions to 11(3 - x) < -2x + 6
What is inequality?Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
The given inequality is 11(3 - x) < -2x + 6
We need to separate the variable x.
11(3 - x) < -2x + 6
33-11x<-2x+6
Let us shift -2x from RHS to LHS and 33 from LHS to RHS
2x-11x<6-33
Divide both sides by -9
-9x<-27
x<3
Therefore the solution to inequality 11(3 - x) < -2x + 6 is x<3.
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When Mt. St. Helens erupted in 1980, it reduced the elevation of the summit from 9,677 ft to 8,363 ft. By what percentage was the volcano's height reduced?
Answer:1314 or 13.14%
Step-by-step explanation:yes
Simplify each expression. y¹/₂ . y³/₁₀
Simplify the expression by applying the index rule: a^mx a^n = a^m+n.
y¹/₂ . y³/₁₀
y¹/₂ . y³/₁₀ = y¹/₂ +³/₁₀
¹/₂ +³/₁₀ = 4/5
y¹/₂ +³/₁₀ = y^ 4/5
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lowest common multiple of 18 and 42 x
Answer:
I'm assuming you inserting the variable x was a mistake.
Step-by-step explanation:
The least common multiple of 18 and 42 is 126.
[tex]\bold{Step-by-step}[/tex]
[tex]\mathrm{"LCM"}[/tex]
[tex]18 \times 7 = 126\\42 \times 3 = 126[/tex]
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given ij = 3x +3 HI = 3x-1 hj=3x+8 determine the numerical length of hj
if the point I is between points H and J, then the numerical length of hj is 14 units
How to determine the numerical length of hj?The given parameters are
IJ= 3x + 3
HI = 3x - 1
HJ = 3x + 8
The above implies that the point I is between points H and J
So, we have
HJ = HI + IJ
Substitute the known values
3x + 8 = 3x + 3 + 3x - 1
Evaluate the like terms
3x = 6
Divide by 3
x = 2
Substitute x = 2 in HJ = 3x + 8
HJ = 3 x 2 + 8
Evaluate
HJ = 14
Hence, the numerical length of hj is 14 units
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The figure below is dilated by a factor of 33 centered at the origin. Plot the resulting image.
The image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)
How to determine the image of the transformation?The complete question is added as an attachment
The coordinates of the triangle are given as
R = (-4, 1)
S = (-4, 4)
T = (-2, 1)
The transformation is given as
Dilation by a scale factor of 3Centered at the originThe rule of the transformations is
(x, y) = 3(x, y)
So, we have
R' = 3 * (-4, 1) = (-12, 3)
S' = 3 * (-4, 4) = (-12, 12)
T' = 3 * (-2, 1)= (-6, 3)
Hence, the image of the transformation is R' (-12, 3), S' (-12, 12) and T' (-6, 3)
See attachment for the image of the transformation
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Write an inequality that represents
Answer: x ≤ 4.5
Step-by-step explanation:
Since there is a closed circle on 4.5 and the ray is going left we know that x is ≤ 4.5
A total of 639 tickets were sold for the school play .They were either adult tickets or students tickets.There were 61 fewer student’s tickets sold than adults.How many adults tickets were sold ?
Answer:
350
Step-by-step explanation:
Okay, so we have a total of 639 tickets that they were sold. Using both students and adults tickets.
And also we know that the students r 61 fewer than the adults. So X minus 61.
X -61 = 289.
350 -61= 289
It's gonna be a total of 289. And we can check our results, X plus Y. So 350 plus 289. It's gonna be a total of 639.
A student found that a cubic function has zeros 16 and 1-2 i with a leading coefficient of 3 . What is the constant term of this polynomial function with real coefficients?
The constant term of this polynomial function with real coefficients will be - 240.
We are given the zeroes of the equation as:
16 and 1 - 2i
Now, we know that, the imaginary root are always in a pair, so the third root will be:
1 + 2i
This means that the factors of the cubic polynomial will be:
(x - 16)
(x - [1 - 2i])
(x - [1 + 2i])
The leading coefficient is 3, so the polynomial function will be:
y = 3 (x - 16) (x - [1 - 2i]) (x - [1 + 2i])
Now, the constant term will be:
3 (- 16) (1 + 2i) (1 - 2i)
( - 48) (1 - 4i²)
= ( - 48) (5)
= - 240
Therefore, the constant term of this polynomial function with real coefficients will be - 240.
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b. What are the expressions ⁴√x³} and (⁵√y⁴) in exponential form?
Exponential Form
We've all heard the term "exponential." What does that word mean? Exponential means growing faster and faster. However, in mathematics, it represents a formula with one or more exponents. So, we know it as exponential form. I would say that things can grow exponentially as the items being talked about get bigger and faster and faster.
So, we use the following method to write the given expression in exponential.
Expression 1 = ⁴√x³
Expression 2 = ⁵√y⁴
Use n*sqrt{a}x=a^(x/n) to rewrite 4*sqrt{x}3 as x^ (3/4)
similarly, we can write the second equation as
Use n*sqrt{a}x=a^(x/n) to rewrite 5*sqrt{y}4 as y^ (4/5)
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