Missing term i.e., the second term of the sequence is 5.
As the series is in an arithmetic sequence, so we have an equation
[tex]a_{n}[/tex] = a +(n-1)d
Where a = first number of the series
n = number of term
d= common difference
As we know the 3rd term of the sequence, so by this we can find the common difference.
So we have,
9 = 1 +(3-1)d
8=2d
d=4
common difference = 4
Now we have to find the 2nd term or the missing term of the sequence, so we have
[tex]a_{2}[/tex] = 1 +(2-1)4
= 1+ 1×4
= 1+4
= 5
Therefore the 2nd term is 5.
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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. 3,6,12,24,48, .......
The next two terms of the sequence are 96 and 192. And the formula for the nth term of the sequence is [tex]T_{n+1} = 2T_{n}[/tex].
According to the given question.
We have a sequence 3, 6, 12, 24, 48, ..
Since, the first term of the sequence is 3.
The second term of the sequence is 6.
The third term of the sequence is 12.
Here, we can say that the next term is twice the previous term.
So, the next two terms of the given sequence, i.e.
Sixth term = 48 × 2 = 96
Seventh term = 96 × 192
Therefore, the formula for the nth term of the sequence is given by
[tex]T_{n+1} = 2T_{n}[/tex].
Hence, the next two terms of the sequence are 96 and 192. And the formula for the nth term of the sequence is [tex]T_{n+1} = 2T_{n}[/tex].
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prove that the sum of the squares of two consecutive even numbers is a multiple of 4
Answer:
Since the final answer has a factor of 4, it is a multiple of 4.
Step-by-step explanation:
Let the smaller even number be 2n.
The next greater even number is 2n + 2.
(2n)² + (2n + 2)² = 4n² + 4n² + 8n + 4 = 8n² + 8n + 4 = 4(2n² + 2n + 1)
the question is shown in the picture
Answer:
Final Cost of 3 pounds: 7.25
Final cost of p pounds: 3.50p
Step-by-step explanation:
3.50p - 3.25 = ?
3.50(3) - 3.25 = ?
10.50 - 3.25 = $7.25
Write an expression of the cost to buy at least one pound of chicken.
3.50p
I hope this helps!
PLEASE HELP ME WITH THIS!!!!
Julio walks 3 1/2 miles in 1 1/4 hours. Find unit rate
Answer:
3 1/2 ÷ 1 1/4
7/2 ÷ 5/4
7/2 · 4/5
28/10
2.8
Step-by-step explanation:
Please help me I need help
The question is What is the slope of a line perpendicular to the line whose equation is 5x-2y= -10. Fully simplify your answer
Answer:
x=−2+2y/5
Step-by-step explanation:
Add 2y to both sides of the equation.5x=−10+2y
Divide each term in 5x=−10+2y by 5 and simplify.
Divide each term in 5x=−10+2y by 55x5=−105+2y5Simplify the left side
. Cancel the common factor of 5
Cancel the common factor.5x5=−105+2y5Divide x by1.x=−105+y5
Simplify the right side.
Divide
−10 by 5
order from smallest to greatest
urgent !
How many solutions does the equation have?
5(n–2)=5n–10
Answer:
Infinite solutions, regardless of the value of n.
Step-by-step explanation:
[tex]5\left(n-2\right)=5n-10\\5\left(n-2\right)\\5n-5\cdot \:2\\5n-10\\5n-10=5n-10\\5n - 10+10=5n-10 + 10\\5n = 5n\\5n-5n=5n-5n\\0=0\\\mathrm{\:for\:n = \infty,-\infty}[/tex]
Alan deposits $10 per month into his savings account. Which expression could represent the amount he saves, in dollars, in y years?
Answer:
in 1 year Allan would save 120 dollars, this is because, 10x12=120
Step-by-step explanation:
to find out what he would save I 2 years just multiply 120 by 2, 120x2=240, and for 3 years multiply 120 by 3, and so on.
At the Olympic games, many events have several rounds of competition. One of these
events is the men's 100-meter backstroke.
The upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of
the 2012 Olympics. The lower dot plot shows the times of the same 8 swimmers, but in the
semifinal round.
Final round
Semifinal round
distribution.
56
56.5
The center of the semifinal round distribution is
distribution.
57
Time (seconds)
The variability in the semifinal round distribution is
V
57.5
v
58
the center of the final round
the variability in the final round.
The 100–meter backstroke swimming times of the 8 swimmers during the semifinal and the finals of the Olympic games gives;
First part;
The center of the semifinal round is approximately 57.3625
The variability in the semifinal round is 0.0998
Second part;
The center of the final round is approximately 57.0125
The variability in the final round is 0.3336
How can the center and variability of the data in the dot plot be found?The times of the swimmers in the semifinal round are;
56.7, 57.2, 57.3, 57.3, 57.4, 57.5, 57.7, 57.8
The central value is given by the mean of the data, is found as follows;
(56.7+57.2+57.3+57.3+57.4+57.5+57.7+57.8)/8 = 57.3625
The variability is given by the standard deviation which is found by the formula;
[tex] \sigma = \sqrt{ \frac{ x_{i} - \mu}{n} } [/tex]
Where;
[tex]x _{i} = the \: ith \: value[/tex]
[tex] \mu = the \: mean[/tex]
The standard deviation found using the given values above and an online tool is presented as follows;
[tex] \sigma = \sqrt{ \frac{ x_{i} - 57.3625}{8} \approx 0.316 } [/tex]
The variance ≈ √(0.316) ≈ 0.0998Second part;
In the final, we have the following values from the dot plot;
56, 56.6, 56.6, 57, 57.1, 57.2, 57.7, 57.9
From the above values, using an online calculator, the center, which is taken as the mean is 57.0125
The variance for the final, [tex] \sigma^2 [/tex] ≈ 0.3336
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I need help in those questions please
The other root of the given quadratic equation is a = ± 3/√2.
Given that, x=2 and x²+ax+12=0.
What are the roots of quadratic equations?The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
Now, put x=2 in x²+ax+12=0 and find the value of a.
That is, 2²+2a+12=0
⇒4+12+2a=0
⇒16+2a=0
⇒2a=-16
⇒a=-8
So, the value of a is -8.
Put (0, 6) and (4, 6) in the function y=2x²+bx+c and find the value of b and c.
That is, 6=2(0)²+b(0)+c
⇒ c=6
6=2(4)²+b(4)+c
⇒ 6 = 32+4b+c
⇒ -26 = 4b + 6
⇒ 4b = -32
⇒ b = -8
So, the value of b is -8 and the value of c is 6.
Put x=a (root) in the equation 2x + x/a -9 = 0 and find the other root.
That is, 2a²+a/a -9 = 0
⇒ 2a² - 9 = 0
⇒ a²=9/2
⇒ a = ± 3/√2
Therefore, the other root of the given quadratic equation is a = ± 3/√2.
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At a convention, 192 speakers gave one or more presentations of varying lengths. The histogram
summarizes the total presentation time, in hours, of each speaker.
Number of speakers
90
80
70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7
Total presentation time (hours)
What interval contains the 25th percentile for this data?
The 25th percentile of the data is represented by the 0 to 1 hour range.
48 speakers, or around 25% of the total of 192 speakers, are present.
According to the graph, 60 presenters gave presentations that lasted between 0 and 1 hours.
This means that 48 is between0 and1.
A score that compares a certain score to the scores of the other group members is known as a percentile. It shows the percentage of scores that a particular score outperformed.
A person's performance is gauged by using the percentile calculation to compare it to others. A student's test score is compared to that of other applicants using the percentile approach.
Therefore, the 0 to 1 hour period contains the data's 25th percentile.
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Noah is buying a pair of jeans and using a coupon for 10% off.
The total price is $56.70, which includes $2.70 in sales tax.
Noah's purchase can be modeled by the equation:
`x-0.1x+2.70=56.70`
What does the solution to the equation mean in this situation?
Answer: The answer to this equation is 53.91
HELP Finding the initial amount and rate of change given a table for a linear function
The initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively
How to find the initial amount and rate of change given a table for a linear function?The table of linear function represents the given parameter
On the table, we have the following points
(x, y) = (6, 467) and (10, 647)
The rate of change is calculated as
Rate = (y2 - y1)/(x2 - x1)
So, we have
Rate = (647 - 467)/(10 - 2)
Evaluate
Rate = 22.5
This means that the rate of change is $22.5
The initial amount is calculated as
y = m(x - x1) + y1
Where
m = 22.5
So, we have
y = 22.5(x - x1) + y1
Using one of the points, we have
y = 22.5(x - 6) + 467
Set x = 0
So, we have
y = 22.5(0 - 6) + 467
Evaluate
y = 332
Hence, the initial amount and rate of change given a table for a linear function are $332 and $22.5, respectively
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Answer the questions by drawing on the coordinate plane below.
(a) Draw the image of
ΔABC
∆ABC
under the dilation with scale factor 3 and the origin as the center of dilation. Label the image
ΔA'B'C'
∆A′B′C′
. Make sure to include the coordinates of A’, B’, and C’.
(b) Draw the image of
ΔDEF
∆DEF
under the dilation with scale factor
−12
−12
and the origin as the center of dilation. Label the image
ΔD'E'F'
∆D′E′F′
. Make sure to include the coordinates of D’, E’, and F’.
Answer:
Answer:
(b) Draw the image of
ΔDEF
∆DEF
Step-by-step explanation:
14x futher simplfied
Answer:
14x cannot be simplified any further.
Answer:
No, 14x can not be further simplified.
Step-by-step explanation:
I hope this helps.
98!/100! x 10 (! = the number times every number before it and it) ex: 4! = 1 x 2 x 3 x 4
The value of the factorial expression is 99/10
How to evaluate the factorial expression?The expression is given as
98!/100! x 10
The above expression implies that we multiply 10 by the quotient of 98! and 100!
This can be done directly using a calculator, and it can be solved step by step
The step by step procedure is as follows
Expand the denominator
98!/100! x 10 = 98!/100 * 99 * 98! x 10
Evaluate the quotient
98!/100! x 10 = 1/100 * 99 x 10
This gives
98!/100! x 10 = 1/10 * 99
Evaluate the product
98!/100! x 10 = 99/10
Hence, the value of the factorial expression is 99/10
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Lindsey is building a skateboard ramp. She wants the ramp to be 1 foot tall at the end and she wants it to make a 15^{\circ} angle with the ground. What length of board should she buy for the ramp itself? Round to the nearest foot.
The term "length" is used to describe an object's size or the separation between two points. Lindsey must buy 4 feet of the board for the ramp itself.
What is meant by length?The term "length" refers to the measurement or size of something from end to end. In other terms, it is the greater of the upper two or third dimension of a geometric shape or object.
Distance exists estimated in length. The length contain the dimension of distance in the International System of Quantities. The majority of measurement systems select a base unit for length from which all other units exists derived. The meter serves as the foundational unit of length in the International System of Units.
A rectangle, for instance, has length and width as its dimensions.
1/x = 15°
x = 1/sin 15°
simplifying the above equation, we get
x = 3.9ft
x ≈ 4 ft
Therefore, the value of x ≈ 4 ft.
Lindsey must buy 4 feet of the board for the ramp itself.
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What is 45% of 315. I need work shown in explanation area
45% of 315 = 141.75
When you are using a % number convert it into a decimal ( 45% would be 0.45 or 55% would be 0.55 ). After you convert it into a decimal you can multiply it by the number ( Here it would be 315 )
0.45 x 315 = 141.75
Answer:
141.75
Step-by-step explanation:
To do this question, first, we can write 45% as 45/100.
Now, we have to multiply.
45/100x315
=141.75
Hope that helped!
:D
whta slope line goes through (4,5) &(-1,-5)
Answer:
y = 2x - 3
Step-by-step explanation:
1) Find the slope
The slope of any function, if given the coordinates of at least two of the points it crosses, is given by the formula [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].
We are given the points (4, 5) and (-1, -5), therefore, we can substitute their values:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-5)}{4 - (-1)} = \frac{10}5 = 2[/tex]
2) Find the line's equation
We can find the line's equation by substituting one of the given points and the slope we just found into the formula [tex]y - y_1 = m(x - x_1)[/tex]:
[tex]y - 5 = 2(x - 4) \\ \to y - 5 = 2x - 8 \\ \to y = 2x - 3[/tex]
Answer: 2x - 3.
Step-by-step explanation: I took the test.
Negative 3 times negative 8
Answer:
Step-by-step explanation:
-24
Hello! Please help me with this. I'm very desperate lol. Its 16. Ill give brainliest
Answer:
You showed the right work and got the right answer!
x = 6
Step-by-step explanation:
Since B is in the middle of A and C, AB + BC = AC
So,
2x - 11 + 8 = x + 3
x - 3 = 3
x = 6
Please help!:)))))))))))
Answer:
one way to name the symbol is our and another way to name the symbol is rco
(question in the in image above the other side if angle Q is 113
Find x
Answer:
x = 85
Step-by-step explanation:
the exterior angles of a polygon sum to 360°
note the exterior angle at P = 180° - 90° = 90°
sum the 4 exterior angles and equate to 360
x + 72 + 113 + 90 = 360
x + 275 = 360 ( subtract 275 from both sides )
x = 85
A store sells a water blaster for $26. They bought it for $20. What is the markup percent?
The markup percent of the water blaster in the store is 30%
How to calculate the markup percent of the water blaster ?The store sells a water blaster for $26
They bought it for $20
New price is $26
Original price is $20
The markup percent can be calculated as follows
26-20/20 × 100
= 6/20 × 100
= 0.3 × 100
= 30%
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given: ∆abc with vertices a(-3,0), b(0,6), and c(4,6) Find the equations of the three perpendicular bisectors in abc.
The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.
What are the equations of the perpendicular bisectors of the triangle ABC?
Triangles are polygons with three sides and three perpendicular bisectors, whose equations need the informations of slopes and midpoints of each side. Bisectors are lines that partitions line segments in two parts of equal length.
First, determine the midpoints of each side:
Side AB
M₁(x, y) = 0.5 · (- 3, 0) + 0.5 · (0, 6)
M₁(x, y) = (- 1.5, 0) + (0, 3)
M₁(x, y) = (- 1.5, 3)
Side BC
M₂(x, y) = 0.5 · (0, 6) + 0.5 · (4, 6)
M₂(x, y) = (0, 3) + (2, 3)
M₂(x, y) = (2, 6)
Side AC
M₃(x, y) = 0.5 · (- 3, 0) + 0.5 · (4, 6)
M₃(x, y) = (- 1.5, 0) + (2, 3)
M₃(x, y) = (0.5, 3)
Second, determine the slope of the perpendicular bisectors:
Side AB
m = (6 - 0) / [0 - (- 3)]
m = 2
m' = - 1 / m
m' = - 1 / 2
Side BC
m = (6 - 6) / (4 - 0)
m = 0
m' = - 1 / m
m' = NaN (Vertical line)
Side AC
m = [4 - (-3)] / (6 - 0)
m = 7 / 6
m' = - 1 / (7 / 6)
m' = - 6 / 7
Third, derive the equations of the bisectors:
Side AB
b = 3 - (- 1 / 2) · (- 1.5)
b = 9 / 4
y = - (1 / 2) · x + 9 / 4
Side BC
x = 2
Side AC
b = 3 - (- 6 / 7) · (0.5)
b = 24 / 7
y = - (6 / 7) · x + 24 / 7
The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.
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Elemer travels 66 miles per hour for 10 hours .find the distance traveled in miles
Answer: 660 miles
Step-by-step explanation:
66 miles * 10 hours/1 hour =
66*10/1=
66*10=660 miles
Find the eighth term of each geometric sequence. -30,7.5,-1.875, . . . . .
The eighth term of the given geometric sequence is: 0.00183.
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: -30, 7.5, -1.875, ....
Here, [tex]\frac{7.5}{-30}=\frac{-1.875}{7.5}=-0.25[/tex]
That is, the given geometric sequence has a₁ = -30 and r = -0.25
The nth term of a geometric sequence is given by: [tex]a_n=a_1(r^{n-1})[/tex]
For n = 8, [tex]a_8=(-30)(-0.25)^7[/tex] ≈ 0.00183
Hence, The eighth term of the given geometric sequence is: 0.00183.
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Solve p3 = −512.
pls help due in 1 hour
Answer:
-170 2/3
Step-by-step explanation:
Divide both sides by 3 to get p by itself
p = -512/3
Simplify
- 170 2/3
Answer:
p=−8
Step-by-step explanation:
Let's solve your equation step-by-step.
[tex] \rightarrow \sf \: p {}^{3} =−512[/tex]
Step 1: Take cube root.
[tex] \sf p={(−512) }^{ ( \frac{1}{3} )}[/tex]
[tex] \sf \: p=−8[/tex]
Write an equation in point-slope form of the line having the given slope that contains the given point.
m=-3/4, (8,-1)
The equation in point-slope form of the line having the given slope that contain the given point m=[tex]-\frac{3}{4}[/tex] and (8,-1) is [tex]y+1=-\frac{3}{4}(x-8)[/tex]
Given,
m = [tex]\frac{-3}{4}[/tex]
The point = (8,-1)
The point-slope form of the line
[tex](y-y_{1} )=m(x-x_{1})[/tex]
Substitute the values in the equation
[tex](y-(-1))=-\frac{3}{4}(x-8)\\ y+1=-\frac{3}{4}(x-8)[/tex]
Hence, the equation in point-slope form of the line having the given slope that contain the given point m=[tex]-\frac{3}{4}[/tex] and (8,-1) is [tex]y+1=-\frac{3}{4}(x-8)[/tex]
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