The common difference d is 2.2 and the first term a1 is -9.
How to find the a1 and d?The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.
The formula of Arithmetic progression is
a(n) = a1 + (n - 1)d
given that the two terms of arithmetic sequence,
a4 = -2.4 and a6 = 2.
now, find the common difference d.
a(n) = a1 + (n - 1)d
Let take a(n) = a6 and a1 = a4.
a6 = a4 + (6 - 4)d
a6 = a4 + 2d
now substitute the values of a6 and a4
2 = -2.4 + 2d
2 + 2.4 = 2d
d = 4.4/2
d = 2.2
so, the common difference d is 2.2.
then, find the term a1.
take the formula
a(n) = a1 + (n - 1)d
now, substitute a(n) = a4 and d = 2.2.
-2.4 = a1 + (4-1)d
-2.4 = a1 + 3d
-2.4 = a1 + 3(2.2)
-2.4 = a1 + 6.6
a1 = -6.6-2.4
a1 = -9.
so, the first term a1 is -9.
Hence, the common difference d is 2.2 and the first term a1 is -9.
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A pendulum moving in simple harmonic motion is modeled by the function , where s is measured in inches and is measured in seconds. determine the first time when the distance moved is 4 inches.
The maximum displacement, the frequency, and the time required for one cycle are 1/5 inch, 1/π Hz and π sec.
What is displacement?A displacement is a vector in geometry and mechanics that has a length equal to the shortest distance between a point P's initial and final positions. It calculates the length and angle of the net motion, or total motion, in a straight line from the starting point to the destination of the point trajectory. The translation that links the starting point and the ending point can be used to spot a displacement.
Therefore, the instantaneous speed is different from velocity, which is the rate at which the distance traveled along a particular path changes over time. The temporal rate of change of the position vector can also be used to describe velocity.
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Add or subtract as indicated.
25.32 + 109.2 + 8.574
Rob has $1.65 in nickels and dimes.He has 25 coins in all. How many of each kind of coin are there
rob has 8 dimes and 17 nickels in $1.65
WHAT ARE LINEAR EQUATION ?There is only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All the points fall on the same line when the values that together make a linear equation true are determined and plotted on a coordinate grid.
CALCULATIONLet n represent nickels & d dimes
given: n + d = 25 #1 (number of coins)
given: .05n + .10d = 1.65 #2 (amount in dollars)
n = 25 - d #3 (rewrite of #1)
.05(25 -d) + .10d = 1.65 (substitute #3 in #2)
1.25 - .05d + .10d = 1.65 (multiply out the left side)
.05d = .40 (collection of like terms)
d = 8 (divided both sides by.05)
n + 8 = 25 (substitute answer for d in #1)
n = 17 (subtract both sides by 8)
There are 8 dimes and 17 nickels.
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I'm more sophisticated than my little sister. I save my money in a bank account that pays me 3% interest on the money in the account at the end of each month. (If I take my money out before the end of the month, I don't earn any interest for the month.) I started the account with $50 that I got for my birthday. How much money will I have in the account at the end of 10 months? How many months will it take to have at least $100? Justify your answer with a mathematical model of the problem situation.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per \underline{month}} \end{array}\dotfill &1\\ t=\underline{months}\dotfill &10 \end{cases} \\\\\\ A=50\left(1+\frac{0.03}{1}\right)^{1\cdot 10} \implies A=50(1.03)^{10}\implies A \approx \text{\LARGE 67.20}[/tex]
well, let's check how long till you'd have $100 first
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$100\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per \underline{month}} \end{array}\dotfill &1\\ t=\underline{months} \end{cases}[/tex]
[tex]100=50\left(1+\frac{0.03}{1}\right)^{1\cdot t} \implies 100=50(1.03)^t\implies \cfrac{100}{50}=1.03^t \\\\\\ 2=1.03^t\implies \log(2)=\log(1.03^t)\implies \log(2)=t\log(1.03) \\\\\\ \stackrel{\textit{about 23 months and 13 days}}{\cfrac{\log(2)}{\log(1.03)}=t\implies \text{\LARGE 23.45}\approx t}[/tex]
The larger of two numbers is 7 more than 5 times the smaller. If the sum of the two numbers is 31, what are the two numbers
Answer: x=27 y=4
Step-by-step explanation:
Let the larger of two numbers is x and the smaller of two numbers is y
Hence,
[tex]\displaystyle\left \{ {x-5y=7} \atop {x+y=31}} \right.\\\\\left \{ {{x-5y=7} \atop {x+y-y=31-y}} \right. \\\\\left \{ {{x-5y=7\ \ \ \ \ (1)} \atop {x=31-y}\ \ \ \ (2)} \right. \\[/tex]
Substitute equation (2) into equation (1):
[tex]31-y-5y=7\\31-6y=7\\31-6y+6y=7+6y\\31=7+6y\\31-7=7+6y-7\\24=6y\\[/tex]
Divide both parts of the equation by 6:
[tex]4=y\\Hence,\\x=31-4\\x=27[/tex]
In this problem, you will investigate the relationships among three points of concurrency in a triangle.
d. Make a conjecture about the relationships among the circumcenter, centroid, and orthocenter.
The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. The circumcenter, centroid, and orthocenter are all collinear.
What is the relationship between the centroid circumcenter and orthocenter?The circumcenter, centroid, and orthocenter are all collinear.
The centroid separates the line connecting the circumcenter and orthocenter in the proportion of 2 :1
i.e, CSOC = 21.
Where, C-Coordinate of the centroid. O-Coordinate of the orthocenter.
The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. A centroid is the point at which the lines drawn from the midpoints of each side of a triangle intersect at the opposite vertex.
Any triangle's orthocenter, centroid, and circumcenter are collinear. The centroid divides the distance between the orthocenter and the circumcenter in a 2:1 ratio. The line connecting these three points is known as the triangle's Euler line. to represent the ABC triangle's circumcircle.
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(1+2)+6=1+(2+6) which property is this
Answer:
Associative.
Step-by-step explanation:
The associative property is the property that means an equation's result will be the same regardless of grouping the factors together or reversing the equation.
e.g
[tex](a - b) \times c = c \times (b-a)[/tex]
Figure ABCD is a rhombus. Find the
value of x.
B
5x-8
D
A
3x + 10
x = [?]°
A Figure ABCD is a rhombus. The angles of A and C are equal by alterenate interior angle. The value of x in the figure ABCD rhombus is 9 degree.
What is a rhombus?We know that rhombuses are a particular type of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal.
The Solution to an equation is finding values of the variable in the considered equation for which the equation considered evaluates to be true.
For a solution, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, thus solution to a system is the intersection of all its equation at single point
WE know that the diagonals of a rhombus bisect each other, we know that triangle DEC is a right triangle.
Since the side lengths of a rhombus are equal, so the angles of A and C are equal by alterenate interior angle.
Now, 5x-8 = 3x + 10
i.e. 5x - 3x = 10 + 8
i.e. 2x = 18
i.e. x = 9
Therefore the value of x in the figure ABCD is 9 degree.
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Over the last 3 evenings, Heather received 61 phone calls at the call center. She received 7 more calls on the second evening than on the first evening. On the third evening, she received 2 times as many calls as the second evening. How many phone calls did she receive each evening?
Answer:
for real even great Britain cant get this because ya
Step-by-step explanation:
You buy a new car for $22,000. The value of the
car decreases by 12.5% each year.
Answer:
Thus the value of the car decreases by $2,750 every year.... Making it $19,250 in the first year and $16,500 in the second
Step-by-step explanation:
12.5/100×22,000
2750
Determine the following attributes of the graph below please i only have 8 mins to turn this in 20 points pleaseeee
For the following function, we have that:
The domain is 0 < x ≤ 4.The range is -2 ≤ y ≤ 2.The x-intercepts are x = 1 and x = 3, that is, points (1,0) and (3,0).The y-intercept is y = 2, that is, point (0,2).The maximum value on the interval [1,4] is of 2, at point (4,2).The minimum value on the interval [1,4] is of -2, at point (2,-2).What are the domain and the range of a function?The domain of a function is the set that contains all the values of the input.The range of a function is the set that contains all the values of the output.In a graph:
The domain is given by the x-values, the horizontal axis.The range is given by the y-values, the vertical axis.Hence, for the graph in this problem, we have that:
The domain is 0 < x ≤ 4.The range is -2 ≤ y ≤ 2.What are the intercepts of a function?The x-intercept of a function is given by the value of x when f(x) = 0, that is, the value of x when the function crosses the x-axis.The y-intercept of a function is given by the value of f(x) when x = 0, that is, the value of y when the function crosses the y-axis.Hence:
The x-intercepts are x = 1 and x = 3, that is, points (1,0) and (3,0).The y-intercept is y = 2, that is, point (0,2).What is the maximum and the minimum value?We have to look at the values of y on the interval, hence:
The maximum value on the interval [1,4] is of 2, at point (4,2).The minimum value on the interval [1,4] is of -2, at point (2,-2).More can be learned about functions at https://brainly.com/question/24808124
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Write each number as a percent.
1(2/5)
Simplify.
8√2 / 6-3√8
The rationalized expression in general term is given by: (-8 -4√2) / 3
What is rationalization?Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.
As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.
(8√2 / 6-3√8 ) Multiply by ( 6+3√8)/( 6+3√8)
(8√2 / 6-3√8 )( 6+3√8)/( 6+3√8)
8√2(6+3√8) / (6-3√8)² Expand the denominator using the FOIL method.
8√2(6+3√8) / (36 - 18√8 + 18√8 - 72)
8√2(6+3√8) / -36
48√2 + 24√2√8 / -36 ::::. √8 = 2√2
48√2 + 96 / -36
-12(4√2 + 8) / 12x3
(-8 -4√2) / 3 is the result.
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Determine whether each sequence is geometric. If so, find the common ratio. 10,4,1.6,0.64, . . . . .
The given sequence is geometric, with common ratio = 0.4.
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: 10, 4, 1.6, 0.64, ....
Here, [tex]\frac{4}{10}=\frac{1.6}{4}=\frac{0.64}{1.6}=0.4[/tex]
That is, the given sequence follows the only necessary condition for a sequence to be geometric.
Hence, The given sequence is geometric, with common ratio = 0.4.
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The average professional hockey player makes $2.78 million a year.
They play an average of 82 games.
How much does the average hockey player make per game?
A. $33,900.00
B. $3,390.00
C. $34,000.00
D. $3,400.00
E. None of the above
Answer:
$34,000.00
Step-by-step explanation:
[tex]2,780,000/82 = 33,902.439\\33,902.439 ~ 34,000.00[/tex]
The average hockey player makes per game is an amount of $34,000.00 which is the correct option would be option (A).
What is the division operation?In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.
For example 4/2 = 2
The average professional hockey player makes $2.78 million a year.
$2.78 million = $2,780,000
They play an average of 82 games.
The average hockey player makes per game = 2,780,000 / 82
Apply the division operation to get the answer.
The average hockey player makes per game = 33,902.439
The average hockey player makes per game = $33,900.00
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can someone please help me
for the first one x = 12
second one is 2
Answer:
x = 12
x = 2
Step-by-step explanation:
Basically the triangles are congruent. Therefore, the sides are equal to each other. Set both equations equal to each other and solve for x.
Nicolas has 1400 pokemon cards. Of these cards, 40% are water pokemon and 15% are considered rare pokemon, the rest are rock pokemon. How many rock pokemon cards does Nicolas have? (I have completely forgotten this skill)
Answer:
630 rock cards
Step-by-step explanation:
aight so 40 % of 1400 is 560 , and 15% of 1400 is 210 . add those and you get 770 . so you got 770 water and rare . you subtract that by 1400 and you got 630 !!
Answer: 476 rock type pokemon cards
Step-by-step explanation: Let's do this! 40% of 1400 is 560, and 15% of 560 is 84. 560 - 84 = 476.
The sun is at a focus of Earth's elliptical orbit.
a. Find the distance from the sun to the other focus.
The distance from the sun to the other focus is 5.01 × 10⁹ m.
What is the distance from the sun?
(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;
2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.
(b) To express this in terms of solar radii, we set up a ratio;
(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2
Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.
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Complete question is;
The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.
Solve the equation.
2|2x+3|=|x-3|
There should be two solutions.
Please show the steps and give an explanation on how to solve it and why.
Answer:
x= -3
Step-by-step explanation:
[tex]2(2x + 3) = x - 3 \\ 4x + 6 = x - 3 \\ 4x = x - 3 - 6 \\ 4x - x = - 3 - 6 \\ 3x = - 9 \\ x = \frac{ - 9}{3} \\ x = - 3[/tex]
Answer:
[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]
Step-by-step explanation:
Given absolute value equation:
[tex]2|2x+3|=|x-3|[/tex]
The absolute value of a number is its positive numerical value.
Therefore, the expressions inside the bars should be set to both positive and negative. Rewrite the absolute value equation as four equations without absolute value bars and simplify:
[tex]\textsf{Positive = Positive}: \quad 2(2x+3)=x-3[/tex]
[tex]\textsf{Positive = Negative}: \quad 2(2x+3)=-(x-3)[/tex]
[tex]\begin{aligned}\textsf{Negative = Positive}: \quad -2(2x+3) &=x-3\\ \implies 2(2x+3) &=-(x-3)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Negative = Negative}: \quad -2(2x+3) &=-(x-3)\\ \implies 2(2x+3)&=x-3\end{aligned}[/tex]
From inspection of the equations:
Positive = Positive is equal to Negative = Negative, and Negative = Positive is equal to Positive = Negative,so there are only two unique equations to be solved.
Equation 1
[tex]\begin{aligned}2(2x+3) & =x-3\\4x+6 & = x-3\\4x+6-x&=x-3-x\\3x+6&=-3\\3x+6-6&=-3-6\\3x & =-9\\\dfrac{3x}{3} & = \dfrac{-9}{3}\\ x&=-3 \end{aligned}[/tex]
Equation 2
[tex]\begin{aligned}2(2x+3)&=-(x-3)\\4x+6&=-x+3\\4x+6+x&=-x+3+x\\5x+6&=3\\5x+6-6&=3-6\\5x &=-3\\ \dfrac{5x}{5}&=\dfrac{-3}{5}\\x &=-\dfrac{3}{5} \end{aligned}[/tex]
Therefore, the solutions are:
[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]
Which example illustrates public scientific communication?
A scientist collaborates with other scientists to plan an experiment.
A scientist sends a preview copy of a journal article to some colleagues.
A federal government agency holds a press conference to describe the response to and the dangers of a new virus epidemic.
A federal government agency publishes an article in a professional scientific journal detailing technical details of a new virus.
The example that illustrates public scientific communication is D. a federal government agency publishes an article in a professional scientific journal detailing technical details of a new virus.
What is communication?Communication simply had to do with how messages are passed from the sender to the audience or the other party.
In this case, the example that illustrates public scientific communication is a federal government agency publishes an article in a professional scientific journal detailing technical details of a new virus.
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Chen buys 11 books for $77. Each book has the same price. What is the price of each book? Show the multiplication or division fact you used to solve the problem?
Answer: $7 per book
Step-by-step explanation:
$77 for 11 books, so we do 77 ÷ 11 = 7
Find the first five terms of each sequence. a n =-2 n+3
The formula for estimating the nth term of an arithmetic sequence is:
a n = a₁ + (n-1)d
The first five terms of a n = -2n + 3 = 1, -1, -3, -5, -7
What is meant by arithmetic sequence?A succession of numbers merged together to make a sequence exists comprehended as an arithmetic sequence.
A series of numbers named an arithmetic progression or arithmetic sequence (AP) contains a constant difference between the terms.
The formula for estimating the nth term of an arithmetic sequence exists:
a n = a₁ + (n-1)d
The four quantities in the formula exist a n, a₁, n, d.
The first 5 terms are a n = -2n + 3
a₁ = -2 + 3 = 1
a2 = -4 + 3 = -1
a3 = -6 + 3 = -3
a4 = -8 + 3 = -5
a5 = -10+3 = -7
Therefore, the first 5 terms of the sequence be 1, -1, -3, -5, -7.
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You want to buy a new iPhone 50 that costs $1330 including taxes(13%). How many hours will you have to work to be able to buy this new phone if you make minimum wage which is $14.25 per hour?
Answer:
105.47 hours
Step-by-step explanation:
1300x0.13=172.9
172.9+1300=1502.9
1502.9/14.25=105.47
help me number 2 please
The following volume quantities are listed below:
a) 2 pints, 1 qt
b) 12 pints, 6 qt
c) 5 pints, 2.5 c
d) 6.75 pints, 3.375 fl oz
How to convert an unit to another by using unit conversions
In this question we must transform a quantity in a unit to another quantity in a unit of the same kind. For instance, if we have a quantity in a mass unit, then we only can convert it into another mass unit.
Herein we have four unit conversion cases for volumes, both pints and quarts are volume units commonly used in the United States. There are the following equivalencies:
1 quart = 2 pints = 4 cups = 32 fluid ouncesNow we proceed to convert each quantity to pints and quarts by cross multiplication:
a) 32 fl oz × 2 pints / 32 fl oz = 2 pints, 32 fl oz × 1 qt / 32 fl oz = 1 qt
b) 24 c × 2 pints / 4 c = 12 pints, 24 c × 1 qt / 4 c = 6 qt
c) 10 c × 2 pints / 4 c = 5 pints, 10 c × 1 qt / 4 c = 2.5 c
d) 108 fl oz × 2 pints / 32 fl oz = 6.75 pints, 108 fl oz × 1 qt / 32 fl oz = 3.375 fl oz
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What is the arithmetic mean between 20 and 56?
Answer:
35, the population size is 2.
The geometric mean of a number and four times the number is 22 . What is the number?
If 22 is the geometric mean of a number and four times the number, then the number is 11.
Geometric mean, like arithmetic mean, is a kind of average and a measure of central tendency.
To solve for the geometric mean, we multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers) etc. In other words, geometric mean is the nth root of the product of n values.
The formula for the geometric mean is given by:
GM = n√x1 x2 . . . xn
Let x = x1 = unknown number
y = x2 = four times the number = 4x
Using the formula in solving geometric mean, plug in the values and variables.
GM = n√x1 x2 . . . xn
22 = √xy
22 = √x(4x)
22 = √4x^2
22 = 2x
x = 11
y = 4x
y = 44
Hence, the number is 11. 22 is the geometric mean of 11 and 44.
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how to do:
5n - 7n = 14
Please show the step by step process! (:
Answer: n=-7
Step-by-step explanation:
5n - 7n = 14
(5-7)n=14
-2n=14
-2n/(-2)=14/(-2)
n=14/(-2)
n=-7
The equation is,
→ 5n - 7n = 14
Solving for the value of n,
→ 5n - 7n = 14
→ -2n = 14
→ n = -(14//2)
→ [ n = -7 ]
Thus, the value of n is -7.
An aeroplane flies 500km in one hour. How long does it take to f a distance of 10925km? for class 4
Answer:
It will take 22 hours
Step-by-step explanation:
10925 ÷ 500 = 21.9 = 22 hours
What is y-8={3}(x+1)y−8=3(x+1)y, minus, 8, equals, 3, left parenthesis, x, plus, 1, right parenthesis written in standard form?
The equation written in standard form is expressed as 3x - y = -11
Linear equation in standard formThe standard form of a linear equation is expressed as Ax + By = C
Given the equation below;
y - 8 = 3(x+1)
Expand
y- 8 = 3x + 3
Collect the like terms
y-3x = 3 + 8
y - 3x = 11
-3x + y = 11
3x - y = -11
Hence the equation written in standard form is expressed as 3x - y = -11
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Find the sum of each finite series. Σ⁸ n=1 (7-n)
The sum of the finite series [tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex] is 20
Given a finite series:
[tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex]
Recall the properties of summation notation:
Σₙ b. f(n) = b Σₙ f(n) where b is a constant.
Σ (a + b) = Σ a + Σ b
[tex]\sum\limits^p_{n=1} {b} =b.p[/tex] where b is a constant
Using the above summation properties, we can write:
[tex]\sum\limits^{8}_{n=1} {(7-n)}=\sum\limits^{8}_{n=1} {7}-\sum\limits^{8}_{n=1} {n}[/tex]
=7 . 8 - (1+2+3+ ...+8)
= 56 - 8/2 (1+8)
= 56 - 4 . 9
= 56 - 36 = 20
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