The explicit equation for this arithmetic sequence is: aₙ = 9 + (n-1)(-8).
What in mathematics is an arithmetic sequence?An arithmetic series is one that has the following formula: a, a + d, a + 2d, a + 3d, a + 4d,... The basic distinction of the sequence is d, and the number an is the first term. An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.
How do you discover the mathematical order?The formula for an arithmetic sequence is given as an=a1+(n1)d, where an a n is a broad term, a1 a 1 is the initial term, and d is the huge distinction. This is done in order to locate the general phrase in the list.
The general form of the explicit equation for an arithmetic sequence is:
an = a1 + (n-1)d
Given that the first term is 9 and the second term is 1,
d = a2 - a1 = 1 - 9 = -8
So the explicit equation for this arithmetic sequence is:
aₙ = 9 + (n-1)(-8)
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Find the distance between G and H on the number line below -12 and -2
The distance between G and H on the number line -12 and -2 is -10.
What is Distance?
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language .
The phrase is widely used metaphorically to refer to a measurement of the degree of difference between two similar objects since spatial cognition is a rich source of conceptual metaphors in human thought.
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
What is number line?
A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It is assumed that each real number and each point on a number line relate to one another.
We are given two point G and H which are represented on number line;
The value G = -12 and H = -2
We have to find the distance between them;
So , we can simply subtract these two values of G and H to get the distance between them;
distance = -12-(-2)
= -12 + 2
= -10
Therefore, the distance between G and H on the number line -12 and -2 is -10.
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Which function represents the reflection over the x-axis of f(x)=x
The fourth option represents the reflection over the x-axis of f(x)=√x. The graph has been attached below. The solution has been obtained by the concept of reflections.
What is reflection?
A flip is the term for a reflection in geometry. The shape is mirrored in a reflection. The line of reflection is a line across which an image will reflect. A reflection is the shape's mirror image. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way.
We are given the function f(x)=√x.
When we replace x with -x, then the graph of the resulting equation i.e.
f(x)=√-x is captured by reflecting the graph of f(x)=√x vertically across the x-axis.
Thus, the reflection of the function f(x)=√x is a vertical reflection across the x-axis.
Hence, the graph below represents the reflection of the function f(x)=√x which is the fourth option.
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frankie already has a pair of basketball shoes that he can wear for the tryout, which makes the new pair a
The new pair of basketball shoes become a "desire" because Frankie already owns a pair that he can use for the tryout. Frankie's new basketball shoes would be viewed as a "need" if he didn't already have a pair for the tryout.
When referring to possessing or acquiring specific commodities, people frequently use the terms "want" and "need" interchangeably. In terms of economics, a need is what a person needs in order to survive. If a certain need is not met, a person may get sick or perhaps pass away. On the other hand, a desire is something that a person hopes to achieve in the near or distant future. In the first instance, Frankie is able to attend the tryout in a pair of basketball shoes that he already has. He could wear the shoes he already owns, thus the new pair of shoes would be his desire. In contrast, Frankie needs a new pair of sneakers in the second scenario because he doesn't have any basketball shoes for the tryout.
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The price of apples is $0.35 per apple. If Kaitlyn paid $14.35 at the grocery store where she bought some apples and spent $12.00 for the rest of her groceries, write an equation that represents her shopping trip
Answer: 0.35x + 12.00 = 14.35
Explanation: You would make sure to include the x since we are unsure of how many apples to bought, we know the total it will be at the other side of the equal sign, she spent 12 on her groceries so we would add that to the number of apples she got.
are the responses to the survey question quantitative or categorical? quantitative b. how many of the respondents said that they expect driverless cars to be common in the next years? round your answer to nearest whole number. 79659 c. how many respondents answered in the range years? round your answer to nearest whole number. 15030
The responses to the survey question are quantitative, as the respondents were asked to provide a numerical answer.
Out of the 79,659 respondents, 79,659 said that they expect driverless cars to be common in the next years.
Out of the 79,659 respondents, 15,030 answered in the range of years. This means that 15,030 respondents provided a numerical answer that was within the range of years.
It is important to note that the survey question was quantitative, so the responses provided by the respondents were numerical. This means that the responses were not categorical, as categorical responses would have been in the form of words or phrases.
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In the year 2016, the total number of metric tons of
copper produced in the world was 495,000.
Each year since, the total number of metric tons of
copper produced has increased on average by about
3.25% over the amount produced the previous year.
Which function models the total number of metric tons
of copper produced in the year that is x years since
2016?
c(x) = 495,000(1.0325)^x
c(x) = 495,000(0.9675)^x
c(x)=495,000(1.325)^x
c(c)=2010(3.25)^x
Answer:
A. C(x) = 495,000 (1.0325)^ x
Step-by-step explanation:
c(x) = 495,000 x (1+3.25%)^x
= 495,000(1.0325)
what is the solution of the system of equations for a graph that intersects at (0,6)
The solution of a system of equations for a graph that intersects at (0, 6) is given by the ordered pair (0, 6).
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines representing a system of linear equations cross each other (intersect), which is depicted by an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.
By critically observing the graph of the lines representing the system of linear equations, you would notice that the correct solution set lies on Quadrant I and it represents the y-intercept of the graph.
In conclusion, the ordered pair (0, 6) represents the point of intersection and solution set to the system of linear equations represented by the graph.
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Simon is a member of The Mighty Manatees, an outdoor swim team. Every practice, his coach tells him to swim a target number of laps. One day, Simon swims 45 laps before practice is canceled due to a thunderstorm. Simon still has 35 laps left to reach his target number. Use an equation to find Simon's target number of laps.
Simon's target number of laps will be 80.
How to calculate the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
In this case, his coach tells him to swim a target number of laps and Simon swims 45 laps before practice is canceled due to a thunderstorm. Simon still has 35 laps left to reach his target number
Let the target number be x. This will be:
x - 45 = 35
x = 45 + 35
x = 80.
The Target number is 80
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Find X and Y.
TEACHING TEXTBOOKS GEOMETRY
The value of the variables 'x' and 'y' will be 47° and 27°, respectively.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Alternate angle - If two lines are parallel then the third line will make z -an angle and z-angles equal angles with the parallel lines.
The equations are given below.
2y = 180° - 126°
2y = 54°
y = 27°
2x + 1 = 180° - 85°
2x + 1 = 95°
2x = 94°
x = 47°
The value of the variables 'x' and 'y' will be 47° and 27°, respectively.
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What is the equation of the circle with a center located at ( 5, 2) and is tangent at the y-axis?
a. x2 + y2 – 10x – 4y + 4 = 0
b. x2 + y2 + 10x – 4y + 25 = 0
c. x2 + y2 + 10x – 4y + 4 = 0
d. x2 + y2 – 10x – 4y + 25 = 0
The equation of a circle with center located at (5,2) and that is tangent to the y-axis is given as follows:
C. x² + y² - 10x - 4y + 4 = 0.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Considering the center, we have that:
(x - 5)² + (y - 2)² = r².
The circle is tangent to the y-axis, meaning that it passes through the point (0, 2), thus the radius is obtained as follows:
r² = 25.
Then the equation in standard form is given as follows:
x² - 10x + 25 + y² - 4y + 4 - 25 = 0.
x² + y² - 10x - 4y + 4 = 0.
Meaning that option C is correct.
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Sammi plans on selling Christmas tree ornaments. She figured a profit of $2. 00 for each item. She thinks one item out of every fifty may be defective and returned for exchange. That will cost her $7. 00
because of shipping and cost of the replacement. Calculate the expected value.
The expected value for each set of 50 items that Sammi sells is $1.82.
The expected value can be calculated by multiplying the profit from each successful sale by the probability of making that sale, and then subtracting the expected cost of each defective item.
Expected value = (Profit from each successful sale * Probability of making that sale) - (Expected cost of each defective item)
Let's assume that Sammi plans to sell 50 items. So, the probability of a successful sale is 49/50 = 0.98. The expected cost of each defective item is $7.
Expected value = ($2 * 0.98) - ($7 * 1/50) = $1.96 - $0.14 = $1.82
So, the expected value for each set of 50 items that Sammi sells is $1.82.
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DATA COLLECTION Rafaella collected data to determine the number of
books her schoolmates were bringing home each evening. Her data is
shown in the mapping. She let x be the number of textbooks brought
home after school and y be the number of students with x textbooks.
a. Express the relation as a set of ordered pairs.
b. What is the domain of the relation?
c. What is the range of the relation?
The relation as a set of ordered pairs is expressed below.
The domain of the relation is {0, 1, 2, 3, 4, 5}.
The range of the relation is {8, 11, 12, 23, 28}.
What is an ordered pair?In Mathematics, an ordered pair can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:
Mathematically, the set of ordered pairs which represents the relation include the following:
Ordered pair = (0, 12)Ordered pair = (1, 8).Ordered pair = (2, 23).Ordered pair = (3, 38).Ordered pair = (4, 11).Ordered pair = (5, 11).Based on the mapping diagram (see attachment), the domain and range of the relation is given by:
Domain = {0, 1, 2, 3, 4, 5}.
Range = {8, 11, 12, 23, 28}.
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g the radius of a sphere is increasing at a rate of 4 mm/s. how fast is the volume increasing when the diameter is 100 mm?
Answer:
125,664 mm³/s
Step-by-step explanation:
V = (4/3)πr³
dV/dt = (4π/3) × 3r² × dr/dt
dV/dt = 4πr² × dr/dt
dr/dt = 4 mm/s
d = 100 mm; r = 50 mm
dV/dt = 4π(50 mm)² × 4 mm/s
dV/dt = 125,664 mm³/s
i don’t know this answer i need help
what is equalivliant to 4a + (–6b) – 3a + 2b
Answer: a-4b
Step-by-step explanation:
Combine like terms
4a-6b-3a+2b
1a-6b+2b
a-6b+2b
a-4b
WRITE Why are all rectangles parallelograms, but all parallelograms are not rectangles? Explain.
Answer:
because they are not equal in size
A survey asked a random sample students if they estimated they spent more or less than an hour a day on social media.
45 percent of the 8th graders estimated they spend less than an hour a day on social media. The solution has been obtained by using concept of frequency.
What is frequency?
The frequency of a specific value in a set of data is how frequently it appears. Typically, we would keep track of data frequency in a frequency table.
We are given that 17 8th graders spent more than an hour a day on social media and 14 8th graders spent less than an hour a day on social media.
The total 8th graders who spent time on social media is 14 + 17 = 31
The percentage of the 8th graders estimated they spend less than an hour a day on social media is
= 14*100/31
= 45.16%
= 45%
Hence, 45 percent of the 8th graders estimated they spend less than an hour a day on social media.
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Candice is an interior designer and she is currently trying to change the look of a room. Candice found that the area of a room could be given by the expression 32+2 and that the area of a rug, which she wants to spread on the floor, is given by the expression 2+24−144. What expression represents the area of the room not covered by the rug?
The expression represents the area of the room not covered by the rug is A(x) = 2x² - 22x + 144.
Area of room = 3x² + 2x
Area of rug = x² + 24x - 144
We have to find the area of the room not covered by the rug.
Area of the room not covered by the rug = Area of the room - Area of rug
= (3x² + 2x) - (x² + 24x - 144)
= 3x² + 2x - x² - 24x + 144
= (3x² - x²) + (2x - 24x) + 144
= 2x² - 22x + 144
Hence, 2x² - 22x + 144 is the required expression for the area of the floor not covered by the rug.
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The graph shows membership costs at a gym. How much was the initial membership fee?
Answer: 30$
Step-by-step explanation:
To find the slope of the equation, you can use the formula (y2-y1)/(x2-x1). Plugging the points the question gives us we can get:
(205-100)/(5-2)
= 105 / 3
= 35
Plugging this information along with a point into the formula y = mx + b:
100 = 35*2 + b
100 = 70 + b
b = 30
y = 35x + 30
To double check this is correct:
y = 35 * 5 + 30
y = 175 + 30
y = 205
(5,205) is a point therefore y = 35x + 30 is the equation
Because the x of the graph represents the number of months, the initial membership fee would be when x = 0.
y = 35*0 + 30
y = 30$
rsti is a parallelogram. what is the value of x 2x+15 x+15
For x = 0, the sides of parallelogram are equal.
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
There are six crucial parallelogram characteristics to be aware of:
Congruent sides are those when AB = DC.
Congruent opposite angels are D = B.
(A + D = 180°) Consecutive angles are supplementary.
All angles are correct if just one of them is.
A parallelogram's diagonals cut each other in half.
A parallelogram is a four-sided, two-dimensional form in geometry. This particular quadrilateral example has equal and parallel opposite sides.
As the sides of parallelogram are parallel and equal,
2x + 15 = x + 15
2x = x
x = 0
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What happens to the energy in the pendulum as it swings from point A to point B?
Potential energy is converted to kinetic energy.
Kinetic energy is converted to potential energy.
Kinetic energy is converted to chemical energy.
O Chemical energy is converted to thermal energy.
The energy in the pendulum as it swings from point A to point B
Potential energy is converted to kinetic energy.
Now, According to the question:
Energy is defined as the ability of an object to do work. Energy can be classified in two different types of energy, Kinetic and potential energy. This two may be the principal ones, but we can see how energy manifests in different ways in nature, like heat, chemical potential energy, solar energy, electric potential energy, and so on.
Energy is constantly changing from kinetic to potential energy, and vice-versa in a pendulum. At the lowest point of the pendulum swing, the pendulum will have reach a state of maximum kinetic energy. This due to it attaining the maximum speed the pendulum can reach due to it's movement. As the pendulum start to rise again, it will start to lose kinetic energy and will gain potential energy. This loss in kinetic energy will cause the pendulum to slow down until it reaches it's max height. At this point the pendulum will have converted all of it's kinetic energy to potential energy.
Hence, Potential energy is converted to kinetic energy.
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Does anyone know the answer to this?? (pls give right answer I really need this one to be correct)
a) Equation would be 5x + (x - 6) + (x - 6) = 180°
b) m∠1 = 180° and m∠2 = 30°
What is the measure of angle?
The term "degree measure" refers to the measurement of an angle in degrees. Because one entire revolution equals 360°, it is divided into 360 parts. Each stage of the revolution represents a degree.
a) The angle measures in a triangle must add up to 180°.
Therefore, the equation to find x is:
5x + (x - 6) + (x - 6) = 180°
b) Solving for x, we get:
x = 36
Therefore, angle m∠1 = (5x) = (5 * 36) = 180° (major angle)
angle m∠2 = (x - 6) = (36 - 6) = 30° (minor angle)
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Need asap pls broooo
In the given parallelogram, the value of g is 116 degrees and that of h is 64 degrees.
What is parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure. A parallelogram is a type of quadrilateral with opposite pairs of sides that are parallel and equal. The diagram depicts a parallelogram ABCD with AB II CD and AD II BC. In addition, AD = BC and AB = CD. Non-Example: A trapezium is a parallelogram's non-example.
Here,
Since the given figure is parallelogram. Opposite angles are equal.
g=116 degree
h=64 degree
The value of g is 116 degrees and that of h is 64 degrees in the given parallelogram.
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Rewrite the expression 7(×-20)
Answer: 7x - 140
The expression 7(x-20) is a product of 7 and a grouping of x-20. To simplify this expression, we use the distributive property, which states that we can multiply the 7 by each term inside the grouping. So, 7(x-20) becomes 7x - 140. This is because 7x is the product of 7 and x, and 140 is the product of 7 and 20.
Step-by-step explanation:
can somebody help me with this pls:Simplify: 8-2
Answer:
Step-by-step explanation:
I think it's 6 but I am not positive. I would double check it
Cedric and Insha solved the same equation using the calculations below.
Cedric’s Work
Insha’s Work
z minus 4.5 = negative 1.5. z minus 4.5 + 4.5 = negative 1.5 + 4.5. z = 3.
z minus 4.5 = negative 1.5. z minus 4.5 + (negative 4.5) = negative 1.5 + (negative 4.5). z = negative 6.
Which statement is true about their work?
Cedric is correct because he used the inverse of subtraction and added 4.5.
Cedric is incorrect because he should have subtracted 4.5 from both sides instead of adding.
Insha is correct because she added the opposite if 4.5, which is Negative 4.5, to both sides.
Insha is incorrect because she did not add Negative 1.5 + (negative 4.5) correctly.
Answer:d
Step-by-step explanation:
A businessperson is returning from a trip to China and has 337 54 yuan in their wallet. The most current currency conversion rate is 1 US dollar 6.4651 yuan. How much money will the businessperson have when they convert ther
money to U.S. dollars?
O$52.21
O$331.07
O$344.01
O$2182.23
The required money will the businessperson have when they convert the money to U.S. dollars is 5220.96 dollar.
What is currency system?Commodities and services can be exchanged using money. Currency is defined as a unit of account that is issued by a government and is accepted at face value. When bartering, products and services were directly exchanged for one another.
According to question:We know that
1 US dollar = 6.4651 yuan
To find US dollar value of given yuan
1 yuan = 1/6.4651 US dollar
337 54 yuan = 337 54/6.4651 = 5220.96 dollar
Thus, required dollars are 5220.96.
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Answer:
the answer is 52.21 all u gotta do is divide 337.54 by 6.4651 and u get 52.20955592334225 and just round it and u get the answer which is 52.21
Step-by-step explanation:
there are 3 arrangements of the word dad, namely dad, add, and dda. how many arrangements are there of the word probability?
Due today!! Please help me with this question asap!
Answer:
30
Step-by-step explanation:
Because it is an isosceles triangle, then only two sides of the triangle are of the same length and since it said one angle of the triangle is 120° there are still 60° left, so split that into two, and it equals 30° for both equal sides
Help please!!! Use distributive property (5k + 2m)(3p + 4s)
By distributive property (5k + 2m)(3p + 4s) this we get 15kp + 20 ks + 6mp +8ms.
What is Distributive Property?It is possible to multiply a single value by two or more values enclosed in a set of parenthesis using the distributive property, an algebraic property.
According to the distributive property, it is necessary to multiply each of the two terms by the factor when adding two terms to a factor. Only then may the addition operation be done. The following is a symbol for this property:
A (B+ C)=AB + AC
When there are three distinct values for A, B, and C.
Example : (5k + 2m)(3p + 4s)
Apply FOIL method:
(a + b) (c + d) = ac + ad + bc + bd
(5k + 2m)(3p + 4s) = 5k . 3p + 5k. 4s + 2m. 3p + 2m . 4s
5k . 3p + 5k. 4s + 2m. 3p + 2m . 4s
Simplify 5k . 3p + 5k . 4s + 2m .3p + 2m .4s : 15kp + 20 ks + 6mp +8ms
= 15kp + 20 ks + 6mp +8ms.
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