We have explained all the steps to solve an infinite arithmetic sequence.
What is an arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term is the sum of the previous term and a constant called the common difference.
When it comes to solving an infinite arithmetic sequence, you can use the following formulas:
The n-th term of an arithmetic sequence can be represented as a+(n-1)d, where "a" is the first term, "d" is a common difference, and "n" is the position of the term in the sequence.
The sum of the first n terms of an arithmetic sequence is represented as S_n = n/2(2a + (n-1)d), where "a" is the first term, "d" is a common difference, and "n" is the number of terms.
If a sequence is infinite, the sum of all terms can be represented as S_inf = a/(1-r) where "a" is the first term and "r" is the common ratio (r=1+d)
Hence, we have explained all the steps to solve an infinite arithmetic sequence.
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what does it mean for a function to be differentiable?
When a point has a defined derivative, the point is where a function can be differentiated.
What is differentiable function?
Calculus functions in one variable that have a derivative at every point in their domain are said to be differentiable functions. At every interior point within the domain of a differentiable function, the tangent line to the graph is invariably non-vertical.
No break, cusp, or angle exists in a differentiable function. Continuous functions are never differentiable, but differentiable functions can never be continuous.
If the derivative of a function exists at every point within its domain, the function is said to be differentiable. In particular, f′(a) exists in the domain if a function f(x) is differentiable at x = a.
When a point has a defined derivative, the point is where a function can be differentiated. This indicates that the tangent line's slope from the points on the left is getting close to matching the tangent line's slope from the points on the right.
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Which of the following tables represents a multiplicative relationship?
Answer:
B is the answer
Step-by-step explanation:
A multiplicative relationship means that 2 quantities can be expressed as multiples of each other
can somebody please tell me how we can answer this
The final velocity and displacement after 5 seconds are 19.3m/s and 59m and the acceleration is 0.7m/s²
What are Equations of MotionThe equations of motion are a set of mathematical equations that describe the motion of an object in terms of its position, velocity, and acceleration. These equations are used in physics, engineering, and other fields to predict and analyze the motion of objects.
The equations are;
v = u + at ...eq(i)
v² = u² + 2as ...eq(ii)
s = ut + 1/2 at² ...eq(iii)
2.
From the first equation of motion;
v = u + at
v = 4.3 + 3(5)
v = 19.3m/s
The displacement after 5 minutes will be
From third equation of motion;
s = ut + 1/2 at²
s = 4.3 * (5) + 1/2(3)(5)²
s = 59m
1)
distance = 1.0 * 10²m
time = 12.11s
acceleration = ?
Acceleration = velocity / time
velocity = distance / time
velocity = 1.0×10² / 12.11
velocity = 8.23m/s
acceleration = velocity / time
acceleration = 8.23 / 12.11
acceleration = 0.7 m/s²
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How do you find the ratio of a line segment joining?
The ratio ( m :n ) of the line segment joining the given points is calculated by using the formula x = ( mx₂ + nx₁ ) /(m+ n) and y = ( my₂ + ny₁ ) /(m+ n) provided all the three coordinates points should be given.
As given in the question,
Let the line segment be formed by joining the two endpoints (x₁, y₁) and ( x₂ ,y₂ ).Point (x, y) divides the line segment formed by above mentioned coordinates in the ratio m : n.Equation formed to calculate the ratio of the line segment is given by : x = ( mx₂ + nx₁ ) /(m+ n) and y = ( my₂ + ny₁ ) /(m+ n) .Provided the value of all the three coordinates should be given.Solve both the equation by any method and get the ratio which divides the given line segment.Therefore, the ratio divides the given segment can be calculated by the formula x = ( mx₂ + nx₁ ) /(m+ n) and y = ( my₂ + ny₁ ) /(m+ n) .
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Select all the inequalities that have symbols that will be reversed when the variable is isolated.
–10. 5 < 3a
b6 ≤ 7
–4. 5c > 9
–215 ≤ –52d
e – 13 ≥ 11
Option - C and D : -4.5c > 9 and -215 ≤ -52d will have its inequalities that have symbols that will be reversed when the variable is isolated .
Anytime you are multiplying or dividing an inequality by a negative you must reverse the inequality symbol .
Inequalities in mathematics specify the connection between two non-equal quantities. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. However, a variety of inequalities are employed to compare the values, whether they are less than or more than.
The different inequality symbols, properties, and methods for resolving linear inequalities in one variable and two variables will all be covered in this article along with examples. "A connection is called an inequality if two real numbers or algebraic expressions are connected by the symbols ">,",“<”, “≥”, “≤”, An inequality statement in algebra uses the inequality symbol to illustrate the relationship between two expressions.
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a rectangle has its base on the x acis and its upper two vetivies on th eporabloa 16-x^2what is the maximum area the rectangle can have
The maximum area the rectangle can have, is 2.31 square unit.
In the given question, a rectangle has its base on the x axis and its upper two vertices on the parabola 16 - [tex]x^2[/tex].
We have to find the maximum area the rectangle can have.
Let Length is x and width is y.
So, Area of Rectangle = length × breadth
Area of Rectangle = xy
Since, base is on the x - axis, therefore, length will be 2x.
Now, Area of Rectangle = 2xy
The given parabola y = 16 - [tex]x^2[/tex]
Area of Rectangle = 2x(16 - [tex]x^2[/tex])
Area of Rectangle = 32x - 2[tex]x^3[/tex]
For Largest Area find derivative of Area and set equal to zero.
A'(x) = 32 - 6[tex]x^2[/tex]
Now equating equal to zero
32 - 6[tex]x^2[/tex] = 0
Subtract 32 on both side, we get
- 6[tex]x^2[/tex] = - 32
Divide by -6 on both side, we get
[tex]x^2[/tex] = 5.33
Taking square root on both side, we get
x = 2.31
Hence, the maximum area the rectangle can have, is 2.31 square unit.
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math city has eight streets, all of which are straight. no street is parallel to another street. one police officer is stationed at each intersection. what is the greatest number of police officers needed?
The greatest number of police officers needed is 28.
In a scenario where there are n straight lines in a city, and none of the lines are parallel to each other, the maximum number of police officers needed at the intersections can be determined by using the summation formula. The summation formula for the series of numbers from 1 to n-1 is (n-1) * n / 2.
Thus, if there are 8 straight lines in a city, the maximum number of police officers needed at the intersections is (8-1) * 8 / 2 = 28. This is because there will be 8-1 = 7 intersection points in total, and at each intersection point, one police officer is needed.
It's important to note that this is the maximum number of officers needed and it assumes that all lines are intersecting at different points. In case of any parallel lines this number would be less.
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The surface area of this cone is 5,633.16 square millimeters. What is the slant height of this
cone?
Use ≈ 3.14 and round your answer to the nearest hundredth,
Therefore , the solution of the given problem of surface area comes out to be slant height 43 mm.
Definition of surface areaHow much surface area it occupies is a decent indication of its total size. The surroundings is taken into account while calculating the squared of a right triangle. Anything's overall size is determined by its surface area. The volume of water inside a cuboid is the total of the volumes on each of the six horizontal sides. To determine the box's dimensions, use the formula below: The region is the same in 2lh, 2lw, and 2hw (SA). The overall area of the adaptable shape serves as a representation of the region.
Here,
Given :
Surface area = 5633.16 square millimeters
and
slant height = x
radius = 26 mm
So,
=> SA = πr² + πrl = 5633.16
=>SA = π(r² + rl) = 5633.16
=> SA = 3.14 ( 26² + 26* l) = 5633.16
=> SA = 2122.64 + 81.64l = 5633.16
=> SA = 81.64* l = 5633.16 - 2122.64
=> 81.64*l = 3510.52
=> l = 3510.52/81.64
=> l = 43 mm
Therefore , the solution of the given problem of surface area comes out to be slant height 43 mm .
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Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix.
2 5 5
5 2 5 = λ -3, 12
5 5 2
Find P and D
the value of p and d are P = [v1, v2, v3] = [[-1, 1, 1], [1, 1, 1], [1, 1, 1]] and
D = [[-3, 0, 0], [0, 12, 0], [0, 0, 12]] To diagonalize a matrix A, initially the value of eigenvalues and eigenvectors to be find. The eigenvalues of the matrix are λ = -3 and 12.
The eigenvectors for λ = -3 are obtained by the solutions to the equation given as:
(A - λI)v = 0 then,
(A + 3I)v = 0
hence
| 2 5 5 | |v1| | 0|
| 5 2 5 | . |v2| = | 0|
| 5 5 2 | |v3| | 0|
hence The solution obtained by the equation is given by:
v1 = -v2 + v3
The eigenvectors for λ = 12 are obtained by the solutions to the equation:
(A - λI)v = 0
Which is:
(A - 12I)v = 0
Which is:
| -10 -5 -5 | |v1| | 0|
| -5 -10 -5 | . |v2| = | 0|
| -5 -5 -10 | |v3| | 0|
hence The solution obtained is :
v1 = v2 = v3
So the eigenvectors are:
v1 = [-1, 1, 1] for λ = -3
v2 = v3 = [1, 1, 1] for λ = 12
The matrix P is the matrix whose columns are of the eigenvectors of A:
P = [v1, v2, v3] = [[-1, 1, 1], [1, 1, 1], [1, 1, 1]]
The matrix D is the diagonal matrix whose diagonal elements are of the eigenvalues of A:
D = [[-3, 0, 0], [0, 12, 0], [0, 0, 12]]
therefore , A can be diagonalized as A = PDP^-1
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Ms. Adams needs to make 50 ml of 15% saline solution. However, she only has bottles of 7.5% and 20% solution. How many milliliters of each does she need to mix?
Answer: 20 mL of 7.5% solution and 30 mL of 20% solution
Step-by-step explanation:
Let the amount of 7.5% solution in mL be [tex]x[/tex] and the amount of 20% solution in mL be [tex]y[/tex].
Then, we know that [tex]x+y=50[/tex] (from the total amount) and that [tex]0.075x+0.20y=50(0.15)[/tex] from the concentration.
[tex]x+y=50 \implies y=50-x\\\\\therefore 0.075x+0.20(50-x)=50(0.15)\\\\0.075x+10-0.20x=7.5\\\\-0.125x=-2.5\\\\x=20\\\\\implies y=50-20=30[/tex]
Five less than a number (n) 28 is . Which equation shows this relationship?
4. One root of a quadratic
equation is 5+i
a. What is the other root?
b.What is the sum of the roots?
c. What is the product of the roots?
d. What is the equation?
The quadratic equation is x²+10x+26=0
What are quadratic equations?A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.
Given here: Complex root of a quadratic equation is 5+i
And we know that complex roots always occur in pairs.
Thus the other root must be its conjugate as 5+i
The sum of roots will be given by 5+i+5-i=10
and product of the roots is given by (5+i) (5-i)=25-(-1)
=26
∴ The quadratic equation is x²+10x+26=0
Hence, The roots are 5+i , 5-i
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The question is attached below - Attached below
Step-by-step explanation:
the formula for the circumference of a circle is
2×pi×r
well, does this look familiar ?
our given circumference is
2×pi×sqrt(2)
so, clearly, r (radius) = sqrt(2).
the area of a circle is
pi×r²
so, for our circle that means
pi×sqrt(2)² = 2pi ft²
An Isosceles triangle and a square have the same perimeter. Find the side lengths of the triangle.
triangle base: 3x
triangle height: 2x+1
square length: 4
Answer: 5, 5, 6
How you get this answer?
The sides of the triangle based on the information will be 5 unit, 5 units and 6 units.
How to calculate the triangle?From the information, we are given that the isosceles triangle and a square have the same perimeter and we want to find the side lengths of the triangle.
It should be noted that a isosceles triangle has two sides that are equal. In this case, the perimeter of the square and Triangle is the same. The perimeter will be:
= 4 + 4 + 4 + 4
= 16 units.
Therefore, the sides of the triangle will be calculated thus:
3x + 2x + 1 + 2x + 1 = 16
7x + 2 = 16
7x = 16 - 2
7x = 14
Divide
x = 14 / 7
x = 2
The sides will be:
3x = 3 × 2 = 6
2x + 1 = 2(2) + 1 = 5
2x + 1 = 2(2) + 1 = 5
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Belinda is thinking about buying a house for $179,000. The table below shows the projected value of two different houses for three years:
Answer:
A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Part A :
If a function is linear, then the function values have equal differences.
If a function is exponential, the function values have equal ratios.
For car 1 :
36450 / 40,500 = 9/10
32805 / 36450 = 9/10
Values of car have equal ratios.
This is exponential function.
For car 2 :
39000 - 42000 = -3000
36000 - 39000 = -3000
Values of car have equal differences
This is linear function.
Part B :
The initial value of car is 45,000.
For car 1 :
f(1) = 40,500, f(2) = 36,450, ............
For car 2 :
f(1) = 42,000, f(2) = 39,000, ..........
Part C :
For car 1 :
f(13) = = 11438.396
For car 2 :
f(13) = = 6000
There is a significant difference in the values of the car after 13 years. The value of the car 1 is greater.
Hence the value of the car 1 is described by an exponential function and that of car 2 by linear function. The value of car 1 is greater after 13 years.
Step-by-step explanation:
An equilateral triangle and an isosceles triangle share a common side. What is the measure of ∠ ABC?
The measure of ∠ ABC is 112°
How determine the measure of ∠ ABC?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a shape with its angles.
Triangle BCD is an equilateral triangle. So all the angles are equal, that is 60° each.
∠ ADB = 64° (base angle of an isosceles triangle are equal)
∠ ABD = 180° - 64° - 64° (sum of angles in a triangle is 180°)
∠ ABD = 52°
∠ ABC = ∠ ABD + ∠ CBD
∠ ABC = 52° + 60°
∠ ABC = 112°
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Two different drugs, X and Y, are currently in use to treat a certain condition. About 7 percent of the people using either drug experience side effects. A random sample of 75 people using drug X and a random sample of 150 people using drug Y are selected. The proportion of people in each sample who experience side effects is recorded.
Therefore ,option C is correct since the percentage sample would need to be higher than 100 to produce a significant result.
What is a percentage?A percentage is a subdivision by 100, also referred to as percent. A percentage, which is defined as "per 100," denotes a component of an overall amount. For instance, 45% represents the number 45 out of 100. Calculating a percentage is the process of finding the proportion of a whole given terms of 100. There are choices for fraction computation and using online calculators.
Given:
A random selection of 75 drug users of drug X and just a random selection of 150 drug users of drug Y are chosen,
Most statisticians agree that you need a 100 sample size to get any kind of statistically meaningful findings. You should absolutely poll each and every person in a population of less than 100.
The representative sample for medication X is therefore insufficient.
Therefore ,option C is correct since the sample would need to be higher than 100 to produce a significant result.
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03.06 LC)
Which is the standard equation of the hyperbola centered at the origin, with a vertical transverse axis and values of a = 7 and b = 10?
The standard equation of hyperbola centered at the origin with the given values is x^2 / 49 - y^2 / 100 = 1 .
What is Hyperbola ?
a plane curve generated by a factor so moving that the difference of the distances from two constant points is a consistent : a curve formed by way of the intersection of a double right circular cone with a plane that cuts each halves of the cone.
Given,
The standard equation of the hyperbola centered at the origin with given values a=7 and b=10 .
[(x2 / a2) – (y2 / b2)] = 1.
vertical axis with values a = 7 and b=10 .
[(x2 / a2) – (y2 / b2)] = 1.
(x^2 / 7*7) - ( y^2/ 10*10) = 1
x^2 / 49 - y^2 / 100 = 1
Hence , the standard equation of hyperbola centered at the origin with the given values is x^2 / 49 - y^2 / 100 = 1 .
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What type of chart can graph 2 different types of data?
A combination chart can be made up of the area, bar, column, dot, and line charts.
Bar charts are one of the most common data visualizations. Each data series can be represented by a different type of chart. They are all then displayed simultaneously on the same chart.
Adding a chart type that displays over another chart type can give you an immediate comparison of two or more data series over a dimension such as time.
Combination charts enable you to compare different series of data through different types of charts on the same axes simultaneously. This is useful for visualizing large quantities of data in varied formats.
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sarahs aunt gave her 5$ for her birthday sarahs grandma gave her ten times as much as her aunt. sarah's uncle gave her $18. how much money did sarah receive for her birthday.
Therefore , as a result the unitary method answer to the given problem is to determine the total or difference: 73.
What does unitary method mean?The unitary technique is a way of problem-solving where you first calculate the amount of a single component, then multiple that value to get the answer. Simply put, a single system value is extracted from a sourced multiple using the unit method. For illustration, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent.
Here,
Given :
Devise 18 + 5 + 5 * 10 based on the given conditions. Do the math: 18 + 5 + 50 to get the product or quotient.
Determine the difference or total: 23 + 50\s=> Determine the difference or total: 73
The answer is: 73.
As a result, the unitary method's answer to the given problem is to determine the total or difference: 73.
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9. Marry plays a game of throwing a ball at a target.
The table shows information about the probability of each possible score.
0
1
*
2
3
4
Score
0.09
Probability
X
3x
0.16
0.21
Marry is three times more likely to score 2 points than to score 1 point.
a) Work out the value of x.
b) Mary plays the game twice.
Work out the probability of Mary scoring a total of 8.
5
0.30
6.......
Answer:
6.97%
Step-by-step explanation:
a) To work out the value of x, we can use the information given that "Marry is three times more likely to score 2 points than to score 1 point". We know that the probability of scoring 1 point is x, and the probability of scoring 2 points is 3x.
So we can set up the equation:
3x = probability of scoring 2 points
x = probability of scoring 1 point
We know that 3x = probability of scoring 2 points = 0.16
So we can solve for x by dividing both sides by 3:
x = 0.16 / 3 = 0.05333
b) To work out the probability of Mary scoring a total of 8, we can use the information from the table and the formula for the probability of a specific outcome when playing the game twice.
We know that the probability of scoring 4 points in one game is 0.21, so the probability of scoring 4 points twice is (0.21)^2 = 0.0441
We also know that the probability of scoring 2 points in one game is 3x = 3(0.05333) = 0.16, so the probability of scoring 2 points twice is (0.16)^2 = 0.0256
We can add these probabilities together to find the total probability of scoring 8 points:
0.0441 + 0.0256 = 0.0697 or 6.97%
So the probability of Mary scoring a total of 8 is 6.97%.
Are the two lines in the picture parallel, perpendicular, skew or neither? Be sure to explain your reasoning
Answer:
i think Parallel
Step-by-step explanation:
they are not perpendicular as the lines are not intersecting
they are not skewed because they go in same direction
and they are parallel because they never meet and go in same direction
my school's math club has 6 boys and 8 girls. i need to select a team to send to the state math competition. we want 6 people on the team. in how many ways can i select the team to have more girls than boys?
By 2228 ways i can select the team to have more girls than boys
We have, total number of boys = 6, while the total number of girls = 8
Total size of team = 6
Condition given: In every case the total number of girls should be more than the total number of boys.
As for that we can choose the team like
(6G, 0B) + (5G, 1B) + (4G, 2B)
Making the combination as per above arrangements:
We will get it as:
=8C6*6C0+8C5*6C1+8C4*6C2
As we know,
The formula of combination is:
[tex]$${ }_n C_r=\frac{n !}{r !(n-r) !}$$[/tex]
[tex]${ }_n C_r=$[/tex] number of combinations
n= total number of objects in the set
r= number of choosing objects from the set
So, applying the concept of combination in the above,
So, from above we can write it as:
8C6*6C0+8C5*6C1+8C4*6C2
=[tex][\frac{8!}{6! \times 2!}\times \frac{6!}{6!\times 0!}]+[\frac{8!}{5!\times 3!}\times \frac{6!}{5!\times 1}]+[\frac{8!}{4!\times 4!}\times \frac{6!}{2!\times 4!}]\\\\[/tex]
[tex][\frac{8 \times7\times6! }{6!\times2} \times \frac{1}{1}]+[\frac{8\times7\times6\times5!}{5!} \times \frac{6\times5!}{5!}]+[\frac{8\times7\times6\times5\times4!}{4!\times24} \times \frac{6\times5\times4!}{4!\times2}][/tex]
[28*1]+[336*6]+[70*2]
=28+2016+140
=2228
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A new health drink has 140% of the recommended daily allowance (RDA) for a certain vitamin. The RDA for this vitamin is 40mg. How many milligrams of the vitamin are in the drink?
The drink contains 56mg of the vitamin while RDA is only 40mg.
What is milligram?The SI unit of mass, the kilogramme, is 1000,000,000 times larger than the milligramme (mg), which is a unit of mass. Using a lowercase m and lowercase g, a milligramme is abbreviated as mg.
There are 1000 milligrammes in a gramme, hence the use of the prefix milli to denote the thousandth.
There are 10-6 kilogrammes in a milligramme. When describing drug doses, milligrammes are frequently used.
We have to count 140% of the RDA to find the how much vitamins its contains.
Here, RDA = 40mg
140% × 40
140/100 × 40
1.4 × 40
56mg
Thus, the drink contains 56mg of the vitamin while RDA is only 40mg.
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In the community park, there are 7 oak trees and 4 maple trees. Which ratios show the number of oak trees to the number of maple trees
There are 7 oak trees and 4 maple trees in the community park, so the ratio of oak trees to maple trees can be written as 7:4.
What is ratio?
A ratio is a way of comparing two or more quantities. It is a way of expressing the relationship between two numbers in terms of their size. A ratio can be written in different ways, such as in the form of a fraction, as a decimal, or as a whole number.
We can also write the ratio in different ways, such as:
7/4 = 1.75 oak trees for every 1 maple tree
35:20 = 35 oak trees for every 20 maple trees
14:8 = 14 oak trees for every 8 maple trees
All of these ratios represent the same proportion, which is 7 oak trees to 4 maple trees.
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8. A man standing on the top of a building. He knows that he is 180 ft up in the building. The
tree is 86 ft from the base of the building. What would the angle of depression be from where
the man is to the tree?
The angle of depression from the man to the tree will be 64.46°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
A man standing on the top of a building. He knows that he is 180 ft up in the building. The tree is 86 ft from the base of the building.
The angle of the depression is calculated as,
tan θ = 180 / 86
tan θ = 90 / 43
θ = tan⁻¹ (90 / 43)
θ = 64.46°
The angle of depression from the man to the tree will be 64.46°.
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MathXL for School Practice & Problem Solving
7.PS-13
Question Help
Shopping Two friends shop for fresh fruit. Elena buys a watermelon for $6.75 and 3 pounds of cherries. Taniy buys a
pineapple for $2.45 and 2 pounds of cherries. Use the variable p to represent the price, in dollars, per pound of cherries.
Write and simplify an expression to represent how much more Elena spent.
The expression represents how much more Elena spent than Taniy.
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Due
An expression that represents how much more Elena spent than Taniy is 4.3 + p.
How to write and simplify an expression to represent how much more Elena spent?Assuming the variable p, represents the price, in dollars, per pound of cherries, the amount of money Elena spent in buying a watermelon for $6.75 and 3 pounds of cherries is given by:
Elena = 3p + 6.75.
For the amount of money Taniy spent in buying a pineapple for $2.45 and 2 pounds of cherries is given by:
Taniy = 2p + 2.45
For the difference, we have:
Elena's cost = 3p + 6.75 - (2p + 2.45)
Elena's cost = 3p + 6.75 - 2p - 2.45
Elena's cost = 4.3 + p
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Find the values of x for which the series converges. (enter your answer using interval notation.) [infinity] (x + 9)n n = 1 find the sum of the series for those values of x.
For the series to converge, the limit as n approaches infinity of (x + 9)n must be less than 1.
What is value?Value is an important concept in economics and business that refers to the worth of a product, service, or asset. It is a measure of the relative worth of something compared to other similar items. Value can be determined by a variety of factors, such as the quality, condition, and availability of an item. It can also be based on a customer's perception or opinion of a product or service. Values can vary from person to person, and can even change over time. Ultimately, value is a subjective concept that is determined by the beliefs and preferences of individuals.
This can be expressed as x + 9 < 1, so the values of x for which the series converges is x < -8. The sum of the series for these values of x is the geometric series:
Sum = (x + 9)1 / (1- (x + 9)) = -8.
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How do I partition a directed line segment?
The point of partition of the line segment AB in the ratio 2:3 with endpoints at A(9,5) and B (4,-5) is (7,1) .
What is Partition ?
The Simple words Partition means to separate or to divide . and
we know that , the point of partition of the line segment AB in the ratio a:b , can be calculated using the formula :
[tex]P=\frac{bA+aB}{a+b}[/tex] ;
Substituting the values of end points A(9,5) and B (4,-5) and the ratio [tex]a=2[/tex] , [tex]b=3[/tex] ,
we get ;
P = [tex]\frac{3(9,5) +2(4,-5)}{2+3}[/tex] = [tex]\frac{(27,15) + (8,-10)}{5}[/tex] = [tex]\frac{(35,5)}{5}[/tex] ;
Simplifying further ,
we get ;
P = (7,1) .
Therefore , the point of partition P is (7,1) .
The given question is incomplete , the complete question is
How do I find the point that partitions the segment AB into a 2:3 ratio with endpoints at A(9,5) and B (4,-5) ?
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timed please be quick
Which statement describes the system of equations?
It has one solution (–5, 5).
It has one solution (5, –5).
The system has no solution.
The system has infinitely many solutions.
A statement which best describes the system of equations include the following: A. It has one solution (–5, 5).
What is a point of intersection?In Mathematics, a point of intersection is the location on a graph where two (2) lines intersect, or cross each other, which is typically represented as an ordered pair containing the point that corresponds to the x-axis and y-axis on a cartesian coordinate.
In this scenario, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
3x - 4y = -35 ........equation 1.
3x + 4y = 5 ........equation 2.
Based on the graph (see attachment), we can reasonably and logically deduce that the given system of equations has only one true solution, and this is the point of intersection of the lines on the graph representing each of them, which is given by the ordered pair (-5, 5).
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