a. (F) If the sequence {n} converges, then the series an must converge. This statement is false.
The convergence of a sequence does not necessarily imply the convergence of the corresponding series.
b. (T) If a sequence is bounded and monotonic, then the sequence must converge.
This statement is true.
This is known as the Monotone Convergence Theorem.
c. (F) The nth-term test can show that a series converges.
This statement is false.
The nth-term test can only determine the divergence of a series, not its convergence.
d. (T) If the sequence of partial sums converges, then the corresponding series must also converge.
This statement is true.
This is known as the Cauchy criterion for convergence of a series.
e. (F) The harmonic series diverges since its partial sums are unbounded. This statement is false.
The harmonic series diverges because its terms do not approach zero.
f. (F) sinn is not an example of a p-series.
This statement is false. sinn is not a p-series since its terms do not have the form 1/n^p, where p is a positive constant.
g. (T) If a convergence test is inconclusive, you may be able to prove convergence/divergence through a different test.
This statement is true.
There are many convergence tests available, and if one test fails, it may be possible to apply a different test to determine convergence or divergence.
h. (F) If a series diverges, it does not necessarily mean that the corresponding sequence diverges.
This statement is false.
The divergence of the series implies that the corresponding sequence does not converge.
i. (F) If an alternating series fails to meet any one of the criteria of the alternating series test, then the series is not necessarily divergent. This statement is false. If an alternating series fails the alternating series test, it could be convergent or divergent, and further analysis is required to determine its convergence/divergence.
j. (F) Given that an > 0, if an converges, then -1an must converge. This statement is false.
The convergence or divergence of -1an depends on the original convergence or divergence of the series an.
The sum of the series is 14/3.
For the infinite geometric series with first term a=7 and common ratio r=-1/2:
The series converges since the absolute value of the common ratio r is less than 1, which is a necessary and sufficient condition for convergence of a geometric series.
The sum of the series is given by:
S = a / (1 - r) = 7 / (1 + 1/2) = 7 / (3/2) = 14/3.
Therefore, the sum of the series is 14/3.
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Assume that all sequences and series mentioned below are infinite sequences and infinite series, where an is the nth term of the sequence/series.
a. False. The convergence of a sequence does not guarantee the convergence of the corresponding series.
b. True. If a sequence is bounded and monotonic, then it must converge by the monotone convergence theorem.
c. False. The nth-term test only shows whether a series diverges. It cannot be used to show that a series converges.
d. True. If the sequence of partial sums converges, then the corresponding series must also converge.
e. False. The harmonic series diverges because its partial sums are unbounded, not because they are bounded from above.
f. False. sinn is not an example of a p-series. A p-series is of the form ∑n^(-p), where p>0.
g. True. If a convergence test is inconclusive, then we can try using a different test to determine convergence/divergence.
h. False. If an diverges, then we cannot determine whether a converges or diverges without further information.
i. False. An alternating series can be convergent even if it fails to meet one of the criteria of the alternating series test.
j. True. If an>0 and an converges, then -1an must also converge.
The infinite geometric series with first term a=7 and common ratio r=0.5 is given by: 7 + 3.5 + 1.75 + ...
This series converges because |r|=0.5<1. The sum of an infinite geometric series with first term a and common ratio r is given by:
sum = a / (1 - r)
In this case, we have:
sum = 7 / (1 - 0.5) = 14
Therefore, the sum of the series is 14.
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Hector is mixing fruit punch in a 40-cup punch bowl for a party. He plans to
add at least 24 cups of fruit juice to the bowl before adding ginger ale.
Identify the graph that represents the amounts of fruit juice and ginger ale he
can use, and then identify a valid solution. (The graph shows the overlapping
solution region only, not the shading for each inequality.)
The graph that represent the amounts of fruit juice and ginger ale he can use, and the valid solution is: A. valid solution (28, 8).
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of cups of fruit juice and number of hours clearing tables respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of cups of fruit juice.Let the variable y represent the number of cups of ginger ale.Since Hector is mixing fruit punch in a 40-cup punch bowl for a party, an inequality which models this situation is given by:
x + y ≤ 40.
Additionally, Hector plans to add at least 24 cups of fruit juice to the bowl before adding ginger ale:
x ≥ 24.
Based on the graph (see attachment), we can logically deduce that a valid solution to the given system of inequalities is the overlapping solution region, which is given by the ordered pair (28, 8).
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find the equation of the line given (4,-2) and (3,10)
Answer:
y-(-2)=-12(x-4)
Step-by-step explanation:
Use Slope point Form to solve this equation. Follow the steps in the image.
-Hope this helped
what is the length of AB
Answer:
AB ≈ 5.2
Step-by-step explanation:
given ∠ CAD = ∠ BAD = Θ
then AD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides , that is
[tex]\frac{BD}{CD}[/tex] = [tex]\frac{AB}{AC}[/tex] ( substitute values )
[tex]\frac{4.1}{4.3}[/tex] = [tex]\frac{AB}{5.5}[/tex] ( cross- multiply )
4.,3 AB = 4.1 × 5.5 = 22.55 ( divide both sides by 4.3 )
AB ≈ 5.2 ( to one decimal place )
In the coordinate plane point a has coordinates of A (-5,8). Which is further from a point B or point C given that they have coordinates of B(1,0) and C(-10,16)
The point that is further from point A is point B
How to find length of lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points A (-5, 8) and B(1, 0) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-5 - 1)² + (8 - 0)²}
d =√{36 + 64}
d = √100
d = 10 units
distance between points A (-5, 8) and C(-10, 16) is calculated as follows
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
d =√{(-5 + 10)² + (8 - 16)²}
d =√{25 + 64}
d = √89
d = 9.43 units
comparing both points shows that point B shows further away
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Which of the following expressions are polynomials? Justify your answer:(1) 8(ii) √3x² - 2x(iii) 1 - √5x(iv) 1/5x-2 +5x+7(v)(x-2)(x-4)/X(vi)1/x+1(vii)1/7 a^3 - 1/√3a^2 + 4a-7(viii) 1/2xa. Polynomials: (ii), (vi), (vii)b. Polynomials: (i), (ii), (iv), (vii)c. Polynomials: (ii), (iii), (iv), (vii)d. Polynomials: (i), (ii), (vii)
B) Therefore, the polynomials among the given options are (i), (ii), (iv), and (vii).
A polynomial is a mathematical expression made up of constants, variables, and non-negative integer exponents.
It can have no variable at all, one variable or multiple variables.
A polynomial can't have a negative exponent. It never has division by a variable. Based on this definition, options
(iii) 1- √5x
(v) (x-2)(x-4)/x
(vi) 1/x+1, and
(viii)1/2xa
are not polynomials because they have fractional exponents or negative exponents.
Therefore, the polynomials among the given options are (i), (ii), (iv), and (vii) because they do not have fractional or negatice exponent.
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please solve two answers
The function f(x) is f(x) = -2/3 x -8. The function g(x) is g(x) = -1/6 x - 2
What is a function?
A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain.
Given that f(x) is a linear function. The value of f are f(-9) = -2 and f(-3) = -6.
Assume that, f(x) = ax + b
Now putting x = -9 in f(x) = ax + b:
f(-9) = a(-9) + b
Putting f(-9) = -2
-2 = -9a + b ....(i)
Now putting x = -3 in f(x) = ax + b:
f(-3) = a(-3) + b
Putting f(-3) = -6
-6 = -3a + b .....(ii)
By using the elimination method solve equation (i) and (ii).
Subtract equation (ii) from equation (i)
-9a + b = -2
-3b + b = -6
(+) (-) (+)
__________
-6a = 4
Divide both sides by -6:
a = -4/6
a = -2/3
Putting a = -2/3 in equation (i)
-6 = -3(-2/3) + b
-6 = 2 + b
b = -6 - 2
b = -8
Therefore, f(x) = -2/3 x -8
Now compare f(x) = -2/3 x -8 with f(x) = ax + b
a = -2/3 , b = -8
The y-intercept of f(x) is b = -8
The x-intercept of f(x) is b/a = -8/(-2/3) = 12
The y-intercept of g(x) is 6 more than f(x). Thus the y-intercepts of g(x) is 6 + (-8) = -2
The x-intercept of g(x) is 12.
Assume that the linear equation of g(x) is g(x) = hx + k
The y-intercept of g(x) is k = -2
The x-intercept of g(x) is k/h = 12
Putting k = -2:
-2/h = 12
h = -2/12
h = - 1/6
The linear equation of g(x) is g(x) = -1/6 x - 2
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What causes dilated eyes?
Dilated eyes cause ,A traumatic injury, drug/medication side effects, or dilating eye drops after an eye checkup may all contribute to the illness.
Why, for no apparent reason, are my eyes super dilated?A physical or psychological condition, certain substances or prescriptions, or an injury could be the cause of this. The term "blown pupil" is occasionally used by doctors to describe more severe mydriasis when the pupils are fixed and dilated. This disorder may be a sign of brain damage brought on by a stroke or other physical trauma.A traumatic injury, drug/medication side effects, or dilating eye drops after an eye checkup may all contribute to the illness. While unexpected pupil dilation may be the result of a medical illness, it can also happen naturally owing to changes in light and emotional events.To learn more about Dilated eyes refer to:
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In LMN MN=15cm, LP is perpendicular to MN, LP=100 angle PLN=PNL state the length of PN. Give reason for your answer. PLS HELP ME
Therefore , the solution of the given problem of triangle comes out to be PN =100 cm .
A triangle is what exactly?An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having angles A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.
Here,
Given :
MN = 15 cm
and
LP = 100
and
ΔPLN=ΔPNL
Length of PN:
Since
=> PN = LP
=> PN =100 cm
Therefore , the solution of the given problem of triangle comes out to be
PN =100 cm .
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Divide (36z^2y^6-12z^6y^6) divided by (4z^5y^2)
Therefore , the solution of the given problem of algebraic comes out to
be 9y⁴ /z³ - 3zy⁴.
What is algebraic in mathematics?Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we use numbers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we use variables such as x, y, and z in addition to numbers.
Here,
Given:
=> (36z²y⁶ - 12z⁶y⁶) / 4z⁵y²
=> 9y⁴ /z³ - 3zy⁴
thus , we get the solution for the given algebraic expression.
Therefore , the solution of the given problem of algebraic comes out to
be 9y⁴ /z³ - 3zy⁴.
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Jake filled a bucket with 2 7/8 gallons of water. He then poured out 1/3 gallons of water. How much water remained in the bucket.
Thanks!
Answer: 2.54167 another way to write it 2 13/24 gallons of water jake put in his water.
Step-by-step explanation:
What is the solution for X?
By virtue of the properties of congruency of sides of opposite sides, the solution of x is 5 as 4/x-3 = x-7/35.
what is solution ?a number or values that, when used as a substitution for one or more variables in an equation, make the equation true. For instance, the answers to the equation x2 = 4 are 2 and -2. a method or technique for solving a problem. an explanation of a solution. specifically: a collection of variable values that satisfy an equation. A number that can be entered as the variable's replacement in an equation serves as the solution. 6+5=11 is correct according to the formula 3(2)+5=11. The answer is therefore 2,
given
AB / CD = EF/GH
4/x-3 = x-7/ 35
x = 5
so By virtue of the properties of congruency of sides of opposite sides, the solution of x is 5 as 4/x-3 = x-7/35.
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How can you break apart the factor 4 into equal addends to find the factor 4x7
We can add the factor 4 seven times to find the product 4 × 7.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number. a × b means that a is added to itself b times or b is added to itself a times.
So we know that multiplication is basically addition of one of the numbers up to the times as that of the other number.
Given, we have to find the product of 4 × 7, in terms of addition, by using the factor 4.
The meaning of the product of 4 and 7 is that 4 is adding to itself 7 times or 7 is adding to itself 4 times.
Since we need to break the product in terms of 4 as addends, we can write,
4 × 7 = 4 + 4 + 4 + 4 + 4 + 4 +4
Hence we can break 4 as 7 equal addends to find the given product.
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Slope intercept form
The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept
What is standard form form?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5.
When an equation is given in this format, finding both intercepts is rather simple (x and y). Additionally, when resolving systems of two linear equations, this form is highly helpful.
It is possible to determine the x- and y-intercepts of the corresponding line when we have a linear equation in standard form.
In some circumstances, we might want to convert an equation written in a different form to standard form (for instance, while solving systems of equations).
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Use transformations to solve the inequality. Write down all the steps
Answer: [tex]f \ge 26[/tex]
Work Shown:
[tex]-\frac{1}{2}f \le -13\\\\-2*(-\frac{1}{2}f) \ge -2*(-13)\\\\f \ge 26[/tex]
To isolate the variable f, we multiply both sides by -2.
Multiplying both sides by a negative number will flip the inequality sign.
What is the 3rd exponent called?
The exponent of 3 in 3^3 is 3, also called "cubed" or "3 raised to the 3rd power".
Katie would go to the park everyday and each day she recorded how many dogs were in the park. Day 1: there was 4 dogs , Day 2: 3 dogs , day 3: 6 dogs , Day 4:1 dog and day 5: 8 dogs. Over the next 3 weeks the same amount of dogs turned up each day. How many dogs turned up each day did she see over 3 weeks?
The total number of dogs that turned up per day for the 3 weeks are;
Day 1 = 12 dogs
Day 2 = 9 dogs
Day 3 = 18dogs
Day 4 = 3 dogs
Day 5= 24 dogs
To find the total number of dogs:If the same amount of dogs turned up each day over the three weeks then we have;
For week 1
Day 1 = 4 dogs
Day 2 = 3 dogs
Day 3 = 6 dogs
Day 4 = 1 dog
Day 5 = 8 dogs
Total for the week = 22 dogs
For week 2
Day 1 = 4 dogs
Day 2 = 3 dogs
Day 3 = 6 dogs
Day 4 = 1 dog
Day 5 = 8 dogs
Total for the week = 22 dogs
For week 3
Day 1 = 4 dogs
Day 2 = 3 dogs
Day 3 = 6 dogs
Day 4 = 1 dog
Day 5 = 8 dogs
Total for the week = 22 dogs
For the 3 weeks
Day 1: 4 x 3dogs = 12 dogs
Day 2: 3 x 3dogs = 9 dogs
Day 3: 6 x 3dogs = 18dogs
Day 4: 1 x 3dogs = 3 dogs
Day 5: 8 x 3dogs = 24 dogs
Total dogs seen in the 3 weeks = 66 dogs
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Find the value of y so that the line through the pair of points has the given slope.
The line through the points (4, 3) and (-1, y) with slope 1.
y=?
The value of y so that the line has a slope of 1 is given as follows:
y = -2.
How to obtain the slope of a linear?The slope of a linear function represents the rate of change of the output variable y relative to the input variable x.
Hence, given two points, the slope is calculated as the change in y divided by the change in x.
The points for this problem are given as follows:
(-1, y) and (4,3).
The change in y is of:
3 - y
The change in x is of:
4 - (-1) = 5.
The slope will have a value of one when:
(3 - y)/5 = 1
3 - y = 5
y - 3 = -5
y = -2.
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Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
Which of the following shapes are rectangles?
A rectangle has four sides and angles at 90 degree.
What is a rectangle?A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square. A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
Given: shape of a rectangle
A rectangle is closed flat shape, having four sides, and each angle equal to 90 degrees. The opposite sides of the rectangle are equal and parallel.
Hence, A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles (90°).
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Please help, i dont really understand this lol
Answer:
A) [tex]x>-2[/tex]
Step-by-step explanation:
[tex]x+4>-x \\ \\ 2x+4>0 \\ \\ 2x>-4 \\ \\ x>-2[/tex]
Asher is able to sell his cell phone on two different websites, A and B. In the table, the different rates are represented by the functions A(t) and B(t), where t is time in months.
t (months) 1 2 3
Website A
A(t) = 50(0. 85)t 42. 50 36. 13 30. 71
Website B
B(t) = 50 − 5t 45 40 35
In what month will the price of his phone be less with website B than website A?
a
5
b
6
c
7
d
8
As per the given functions A(x) and B(x), at the month 8th the price of his phone be less with website B than website A.
The term function in math is known as a relationship between inputs where each input is related to exactly one output.
Here we have given that Asher is able to sell his cell phone on two different websites, A and B.
And in the given table, the different rates are represented by the functions A(x) and B(x), where t is time in months.
While we looking into the given question, we have identified that there are two functions are listed as follows:
A(x) = 80(0.86)ˣ
B(x) = 80 - 8t
When we plot the function on the graph, then we get the graph like the following,
Through the graph, we have identified that on the point of (8, 23.93) and (8,16) has been the resulting point.
Therefore, the correct option is (d).
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5 of 8 18 seconds A Given that A, O & B lie on a straight line segment, evaluate acute ZCOD. C (3x+88) this question ZCOD = 46 0 (x +36) (2x-4) The diagram is not drawn to scale. D B
On solving the provided question, we can say that A,O, B lie on a straight line segment, so, angle COD=46°
what are angles?An angle is a form in Euclidean geometry made composed of two rays, called the angle's sides, that meet at a point in the middle known as the angle's vertex. In the plane where the rays are placed, two rays can produce an angle. An angle is also produced when two planes intersect. They're known as dihedral angles. In plane geometry, an angle is the form that two rays or lines with a common termination might take. The Latin word "angulus," which means "horn," is where the English word "angle" comes from. The two rays, also known as the sides of the angle, have a common termination known as the vertex.
A,O, B lie on a straight line segment.
We know that
straight line has = 180
angle AOC=3x+88
angle COD=(x+36)
Angle DOB = (2x - 4)
[tex]AOC+ COD+ DOB=180\\(3x+88)+(x+36)+(2x-4)=180\\6x+190=180\\ x=60/6=10 \\COD=x+36=10+36=46\\[/tex]
so, angle COD=46°
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A linear relationhip i hown in the table. Time (hour) 2 4 6 8
Ditance (mile) 4 8 12 16
I the linear relationhip alo proportional? Explain. No, the contant of proportionality i 2. Ye, the contant of proportionality i 2. No, there i no contant of proportionality. Ye, there i no contant of proportionality
The value of k is 4. So the constant of proportionality is 4.
In the given question, a linear relationship is shown in the table.
Time (hour) 2 4 6 8
Distance (mile) 4 8 12 16
We have to find the linear relationship also proportional.
When determining if two ratios or fractions are equivalent, the proportion formula is utilized. One way to express the percentage formula is as a: Whereas a and d are the extreme terms and b and c are the mean terms, b::c: d = a/b = c/d.
y ∝ x is the supplied proportional equation.
Additionally, y = kx, where k is the proportionality factor.
It shows that the expressions printed on the left and right sides have an equal relationship.
Let k be the proportionality constant for the given data.
Now , the value of k is determined by x = {2, 4, 6, 8}.
The values of distances be y = {8, 16, 24, 32}.
The proportionality constant is now provided by y = kx.
Divide by x on both sides of the equation, we get
k = y/x
Substituting the values in the equation, we get
k = 8/2
k = 4
k = 16/4
k = 4
Hence, the value of k is 4. So the constant of proportionality is 4.
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The constant of proportionality is 4.
A linear relationship (or linear association) is a statistical term used to describe a straight-line relationship between two variables. Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + b.
The constant of proportionality is the ratio between two directly proportional quantities. Two quantities are directly proportional when they increase and decrease at the same rate. The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.
Let the proportionality constant be k
Noe the value of proportionality constant k is determined by
The values of time be x = {2,4,6,8}
The values of distance be y = {8,16,24,32}
Now, the constant of proportionality is given by
y = kx
Divide by x on both sides of the equation, we get, k = y/x
Substituting the values in equation, we get
K = 8/2 = 4
And k = 16/4 = 4
Therefore the value of k is 4.
hence, the constant of proportionality is 4.
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what is 3,000x9,000,628?!!!!!!!!!!!!!!!!!!!!!!!
Answer: 3,000 x 9,000,628 = 27,001,884,000 ✅
Step-by-step explanation:
It is the result of multiplication of 3,000 with 9,000,628.
PLEASE GIVE ME THE BRANLIEST PLEASXE IM BEG
Answer:
27,001,894,000
put it in a calculator
What is a solutions grade 7?
Step-by-step explanation:
Grade 7 Science. Solutions… a review. A homogeneous mixture They appear as ONE substance Examples: tap water, vinegar, gold jewelry.
if a sound traveling through a medium has a frequency of 520 Hz and a wavelength of 6.92 m, what is its speed??
The speed of the sound traveling through the medium is 3590.4 m/s.
What is speed of sound?
The speed of sound is the distance traveled by a sound wave per unit time.A sound wave is a pressure disturbance that propagates through the medium through the interaction of particles. When one particle is perturbed, it exerts a force on the next adjacent particle, thus perturbing that particle from rest and transporting energy through the medium.
The speed of a sound wave can be calculated using the formula,
[tex]speed = frequency \times wavelength[/tex]
Where frequency is measured in Hertz and wavelength is measured in meters .
Putting in the given values,
speed = 520 x 6.92
So, speed = 3590.4 m/s
Therefore, the speed of the sound traveling through the medium is 3590.4 m/s.
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How do you solve a factor by step by step?
Therefore , the solution of the given problem of factor comes out to be
the factor can be solved by listed below steps.
What is a factor?A factor seems to be a variable that is multiplied by another to produce a result. A multiplication puzzle has a product as its answer. Consider an arithmetic problem as the process of multiplying the factors to obtain the product. For instance, the factors of 8 are 2 and 4: A number may have only two components or many other factors.
Here,
There are four main steps in the Solve via Factoring process:
1) Use addition or subtraction to transfer all terms around one part of the equation, typically the left.
2) Completely factor the equation.
3) Solve by setting each element to zero.
4) Identify each of the Step 3 answers as a solutions to the initial problem.
Therefore , the solution of the given problem of factor comes out to be
the factor can be solved by listed above steps.
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The sum of the measures of five exterior angles of a hexagon is 257°
. What is the measure of the sixth exterior angle?
Find x if QT is an angle bisector. Round to the nearest tenth.
18
S
T
32
21
X
R
Rounding to the nearest tenth: x = 7.6
What is an angle bisector?
An angle bisector is a line or segment that divides an angle into two congruent angles. It is called an angle bisector because it bisects, or cuts in half, the measure of the angle. An angle bisector can also divide the angle into two angles of different measures if the angle is not congruent.
In order to find x, we can use the Angle Bisector Theorem which states that the ratio of the length of the segment from the vertex of the angle bisector to the sides of the angle is equal to the ratio of the length of the other two segments formed by the angle bisector.
In this case, we know that QT is an angle bisector of angle X, so we can set up the following proportion:
(ST/x) = (TR/XT)
We are given that ST = 21, TR = 32 and XT = 18
Solving for x:
x = (21*18) / (32+18) = 378 / 50 = 7.56
Hence, Rounding to the nearest tenth: x = 7.6
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Why is geometry vocabulary important?
Geometry vocabulary assisted us in continuing to lay the groundwork for thinking critically, clearly, and profoundly. So even if you might not want to or even be able to recall the geometry vocabulary, it nonetheless had a role in your mental growth and helped you become the thoughtful adult you are today.
Who named geometry?The father of geometry, Euclid was a brilliant mathematician. Learn more about Euclid and the history of some of the math ideas we use today to see how important they have become.
The terms "ge" and "metria," which both imply "measuring," are the origins of geometry. For more than 2000 years, the Greeks' method of approaching geometry has served as the foundation for geometry.
The study of various mathematical or actual-world forms, figures, and sizes is known as Geometry. We learn about various angles, transformations, and similarities between the forms in geometry. The point, line, and plane are the main building blocks of geometry.
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Geometry vocabulary assisted us in continuing to lay the groundwork for thinking critically, clearly, and profoundly. So even if you might not want to or even be able to recall the geometry vocabulary, it nonetheless had a role in your mental growth and helped you become the thoughtful adult you are today.
What is the role of vocabulary development in mathematics?Understanding vocabulary has a significant role in general comprehension in many subject areas, including mathematics. There are several, tried-and-true techniques for teaching vocabulary across all subject areas. The growth of mathematical competency depends on the teaching and learning of the mathematical language.
Our continued development of the foundations required to think critically, clearly, and thoroughly was made possible by our language in geometry. Therefore, even if you might not want to or even be able to recall your geometry vocabulary, it nevertheless had a role in your mental growth and helped you become the thoughtful adult you are today.
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Lin has a summer reading assignment. After reading the first 30 pages of the book, she plans to read 40 pages each day until she finishes. Lin makes the graph shown here to track how many total pages she'll read over the next few days.
After day 1, Lin reaches page 70, which matches the point (1,70) She made it on her graph. After day 4, Lin reaches page 190, which does not match the point (4,160) She made it on her graph. Lin is not sure what went wrong since she knows she followed her reading plan.
Sketch a line showing Lin's original plan on the axes.Click on the graph and select edit to complete the graph. Once done, hit save and close to see your completed graph.
What does the vertical intercept mean in this situation? How do the vertical intercepts of the two lines compare?
What does the slope mean in this situation? How do the slopes of the two lines compare?
1. The graph of Lin mistake is shown below.
2. The Vertical intercept of Lin graph is less than the correct graph.
3. The slope of Lin graph (m= 30) is less than Correct graph (m=40).
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
1. Lin started with reading 30 pages.
Then, after 1sr day she will read the 40 pages per day.
So, if number of days represented by x- coordinates and number pages pages by y- coordinate we get
On first day (0. 30)
On second day (1, 30+40)= 91. 70)
On third day (2, 70+40)= (2, 110)
On fourth day (3, 110+40) = (3, 150)
and, On fifth day (4, 150+40)= (4, 190)
Hence, Line made mistake as after 4 days he completed 190 pages.
2. The Vertical intercept of Lin graph is less than the correct graph.
3. The slope of Lin graph (m= 30) is less than Correct graph (m=40).
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