Answers
A coordinate that is a solution to the first equation but not a solution to the system of equations is (3, 1.5).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
a) Given that, the graph shows the equations y= - 1/2x+3 ------(i) and y=2x-2 ------(ii).
From the graph, the solution is (2, 2)
b) Put x=1 in equation (i), we get
y= -1/2(1)+3
y= 2.5
Put x=2 in equation (i), we get
y= -1/2(2)+3
y= 2
Put x=3 in equation (i), we get
y= -1/2(2)+3
y= -1/2 (3)+3
y= -1.5+3
y= 1.5
So, a coordinate that is a solution to the first equation is (3, 1.5)
Therefore, a coordinate that is a solution to the first equation but not a solution to the system of equations is (3, 1.5).
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Related Questions
Write a paragraph summarizing how Chandragupta Maurya built and ruled the Mauryan Empire. Use these words or phrases in your summary: kingdoms, conquer, unite, force, central government.
Answers
The Maurya Empire was founded in 322 B.C. by Chandragupta Maurya, after overthrowing Dhana, the king of the Nanda dynasty. Chandragupta initiated battles to defeat and conquer the kingdoms left by Alexander the Great and gained additional lands west of the Indus River by force. He enlarged his power westward across central and western India, and by 320 B.C., the empire had fully occupied Northwestern India. Chandragupta Maurya became the first emperor to unite India into one state, under a central government.
Who is Chandragupta Maurya?Chandragupta Maurya was the creator of the Maurya Empire in ancient India. He established one of the largest empires on the Indian subcontinent.
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if the positive numbers from 1 to 116, inclusive, are written on a piece of paper, then the sum of all of the numbers that are written on the paper is
Answers
The sum of all the positive numbers from 1 to 116, inclusive, is 6350.
The sum of the first n positive integers can be found using the formula n(n+1)/2. In this case, n=116, so the sum of all the positive numbers from 1 to 116, inclusive, is 116 * 117 / 2 = 6350. This formula can be useful in a variety of mathematical and real-world applications, such as finding the total number of objects in a sequence or the total distance traveled by an object moving at a constant speed.
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El largo de un terreno rectangular es 10 cm más que cuatro veces su
ancho. El perímetro es 70 cm. Halla las dimensiones.
Answers
multiplicativa, x=5 is Halla las dimensiones.
Describe the dimension formula with an example.The physical quantity is correctly described in terms of its fundamental unit according to the formulation of the dimensional formula. For instance, the formula for dimensional force is F=[MLT2]. It's because the unit of force is the Newton, or kg/s2.
Finding the required dimensiones:De acuerdo con las condiciones dadamultiplicativa s, plantear: 2x(10+x+4x) = 70 Aplicar la ley multiplicativa de distribución: 20+2+8x= 70
Reordenar los términos desconocidos al lado izquierdo de la ecuación: 2x+8x= 70-20
Combinar como términos: 10x = 70-20
Calcular la suma o diferencia: 10x = 50
Dividir ambos lados de la ecuación por el coeficiente de la variable: = 50 10
Calcular los dos primeros términos: a = 5
Therefore, Halla las dimensiones is x=5.
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Higher Order Thinking Write a word problem involving addition of two mixed
numbers with unlike denominators where the answer is 12 1/10
Answers
The word problem would be "John has two pieces of rope. The first piece is 9 feet long and the second piece is 7 and 4/5 feet long. How long is the combined length of the two pieces of rope in feet and inches? ".
What is the word problem?
A word problem in mathematics is a problem that is described in words, rather than with mathematical symbols and equations. It presents a real-life situation and asks the reader to use mathematical concepts and skills to find a solution.
John has two pieces of rope. The first piece is 9 feet long and the second piece is 7 and 4/5 feet long. How long is the combined length of the two pieces of rope in feet and inches? The answer is 12 1/10 feet.
Hence, the word problem would be "John has two pieces of rope. The first piece is 9 feet long and the second piece is 7 and 4/5 feet long. How long is the combined length of the two pieces of rope in feet and inches? ".
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the heights of a group of students, in centimeters, are 158, 162, 172,.157, 161.com. A) caculate the mean heaight . B) another student joins the group. his height is 169cm. calculate the new mean height?
Answers
Step-by-step explanation:
So basically To find the mean you have to add all the numbers and divide by how many numbers you have, but to do that you have to make sure the numbers are lined up correctly so
157,158,161,162,172 ( Correct Order ) Smallest to biggest now add these up
157 + 158 + 161 + 162 + 172 = 810 / 5 = 162
The mean height is 162 cm
The new mean height
Again we're going to do the same thing
157 + 158 + 161 + 162 + 169 + 172 = 979/6 = 163.16666 = 163 cm
Hence the first mean height is 162 cm and the new mean height is 162 cm
If you want to solve the equation by completing the square, then rearrange the equation as x2−6x=11
and add 9 to each side.
If you want to solve the equation by using the quadratic formula, rearrange the equation as x2−6x−11=0
and substitute the values of 1, −6
, and −11
into the formula
Round to the nearest hundredth.
Answers
3±2√5 is the solution of the equation x²−6x=11
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given equation is s x²−6x=11
By completing the square, then rearrange the equation as x²−6x=11
add 9 to each side.
To find the solution of equation by quadratic formula, substitute 11 on both sides
x²−6x-11=0
a=1, b=-6 and c=-11
x=-b±√b²-4ac/2a
=6±√36+44/2
=6±√80/2
=3±2√5
Hence, 3±2√5 is the solution of the solution of the equation x²−6x=11
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Which equation correctly represents the situation: A campground charges $5 plus $ 25 per person for rent. Use x and y for the unknown variables.
Answers
Answer:
25x+5y
Step-by-step explanation:
Write an equation that represents the graph
Answers
?+6=2+7 what is the missing number
Answers
Answer:
3
Step-by-step explanation:
Answer:x=3 I hope this helps pls mark brainlist and give some love to the other person that answered
Step-by-step explanation:
x+6=2+7 I put a x where the missing number is
Add the number
X+6=9
Move the constant to the right-hand side and change its sign
X=9-6
Subtract the numbers
You will get your answer 3
X=3
(c) Given that
f(x)=e^{-3x}-4.
g(x)=ln(\frac{1}{x+2}),
TER
x>-2
(i) state the range of f
(ii) find f(x),
(iii) express fg(x) as a polynomial in r.
Answers
The range of function f(x) is Range: (-4,∞), {y|y>-4}.
What is range of a function?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
The given functions are f(x)=e⁻³ˣ -4, x∈R
g(x)=ln(1/x+2), x>-2
(i)
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (-∞,∞), {x|x∈R}
Range: (-4,∞), {y|y>-4}
(ii)
To find the inverse, interchange the variables and solve for y.
f⁻¹(x)=-ln(x+4)/3
(iii) Here, fg(x) is
Replace x by ln(1/x+2) in f(x), we get[tex]fg(x)=e^{-3(ln(\frac{1}{x+2} ))}-4[/tex]
Therefore, the range of function f(x) is Range: (-4,∞), {y|y>-4}.
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Convert the angle 3 radians to degrees, rounding to the nearest 10th.
Answers
Answer: 172.0 degrees
Step-by-step explanation:
In 180 degrees, there are [tex]\pi[/tex] radians. That means each radian is equal to:
[tex]\frac{180}{\pi }[/tex]
= 57.3248408
Then we simply multiply that by 3 to get:
3 * 57.3248408
= 171.974522
Rounded to the nearest tenth is 172.0
Answer:
172
Step-by-step explanation
180 degrees is equal to one pi.
That means each radian is equal to:= 57.3248408
Then multiply that number by 3
Written out is: 3 x 57.3248408 = 171.97452
When rounded to the nearest tenth is 172.0
Cans of soft drinks cost $0.30 in a certain vending machine. What is the expected value and variance of daily revenue (Y) from the machine, if X, the number of cans sold per day has E(X) = 125, and Var(X) = 50?
(a) E(Y) = 37.5, Var(Y) = 50
(b) E(Y) = 37.5, Var(Y) = 4.5
(c) E(Y) = 37.5, Var(Y) = 15
(d) E(Y) = 37.5, Var(Y) = 30
(e) E(Y) = 125, Var(Y) = 4.5
Answers
The correct option is (b) as the expected value and variance of daily revenue are 37.5 and 4.5 respectively.
What is meant by variance?
Consider the expected value to be the average value. The expected value of X when it is a discrete random variable is the exact mean of the relevant data.
The difference between the actual numbers and the average should be viewed as the variance. A greater range of values is indicated by a higher variance. A spread of measure for a random variable distribution that quantifies how much a random variable's values deviate from its expected value is called variance. Frequently, V(X) is used to represent the variance of random variable X.
Given,
Cost of soft drink c = $0.30
Expected value of the number of cans sold per day E(X) = 125
Variance of number of cans sold per day V(X) = 50
So,
Expected value of daily revenue E(Y) = c * E(X) = 0.3 * 125 = 37.5
Variance of daily revenue V(Y) = c² * V(X) = 0.3² * 50 = 4.5
Therefore the expected value and variance of daily revenue are 37.5 and 4.5 respectively. The correct option is (b).
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1. A soft-drink manufacturer can produce 1000 case of soda in a week at a total cost of GHC6,000, and 1,500 cases of soda at a cost of GHe8,500. Fid the manufacturer's weekly fixed costs and marginal cost per case of soda.
Answers
Total Cost = Fixed Cost + Variable Cost
Variable Cost = Marginal Cost * Quantity
At 1000 cases of soda, the variable cost is GHC6,000, and the total cost is GHC6,000. So the fixed cost at this quantity can be found as:
Fixed Cost = Total Cost - Variable Cost
Fixed Cost = GHC6,000 - (1000 * GHC6/1000) = GHC6,000 - GHC6 = GHC0
This means the manufacturer has no fixed costs at this quantity of 1000 cases.
Next, we can find the marginal cost per case of soda by calculating the change in the variable cost as the quantity changes from 1000 to 1500 cases.
Variable Cost = Total Cost - Fixed Cost
Variable Cost = GHC8,500 - GHC0 = GHC8,500
Marginal Cost = (Variable Cost at 1500 cases - Variable Cost at 1000 cases) / (1500 - 1000)
Marginal Cost = (GHC8,500 - GHC6,000) / 500 = (GHC2,500) / 500 = GHC5
So the manufacturer's marginal cost per case of soda is GHC5.
Note: The fixed cost is assumed to be zero because the information provided does not specify any fixed costs. This may not necessarily be the case in a real-world scenario.
If I took 420 minutes a day in school (that would be 7 hours a day in school), and there is 4 weeks in a month, and all together we spend time in 10 months in school, if 1 hours is 60 minutes, then how much minutes and days to we spend in school.
Answers
The number of minutes attends school in 10 month is 100800 minutes.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, I took 420 minutes a day in school (that would be 7 hours a day in school).
There is 4 weeks in a month, if each week they attend 6 days school
Then, number of minutes attends school in a week is
420×6
= 2520 minutes
The number of minutes attends school in a month is
2520×4 =10080 minutes
The number of minutes attends school in 10 month is
10080×10 =100800 minutes
Therefore, the number of minutes attends school in 10 month is 100800 minutes.
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Choose the lotion brand with lowest price per ounce. (2 points)
Brand A: 24 ounces for $2.25
Brand B: 40 ounces for $3.75
Both brands have the same price per ounce.
Not enough information is given.
Brand B
Brand A
Answers
Answer: Brand A: 24 ounces for $2.25
Brand B: 40 ounces for $3.75
Price per ounce for Brand A = $2.25 / 24 ounces = $0.09375
Price per ounce for Brand B = $3.75 / 40 ounces = $0.09375
Both brands have the same price per ounce.
Step-by-step explanation:
Ariana Garnde is coming to north gulfport middle school for fundraising concer! nevaeh is selling this week, she sold 3 kids and 9 adult tickets for a total of $75. Last week, she sold 8 kids tickets and 6 adult tickets for $67. how much was each adult ticket, and how much was each kids tickets, i need graph solution, subtituion and elimination.
Answers
There are seven kids tickets and 4 adult tickets.
What is simultaneous equation?
We know that we have to solve the simultaneous equation here;
Let cost of one kids ticket be x and the cost of one adult ticket be y
3x + 9y = 75 ---- (1)
8x + 6y = 67 ----- (2)
We then have that multiplying (1) by 8 and (2) by 3
24x + 72 y = 600 ---- (3)
24x + 18 y = 201 --- (4)
Subtract (4) from (3)
54 y = 399
y = 7
Then;
3x + 9(7) = 75
x = 4
We are going to end up having that there are seven kids tickets and 4 adult tickets.
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If I took 420 minutes a day in school (that would be 7 hours a day in school), and there is 4 weeks in a month, and all together we spend time in 10 months in school, if 1 hours is 60 minutes, then how much minutes and days to we spend in school.
Answers
Doing some changes of units we will see that you spend 84,000 minutes or 58.33 days in school.
How many minutes and days are spent in school?Here we need to do some changes of units.
First, we know that you spent 7 hours a day in school, and you go to school 5 days per week, so in a week you spend:
5*7 = 35 hours.
There are 4 weeks per month, so in a month you spent:
4*35= 140 hours.
And there are 10 months (where you go to school), then the total number of hours is:
140*10 = 1400 hours.
Now, we know that:
1 hour = 60 min
Then the total number in minutes is:
M = 1400*60min = 84,000 minutes.
And we know that:
1 day = 24 hours, then the total number in hours is:
H = 1400/24 days = 58.33 days.
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The US National Science Foundation collects data on the dollar amount for a grant given to a scientist in the Engineering field. A sample of this year’s grants is: (given in thousands of dollars)
22 5 26 23 27 50 100 70 90 25
Calculate and interpret the following statistics (show work to receive credit).
a. Median b. Q1 c. Q3 d. IQR e. Range
Answers
The statistics interpreted from the given data is:
a. Median = 26.5
b. Q1 = 22.5
c. Q3 = 60
d. IQR = 37.5
e. Range = 95
The given data sample of this year’s grants(given in thousands of dollars) in ascending order is :
5 22 23 25 26 27 50 70 90 100
The median of a data set is the middle value when the data is arranged in ascending or descending order. When number of values is even, there are two values in the middle, so we take the average of the two. So the median is
= (26 + 27)/ 2
= 26.5
The first quarter or the lower quartile (Q1), is the value under which 25%, that is first quarter of the data points are found when they are arranged in increasing order. Here Q1 is 0.25*10, that is 2.5th value, but its not possible. So we should interpolate
Q1 = 22.5
Similarly third quartile, Q3 is the value under which 75% of the data points are found when they are arranged in increasing order. So
Q3 = (70 + 50)/2
= 60
And inter quartile range (IQR)
= Q3 - Q1
= 60 - 22.5
= 37.5
Range is
= 100 - 5
= 95
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Suraj took a slice of pizza from the freezer and put it in the oven. The pizza was heated at a constant rate.
The table compares the pizza's temperature (in degrees Celsius) and the time since Suraj started heating it (in minutes).
Time (minutes) Temperature (degrees Celsius)
4
44
25
2525
6
66
40
4040
8
88
55
5555
How long did it take the pizza to reach
100
100100 degrees Celsius?
Answers
To reach a temperature of 100 degrees the pizza would take 750 minutes.
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
Since the pizza was heated at a constant rate, we can model the experiment as a line, where the slope represents how fast the pizza was heated.
The slope is given as:
m = (y2 - y1)/(x2 - x1)
Let
(x1,y1) = (6, 40)
(x2,y2) = (8, 55)
m = (55 - 40) / ( 8 - 6 )
m = 7.5 degrees per minute.
The pizza heats up an average of 7.50 degrees per minute
To reach a temperature of 100 degrees the pizza would take:
(100)(7.50) = 750 minutes.
Hence, to reach a temperature of 100 degrees the pizza would take:
(100)(7.50) = 750 minutes.
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There is a better look of it! Just answer this one- For each team, find the unit rate games per loss.
Answers
0.156 is the unit rate games per loss.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Plug in the values from the table to the above formula.
Slope is nothing but rate of change.
m=17-12/68-36
m=5/32
m=0.156
Hence, 0.156 is the unit rate games per loss.
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Find the area of the figure
Answers
Answer:
202.5 square yards.
Step-by-step explanation:
We know the whole square is 15 * 15 = 225
Now, we need to find the area of the triangles and subtract that.
We can predict that the sides are 3 and 7.5. Doing that we get the area of 11.25 for each.
225- (11.25*2)=202.5
nirav just opened a savings account paying 2 percent interest, compounded annually. after four years, the savings account will be worth $5,000. assume there are no additional deposits or withdrawals. given this information, nirav: a. will earn simple interest on his savingg every year for four yearsb. has an account currently valued at $5,000c. could have deposited less moneytoday and still had $5.000 in four years if the account paid a higher rate of interestd. could earn more interest on this account if the interest earnings were withdrawn anuallye. will earn the same amount of interest each year for four years
Answers
Answer:
c. could have deposited less money today and still had $5,000 in four years if the account paid a higher rate of interest
Step-by-step explanation:
Nirav just opened a savings account paying 2 percent interest, compounded annually. After four years, the savings account will be worth $5,000. Assume there are no additional deposits or withdrawals. Given this information, Nirav:
a. will earn simple interest on his saving every year for four years
False. Problem states it's compound interest.
b. has an account currently valued at $5,000
False. Problem states account will be worth $5,000 in 4 years.
c. could have deposited less money today and still had $5,000 in four years if the account paid a higher rate of interest
True. With a higher interest rate, he would earn more interest, so he could start with less money and still end up with $5000 at the end of 4 years.
d. could earn more interest on this account if the interest earnings were withdrawn annually
False. If he withdraws money periodically, there is less principal to earn interest on, so he will earn less interest overall.
e. will earn the same amount of interest each year for four years
False. Since compound interest earns interest on interest, all else being equal, compound interest earns more interest than simple interest.
Complete the steps for factoring 2x3 - 36x2 + 162x by writing words, numbers,
or expressions in the blanks.
2x336x2 + 162x =
(x²-18x+81)
=________ [x²-2(___)x+ ( )²]
(x-
_)(x-.
= 2 x (x-_9_²
Factor out
Rewrite the trinomial.
Use the
pattern.
Simplify.
Answers
Therefore , the solution of the given problem of expression comes out to be 2x[(x-9)²] is the simplified factor.
What is expression ?There is a need for mathematical variable operations such addition, multiplication, multiplication, and division. When combined, they produce the following: A mathematical operator, some data, and an equation A statement of fact is composed of values, parameters, plus operations like additions, subtractions, multiplications, and divisions. It is possible to contrast and compare various sentences and words.
Here,
Given :
=> 2x³ - 36x² + 162x
=> 2x(x²-18x+81)
=> 2x[ x² - 2 (9)x + (9)²]
=> 2x[(x-9)²]
Thus ,
factor comes out to be 2x[(x-9)²].
Therefore , the solution of the given problem of expression comes out to be 2x[(x-9)²] is the simplified factor.
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Peter wants to estimate the mean value rolled on a fair number cube. He has generated four samples containing five rolls of the number cube as shown in the table below. Which sample will result in the greatest mean?
Answers
The sample that have the greatest mean is sample {4, 5, 2, 4, 3, 6}
The correct option is D.
What is sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of potential experiment results. Depending on the experiment, a sample area could contain a variety of results.
Given:
Peter wants to estimate the mean value rolled on a fair number cube.
He has generated four samples containing five rolls of the number cube, as shown in the table below.
The mean of the data sample 1:
(1 + 4 + 5 + 2 + 4 + 3)/6 = 3.167
The mean of the data sample 2 = 3.83
The mean of the data sample 3 = 3.67
The mean of the data sample 4 = 24/6 = 4
Therefore, the mean of the data sample 4 has greatest mean.
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The complete question:
Peter wants to estimate the mean value rolled on a fair number cube. He has generated four samples containing five rolls of the number cube, as shown in the table below. Which sample will result in the greatest mean? Sample Data Sample 1 4 5 2 4 3 Sample 2 2 2 6 5 6 Sample 3 4 6 3 4 2 Sample 4 5 2 4 3 6
How to find angle in trapezoid given one angle.
Answers
The measure of angle, m<U as required to be determined is; 115°.
What is the measure of the angle U?It follows from the task content that the geometric figure STUV is a trapezoid.
On this note, it follows that; TU and SV are parallel lines; TU || SV.
Consequently, m<U + m<V = 180°.
where, m<V = 65°.
m<U = 180° - 65°
= 115°.
Consequently, the measure of m<U = 115°.
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what is the graph of the function rule? y = -3/4x+4
Answers
The graph of function y = - 3/4x + 4 is shown in figure.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The equation is,
⇒ y = - 3/4x + 4
Clearly, The equation shows the equation of line with slope (m) - 3/4 and y - intercept at point 4.
So, The graph of function y = - 3/4x + 4 is shown in figure with y - intercept at point 4.
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The cost of direct materials transferred into the Bottling Department of Mountain Springs Water Company is $27,225. The conversion cost for the period in the Bottling Department is $7,596. The total equivalent units for direct materials and conversion are 60,500 liters and 63,300 liters, respectively. Determine the direct materials and conversion cost per equivalent unit. Round your answers to the nearest cent.
Answers
Cost of direct materials per equivalent unit = $0.45.
Conversion cost per equivalent unit = $0.12.
What is FIFO method?The FIFO method is the First In First Out method. It is an accounting method used for cost flow assumption purposes in the cost of goods sold calculation.
In the Bottling Department,
The cost of direct materials transferred = $27,225.
The conversion cost = $7,596.
The total equivalent units for,
Direct materials = 60,500 liters.
conversion = 63,300 liters.
By using FIFO method,
The cost of Direct materials per equivalent unit = [tex]\frac{27,225}{60,500}[/tex]
=$0.45
Conversion cost per equivalent unit = [tex]\frac{7596}{63,300}[/tex]
= $0.12
Hence, the cost of direct materials and conversion cost per equivalent unit is $0.45 and $0.12 respectively.
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Use Figure 1 to evaluate the trigonometric function.
Answers
The values of the trigonometric functions for the angle theta in Figure 1 are:
sin (theta) = 0.6 ,cos (theta) = 0.8, tan (theta) = 0.75.
A right triangle with sides of 3, 4, and 5 units is shown in Figure 1. The definitions of sine, cosine, and tangent allow us to evaluate the trigonometric properties of the triangle's angles as follows:
Theta = opposite / adjacent = 3 / 4 = 0.75 Tan = opposite / adjacent = 3 / 5 = 0.6 Cos = adjacent / hypotenuse = 4 / 5 = 0.8
As a result, the trigonometric functions' values for the angle theta in Figure 1 are as follows:
Tan(theta) = 0.75, sin(theta) = 0.6, cos(theta), and 0.8.
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What is the sum of the first 45 terms of an arithmetic sequence if the sum of its 18 th and 28 th term is 36?
Answers
The simplest arithmetic progression satisfying the given condition is the constant progression with all 45 terms equal to 18. The sum of that progression is 45×18=810. If we assume there's enough information to deduce the answer, that must be it.
The reason the sum of the 18th
and 28th terms are enough to determine the sum is the symmetric placement of those two terms about the center of the progression.
The sum of 45 terms of the arithmetic progression whose sum of 18 th and 28 th terms is 36 is given by 810.
Let the first term of the arithmetic progression be A and the common difference for the same be D.
So 18th term of the progression is = A + (18 - 1) D = A + 17D
28th term of the progression is = A + (28 - 1) D = A + 27D
Given that the sum of the 18th and 18th terms of the progression is 36.
So, A + 17D + A + 27D = 36
2A + 44D = 26
So now the sum of 45 terms of the arithmetic progression is given by,
= 45/2 [2A + (45 - 1)D]
= 45/2 [2A + 44D]
= (45/2) * 36
= 45 * 18
= 810
Hence the sum of 45 terms of the arithmetic progression whose sum of 18 th and 28 th terms is 36 is given by 810.
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show that the additive inverse, or negative, of an even number is an even number using a direct proof.
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Let x be an even number. Then, x = 2k for some integer k. The negative of x, -x, is equal to -2k, which is also an even number. Thus, the additive inverse of an even number is an even number.
An even number is any number that can be divided by 2 without any remainder, meaning that it can be written in the form x = 2k for some integer k. The additive inverse, or negative, of an even number, x, is -x. By definition, this is equal to -2k. As -2k can still be divided by 2 without any remainder, it is also an even number.
This can also be understood by looking at the positive and negative sides of the number line. If x is an even number, then it is two units away from 0. Therefore, -x is also two units away from 0, which means it is an even number. This shows that the additive inverse of an even number is an even number.
To prove this, we can look at a specific example. Let x = 8. Then, 8 = 2x4. The negative of 8, -8, is equal to -2x4, which is still an even number. Thus, this proves that the additive inverse of an even number is an even number.
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