With a plane containing 40 lines, no 2 of which are parallel , here are 43 points where exactly 2 lines intersect.
In a plane that contains 40 lines, we are asked to find the number of points where exactly 2 lines intersect. Let's call this number "x".
Since every line intersects exactly 2 points, the total number of line intersections is equal to 2x. In other words, if we add up the number of intersections at each point, the total number should equal 2x.
The problem states that there are 3 points where exactly 3 lines intersect, 4 points where exactly 4 lines intersect, 5 points where exactly 5 lines intersect, and 6 points where exactly 6 lines intersect. At the same time, it states that there are no points where more than 6 lines intersect.
To calculate the total number of intersections, we need to multiply the number of lines that intersect at each point by the number of points, and then add them up. In mathematical terms:
2x = 3 * 3 + 4 * 4 + 5 * 5 + 6 * 6
Expanding the right side of the equation:
2x = 9 + 16 + 25 + 36
= 86
Dividing both sides of the equation by 2:
x = 43
So there are 43 points where exactly 2 lines intersect.
This is because at each point where exactly 2 lines intersect, the number of intersections is equal to the number of lines. In total, these 43 points account for 86 line intersections, which is half of the total number of line intersections in the plane.
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A toy rocket is launched from a 5.6 m high platform in such a way that its height, h (in meters), after t seconds is given by the equation h= - 4.97t^2+ 38.5t + 5.6. How long will it take for the rocket to hit the ground?
The toy rocket will hit the ground after approximately 3.86 seconds.
Calculating time for toy rocket to reach groundThe rocket will hit the ground when its height is equal to zero, so we can use the equation h = -4.97t^2 + 38.5t + 5.6 to find the value of t that satisfies this condition. To do this, we set h equal to zero and solve for t:
0 = -4.97t^2 + 38.5t + 5.6
-5.6 = -4.97t^2 + 38.5t
4.97t^2 - 38.5t - 5.6 = 0
This is a quadratic equation and can be solved using the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Where a = 4.97, b = -38.5, and c = -5.6.
Plugging in these values, we get:
t = (-(-38.5) ± √((-38.5)^2 - 4 * 4.97 * -5.6)) / (2 * 4.97)
t = (38.5 ± √(1466.25 + 113.92)) / 9.94
t = (38.5 ± √1580.17) / 9.94
The square root of 1580.17 is 39.67, so:
t = (38.5 ± 39.67) / 9.94
t = (38.5 + 39.67) / 9.94 or (38.5 - 39.67) / 9.94
The first solution gives us a time of approximately 3.86 seconds, while the second solution is negative and therefore represents an unrealistic result.
The toy rocket will hit the ground after approximately 3.86 seconds.
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what is R30 into shillings?
Answer:
Step-by-step explanation:
The exchange rate between the South African Rand (ZAR) and the Kenyan Shilling (KES) fluctuates daily. As of my training data cut off in 2021, the exchange rate was approximately 1 ZAR = 10.87 KES.
So, 30 South African Rand would be equivalent to approximately 329.10 Kenyan Shillings. However, it is important to note that exchange rates can change over time, so it is always a good idea to check a reliable source for the most up-to-date conversion rate before making any currency exchanges.
A square and a rectangle have the same perimeter. The square has an area of 81 sq. inches and the rectangle has a width of 5 in. What is the area of the rectangle?
Answer:
Area of rectangle = [tex]\mbox{\large \boxed{\textrm{65 sq. inches}}}[/tex]
Step-by-step explanation:
Let square side = [tex]a[/tex]
Area of square [tex]A = a^2[/tex]
Given [tex]A = 81[/tex] and equating it to [tex]a^2[/tex]
[tex]a^2[/tex] [tex]= 81\;in^2[/tex]
[tex]a = \sqrt{81} = 9\;in[/tex]
Perimeter of square = [tex]4a = 4\cdot 9 = 36 \;in[/tex]
If [tex]l[/tex] = length of the rectangle and [tex]w[/tex] = width
Perimeter P of rectangle = [tex]2(l + w)\\[/tex]
Given perimeter of rectangle = perimeter of square we get
[tex]2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18[/tex]
Given
[tex]w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\[/tex]
[tex]\\\\\textrm{Area of rectangle } = l \times w\\\\= 13 \times 5 \\\\= 65 \;sq.\;inches[/tex]
Triangle ABC is a right triangle.
B
(X-10)
(2X+40)
Which equations can be used to find the value of x? Check all that apply.
X+90+(x-10)- 180
OX+90+(2x+40)-180
Save and Exit
Next
The expression to measure {x} can be written as -
{x - 10} + {2x +40} + 90 = 180
What is Pythagoras theorem?We can write the Pythagoras theorem as - The sum of the squares of the base and perpendicular is equal to the square of the hypotenuse.
Mathematically -
(hypotenuse)² = (base)² + (perpendicular)²
Given is a right triangle ABC
We an write the expression to measure {x} as -
{x - 10} + {2x +40} + 90 = 180
Therefore, the expression to measure {x} can be written as -
{x - 10} + {2x +40} + 90 = 180
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What is the r-value of the following data to three decimal places?
X. Y
4. 23
5. 12
8. 10
9. 9
13. 2
Note that the r-value of the above data is : -0.903 (Option A)
What is R-value?In mathematics, the r-value typically refers to the correlation coefficient, which measures the strength and direction of the linear relationship between two variables.
With regard to the above data:
A) Find the Sum of the X values: 4 +5+8+9+13 = 39
B) Find the Sum of the Y values: 23 +12 +10 +9 +2 = 56
C) Find the Sum of x^2: 4^2 + 5^2 + 8^2 + 9^2 +13^2 = 355
D) The sum of the Y^2's: 23^2 + 12^2 + 10^2 + 9^2 + 2^2 = 858
E) Sum of x *y's: 4*23 + 5*12 + 8*10 + 9*9 + 13*2 = 339
N = number of sets = 5
Numerator of r = (E - A*B/N) = 339-39*56/5 = 339 - 436.8 = -97.8
Denominator of r = SQRT(C-A^2/N) x SQRT(D-B^2/N) =
SQRT(355-39^2/5) x SQRT(858-56^2/5) =
SQRT(50.8) x SQRT(230.8) =
7.1274 x 15.1921 =
108.2803
r = -97.8 / 108.2803
r = -0.903
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The solution set of an equation of a circle is all of he points that lie on the circle.
A. True
B. False
1/2of 2/3 =1/2 of _ Third(s)= _third(s)
Answer: 1/2of 2/3 = 1/2 of 2 Third(s)= 1 third
peter sets up a neurological study in which he wants to investigate three pre-defined groups of patients. each group of patients is already diagnosed with the same neurological syndrome. peter not only examines the average score for each group of patients, but also the scores for each individual patient. peter's study is an example of...
Peter's study is an example of a cross-sectional clinical study that investigates three pre-defined groups of patients with the same neurological syndrome by examining both the average score for each group and the scores for individual patients.
Cross-sectional study that compares three groups of patients with the same neurological syndrome. In this type of study, the researcher examines the groups at a specific point in time to obtain information about the prevalence, incidence, and characteristics of the disease or condition being studied. By examining both the average score for each group and the scores for individual patients, Peter is able to draw conclusions about the relationship between the neurological syndrome and the factors being studied. This type of study can help to identify risk factors, determine the efficacy of treatments, and guide future research in the field.
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The graph below is a discrete function:
8
246
0 2
A True
B) False
f(x)
6
8 10
12
14
Answer: A.
Step-by-step explanation:
- f(x) = 4x, g(x) = 9x¹/2; x = 9
The value of the functions at 9m is
3627What is the value of the functions at x=9?Generally, In mathematics, a function is a rule that maps one set of values (the domain) to another set of values (the range). The values in the range are determined by applying the function to the values in the domain.
Functions can take many forms and be expressed in different ways, including:
Linear functions: a function that produces a straight line when graphed. It has the form f(x) = mx + b, where m is the slope of the line and b is the y-intercept.
Quadratic functions: a function that produces a parabola when graphed. It has the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
Therefore, this function
- f(x) = 4x
g(x) = 9x¹/2
for
F(x)=4x
F(9)=4*9
f(9)=36
for
g(x) = 9x¹/2
g(9)=9√9
=27
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1. a certain type of tomato seed germinates 43% of the time. a backyard farmer planted 10 seeds. what is the probability that 2 or fewer germinate?
The probability that 2 or fewer tomato seeds germinate out of 10 planted, given a germination rate of 43%, is 0.586 or 58.6%.
To calculate the probability that 2 or fewer seeds germinate, we need to use the binomial distribution, where:
n is the total number of trials (plantings)p is the probability of success (a seed germinating)x is the number of successes we want to calculate the probability forIn this case, n = 10, p = 0.43, and we want to find the probability that 0, 1, or 2 seeds germinate. We can calculate this probability as the sum of the probabilities of each of these outcomes:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
where X is the random variable representing the number of seeds that germinate.
Using the binomial distribution formula, we can calculate the probability of each outcome:
P(X = k) = (n choose k)[tex]* p^k * (1 - p)^{(n - k)}[/tex]
where (n choose k) is the binomial coefficient, equal to [tex]n! / (k! * (n - k)!)[/tex].
Plugging in the values, we get:
P(X = 0) = (10 choose 0) [tex]* 0.43^0 * 0.57^{10}[/tex] = 0.057
P(X = 1) = (10 choose 1) [tex]* 0.43^1 * 0.57^9[/tex] = 0.205
P(X = 2) = (10 choose 2) [tex]* 0.43^2 * 0.57^8[/tex] = 0.324
Therefore,
[tex]P(X \leq 2)[/tex] = [tex]0.057 + 0.205 + 0.324[/tex] = 0.586
So the probability that 2 or fewer seeds germinate is 0.586, or 58.6%.
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PLEASE HURRY!! Which of the following statements are true regarding the graph of this linear function? Select all that apply.
The slope of the line, 9.75, is the amount of money she makes per hour of work. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
The definition of amount?Extent, volume, and supply are all nouns. the sum of two or more amounts; the complete worth, impact, or importance of anything.
What is an example of a number?A number is a mass or accumulation, especially of something impossible to count: amount of The appropriate quantity of sand wasn't delivered. Animals were kept on a small amount of land. He donated money on a regular basis to a charity.
We know that slope =
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, slope m is
[tex]$m=\frac{53 -14}{8 -4 }[/tex]
[tex]$m=\frac{39}{4 }[/tex]
m = 9.75
And putting the value in y-intercept form we have
y = 9.75x – 25
Therefore, The slope of the line, 9.75, is the amount of money she makes per hour of work. The y-intercept of the line, -25, is the amount of money she starts with, since she owes her sister $25 and has worked 0 hours.
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you have a recipe that indicates to use 2 parts of milk for every 7 parts of flour. You use 8 cups of milk. How much flour do you need?
(Also complete the ratio table below pls)
Milk(cups) 2 , 4 _ , 8
Flour (cups) 7 , _ , 21 , _
Answer:
28 cups of Flower
Ratio Table:
2,4,6,8
7,14,21,28
Step-by-step explanation:
2x4/7x4=8/28
Multiply the polynomials. (2x+y)·(4x^2-2xy+y^2)
Answer:
Step-by-step explanation:
The answer is 4x^2y+8x^3+y^2-2xy
The diameter of each of the three circular lights in a traffic signal is 7 inches. In this activity, you will find the total area of the three lights.Part C What is the total area of all three circular lights?
Answer:
The area of a circle can be found using the formula A = πr^2, where r is the radius of the circle. If the diameter of each circular light is 7 inches, the radius would be half of that, or 3.5 inches.
Therefore, the area of one circular light would be:
A = π * 3.5^2 = 3.5^2 * π = 12.25 * π square inches.
Since there are three circular lights, the total area of all three would be:
3 * 12.25 * π = 36.75 * π square inches.
Step-by-step explanation:
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The figure shown has two parallel lines cut by a transversal:
A pair of parallel lines is shown, crossed by a transversal. Angles are identified as 1, 2, 3, 4, 5, 6, 7, and 8. Angles 1-4 are on the top line clockwise from upper left. Angles 5-8 are on the lower line clockwise from upper left.
Which angle is an alternate interior angle to ∠3?
∠5 is the alternate interior angle of ∠3.
What is transversal?
A transversal is a line that, at two different points in the geometry, cuts through two lines in the same plane. Various types of angles in pairs, including consecutive interior angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.
When a transversal intersects two parallel lines, the angles that are created inside are equal to the alternate pairs of that transversal. Alternate interior angles are what they are called.
Line m and line n are parallel and line l is transversal.
The alternate pairs of that transversal are ∠3 and ∠5.
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Miss carol spendmore is not good at budgeting her money. She initially haf $500 in the bank. She lent her friend $65 this month and she notices that her bank account is declining by $15 dollard per day. Determine the rate of cHange
Miss Carol's bank account is losing money at a daily rate of $15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.
We must calculate Miss Carol's account balance's daily decline in order to ascertain the rate of change in her bank account.
Since Miss Carol lent her friend $65 this month, her account balance is reduced by $65, leaving her with $500 - $65 = $435.
The information that her account is losing $15 every day can then be put to use. We can write this as:
Rate of change = -$15 per day
The negative symbol signifies a declining amount on her account.
Therefore, Miss Carol's bank account is losing money at a daily rate of
$15, After giving money to her friend, Miss Carol's account balance fell by $65 leaving her with $435.
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consider the function graphed below. What is the average rate of change of the function over the interval (2,3)?
The average rate of change of the function over the interval [2,3] will be around 3.
What is a function?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
For example to draw the equation y = 3x +2 this will draw a straight line in the coordinate geometry.
The rate of change is given by dy/dx
The average rate of change can be given as:
= (difference in y coordinate)/(difference in x coordinate)
= Δy/Δx
Average rate of change = ( 11 - 8 )/(3 - 2 )
= 3
Hence, the average rate of change is 3
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If f(x)=-2x+4 and g(x)=x^2-5x, find all values of x for which f(x)=g(x)
The values of x for which f(x) = g(x) are -1 and 4
How to determine the values of xFrom the question, we have the following parameters that can be used in our computation:
f(x) = -2x + 4
g(x) = x^2 - 5x
Using the above as a guide, we have the following:
Plot the graphs of f(x) and g(x) on the same planeWrite out the x coordinate of the intersectionUsing the above as a guide, we have the following:
x = -1 and x = 4
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Which one of the following best defines the notion of the significance level of a hypothesis test?
The probability of committing type 1 error best describes notion of significance level of hypothesis test.
What is probability?
Probability is a mathematical concept used to measure the likelihood or chance of an event occurring. It is expressed as number between 0 and 1, where 0 represents an impossible event, and 1 represents certain event. The probability of an event is calculated by dividing number of favorable outcomes by total number of possible outcomes. Probability is used in various fields, including statistics, economics, finance, and science. It is used to make predictions, assess risk, and make informed decisions. Probability theory helps to explain random phenomena, such as the outcomes of a coin toss or the probability of a disease occurring in a population.
Complete Question:
Which one of the following best describes the notion of the significance level of a hypothesis test?
i) the probability of committing a type 1 error
ii) the probability of committing a type 2 error
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An athletic track is given in the figure.
The two straight parts are 80 m long.
The total length of the track is 400 m.
Find the radius of the curved part of the track
on both sides.
Subtract the length of the two straight parts
from the entire length of the track.
SOMEONE HELLPPPP IM SCAREDDDDD
Answer: AE
Step-by-step explanation:
if you look at the picture you can tell that Ae is a ray because rates tend to have 2 points and 2 sides one going on forever. that's why there's an arrow near "a"
Find the equation of the line that passes through (1,3) and is perpendicular to
y=2x-1.
Leave your answer in the form ax+by=c
Where a, b and c are integers.
Answer:
Equation of perpendicular line:
[tex]\boxed{\quad y=-\dfrac{1}{2}x+\dfrac{7}{2}\quad }[/tex]
Step-by-step explanation:
Generalized lope-intercept form of a line is y = mx + b [1]
where
m = slope
b = y-intercept
Equation of the given line is y = 2x - 1 [2]
We are asked to find the equation of the line perpendicular to this and also passes through (1, 3)
Jack washes cars no monday he washed 18 cars for $90 on tusday he washed 9 cars for $45 on wadnesday he washed 12 cars for $60 what si the rate of change of jakes earnings
The rate of change of Jakes earning is, 0 or no change.
What is the rate?Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.
So formula for the rate is,
m = change in one quantity/change in another quantity = Δy/Δx
On Monday, Jake earned $90 by washing 18 cars.
Therefore, his earning rate was:
= $90 / 18 cars
= $5 per car
On Tuesday, Jake washed 9 cars and earned $45.
Therefore, his earning rate was:
= $45 / 9 cars
= $5 per car
On Wednesday, Jake washed 12 cars and earned $60.
Therefore, his earning rate was:
= $60 / 12 cars
= $5 per car
We can see that Jake's earning rate remained constant over the three days at $5 per car.
Therefore, the rate of change of Jake's earnings is 0, or no change.
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OnOff
Question
A composite figure is shown.
What is the total area of this figure?
164 sq. cm.
136 sq. cm.
216 sq. cm.
160 sq. cm.
Answer:
164 cm^2
Step-by-step explanation:
lets find square of triangle first
corner ABD is 90 degrees coz corner ABC is 180 degrees and EBC is 90
(sum of all angles of a quadrilateral is 360,
B = 360 - C - F - E
360 - 90 - 90 - 90 = 90)
BD = CF - DE
BD = 16 - 8 = 8 cm
S ABD = AB * BD / 2 (coz corner B is 90 degrees)
S ABD = 13 * 8 / 2 = 13 * 4 = 52 cm^2
lets find square of BEFC next
S BEFC = CF * EF ( B = C = F = E = 90 so thats a rectangle)
S BEFC = 16 * 7 = 70 + 42 = 112 cm^2
finally lets find total area
S = S ABD + S BEFC = 52 + 112 = 164 cm^2
34.2 million americans, or 10.5% of the population, had diabetes in the year 2018. a simple random sample of size 100 is chosen from the population to study this disease. let be the total number of people in our sample that have diabetes. what is the distribution of ?
The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution, with a probability of success of 10.5%.
The binomial distribution has certain properties, such as the mean and variance, that can be used to make inferences about the population. For example, the mean of the distribution is given by:
μ = np
where n is the sample size and p is the probability of success.
The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution. The binomial distribution describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
In our case, a success is a person with diabetes, and the probability of success is the prevalence of diabetes in the population, which is 10.5%. The number of trials is 100, which is the sample size. Therefore, the distribution of the number of people with diabetes in our sample can be written as:
X ~ B(100, 0.105)
Where X is the random variable representing the number of people with diabetes in our sample, and B(100, 0.105) denotes the binomial distribution with 100 trials and a probability of success of 0.105.
In our case, the mean number of people with diabetes in our sample is:
μ = 100 x 0.105 = 10.5
This means that we expect, on average, to find 10.5 people with diabetes in our sample of 100.
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Klaus is cycling at a speed of -8 miles per hour. If he starts at the same position as Rachel (zero) , what will his position be after 60 minutes?
Klaus will be ____ miles be hind where he started, and ___ miles away from Rachel.
Klaus wil be behind where he started with a distance of 8miles
What is distance?Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
Distance can also be defined as the space or gap between two points.
Velocity = distance/time
distance = velocity × time
time = 60minutes = 1hr
therefore the distance made by Klaus in 60 minutes =
= 8 ×1
= 8miles
therefore within 60 minutes Klaus will cover a distance of 8miles from where he started.
Klaus and Rachel will be at same position with the same speed
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A geolo
gistis going to ship two granite specimen weighs 22 pounds and the crate weighs 20pounds the shipping crate weighs 8pounds the shipping crate is what percentage of the total weight of the shipment
The percentage of the shipping crate when compared to the total weight of the shipment would be = 16%
How to calculate the percentage of shipping crate?The weight of two granite specimen = 22 pounds
The weight of the crate = 20 pounds
The weight of shipping crate = 8 pounds
The total weight of the whole shipment = 22+20+8 = 50 pounds.
Therefore the percentage of shipping crate as compared to the total weight;
= 8/50 × 100/1
= 800/50
= 16%
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MODELING REAL LIFE Scientists rope off two excavation sites. Site A is rectangular with a length of $60$ meters and a width of $40$ meters. Site B is similar in shape to Site A but has a length of $45$ meters. How much rope is needed for both sites?
m=
By using unitary methods, the amount of rope is needed for both sites is 350 meters.
Unitary method is a mathematical problem-solving technique that involves finding the value of one unit and using it to calculate the value of other units.
Let's start by looking at Site A, which is a rectangular area with a length of 60 meters and a width of 40 meters. To surround this area with rope, we need to measure the perimeter, which is the distance around the site.
=> Perimeter = 2 (length + width)
=> 2(60 + 40)
=> 2 x 100
=> 200 meters
Therefore, we need 200 meters of rope to surround Site A.
Now let's move on to Site B, which is also rectangular but has a length of 45 meters. To find the width of Site B, we can use the fact that it is similar in shape to Site A. Similar shapes have the same angles and proportional sides, so we can use a unitary method to find the missing dimension.
The length ratio of Site B to Site A is
=> 45/60 = 3/4
Since the shapes are similar, the width of Site B must also be 3/4 of the width of Site A.
Width of Site B = 3/4 x 40 = 30 meters
Now we can use the same formula as before to find the perimeter of Site B:
Perimeter = 2 (length + width)
=> 2(45 + 30)
=> 2 x 75
=> 150 meters
Therefore, we need 150 meters of rope to surround Site B.
To find the total amount of rope needed for both sites, we simply add the two perimeters:
Total rope needed = 200 + 150 = 350 meters
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The sum of two numbers is 14. Four less than twice the smaller number is equal to the larger number x. Find the larger number.
The Larger number is 8
What is a linear equation in one variable?
The fundamental equation used to represent and solve for an unknown quantity is a linear equation in one variable. It is always a straight line, and it is simply shown graphically. A mathematical statement is simply represented by a linear equation.
Given that, the sum of two numbers is 14 and the larger number is four less than twice the smaller number
let the larger number be 'a' and the smaller be 'b'
from the question,
a + b = 14 .....eq 1
a = 2b - 4 .....eq 2
By substituting eq 2 in eq 1:
2b - 4 + b = 14
3b - 4 = 14
3b = 14 + 4 = 18
b = 6
a = 2b - 4 = 2*6 - 4 = 8
Therefore, The two numbers are 8, 4
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