By answering the presented question, we may conclude that Therefore, equation the two numbers are either 3 and 4, or 4 and 3.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
the system of equations:
[tex]x + y = 7\\x * y = 12 \\y = 7 - x\\x * (7 - x) = 12\\7x - x^2 = 12\\x^2 - 7x + 12 = 0\\(x - 3)(x - 4) = 0\\If x = 3, then y = 4\\If x = 4, then y = 3\\[/tex]
Therefore, the two numbers are either 3 and 4, or 4 and 3.
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For the function f(x) = 2 (x − 1), find ƒ−¹(x).
Answer:
To find ƒ⁻¹(x), we need to solve for x in terms of ƒ⁻¹(x).
So, we start with the equation:
x = 2 (ƒ⁻¹(x) - 1)
We isolate ƒ⁻¹(x) by dividing both sides by 2 and adding 1 to both sides:
ƒ⁻¹(x) = (x/2) + 1
Therefore, the inverse of the given function f(x) is:
ƒ⁻¹(x) = (x/2) + 1
Use synthetic division to find the quotient and remainder when 0.9x^3 +0.8x is divided by x+0.7
The quotient is 0.9x² + 0.17x - 0.259, and the remainder is 0.181.
Describe Division?Synthetic division is a simplified method of dividing a polynomial by a linear factor of the form (x-a). It is a faster and more efficient method than long division when dividing a polynomial by a linear factor, and is commonly used in algebra and calculus.
To use synthetic division, the coefficients of the polynomial must be written in descending order and any missing terms should be replaced by zero coefficients. The divisor must be a linear factor of the form (x-a), where 'a' is a constant.
Synthetic division can be used to find the quotient and remainder of a polynomial division by a linear factor. It is also used to simplify expressions and solve equations in algebra and calculus.
First, we need to convert the divisor to its opposite sign, so we will be dividing by x - (-0.7) = x + 0.7
The coefficients of the dividend are 0.9, 0.8, 0, 0, so we will set up our synthetic division table as follows:
-0.7 | 0.9 0.8 0 0
| -0.63 -0.259 0.181
|____________________
0.9 0.17 -0.259 0.181
The quotient is 0.9x² + 0.17x - 0.259, and the remainder is 0.181.
Therefore, 0.9x³ + 0.8x = (x + 0.7)(0.9x² + 0.17x - 0.259) + 0.181.
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The quotient is 0.9x² + 0.17x - 0.259, and the remainder is 0.181.
Describe Division?A more straightforward way to divide a polynomial by a linear factor is by synthetic division. (x-a).
The polynomial's coefficients must be written in descending order and any missing terms should be substituted with zero coefficients in order to apply synthetic division. A linear factor of the type (x-a), where "a" is a constant, must be used as the divisor.
To determine the quotient and remainder of a polynomial division by a linear factor, utilise synthetic division. In algebra and calculus, it is also used to resolve equations and simplify statements.
We will divide by in order to first change the divisor to its opposite sign x - (-0.7) = x + 0.7
Since the dividend's coefficients are 0.9, 0.8, 0, 0, we will set up our artificial division table as follows:
-0.7 | 0.9 0.8 0 0
| -0.63 -0.259 0.181
|____________________
0.9 0.17 -0.259 0.181
The quotient is 0.9x² + 0.17x - 0.259, and the remainder is 0.181.
Therefore, 0.9x³ + 0.8x = (x + 0.7)(0.9x² + 0.17x - 0.259) + 0.181.
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23. 3 kg आलु र 2 kg प्याजको जम्मा मुल्य रु 240 आलुको दरमा 20% से वृद्धि र प्याजको दरमा 10% से कमी हुँदा 5kg आलु र 7 kg प्याजको जम्मा मुल्य रु 618 पर्न आउँछ भने 1 kg प्याजको मुल्य, 1 kg आलुको मुल्यभन्दा कति प्रतिशतले बढी वा कम हुन्छ ? पत्ता लगाउनुहोस् | The toptal cost of 3kg potato and 2 kg onion is Rs. 240. If the rate of potato increases by 20% and the rate of onion decreases by 10%, the total cost of 5 kg potato and 7 kg onion will be Rs. 618. By what percent the cost of 1 kg onion is more
Step-by-step explanation:
Here , the eqn is given as,
Let 1 kg onion cost Rs. y and 1kg potato cost Rs. y then,
3x + 2y= 240....eqn i
The When rate of potato increases by 20 percent,
New rate of unit kg potato becomes,
[tex]x \: + \: 20\% \: of \: x[/tex]
i.e. Rs.6x/5
And when price of onion decreases by 10% ,
New unit price is ,
[tex]y - 10\% \: of \: y[/tex]
i.e. Rs.9y/10
Now the second eqn becomes ,
20x + 21y= 2060
By using elimination method we get x= Rs 40 and y= Rs.60
Finally, we have to find percent change i.e
{(cost of 1kg onion - cost of 1kg potato)/ cost of 1kg potato}x 100%
This gives the ans as 50%
A blue balloon usually costs $0.34. Today it is on sale for $0.16. If Francesca buys a balloon today, how much will she save?
Answer:18 cents.
Step-by-step explanation: I did the math.
Hope this helps <3
She will save $0.18
To find the answer, you use the amount of what it usually costs and subtract the sale price to get the amount she saves.
$0.34 - $0.16 = $0.18
DIlate by a scale factor of 3
Dilation is a transformation that changes the size of an object while keeping its shape the same.
In this case, the scale factor of 3 tells us that the triangle will be three times larger than the original triangle.
To perform the dilation, you would take each vertex of the triangle and multiply the x-coordinate and y-coordinate by 3. For example, if one vertex of the original triangle had coordinates (x, y), the coordinates of that same vertex in the dilated triangle would be (3x, 3y).
It's also worth noting that the dilation is done with respect to a fixed point called the center of dilation. You can think of this point as the "pivot" around which the dilation occurs.
The center of dilation is typically represented by the letter "O".
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Help with math problems
The graph that shows the solution set of 7 ≤ n + 5 include the following: A. graph A.
What is an inequality?In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).In this exercise, we would determine the solution set by evaluating the given equation 7 ≤ n + 5 as follows;
7 ≤ n + 5
7 - 5 ≤ n + 5 - 5
2 ≤ n
n ≥ 2
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What scale factor was used to dilate point D? D(-1,-1)-D'(4,4)
Answer:
Step-by-step explanation:
scale factor is -4
D(-1 , -1) and if you divide either the x coordinate or the y coordinate by
4 - you get negative four which is the scale factor.
Please help me describe how to simplify this expression.
we have successfully simplified the expression x⁵-x³ into x³(x + 1)(x - 1). This can be useful for further algebraic manipulation or simplification in larger expressions.
How to simplify?
To simplify the expression x⁵-x³, we can factor it using the distributive property of multiplication. First, we can factor out x³ from both terms:
x⁵ - x³ = x³(x² - 1)
Now, we can further simplify by recognizing that x² - 1 is a difference of squares, which can be factored into (x + 1)(x - 1). So, we have:
x⁵ - x³ = x³(x² - 1) = x³(x + 1)(x - 1)
This is the fully simplified form of the expression. We can also expand the expression to verify that it is equivalent to the original expression:
x³(x + 1)(x - 1) = (x³ * x) + (x³ * -1) + (x³ * 1) + (x³ * -1) = x⁴ - x³ + x³ - x³ = x⁴ - x³
So, we have successfully simplified the expression x⁵-x³ into x³(x + 1)(x - 1). This can be useful for further algebraic manipulation or simplification in larger expressions.
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2
A tire is sold at a discount of 10%. It is sold for $45. Find the usual price of the tire.
Answer:
Step-by-step explanation:
50$ (Sorry for the mistake, it’s a little hard for me to give such assignments, if the translator would translate correctly, then there would be no mistake, sorry again)
Answer:
Step-by-step explanation:
A tire is sold at a discount of 10%. It is sold for $45. Find the usual price of the tire.
from the question you understand that $45 is 90% of the original price (100%-10%=90%), so we divide 45 by 90 and multiply by 100 and we find the original price
45 : 90 x 100 =
0.5 x 100 =
50$
----------------------------
50$ - 10% = 45
The money spent, M , purchasing burritos at a particular fast food restaurant varies directly with the number of burritos purchased, B . When 4 burritos are purchased, $18 is spent. How much money is spent if 20 burritos are purchased?
In a particular country, there are 11 200 registered female soccer players and 14 000 registered male soccer players.
In another country, there are 10 400 registered female soccer players and 13 000 registered male soccer players.
Is the ratio of female players to male players the same for both countries?
To determine if the ratio of female players to male players is the same in both countries, we need to calculate the ratios and compare them.
For the first country,
let female players be f1,male players be m1
the ratio of female players to male players is:f1:m1 (i.e f1/m1)
11,200 / 14,000 = 0.8
For the second country,
let female players be f2,male players be m2
the ratio of female players to male players is:f2:m2 (i.e f2/m2)
10,400 / 13,000 = 0.8
As we can see, both ratios are the same, which means that the ratio of female players to male players is the same in both countries. Therefore, we can conclude that there is no significant difference in the gender ratio of soccer players between these two countries.
Answer:
The female-to-male ratios for both countries are the same (0.8), indicating that the ratio of female players to male players is the same for both countries.
Explanation:
To determine whether the ratio of female players to male players is the same for both countries, we need to calculate the ratio of female players to male players for each country and compare them.
Country 1: Female-to-male ratio
= 11,200 / 14,000
= 0.8
Country 2: Female-to-male ratio
= 10,400 / 13,000
= 0.8
The radius of a circle is 1. What is the length of an arc that subtends an angle of
6radians?
Answer:
pi/6
Step-by-step explanation:
the full arc of the circle is the circumference = 2pi×r.
since r = 1, we get circumference = 2pi.
the full arc of 2pi is for 360° or 2pi radians (hence the definition).
an angle given in radians for the norm circle with radius = 1 IS therefore already the arc length for that angle.
for 2pi the arc length is 2pi.
for pi/6 the arc length is ... pi/6.
Giving out brainliest to the correct answer!
The nth derivative of g at x = 0 is given by g(n) (0) = (-1)n (n − 1)!
for n ≥ 1.
n+3
What is the coefficient for the term containing 4 in the Maclaurin series
of g?
Choose 1 answer:
1/28
6/7
1/7
3/28
Answer: 1/7
Step-by-step explanation:
d d x ( ∑ n = 0 ∞ c n ( x − a ) n ) = c 1 + 2 c 2 ( a − a ) + 3 c 3 ( a − a ) 2 + ⋯ = c 1/7
1. Julio Carson has a brick home with a replacement value of $100,000. It
is insured for 80% of the replacement value and is in an area that has been
designated fire protection class.
a. Find the amount
of the insurance.
b. Find the annual premium
a) The amount of the insurance or the sum assured by Julia Carson on his brick home is $80,000.
b) The annual premium is $5,148.00.
What is the sum assured?The sum assured represents the fixed amount that the insurance company pays to Julio Carson (the policyholder) if the unpredictable event, such as fire, occurs and damages his brick home.
The purpose of the payment is to reimburse Julio not for the costs incurred but according to the risks undertaken and it is a fixed sum of money unlike the sum insured, which reimburses to cover the costs incurred.
Replacement value of the brick home = $100,000
Sum insured = 80%
= $80,000 ($100,000 x 80%)
b) Annual premium:Monthly premium = $429
Number of insured years = 10 years
Annual premium = $5,148 ($429 x 12)
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I don’t understand please help ?
For the given functions f(x) and g(x), the inverse functions of f and g are:
a. f(g(x)) = x; g(f(x)) = x
ƒ and g are inverses of each other.
b. (g(x)) = x; g(f(x)) = x
ƒ and g are inverses of each other
What are the inverse functions of f and g?The inverse functions of the functions f(x) and g(x),are determined as follows;
a. f(x) = 2x, g(x) = x/2
f(g(x)) = f(x/2)
f(g(x)) = 2(x/2)
f(g(x)) = x
g(f(x)) = g(2x)
g(f(x)) = (2x)/2
g(f(x)) = x
Since f(g(x)) = g(f(x)) = x, ƒ and g are inverses of each other.
b. f(x) = 2x + 1, g(x) = (x -1)/2
f(g(x)) = f((x-1)/2)
f(g(x)) = 2((x-1)/2) + 1
f(g(x)) = x - 1 + 1
f(g(x)) = x
g(f(x)) = g(2x + 1)
g(f(x)) = ((2x + 1) - 1)/2
g(f(x)) = 2x/2
g(f(x)) = x
Since f(g(x)) = g(f(x)) = x, ƒ and g are inverses of each other.
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4. Find the circumference of a circle with a
radius of 4.4 inches. Express your answer in
terms of (Pi)
Step-by-step explanation:
All you would need to do is to use the circumference of a circle equation, C = 2pi(r) or C=pi(d). Since we are given the radius we will use C= 2pi(r).
C=2pi(4.4)
C=8.8pi inches
The function g is related to one of the parent functions
g(x) = −(x − 2)^3
a.) Identify the parent function f.
b.) Use function notation to write g in terms of f.
a. f(x) = x³
b. g(x) = -f(x-2)
Answer:
a) parent: f(x) = x³
b) g(x) = -f(x -2)
Step-by-step explanation:
You want the parent function and the given function written in terms of the parent function for g(x) = -(x -2)³.
a) Parent functionThe parent function is the function that remains after scale factors and translations are removed. In general, a transformed function will look like ...
g(x) = c·f((x-a)/b) +d
which scales the function f(x) horizontally by a factor of b, vertically by a factor of c, and translates the result by (a, d).
Here, we recognize that ...
g(x) = -(x -2)³
has c = -1, a = 2, b = 1, d = 0
and the parent function is ...
f(x) = x³
b) g in terms of fUsing the values for a, b, c, d that we recognized above, we have ...
g(x) = -f(x -2)
__
Additional comment
When scale factors are negative, they reflect the function over the relevant axis. Here, the negative vertical scale factor reflects the function vertically over the x-axis. The translation is 2 units to the right.
The volume of this cube is 64 cubic meters. What is the value of y?
y =
meters
Answer:
y = 4 meters
Step-by-step explanation:
to find a volume of a cube you do (y × y) y
so if Y equals 4 then it would look like this:
(4 × 4)4 which = 64
Suppose the weights of sumo wrestlers are normally distributed with a mean of 330lbs and a standard deviation of 15lbs. An up and coming competitor wants to defeat wrestlers whose weights are in the top 10%. What is the minimum weight of the sumo wrestlers at the highest weight of the league? Round your answer to the nearest whole number, if necessary.
I have to figure out how to use Excel's NORM.INV() function to solve this.
Answer: To use Excel's NORM.INV() function to solve this problem, we can follow these steps:
Determine the z-score corresponding to the top 10% of the distribution. We can use the NORM.INV() function to find this value. Since we want the top 10%, we'll use a probability of 0.9 and a mean of 330lbs and a standard deviation of 15lbs. In Excel, we can use the formula:
=NORM.INV(0.9,330,15,TRUE)
This gives us a z-score of 1.281552.
Once we have the z-score, we can use the formula for a normal distribution to find the corresponding weight. The formula is:
z = (x - μ) / σ
where z is the z-score, x is the weight we're trying to find, μ is the mean weight (330lbs), and σ is the standard deviation (15lbs).
Rearranging this formula to solve for x, we get:
x = z * σ + μ
Substituting in the values we know, we get:
x = 1.281552 * 15 + 330
This gives us a weight of approximately 349lbs.
Therefore, the minimum weight of the sumo wrestlers at the highest weight of the league is about 349lbs, rounded to the nearest whole number.
Step-by-step explanation:
given: MATH is a parallelogram
prove: MT bisects AH
Answer:
Step-by-step explanation:
In a parallelogram, opposite sides are parallel and equal.
MA // HT & AH is transversal.
∠MAG ≅ ∠GHT {Alternate interior angles are equal} --Angle
MA = HT {MATH is a parallelogram} ---> Side
MA // HT & MT is transversal.
∠AMG ≅ ∠HTG {Alternate interior angles area equal} ---->Angle
ΔMGA ≅ ΔTGH { Angle side angle congruent}
AG = HG {CPCT}
MT bisects AH
For function F(x)=-4x+8, evaluate and simplify the different quotient
Thus, the simplification of the given function using difference quotient formula is found as 4.
Explain about the difference quotient formula:The difference quotient is the product of the difference between the function values, f(x + h) - f(x), and indeed the difference between the input values, (x + h) - x, given a function f(x) and two input values, x as well as x + h (where h is indeed the distance between x and x + h).
For the given question:
function F(x) = -4x+8
difference quotient formula:
[f(x + h) -f(x)] / h
Put x = x + h
F(x+ h) = -4(x + h) + 8
F(x+h) = -4x -4h + 8
F(x) = -4x+8
Now,
[f(x + h) -f(x) ]/ h = [-4(x + h) + 8 + 4x - 8]/ h
On simplifying:
[f(x + h) -f(x) ]/ h = 4h/h = 4
Thus, the simplification of the given function using difference quotient formula is found as 4.
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An equilateral triangle is inscribed in a
circle with center O. The triangle is ther
rotated 30° to obtain another equilateral
triangle inscribed in the circle.
Jom kuivad
5. What is m/AOC? ala
120
6. Prove that the diameter through B is
perpendicular to the diameter through C.
Since the triangle was rotated by 30 degrees, the angle AOA' is 30 degrees, as is the angle A'OC. Thus, m/AOC is equal to 60 degrees. To demonstrate that BD is perpendicular to CD, OB = OC, angles AOB and COA are both 60 degrees, and angles BOD and COD are both 60 degrees. BD and CD are both perpendicular to the diameter through A.
What is an equilateral triangle?A triangle is said to be equilateral if all three of its sides are the same length and all three of its angles are exactly 60 degrees. It has three regular sides and is a polygon. When dividing an equilateral triangle into two congruent 30-60-90 triangles, the altitude, median, and angle bisector from any vertex are also the same line.
5. Let's identify the circle's intersection points as the equilateral triangle's A, B, and C. All angles in a triangle that is equilateral are 60 degrees. Point A will change locations when the triangle is rotated by 30 degrees; let's designate this new position A'. Since O is the centre of the circle, the angle AOC remains at 60 degrees. Since the triangle has been turned by 30 degrees, the angle AOA' is 30 degrees, as is the angle A'OC. Thus, m/AOC is equal to 60 degrees.
6. The center of the circle is O, and D is the point where the diameter through B intersects the diameter through C. To demonstrate that BD is perpendicular to CD, the center of the circle, OB = OC, and angles AOB and COA are both 60 degrees, so angle BOC is 120 degrees. Angle BOD is a right angle, and angle OBD is half of angle BOC, so it is 60 degrees. Angle COD is also a right angle, and angle OCD is half of angle BOC, so it is also 60 degrees. Since angles OBD and OCD are both 60 degrees, and they are angles in a triangle, the third angle (angle BDC) must also be 60 degrees.
Therefore, triangle BDC is equilateral, and BD = CD. Since BD and CD are both perpendicular to the diameter through A, BD is perpendicular to CD.
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Emilie has a drawer full of color for ribbons the probability of randomly selecting a green ribbon is 84% which of the following describes the likelihood of selecting a green ribbon
When the probability of an event is high, we can say that the likelihood of that event occurring is also high. Conversely, when the probability of an event is low, the likelihood of that event occurring is also low.
What is probability?
In mathematics, probability is a measure of the likelihood that an event will occur. It is a way of quantifying the uncertainty or randomness associated with an event or set of events. The probability of an event is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur. For example, the probability of flipping a fair coin and getting heads is 0.5, or 50%, since there are two equally likely outcomes (heads or tails) and getting heads is one of them. Probability theory is a fundamental branch of mathematics that has applications in many areas, including statistics, finance, engineering, and computer science, among others.
Here,
The likelihood of selecting a green ribbon from Emilie's drawer is high, since the probability of randomly selecting a green ribbon is 84%. This means that out of all the ribbons in the drawer, 84% of them are green.
Another way to interpret this is that if Emilie were to randomly select a ribbon from her drawer without looking, there is an 84% chance that the ribbon she selects will be green.
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Correct question is "Emilie has a drawer full of color for ribbons the probability of randomly selecting a green ribbon is 84% which describes the likelihood by the example of selecting a green ribbon".
In a group of 55 students 35 students like only subject out of english and science , the ratio of students who like both and who do not like both is 1:2. find students who like both subjects ?
Answer:
n(EnS)= 10
Step-by-step explanation:
n(U)= 55
n(EnS)= x
n"(EuS)"= 2x
n(EuS)= 35
We have,
n"(EuS)"= n(U) - n(EuS)
=55-35
=20
n(EnS) /n"(EuS)" = 1/2
x/20 = 1/2
2x=20
x=20/2
x=10
Therefore, n(EnS) = 10
What is 80% of Mr Kaisers class turned in their homework assignments there are 30 students in Mr kaisers class
Answer:
24 students turned in there homework assignments.
Step-by-step explanation:
80% = .8
30 x .8 = 24
70 adults with gum disease were asked the number of
times per week they used to floss before their
diagnoses. The (incomplete) results are shown below:
(frequency of 6, relative frequency of 4, and cumulative frequency of 5 are blank)
# of
times
floss
per
week
0
1
2
3
4
5
Frequency
6
7
4
11
15
11
6
7
Relative
Frequency
6
0.1571
0.2143
0.1571
0.0857
0.1
Cumulative
Frequency
0.1429
64
0.0857
70
a. Complete the table (Use 4 decimal places when
applicable)
4
15
30
41
47
b. What is the cumulative relative frequency for
flossing 3 times per week?
%
Answer:
a. To complete the table:
# of times floss per week Frequency Relative Frequency Cumulative Frequency
0 6 0.0857 6
1 7 0.1 13
2 4 0.0571 17
3 11 0.1571 28
4 15 0.2143 43
5 11 0.1571 54
6 6 0.0857 60
7 7 0.1 67
Step-by-step explanation:
b. To find the cumulative relative frequency for flossing 3 times per week, we need to add up the relative frequencies for all values of flossing less than or equal to 3.
Cumulative relative frequency for flossing 3 times per week:
= relative frequency for flossing 0 times per week + relative frequency for flossing 1 time per week + relative frequency for flossing 2 times per week + relative frequency for flossing 3 times per week
= 0.0857 + 0.1 + 0.0571 + 0.1571
= 0.4
Therefore, the cumulative relative frequency for flossing 3 times per week is 40%.
=
A rectangular parking lot has a length that is 4 yards
greater than the width. The area of the parking lot is 192
square yards. Find the length and the width.
Answer:
4√3
Step-by-step explanation:
length > width
If width = y
length =4y
Length × width = area
y × 4y = 192
4 y^2 = 192
y^2 = 48
y = 4 √3
25 Points!!!! ASAP
I want to go to the beach next week and I do not want to drive there."
Write the negation of this statement
triangle fun has vertices located at f(-2,-3), u (4,-2), and n (1,2), find the slope of UN. show your work
[tex]U(\stackrel{x_1}{4}~,~\stackrel{y_1}{-2})\qquad N(\stackrel{x_2}{1}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{2 +2}{-3} \implies \cfrac{ 4 }{ -3 } \implies - \cfrac{4 }{ 3 }[/tex]
Lines L and m are parallel. Lines L1 and L2 are transversals. What is m<1 if m<4 - 65? Justify your answer.
Answer:
Refers to the attachment given below!Step-by-step explanation: