Step-by-step explanation:
THE POINT OF INTERSECTION IS WHERE F(x) = G(x)
[tex](x + 3)(x - 1) = (x + 1)(x - 3) \\ {x}^{2} + 2x - 3 = {x}^{2} - 2x - 3 \\ \\ {x}^{2} - {x}^{2} + 2x + 2x - 3 + 3 = 0 \\ 4x = 0 \\ \frac{4x}{4} = \frac{0}{4} \\ x = 0[/tex]
find the y coordinate by plugging in the value of c in any of the function.You will get thw same value
[tex]g(0) = (0 + 1)(0 - 3) \\ g(0) = 1( - 3) \\ g(0) = y = - 3[/tex]
The point of intersection is (0,-3)
Captain Ashley has a ship, the H.M.S Crimson Lynx. The ship is two furlongs from the dread pirate Umaima and her merciless band of thieves.
If her ship hasn't already been hit, Captain Ashley has probability 1/2 of hitting the pirate ship. If her ship has been hit, Captain Ashley will always miss.
If her ship hasn't already been hit, dread pirate Umaima has probability 1/3 of hitting the Captain's ship. If her ship has been hit, dread pirate Umaima will always miss.
If the Captain and the pirate each shoot once, and the pirate shoots first, what is the probability that both the pirate and the Captain hit each other's ships?
The probability would be zero that both the pirate and the captain hit each other's ships.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Captain Ashley has probability 1/2 of hitting the pirate ship.
Dread pirate Umaima has a 1/3 probability of attacking the Captain's ship if it hasn't already.
The captain must miss if the pirate hits, and the requirement that both hits are not satisfied. The requirement that both hits cannot be satisfied if the pirate misses.
Therefore, the probability would be zero that both the pirate and the Captain hit each other's ships.
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A ramp with a constant incline is made to connect to a driveway to a front door. At a point 4 feet from the driveway, the height of the ramp is 12 inches. At a point 6 feet from the driveway, the height of the ramp is 18 inches. What is the rate of change of the ramp’s incline?
The rate of change/slope of the ramp’s incline is found to be 3.
What is meant by rate of change or slope?A line's slope is defined as the change in y coordinate in relation to a change in x coordinate.
The net change in y coordinates is Δy, while it is x in Δx coordinates.As a result, the y coordinate shift in relation to the x coordinate shift could be written as,m = Δy/Δx
where, m is the slope
And, tan θ = Δy/Δx
Such an tan θ is also known as the line's slope.
The slope of a line could be determined by calculating using only two straight line points. The slope of line formula could then be used with two point coordinates.
Now, in response to the question;
To link a driveway to a front door, a ramp with a constant incline is built.
The ramp's height y₁ is 12 inches at a point 4 feet from of the driveway x₁.
The height y₂ of the ramp is 18 inches at a point 6 feet from of the driveway x₂.
The incline of the ramp's rate of change is given by:
Slope = m = tan θ = (y₂ - y₁)/(x₂ - x₁)
The values given in the question;
(x₁, y₁) = (4, 12) and,
(x₂, y₂) = (6, 18)
Put the values in the formula of the slope;
Slope = m = (18 - 12)/(6 - 4)
m = 6/2
m = 3
Therefore the rate of change also called as ramp’s incline is calculated as 3.
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please answer with a explanation
Answer: 10
Step-by-step explanation:
Distance formula = (x2-x1)^2 + (y2-y1)^2
In this circumstance, we have (0,0) and (6,8) as our two points.
(6-0)^2 + (8-0)^2
(6^2) + (8^2)
36 + 64 = 100
Square root the 100.
SQRT of 100 is 10 (perfect square) so your answer is, again, 10.
I hope I managed to help.
Number 6 please help!
Answer:
118 .........................
The coordinates of A and B are-7 and 9. The coordinates of C and D are -4 and 12. Are AB and CD congruent? If yes, what is the length of
each segment?
Ο A) No
OB) yes; -16
OC) yes; 8
OD) yes; 16
The coordinates of A and B are-7 and 9. The coordinates of C and D are -4 and 12. AB and CD are not congruent
What does it men to be congruent?
Congruent refers to objects that are precisely similar in size and shape. The forms stay equal no matter how they are rotated, flipped, or turned. For instance, create two circles with the same radius, cut them out, and stack them.
We'll see that they'll be placed entirely on top of one another and will superimpose one another. This demonstrates that the two circles are similar. Given that they have an equal radius and can be positioned exactly over one another, the circles below are considered to be congruent. "≅" is the sign used to represent the congruence of figures. Since circle A and circle B are similar, we may say the following: Circle B ≅ Circle A.
Lets assume AB and CD are congruent
Then according to Pythagoras theorem
Hypotenuse of AB of right-angled triangle AOB is equal to Hypotenuse of CD of right-angled triangle COD
Hypotenuse AB = Hypotenuse CD
Hypotenuse AB
a² + b² = c²
(-7)² + 9² = c²
49 + 81 = c²
130 = c²
Hypotenuse CD
a² + b² = c²
(-4)² + 12² = c²
16 + 144 = c²
160 = c²
Here, 130 ≠ 160
So, The coordinates of A and B are-7 and 9. The coordinates of C and D are -4 and 12. AB and CD are not congruent
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can anybody help me ?
Answer:
Step-by-step explanation:
A and C
Figure 1 is a triangle with vertices at (18, 6), (12, 15), and (3, 9). It
is dilated twice, using the origin as center both times: once with
a scale factor of 4, and once with a scale factor of 2/3. What are the locations of the vertices of the dilated figures?
The locations of the vertices of the dilated figures are (48,16), (32,40), and (8,24).
This problem can be solved by using the concept of scale factor. Scale factor is useful in finding proportional measurements.
Proportion implies having the same ratio.
Scale factor can be defined as the ratio of the measurement of the model to the measurement of the actual form in the simplest form. In other words, the ratio of any two corresponding lengths in two similar geometric figures is called a scale factor.
If the scale factor is more than 1, that is, scale factor > 1,
then it is an enlargement,
If the scale factor is less than 1, that is, scale factor < 1,
then it is a reduction.
We can obtain the answer by multiplying the given coordinates, first by a scale factor of 4 and then by a scale factor of 2/3.
(18,6) => (18x4, 6x4) => (72,24) => (72x2/3, 24x2/3) => (48,16)
(12,15) => (12x4, 15x4) => (48,60) => (48x2/3, 60x2/3) => (32,40)
(3,9) => (3x4, 9x4) => (12,36) => (12x2/3, 36x2/3) => (8,24)
Therefore, using the concept of scale factor, we get the locations of the vertices of the dilated figures as (48,16), (32,40), and (8,24).
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a rectangular garden is fenced on alls ides with 256 feet fencing. the garden is 8 feet longer than it is wide
The length and width of the rectangular garden is estimated as-
Length = 68 ft width= 60 ftHow to calculate perimeter of the rectangle?A rectangle's perimeter is the total length and distance of its border across all sides. The perimeter of a rectangular box is a linear measurement that is expressed in meters, feet, cm, or yards. Let us first examine the two primary characteristics of a rectangle.
A rectangle's four angles are all 90°.A rectangle's opposite sides are of equal length.The perimeter of the rectangle is given as-
Perimeter = 2(length + width)
perimeter= 256
Let the width of the rectangle be x.
Length is 8 feet longer than width, Thus,
length = x+8
Substitute the values in the formula of perimeter;
256 = 2( x+ 8+ x)
256 = 2( 2x + 8)
128= 2x + 8
120= 2x
x=60
Thus, width = 60 ft.
Length = 60 + 8 = 68 ft.
Therefore, the length and width of the rectangular garden is estimated.
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The complete question is -
A rectangular garden is fenced on all sides with 256 feet of fencing. The garden is 8feet longer than it is wide. Find the length and width of the garden.
O
US
If none of the stories can be represented, select "None of the above
(a) 9x = 99
Felipe finished reading his book in 9 days. Each
day, he read x pages. His book has 99 pages.
Felipe finished reading his book in x days. Each
day, he read 9 pages. His book has 99 pages.
A book is x pages long. Felipe read 9 pages. He
has 99 pages remaining.
A book has two parts. One part is x pages long.
The other part is 9 pages long. The book has 99
pages.
D None of the above
Check
(b) x + 5 = 25
0
Felipe uses 5 eggs to make a cake. He wants to
make x cakes. He needs 25 eggs.
A tray has x eggs. Another tray has 5 eggs.
Together, the two trays have 25 eggs.
Felipe had x eggs. Then his friend gave him 5
eggs. Felipe now has 25 eggs.
Felipe had x eggs in his refrigerator. Then he used
OS of them for his cake recipe. He now has 25
eggs left in the refrigerator.
None of the above
Answer:
Step-by-step explanation:
a travel agent is interested in the average price of a hotel room during the summer in a resort community. the agent randomly selects 18 hotels from the community and determines the price of a regular room with a king size bed. the average price of the room for the sample was $135 with a standard deviation of $25. assume the prices are normally distributed. construct an interval to estimate the true average price of a regular room with a king size bed in the resort community with 99% confidence. around the endpoints to two decimal places, if necessary.
The interval of true average price of a regular room with a king size bed in the resort community with 99% confidence is ( 14.74, 48.89 )
critical value at 0.01 significance level with 17 df = 2.898
x = mean;
99% confidence interval for μ is
(x - t * S) /√n < μ <( x + t * S) /√n;
(135 - 2.898 * 25 )/√18 < μ < (135 + 2.898 * 25)/√18;
14.74< μ< 48.89;
99% CI is ( 14.74, 48.89 ) ;
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the span of a set of vectors is the set of all possible linear combinations of those vectors, and will always include the zero vector
The spam of the sets of vector of all linear combination is 0,
The span of the set {(2, 5, 3), (1, 1, 1)} is the subspace of R 3 consisting of all linear combinations of the vectors v 1 = (2, 5, 3) and,
v 2 = (1, 1, 1).
this defines a plane in R 3.
Since a normal vector to this plane in n = v 1 x v 2 = (2, 1, −3),
the equation of this plane has the form 2 x + y − 3 z = d for some constant d. the plane must contain the origin—it's a subspace— d must be 0.
A linear equation is an equation in which the highest power of the variable is always 1. it is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. A linear equation only has one or two variables.No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line
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-5(1-5k)-4(2k+5) i need help on simplfying this
Answer:
-25+27k
Step-by-step explanation:
-5(1-5k)-4(2k+5)
= -5+35k-8k-20
=-5-20+35k-8k
= -25+27k
<
7. 2x+1> 3 and 3x - 4 ≤ 17
Solve each compound inequality and graph the solution set
Answer:
2x+1>3
2x>4
x=2
3x-4≤17
3x≤21
x=7
Name the segment in the scaled copy that corresponds to segment AD
Segment PS in the scaled copy corresponds to segment AD in polygon ABCD in polygon PQRS. They are similar in appearance and appear in the same location.
What is a polygon?A polygon is a two-dimensional flat shape with straight, fully closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.
Polygon is derived from the Greek word "polugonos." It has evolved into the term "polygon" over time. The term "polygon" means "many" and "gon" means "angled." This is due to the fact that a polygon has numerous angles and corners within its shape.
The Greeks may have been the first to recognize polygons, as there are numerous examples of them recognizing polygons such as the pentagram in their ancient art and writings.
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The lengths of the three sides of a triangle are consecutive integers. If the perimeter is 90 feet, find the value of the longest of the three side lengths
The value of the longest side of the triangle is 31 feet
The perimeter of the triangle is the sum of all its sides.
The formula for perimeter where a, b and c are the three sides of the triangle is given as:
Perimeter = a + b + c
It is given that the sides are consecutive integers and the perimeter is 90 feet, therefore
Let sides be x, x+1 and x+2
Perimeter = x + x+1 + x+2
90 = x + x+1 + x+2
90 = 3 + 3x
87 = 3x
x = 29 feet
The value of the longest side will be x+2, which will be 29+2 = 31 feet
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Examine the following graph of y=−3x+7.
Match each x-coordinate with the corresponding y-coordinate.
x-coordinate=2
x-coordinate=5
x-coordinate=3
x-coordinate=0
-----------------------------------
Answer choices to match with the X coordinates
Y coordinate = -2
Y coordinate = -8
Y coordinate = 7
Y coordinate = 1
Answer:
y = -3(2)+7
y= -6+7
y= 1
(2,1)
y=-3(5)+7
y= -15+7
y= -8
(5,-8)
y= -3(3)+7
y=-9+7
y=-2
(3,-2)
y=-3(0)+7
y=0+7
y=7
0,7)
Step-by-step explanation:
substitute the values of x in the equation
marilyn is going on a class outing to an amusement park. she has $40 to spend. the admission price is $20. she plans to buy a sandwich for $5. a cup of lemonade costs $3.00. write an inequality to show how many cups of lemonade, c, she can buy.
The inequality for the number of cups of lemonade she can buy is :
0 < c < 5.
Marilyn has $40 to spend in the amusement park.
Admission price = $20
So money left = 40 - 20 = $20
Now she plans to buy a sandwich for $5.
So the money left now will be = 20 - 5 = $15
Price of a cup of lemonade = $3
Marilyn can buy at most $15/3 = 5 cups of lemonade.
She can either choose to not buy a cup of lemonade or can buy at most 5 cups of lemonade.
So the inequality for the number of cups of lemonade she can buy will be
0 < c < 5 , where 'c' denotes the number of cups of lemonade.
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WILL CHOOSE THE BRAINLIEST!
The measure of x, that is, the angle OBA is equal to 22.5°.
What is the measure of the missing angle in geometrical system?
Herein we find a geometric system formed by a circle, a diameter and a chord. In the image attached below we present all the possible angles of the geometric system, formed by two isosceles triangles.
According to Euclidean geometry, an isosceles triangle has two sides and two angles of equal length. Then, the sum of the internal angles of the triangle AOB is equal to:
m ∠ AOB + m ∠ OBA + m ∠ OAB = 180°
135° + 2 · m ∠ OBA = 180°
2 · m ∠ OBA = 45°
m ∠ OBA = 22.5°
By taking advantage of the properties of isosceles triangles, the measure of x, that is, the angle OBA is equal to 22.5°.
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Ernie writes this problem:
525 divided by 1500
HINT: The dividend is smaller on this problem.
Select each correct answer. There are THREE.
1500525
1500 over 525
5251500
525 long division enclose 1500
525 ÷ 1500
525 ÷ 1500
5251500
525 over 1500
1500525
1500 long division enclose 525
1500 ÷ 525
THERE IS THREE ANSWERS
The three ways that the problem that Ernie has written can be solved are:
525 ÷ 1500525 over 15001500 long division enclose 525What is division in mathematics?This is the term that is sued to refer to the topic in mathematics that has to do with the ways that numbers can be broken down into smaller units. The number that is being divided is often done with the aid of a divisor.
In this question, the number that is to be divided is 525 and the number that is to do the division is 1500. This can be written as 525 / 1500 for us to see clearly.
When written, we can write this out in the different ways that have been stated above. Hence we would have The three ways that the problem that Ernie has written can be solved are:
525 ÷ 1500525 over 15001500 long division enclose 525The solution is 0.35
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need this answer---i hate geometry so much
TX IS THE OVERALL MAGNITUDE OF THE LINE
TX IS THE OVERALL MAGNITUDE OF THE LINE WHICH IS MADE BY TW+WX
MATHEMATICALLY
TX=TW+WX
[tex](5x - 9) = (3x + 5) + 10 \\ 5x - 9 = 3x + 5 + 10 \\ 5x - 3x = 5 + 10 + 9 \\ 2x =24 \\ \frac{2x}{2} = \frac{24}{2} \\ x = 12[/tex]
HOPE THIS HELPS!!!
PLEASE DO NOT HATE MATHS I'M HERE FOR YOU TO MAKE SURE YOU ENJOY IT.
{(7x+y=14),(-2-y=6):}
Answer:12/8y
Step-by-step explanation:
i took the test
Answer all these questions, and I will give you brainly + 50 Points.
Answer:
Step-by-step explanation: Hello! My name is Madison and I will being helping you how to go about doing these problems! First things first.
1) 50,000 divided by 12 would be 4166.6 repeating.
2)
The temperature at 3:00 p.m. was 7F. By 9.00 p.m. the temperature had dropped by 12 degrees. What was the temperature at 9.00 p.m.?
Answer: The answer is -5
Step-by-step explanation: According to the question it stated that the temperature was 7 degrees at 3pm and by 9pm it dropped 12 degrees so from my answer it would -5 degrees
V
What is the measure of the angle shown?
Answer:
The arrow indicates that the angle terminates in the second quadrant, meaning that its more than 270 deg
A stand in a supermarket can hold 157.5 kg. How many 1.25 kg bags of potatoes will it hold?
Answer:
If a stand can hold 157.5kg
x stand can hold 1.25kg
1=
Answer:
126 bags.
Step-by-step explanation:
157.5 / 1.25
= 126.
d. When would you need to make use of spherical geometry in the real world? Are there any professions that would need to make use of it? How would these professions make use of spherical geometry?
Spherical geometry would be use in the real world practical applications to navigation. Professions that would need to make it use is astronomy.
These professions make use of spherical geometry for making Spherical conic, Spherical distance, Spherical polyhedron, Half-side formula.
What is spherical geometry?Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2 dimensional surface and other terms like "ball" or "solid sphere" are used for the surface together with its 3-dimensional interior.
An important geometry related to that of the sphere is that of the real projective plane; it is obtained by identifying antipodal points (pairs of opposite points) on the sphere.
Locally, the projective plane has all the properties of spherical geometry, but it has different global properties. In particular, it is non-orientable, or one-sided, and unlike the sphere it cannot be drawn as a surface in 3-dimensional space without intersecting itself.
Spherical geometry would be use in the real world practical applications to navigation. Professions that would need to make it use is astronomy.
These professions make use of spherical geometry for making Spherical conic, Spherical distance, Spherical polyhedron, Half-side formula.
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2/3x + 1/3x = x
Simplified
Answer: x=1
Step-by-step explanation:
Answer:
IMS (Infinitely Many Solutions)
Step-by-step explanation:
1. Combine like terms (2/3x + 1/3x) Equation: 1x = x
2. 1x is just x, so the final equation is x = x. When you get an answer like this, it means there are infinitely many solutions.
lim x cot A - A cot x/x-A
x→A
The value of the expression [tex]\lim_{x \to A} \frac{xcot(A)-Acot(x)}{x-A}[/tex] is [tex]cot(A)+\frac{A}{sin^{2}A}[/tex].
The value that a function approaches when the input approaches a certain value is known as a limit. Calculus and mathematical analysis are not possible without limits, which are also required to determine derivatives, continuity, and integrals.
Mathematical expressions consist of at least two variables or numbers, at least one arithmetic operation, and a statement. It's possible to divide, multiply, add, or subtract with this mathematical operation.
Consider the expression,
[tex]\lim_{x \to A} \frac{xcot(A)-Acot(x)}{x-A}[/tex]
Adding and subtracting Acot(A) and A common in the numerator,
[tex]\lim_{x \to A} \frac{xcot(A)-Acot(A)+Acot(A)-Acot(x)}{x-A}[/tex]
Taking cot(A) common,
[tex]\lim_{x \to A} \frac{cot(A)(x-A)+A(cot(A)-cot(x))}{x-A}[/tex]
[tex]\lim_{x \to A} cot(A) + \frac{A(cot(A)-cot(x)}{x-A}[/tex]
Now, using the identity:
cot x = cos x / sin x
[tex]\lim_{x \to A} cot(A) + \frac{A(\frac{cos(A)}{sin(A)} -\frac{cos(x)}{sin(x)}) }{x-A}[/tex]
[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{cos(A)sin(x)-cos(x)sin(A) }{sin(A)sin(x)})[/tex]
By using the identity, sin ( a - b ) = sin(a)cos(b) - sin(b)cos(a)
[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})[/tex]
[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})=\lim_{x \to A} cot(A) +\lim_{x \to A} \frac{sin(x-A)}{(x-A)}\frac{A}{sin^{2}A}[/tex]
[tex]\lim_{x \to A} cot(A) + \frac{A}{x-A}(\frac{sin(x-A)}{sin(A)sin(x)})=cot(A)+1 \cdot \frac{A}{sin^{2}A}[/tex]
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I need help with this!
Answer:
-0.5
Step-by-step explanation:
[tex]\frac{f}{g} =\frac{f(n)}{g(n)} = \frac{4n}{n^2-3n}[/tex]
[tex]\frac{4(-5)}{(-5)^2-3(-5)} =\frac{-20}{40} =\frac{-1}{2}[/tex]
please help with this question and give detailed explanation!! thank you!!
Answer:
[tex]-\sqrt{2}[/tex]Step-by-step explanation:
Make the following operations:
a² + b² = 6aba² + 2ab + b² = 8ab(a + b)² = 8aba + b = [tex]2\sqrt{2ab}[/tex]and
a² + b² = 6aba² - 2ab + b² = 4ab(a - b)² = 4aba - b = [tex]-2\sqrt{ab}[/tex], since a < bThe required value is:
[tex]\cfrac{a+b}{a-b} =\cfrac{2\sqrt{2ab} }{-2\sqrt{ab} } =-\sqrt{2}[/tex]Answer:
[tex]\dfrac{a+b}{a-b}=-\sqrt{2}[/tex]
Step-by-step explanation:
Given:
[tex]a^2+b^2=6ab[/tex]
[tex]0 < a < b[/tex]
Add 2ab to both sides of the given equation:
[tex]\implies a^2+b^2+2ab=6ab+2ab[/tex]
[tex]\implies a^2+2ab+b^2=8ab[/tex]
Factor the left side:
[tex]\implies (a+b)^2=8ab[/tex]
Subtract 2ab from both sides of the given equation:
[tex]\implies a^2+b^2-2ab=6ab-2ab[/tex]
[tex]\implies a^2-2ab+b^2=4ab[/tex]
Factor the left side:
[tex]\implies (a-b)^2=4ab[/tex]
Therefore:
[tex]\implies \dfrac{(a+b)^2}{(a-b)^2}=\dfrac{8ab}{4ab}[/tex]
[tex]\implies \dfrac{(a+b)^2}{(a-b)^2}=2[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^c}{b^c}=\left(\dfrac{a}{b}\right)^c:[/tex]
[tex]\implies \left(\dfrac{a+b}{a-b}\right)^2=2[/tex]
Square root both sides:
[tex]\implies \sqrt{\left(\dfrac{a+b}{a-b}\right)^2}=\sqrt{2}[/tex]
[tex]\implies \dfrac{a+b}{a-b}=\pm\sqrt{2}[/tex]
As 0 < a < b then:
a + b > 0a - b < 0Therefore:
[tex]\implies \dfrac{a+b}{a-b}=\dfrac{+}{-}=-[/tex]
So:
[tex]\implies \dfrac{a+b}{a-b}=-\sqrt{2}[/tex]