find an equation of the tangent line to the given curve at the specified point. y = e^x /x , at the point (1, e)

The measurement of side AC in the given right triangle is 10.12 units.

A triangle having at least one angle measuring 90° is called a right triangle.

Given that, a triangle ABC, right-angled at A,

AB = 15 and BC = 18.1, we need to find AC,

Please refer to the figure attached,

Using Pythagoras theorem,

BC² = AB² + AC²

AC² = BC² - AB²

AC² = (18.1)² - 15²

AC² = 327.61 - 225

AC² = 102.61

AC = 10.12

Hence, the value of AC = 10.12

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The length of the median of the trapezoid is 12.

The area of a trapezoid is given by the formula (1/2)h(b1+b2), where h is the height and b1 and b2 are the lengths of the bases. We know that the area is 60, the height is 5 and b1 = b2 + 4.

So, we can write the equation as follows:

(1/2) * 5 * (b1 + b2) = 60

To find the length of the median of a trapezoid, we need to find the length of the mid-segment. The mid-segment of a trapezoid connects the midpoints of the non-parallel sides. The length of the midsegment is the average of the lengths of the bases.

So, the length of the median is (b1 + b2) / 2.

We can substitute the value of the area to find the lengths of the bases and then use that to find the length of the median.

(1/2) * 5 * (b1 + b2) = 60

(1/2) * 5 * (b1 + b2) = 60

b1 + b2 = 24

b1 = b2 + 4

b2 = 24 - b1

b1 = (24 - b1) + 4

b1 = 24 - b1 + 4

b1 = 28 - b1

b1 = 28 - (24 - b1)

b1 = 4 + b1

b1 = b2 + 4

b1 = b1

So, the lengths of the bases are equal to 14 and 10.

Length of median = (14 + 10) / 2 = 12.

Therefore, The length of the median of the trapezoid is 12.

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When you divide a number by 1/2, it is the same as multiplying the number by 2. Therefore, the result of the division is two times the original number.

Let's say we have a number, X.

When you divide X by 1/2, you can rewrite the equation as:

X ÷ 1/2 = X × 2

Thus, the result of the division is two times the original number, X.

Let's say we have a number, X. When you divide X by 1/2, you are essentially multiplying X by 2. This means that the result of the division is two times the original number. In other words, if you divide X by 1/2, the answer will be 2X. To put it another way, if you take any number, X, and divide it by 1/2, the result will be two times the original number. This is because 1/2 is the same as multiplying the number by 2. For example, if you divide 10 by 1/2, the result will be 20, since 10 multiplied by 2 is 20. Similarly, if you divide 25 by 1/2, the result will be 50, since 25 multiplied by 2 is 50. In conclusion, when you divide any number, X, by 1/2, the result will always be two times the original number.

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The greatest possible weight of the large bag is 1.9n ounces.

Given:

Weight of 10 apples = n ounces

Weight of 1 apple = n/10 ounces

Weight of n apples = n²/10 ounces

It is given that a large bag of n of these apples weighs less than 40 ounces,

= n²/10 < 40

= n²< 400

= n < 20

So, the large bag contains at most 19 apples.

Hence, the weight of the large bag is at most 1.9n ounces, or (19/10)(n) ounces.

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The square root of 13 in decimal form is an non-terminating non-recurring decimal

A decimal number that never ends and never repeats itself is known as a non-terminating, non-repeating decimal.

Such decimals are irrational numbers since they cannot be expressed as fractions.

Examples. Pi is a decimal that doesn't end or repeat.

Since the square root of 13 will result to infinite number the number cannot fully reach the required value but an approximate

Because of this the decimal form of he square root of 13 will lack accuracy

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The rate in centimeters per second, at which the radius is increasing at the instant when the radius is 5 centimeters is 0.16 cm/s.

Using a known value of a function at a certain point along with its rate of change at that moment, one application of derivatives is to estimate an unknown value of a function at a particular point.

Given:

Both radius r and area A is a function of time, so in fact:

A(t) = π [r(t)]²

Deriving this we get that the area changes and the radius changes as:

[tex]\frac{dA(t)}{dt} = 2\pi r(t)\frac{dr(t)}{dt}[/tex]

But,

[tex]\frac{dA(t)}{dt} = 5 \frac{cm^{2} }{s}[/tex]

Considering when r(t) = 5cm at the instant we get,

[tex]5 = 2\pi . 5\frac{dr(t)}{dt}[/tex]

Simplify 5 and take 2π to the other side and divide,

The rate of change of radius is given by:

[tex]\frac{dr(t)}{dt} =\frac{1}{2\pi } = 0.16 cm/s[/tex]

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the height intercept would be 0 given the pool has no water at the beginning.

Which is the vertical intercept?

The vertical intercept (y-intercept) is found by evaluating the function when the input variable, x, is 0 and is always the same as the constant b. It can be thought of as the original value of the function. The horizontal intercept (x-intercept) is the value of the variable x when the function value is 0.

according to the constant dividend growth model

price = d1 / (r - g)

d1 = next dividend to be paid

r = cost of equity

g = growth rate

$2.5 / (0.1 - 0) = $25

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Answer:

x + y ≥ 6 (Melissa exercises for at least 6 hours per week)

x ≤ 11 (Melissa spends at most 11 hours doing cardiovascular work)

y ≤ 4 (Melissa spends at most 4 hours on weight training)

To graph this region, you can plot the constraints on the x-y coordinate plane and shade the area that satisfies all of them.

The first constraint x+y>=6 can be represented by the line y = -x +6

The second constraint x<=11 can be represented by the line y = 11

The third constraint y<=4 can be represented by the line y = 4

The shaded area will be the region that is above and to the right of the line y = -x + 6, below the line y = 11 and below the line y = 4.

Kind of hard to shade a graph without having it in front of me. Hope this helps!

Answer:

livirav737 has provided the correct answer first.

I am merely providing the graph

Step-by-step explanation:

Plotted using online graphing tool Geogebra

The heavily shaded region with ABCD as its corners represents the region corresponding to all 5 inequalities

Note
Though not explicitly stated

You must also have the two additional constraints

x ≥ 0, y ≥ 0

These are called non-negativity constraints to ensure that x and y are not negative. The number of hours exercised on each platform cannot be less than 0

In this particular case, these are not necessary but standard practice is to include them whenever you have a system of inequalities with non-negative variables

The vertices of the polygon before and after dilation are shown below

preimage         Image

J (-5, 3)            J' (-5/2, 3/2)

K (2, 3)            K' (1, 3/2)

L (2, -3)           L' (1, -3/2)

M (-5, -3)        M' (-5/2, -3/2)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The rule used in  transformation is as follows

(x, y) for a scale factor of r → (rx, ry)

Applying the rule to the vertices  of the polygon we have

preimage                                  Image

J (-5, 3)      (1/2 * -5, 1/2 * 3)      J' (-5/2, 3/2)

K (2, 3)       (1/2 * 2, 1/2 * 3)       K' (1, 3/2)

L (2, -3)      (1/2 * 2, 1/2 * -3)       L' (1, -3/2)

M (-5, -3)    (1/2 * -5, 1/2 * -3)     M' (-5/2, -3/2)

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∠3 is congruent to ∠1. Hence, proved.

Two angles are said to be complementary angles if they add up to 90 degrees. In other words, when complementary angles are put together, they form a right angle (90 degrees).

Given that, ∠3 and ∠2 are complementary; m∠2 + m∠3 = 90°---------(I)

From the given figure,

m∠1 + m∠2 = 90°---------(II)

From the given equation (I) and (II), we get

m∠1 + m∠2=m∠2 + m∠3

m∠1 ≅ m∠3

Hence, proved.

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Answer:

58.27 mm (2 d.p.)

Step-by-step explanation:

Assuming the given prism is a rectangular prism, triangles ADC and ACG are right triangles.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Cos trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

AC is the hypotenuse of right triangle ADC.  

Therefore, we can use the cos trigonometric ratio to create an expression for the length of AC:

[tex]\implies \cos\left(36^{\circ}\right)=\dfrac{AD}{AC}[/tex]

[tex]\implies \cos\left(36^{\circ}\right)=\dfrac{42}{AC}[/tex]

[tex]\implies AC=\dfrac{42}{\cos\left(36^{\circ}\right)}[/tex]

AC is the hypotenuse of right triangle ACG.  

Therefore, we can use the cos trigonometric ratio to create an expression for the length of AG:

[tex]\implies \cos\left(27^{\circ}\right)=\dfrac{AC}{AG}[/tex]

[tex]\implies AG=\dfrac{AC}{\cos\left(27^{\circ}\right)}[/tex]

To find the length of AG, substitute the found expression for AC into the expression for AG:

[tex]\implies AG=\dfrac{\frac{42}{\cos\left(36^{\circ}\right)}}{\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=\dfrac{42}{\cos\left(36^{\circ}\right)} \times \dfrac{1}{\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=\dfrac{42}{\cos\left(36^{\circ}\right)\cos\left(27^{\circ}\right)}[/tex]

[tex]\implies AG=58.2654039...[/tex]

[tex]\implies AG=58.27\;\sf mm \;(2\;d.p.)[/tex]

sin T as a fraction in simplest terms is 7/17

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Sin T = opposite/ hypotenuse

The opposite is where the angle T is facing. That is opposite = 7.

The hypotenuse is where the right angle is facing. That is hypotenuse = 17

Thus, Sin T = 7/17

We cannot further simply sin T.

Therefore, the value of sin T as a fraction in simplest terms is 7/17

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The area of a regular octagon inscribed in a circle of radius 4 meters is 45.255 square meters. So, option C is correct

An octagon is a polygon with 8 sides, and a regular octagon has all sides of equal length. To find the area of a regular octagon inscribed in a circle of radius 4 meters, we can use the formula:

Area = (2 * (4^2) * (1 + sqrt(2))) / (4 * tan(pi/8))

Plugging in the values we get:

Area = (2 * (4*cos(pi/8))^2 * (1 + sqrt(2))) / (tan(pi/8)) = 16 * (1 + sqrt(2)) * (sqrt(2) / sqrt(2+ sqrt(2)))

        = 8 * 1/2 * 4 * 4 * sin45°

        = 32√2

        = 45.255 square meters.

Therefore, the area of a regular octagon inscribed in a circle with a radius of 4 meters is 45.255 square meters.

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(a) On writing 299790000 in scientific notation , the value of a is 2.9979 and value of k is 8  .

(b) On writing 0.51 in scientific notation , the value of a is 5.1 and value of k is -1 .

What is Scientific Notation ?

The general form of writing a number in scientific notation is ⇒ [tex]a\times 10^{k}[/tex] ;

Part (a) ;

the number is given to be : 299790000 ;

For writing it in scientific notation, decimal point will be placed after 2 ;

So , the scientific notation of the number is ⇒ [tex]2.9979 \times 10^{8}[/tex] ,

On comparing it with the general form of scientific notation,

we get , a = 2.9979 and k = 8 .

Part (b) ;

the number is given to be : 0.51 ;

For writing it in scientific notation, decimal point will be placed after 5 ;

So , the scientific notation of the number is ⇒ [tex]5.1 \times 10^{-1}[/tex] ,

On comparing it with general form of scientific notation,

we get , a = 5.1 and k = -1 .

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Answer: 1 moles KI = 166.00277 gram using the molecular weight calculator and the molar mass of KI.

Step-by-step explanation

Answer was found by using the molecular weight calculator and the molar mass of KI.

Hope this helps :)

Answer:To write a proportion as a percentage, you first convert it to a decimal and then multiply it by 100.

The proportion of Year 12 pupils in the music club is 32/85.

To convert to a decimal, divide 32 by 85:

32/85 = 0.376

To convert this decimal to a percentage, multiply by 100:

0.376 * 100 = 37.6

So, the proportion of Year 12 pupils in the music club as a percentage is 37.6%.

To convert a proportion to a percentage, you can multiply it by 100.

The proportion of Year 12 pupils in the music club can be represented as 32/85.

Multiplying by 100, we get:

(32/85) * 100 = 37.65

So, 37.65% of the pupils in the school are Year 12 pupils in the music club.

Rounded to 1 decimal place, the answer is 37.7%.

In the video game Rebecca is playing using only addition the expression that represents Rebecca's score after these three turns is  

= 4 + (-6) + (8) + (-1)

Rebecca's energy level after Turn 1 = -2

Rebecca's energy level after Turn 2 = 6

Rebecca's energy level after Turn 3 = 7

Following the rule of the video game the expression is written in steps below

Rebecca is currently at energy level 4

= 4

Turn 1: 6 trees cut

= 4 + (-6)

= 4 - 6

= -2

Turn 2: 8 trees planted

= 4 + (-6) + (8)

= -2 + 8

= 6

Turn 3: 1 tree cut

= 4 + (-6) + (8) + (-1)

= 6 - 1

= 7

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Answer: x = 1

Step-by-step explanation: 4(1-x) = 6(x-1)

 -  4-4x = 6x-6

 -  6x-4x = 6-4

 -  2x = 2

 - x= 1

Answer:

A.  293 dolls each

B.  710 beads

C.  (n+n)/3 >2xy

Step-by-step explanation:

1.  Let A be the number of dolls collected by Gelyn and B the number collected by Geraldine.  

At the start:

 A = 1,178, and

 B = 588

Girlie gets the same number of dolls from both, which we'll say is x.  The situation is then:

Gelyn:  A - x

Geraldine = B - x

Girlie = 2x

After the transfer, we find that A-x = 3(B-x)  [Gelyn had 3 times as many dolls left as Geraldine]

Lets rearrange this last expression:

A-x = 3(B-x)

A-x = 3B-3x

2x=3B-A

Use the values of A and B to find x:

2x=3(588)-(1,178)

2x = 586

x =  293

Gelyn  and Geraldine each gave Girlie 293 dolls.

========

2.  Let A, B, and C stand for the number of beads in Boxes A, B, and C, respectively.  We are told that:

 A + B + C = 4342 [Box A, Box B, and Box C contain 4,342 beads altogether]

and learn that:  

A+18 = B, and  [There are 18 more beads in Box B than Box A]

C = 3B              [There are 3 times as many beads in Box C as in Box B]

How many beads in Box A?

We have three equations.  Lets find a way to substitute so that we can eliminate the unknowns B and C.

Look at:   A + B + C = 4342

If we can rearrange the other equations to express the variables B and C in terms of A, we could solve the problem.

A+18 = B becomes B=A+18  [We can now calculate B from A]

The second, C = 3B, does not have A, but we can use the above expression for B, which will allow C to be expressed as a function of A:

C = 3B

C = 3(A+18)

C = 3A + 64   [We can now calculate C from A]

Use these definitions of B and C in the first equation (substitution):

A + B + C = 4342

A + (A+18) + (3A + 64) = 4342

6A + 82 = 4342

6A = 4260

A = 710   Box A has 710 beads

3.  The sum of x and n divided by 3 more than twice the product of x times y

          (n+n)/3        [The sum of x and n divided by 3]

         >2xy            [more than twice the product of x times y]

Put these together:

    (n+n)/3 >2xy

Answer: (2x-2y-1)(x-y)

Step-by-step explanation:

To factor 2(x-y)² - x+y, we first recognize that the expression is a difference of squares, which means it can be factored into the form (a-b)(a+b). To identify the values of a and b, we can look for common factors between the two terms, which are 2(x-y)² and -x+y.

The common factor between 2(x-y)² and -x+y is x-y. We can factor it out by dividing both terms by x-y:

2(x-y)² - x+y = (x-y) * (2(x-y) - 1)

Now we can write the expression as (x-y)(2x-2y-1) .

As you can see (x-y) is common in both the term, so we can factor it out, and we are left with (2x-2y-1)(x-y)

The least count of Vernier calipers is 0.01cm and The length of the line is 10.23cm

Mean scale division:

The main scale is graduated with one division value equal to 1 mm. The length of the Vernier scale is the same as the n- scale of the Vernier scale and the (n-1) scale of the main scale.

Vernier Scale Division:

The minimum Vernier caliper number is also called the Vernier constant. Defined as the difference between the major and Vernier scales is represented mathematically as:

          VC = 1 MSD – 1 VSD

If the Vernier scale has n divisions, it matches the (n-1) divisions of the main scale. Vernier Caliper :

LC = ( 1 - [tex]\frac{n-1}{n}[/tex])  MSD

According to the problem

1MSD= 1mm

MSR = 10.2cm

Here, 10VSD  = 9MSD

          1VSD   = (9/10)MSD

                      =(9/10)×1mm

                      = (9/10)mm

Least count of Vernier calipers L.C = 1MSD - 1VSD

                                                           =1mm - (9/10)mm

                                                           =0.01mm

Therefore, Least Count (LC) = 0.01cm

Therefore,

Length of the line = MSR + (VSD × L.C)

                             = 10.2 + (3 × 0.01)

                             = 10.2+(0.03)p

                             = 10.23 cm

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The length of each side of the courtyard is 25 meters. Then 35.36 meters long is each walkway.

In the given question, a school has a square courtyard and wants to create diagonal walkways.

The length of each side of the courtyard is 25 meters.

We have to find how long is each walkway.

By dividing the square in half to form a right triangle, you can find the solution. The Pythagorean theorem can then be used to find the hypotenuse.

According the Pythagorean Theorem

[tex]a^2+b^2 = c^2[/tex]

[tex](25)^2+(25)^2=c^2[/tex]

Now solving,

625 + 625 = [tex]c^2[/tex]

[tex]c^2[/tex] = 1250

Taking square root on both side, we get

c = 35.36 meters.

Hence, 35.36 meters long is each walkway.

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Answer: the midpoint

Step-by-step explanation:

Answer: 0

Step-by-step explanation:

We know cos π/3 = 1/2.

Therefore, a = π.

Now, sin π is 0 if you remember the sin graph.
Therefore, answer is 0.

The quadrilateral given is Parallelogram.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

(a) The quadrilateral is sketched as shown in the graph below.

(b) We have to write the equation of four lines AB, BC, CD and AD in the form y = mx + b. m is slope and b is intercept along Y axis.

Coordinates of vertices are A(-5, 2), B(-2, 6), C(3, 5) and D(0,1).

Equation of line AB :

Slope = (6 - 2) / (-2 - -5) = 4/3

Equation in point slope form is

(y - 2) = 4/3(x - -5)

y - 2 = 4/3 x + 20/3

y = 4/3 x + 26/3

Equation of line BC :

Slope = (5 - 6) / (3 - -2) = -1/5

Equation in point slope form is,

(y - 6) = -1/5 (x - -2)

y - 6 = -1/5 x - 2/5

y = -1/5 x + 28/5

Equation of line CD :

Slope = (1 - 5) / (0 - 3) = -4/-3 = 4/3

Equation in point slope form is,

y - 5 = 4/3 (x - 3)

y - 5 = 4/3 x - 4

y = 4/3x + 1

Equation of line AD :

Slope = (1 - 2) / (0 - -5) = -1/5

Equation in point slope form is,

y - 1 = -1/5 (x - 0)

y - 1 = -1/5 x

y = -1/5 x + 1

(c) Opposite sides are having the same slope.

From the sketch, opposite sides are equal.

So quadrilateral is either parallelogram or rectangle.

But if the figure is rectangle, adjacent sides are perpendicular and therefore the product of their slope is -1.

But it is not the case here.

So it is parallelogram.

Hence the given figure is a parallelogram.

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Answer:

(a) There are 2 groups. The treatment group will hear older students describe overcoming challenges. The control group won't hear anything.

Label each student with a different integer from 01 to 40. Go to a line in Table D and read two-digit groups moving from left to right. The first 20 different labels between 01 and 40 identify the 20 students who hear older students talking. The remaining 20 students don't hear anything. Ignore groups of digits from 41 to 00.

(b) Separate the 40 freshmen into 2 groups according to their history of academic performance. Carry out treatment separately in each block to account for the variation due to the history of academic performance.

Step-by-step explanation:

(a) We want to infer the cause and effect between hearing older students talking about their challenges and the students' academic performance.

Claim the 2 groups first;

Clarify the random assignment of people.

(b) The differences between the two kinds of students are expected to affect the response to the treatments in some ways. Randomized block designs are to eliminate the effect.

All the Individuals solutions are solved below:

a) To verify that y = e^m_1x - e^m_2 x/m_1 - m_2 is a solution of the differential equation y" - (m_1 + m_2)y' + m_1 m_2y = 0, we can substitute y into the equation and simplify:

y" = m_1^2e^m_1x - m_2^2e^m_2x

y' = m_1e^m_1x - m_2e^m_2x

so:

y" - (m_1 + m_2)y' + m_1 m_2y = m_1^2e^m_1x - m_2^2e^m_2x - (m_1 + m_2)(m_1e^m_1x - m_2e^m_2x) + m_1 m_2(e^m_1x - e^m_2x/m_1 - m_2) = 0

b) To find the limit of the solution in part (a) as m_1 right arrow m_2, we can use I'Hospital's rule. The limit is:

lim (m_1 -> m_2) e^m_1x - e^m_2 x/m_1 - m_2 = e^m_2x - e^m_2 x/m_2 - m_2 = e^m_2x - e^m_2x - m_2 = -m_2

c) To verify that the limit in part (b) satisfies the differential equation obtained from the equation in part (a) by replacing mi by m_2, we can substitute -m_2 into the equation:

y" - (m_2 + m_2)y' + m_2 m_2y = 0

y" - 2m_2y' + m_2^2y = 0

which is the differential equation of a constant function, and -m_2 is a constant function. Therefore, the limit in part (b) satisfies the differential equation.

It should be noted that the solution y = e^m_1x - e^m_2 x/m_1 - m_2 is a linearly independent solution of the differential equation y" - (m_1 + m_2)y' + m_1 m_2y = 0, and it can be used in combination with the general solution y = c_1e^m_1x + c_2e^m_2x to find the general solution of the differential equation.

Therefore, All the Individuals' solutions are solved.

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Answer:

x > 11/-8

Step-by-step explanation:

1/5(x + 2) -1/4(2-x)> 1/3(x + 4) -1/4(5-x)

=60×1/5(x +2)-60×1/4(2-x)>60×1/3 (x+4)-60×1/4(5-x)

=12(x +2)-15(2- x)> 20(x+4)-15(5-x)

=12x + 24 - 30 + 15x > 20x + 80 - 75 + 15x

=12x + 15x - 20x -15x > 80 -75 -24 +30

=27x -35x > 80 - 99 + 30

=-8x > 11

=-8x/-8 > 11/-8

=x > 11/-8.

Hence the truth set of the inequality is said that (x : x > 11/-8).

The slope of a line that is perpendicular to the line through the points is - 25/123

The change in the y-coordinate relative to the change in the x-coordinate of a line is referred to as the slope of that line. The net change in the y-coordinate is y, while the net change in the x-coordinate is x. As a result, the change in the y-coordinate with regard to the change in the x-coordinate may be expressed as,

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

The reciprocal of the perpendicular line's slope is negative. This implies that you switch the slope's sign to its opposite.

m₁ × m₂ = -1

Where,

m₁ = Slope of the first line

m₂ = Slope of the second line

According to the question

Given

points A (4.95, 5.96) and B (8.01, 21.03)

So the equation of the line passing from these two points will be

(y - y₁) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] (x - x₁)

So the equation we get will be

(y - 5.96) = [tex]\frac{21.03 - 5.96}{8.01 - 4.95}[/tex] (x - 4.95)

⇒ y - 5.96 = 4.92 (x - 4.95)

⇒ y - 5.96 = 4.92x - 24.55

⇒ y = 4.92x - 18.39

This is the required equation passing from the two given points with slope m = 4.92 ⇒ m = 123/25

Now

∵ m₁ × m₂ = -1

∴ (123/25) × m₂ = -1

⇒ m₂ = - (25/125)

Hence, the slope of a line that is perpendicular to the line through the points is - 25/123

To know more about perpendicular lines on brainly : brainly.com/question/18271653

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The slope of a line that is perpendicular to the line through the points is - 25/123

The change in the y-coordinate relative to the change in the x-coordinate of a line is referred to as the slope of that line. The net change in the y-coordinate is y, while the net change in the x-coordinate is x. As a result, the change in the y-coordinate with regard to the change in the x-coordinate may be expressed as,

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

The reciprocal of the perpendicular line's slope is negative. This implies that you switch the slope's sign to its opposite.

m₁ × m₂ = -1

Where,

m₁ = Slope of the first line

m₂ = Slope of the second line

According to the question

Given

points A (4.95, 5.96) and B (8.01, 21.03)

So the equation of the line passing from these two points will be

(y - y₁) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] (x - x₁)

So the equation we get will be

(y - 5.96) = [tex]\frac{21.03 - 5.96}{8.01 - 4.95}[/tex] (x - 4.95)

⇒ y - 5.96 = 4.92 (x - 4.95)

⇒ y - 5.96 = 4.92x - 24.55

⇒ y = 4.92x - 18.39

This is the required equation passing from the two given points with slope m = 4.92 ⇒ m = 123/25

Now

∵ m₁ × m₂ = -1

∴ (123/25) × m₂ = -1

⇒ m₂ = - (25/125)

Hence, the slope of a line that is perpendicular to the line through the points is - 25/123

To know more about perpendicular lines on brainly : brainly.com/question/18271653

#SPJ4

Answer: study dum ahh

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