Which is the equation of a line perpendicular to line AB?​

The simplified expression after rationalizing the denominator is [tex]3\sqrt{55} / 11[/tex].

The given expression is,

[tex]3\sqrt{5} /\sqrt{11}[/tex]                                                equation 1

Name the given expression as equation 1.

To simplify the given expression first we need to rationalize the denominator that is [tex]\sqrt{11}[/tex] .

To rationalize the denominator we need to multiply and divide the given equation 1 by [tex]\sqrt{11}[/tex] . On multiplying and dividing the given equation 1 by [tex]\sqrt{11}[/tex], we will get

[tex]3\sqrt{5} /\sqrt{11}[/tex] = ( [tex]3\sqrt{5}[/tex] ×[tex]\sqrt{11}[/tex])/([tex]\sqrt{11}[/tex] ×[tex]\sqrt{11}[/tex])

On further simplifying the expression , we will get

= ([tex]3\sqrt{5}[/tex] × [tex]\sqrt{11}[/tex])/11 = [tex]3\sqrt{55} / 11[/tex]

So, we can conclude that the simplified expression after rationalizing the denominator is [tex]3\sqrt{55} / 11[/tex].

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Answer:

Could you explain the problem a bit more?

Step-by-step explanation:

Answer:

I believe 72

Step-by-step explanation:

Answer: The amount of long will it take the plant to grow is [tex]5\frac{2}{7}[/tex] weeks.

Step-by-step explanation:

Given data,

A certain days plant grows 1 1/6 inches

It take the plant to grow 6 1/6 inches

Let us assume,

A certain days plant grows = x

It take the plant to grow = y

So ,

we can write,

                       x = 1 and 1/6

                       x = 1*1/6

 L.C.M is '6',

Then,

                      x = (6+1) / 6

                      x = 7/6

Then,

                 y = 6 and 1/6

                 y = 6*1/6

                 y =(1+36) / 6

                y = 37/6

So, divide      y/x = (37/6) / (7/6)

                            = 37/6 * 6/7

 L.C.M is 42

                            = 222/42

                            = 5  12/42

                            = 5  2/7 weeks

Therefore,

        The amount of long will it take the plant to grow is [tex]5\frac{2}{7}[/tex] weeks.

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The equation of the line in point-slope form, which passes through the pair of points located at (0 , 1/2) and (5/7 , 0), is y - 1/2 = -7/10 x

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (0 , 1/2) and (5/7 , 0).

m = (y2 - y1)/(x2 - x1)

m = (0 - 1/2)/(5/7 - 0)

m = (-1/2)/(5/7)

m = -7/10

Using the point slope form, plug in the values of the slope and one point to set up the equation.

(y - y1) = m(x - x1)

where m = -7/10 and (x1 , y1) = (0 , 1/2)

(y - 1/2) = -7/10(x - 0)

y - 1/2 = -7/10 x

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Answer:

no photo

Step-by-step explanation:

we need a photo to decide if answer is correct or not

3 . (4-8) / 2

= 3. (-4) /2

= 3. ( -2)

=  -6

In algebraic equation or polynomial equation is an equation of the frame P=0 where P could be a polynomial with coefficients in a few field, regularly the field of the rational numbers.

algebraic equation, statement of the equality of two expressions defined by applying to a set of factors the algebraic operations, namely, expansion, subtraction, increase, division, raising to a control, and extraction of a root.

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According to the given data" the arithmetic mean of 6 x, 3 x , and 27 is 18" the value of x = 3.

The arithmetic mean or average, or simply the mean or average, is indeed the sum of a set of numbers multiplied by the number of numbers in the set.

One approach is to compute the arithmetic mean. To do this, add all of the values together and divide the total by the number pf values. For example, if you have a set of "n" numbers, add them together as follows: a + b + c + d, and so on. Then divide the total by "n."

If the arithmetic mean of 6 + x, 3 + x ,  27  =  18

So value of x will be as follows:

(6x + 3x + 27)

(6x + 3x + 27)/3 = 18

9x+27/3 = 18

9x +27 = 54

x = (54-27)/9

x  = 27/9

x = 3

According to the given data the value of x = 3.

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The total distance traveled in 2-hour time is 50 miles. (option g)

Shauna drove 75 miles in 3 hours at a constant speed, so the total distance covered in 3 hours is 75 miles to find the distance covered in 2 hours, we first need to find the distance or miles covered in 1 hour

To find the distance Shauna traveled in 2 hours, use the following formula: –

Speed ​​= distance/time

Total distance traveled = 75 miles

Total time = 3 hours = 3 hours

Speed ​​= 75/3

Speed ​​= 25 miles per hour

Distance traveled in 2-hour time is 50 miles.

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The exterior angle is acute, the sum of the farthest interior angles must also be acute, implying that the third angle is obtuse. As a result, every triangle should be obtuse.

An obtuse-angled triangle has one of its interior provides a clear view than 90°.. If one angle in an obtuse triangle measures upwards of 90°, the combination of the remaining two angles is a little less than 90°.

if the exterior angle is acute, this same sum of something like the remote interior angles must also be acute, implying that the third angle is obtuse. As a result, the triangle must be obtuse. Furthermore, because the exterior angle and A form a linear pair, A must be obtuse because consecutive acute angles cannot form a linear pair.

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The solution of the given equation 3(2-c)=-(c+4) is c = 5.

According to the given question.

We have an equation

3(2 - c ) = -( c + 4)

Since, we have to solve the above equation for c.

Therefore, the solution of the above equation is gievn by

3(2 - c) = -( c + 4)  

⇒ 3(2) -3(c) = -c -4  (by distributive law)

⇒ 6 -3c = -c - 4  

⇒ 6 + 4 -3c = -c            (adding 4 both the sides)

⇒ 10 -3c = -c

⇒ 10 = -c + 3c    ( adding 3c both the sides)

⇒ 10 = 2c

⇒ 10/2 = c        (multiply both the sides by 2)

⇒ 5 = c or c = 5

Hence, the solution of the given equation 3(2-c)=-(c+4) is c = 5.

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1. The private college's tuition account can earn $22,251,500 in simple interest at 2.33% in one year.

2. The account would earn $22,512,028 in one year at 2.33% interest compounded daily.

3. The difference between daily compound interest and simple interest is $260,528.

4. If the money is used to pay full scholarships, and the tuition price is $61,000 per year, 4 more students can receive full 4-year scholarships with daily compounding instead of simple interest.

Compound interest adds the earned interest to the principal and periodically compounds the new total, unlike simple interest.

1) Simple Interest:

Principal = $955 million

Period = 1 year

Interest rate = 2.33%

Simple Interest = $22,251,500 ($955,000,000 x 2.33% x 1)

2) N (# of periods) = 365 days

I/Y (Interest per year) = 2.33%

PV (Present Value) = $955,000,000

PMT (Periodic Payment) = $0

Results:

FV = $977,512,028.18

Total Daily Compound Interest = $22,512,028.18

3) The difference between daily compound interest and simple interest is $260,528 ($22,512,028 - $22,251,500).

4) Price of tuition per year = $61,000

Additional earnings from compounding interest = $260,528

Additional students to sponsor for tuition each year = 4.27 ($260,528/$61,000).

Thus, compound interest earns more for the investor than simple interest.

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The number of money farmers made by selling 5732 ducks will be $45856.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Mike sold 5,640 chickens and 5,732 ducks from his farm. He made $79,696. If he sold 5,640 chickens and 5,640 ducks, he would get $78,960.

Form two equations to get the amount:-

5640c + 5732d = 79696

5640c + 5640d = 78960

Solve both the equations by elimination method:-

5640c -5640c + 5732d - 5640d = 79696 - 78960

92d = 736

d = 736 / 92

d = $8

Total amount = $8 x 5732 = $45856

Therefore, the money farmers made by selling 5732 ducks will be $45856.

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The tangent to the given curve at the point (1,0) is: y=6x-6.

The first derivative f'(x), the slope (tangent) of the original curve, may be obtained at every point (x,y) on the curve because the supplied curve is a continuous function, making Eq. 1 differetiable at every x.

The slope of the tangent at x=1 is given by the first derivative of Eq. 1: f'(1)=9(1)2-3=6.

A line that passes through the point (x1, y1) and has a slope of m has the equation:

(y-y1)=m(x-x1) ··· Eq.2 (the point- slope form of linear function)

Here, x1=1, y1=0, and m=f'(x1)=6. Add these numbers to Eq. 2. It is possible to repeat and simplify Eq. 2 as follows: y-0=6(x-1) ⇒ y=6x-6

Consequently, y=6x-6 is the tangent to the given curve at position (1, 0).

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The sum of the infinite geometric series 0.5+0.05+0.005+ . . .  is S = 0.55556

The given geometric series is:

 0.5 + 0.05 + 0.005 + . . .

The common ratio (r) of a geometric series is given by:

  r = a(n) / a(n - 1)

Notice that in the given series:

a(1) = 0.5

a(2) = 0.05

a(3) = 0.005

Hence, the common ratio is

   r = a(2) / a(1) = 0.05/0.5 = 0.1

Since 0 < r < 1, the series is convergent and the sum exists.

Use the sum formula:

S = a(1) / (1 - r)

Substitute a(1) = 0.5 and r = 0.1 into the formula:

S = 0.5 / (1 - 0.1)

   = 0.5 / (0.9)

   = 0.55556

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The equation of the circle that passes through the point (0 , 4) and has a center at the origin is x^2 + y^2 = 16.

Using the distance formula, get the radius of the circle by solving for the distance between the center and the point (0 , 4).

radius = distance = √(x2 - x1)^2 + (y2 - y1)^2

radius = √(0 - 0)^2 + (4 - 0)^2

radius= √0 + 16

radius = 4

The standard form of the equation of the circle is given by (x - h)^2 + (y - k)^2 = r^2, where (h , k) is the location of the center and r is the radius of the circle.

Given the radius and center of the circle, substitute these values to the standard form of the equation of the circle.

(x - h)^2 + (y - k)^2 = r^2

where (h , k) = (0 , 0)

r = 4

(x - 0)^2 + (y - 0)^2 = 4^2

x^2 + y^2 = 16

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The proving of the trigonometric function [tex]\frac{1+\cos A}{\sin A}+\frac{\sin A}{1+\cos A} = 2 cosec A[/tex] that LHS = RHS is shown.

So, [tex]\frac{1+\cos A}{\sin A}+\frac{\sin A}{1+\cos A} = 2 cosec A[/tex]:

LHS = [tex]\frac{1+\cos \mathrm{A}}{\sin \mathrm{A}}+\frac{\sin \mathrm{A}}{1+\cos \mathrm{A}}[/tex]

[tex]=\frac{(1+\cos \mathrm{A})(1+\cos \mathrm{A})+\sin \mathrm{A} \sin \mathrm{A}}{\sin \mathrm{A}(1+\cos \mathrm{A})}\\\begin{aligned}&=\frac{(1+\cos \mathrm{A})^2+\sin ^2 \mathrm{~A}}{(1+\cos \mathrm{A}) \sin \mathrm{A}} \\&=\frac{1+\cos ^2 \mathrm{~A}+2 \cos \mathrm{A}+\sin ^2 \mathrm{~A}}{(1+\cos \mathrm{A}) \sin \mathrm{A}}\end{aligned}\\[/tex]

[tex]\begin{aligned}&=\frac{1+2 \cos A+1}{(1+\cos A) \sin A} \\&=\frac{2+2 \cos A}{(1+\cos A) \sin A}\end{aligned}\\\begin{aligned}&=\frac{2(1+\cos A)}{(1+\cos A) \sin A} \\&=2 \frac{1}{\sin A}\end{aligned}\\=2cosecA[/tex]

= RHS

Hence Proved.

Therefore, the proving of the trignometric function [tex]\frac{1+\cos A}{\sin A}+\frac{\sin A}{1+\cos A} = 2 cosec A[/tex] is shown.

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The correct question is given below:
Prove that:  [tex]\frac{1+\cos A}{\sin A}+\frac{\sin A}{1+\cos A} = 2 cosec A[/tex]

The probability that ht occurs before hh IS 1/3

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

P(HH)=1/4

P(HT)=1/4

p(HT) = ½×p(TH) + ½×1 = p(TH)/2 + 1/2.

p(HH) = p(HH)/2

p(HT) = p(TH)/2 + 1/2

p(TH) = p(HH)/2 + p(HT)/2

p(TT) = p(TH)/2 + p(TT)/2

p(HH) = 0.

p(TH) = p(HT)/2

p(HT) = p(HT)/4 + 1/2

p(TH) = 1/3

p(TT) = p(TH) implies p(TT) = 1/3

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The exact value of the expression is -1/2

Given the following trigonometry value

sin 5π/3

Since the value of π is 180 degrees, hence;

sin 5(180)/3

sin 5(60)

sin 300

This can be written as;

sin(360 - 30) = -sin30

sin(360 - 30) = -(1/2)

Hence exact value of the expression is -1/2

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The four consecutive integers are 121, 122, 123, 124.

We have the sum of four consecutive integers equals to 490

We have to determine those integers.

An integer is a number with no decimal or fractional part. It includes negative and positive numbers, including zero.

Assume the first integer is x. Then, the other integers will be -

x + 1 , x + 2 , x + 3.

Therefore -

x + (x + 1) + (x + 2) + (x + 3) = 490

4x + 6 = 490

4x = 484

x = 121

So -

x = 121

x + 1 = 122

x + 2 = 123

x + 3 = 124

Hence, the four consecutive integers are 121, 122, 123, 124.

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The radius of a table with a circumference of 10 feet is A. 1.6 ft .

A circle's outside boundary is called the circumference and can be measured, or calculated, by using

Circumference = 2πr

where r is the radius of circle.

Now it is given that,

Circumference of table = 10 feet

Since, Circumference = 2πr

⇒ 2πr = 10

⇒ r = 10/2π

⇒ r = 10/6.28

⇒ r = 1.59

⇒ r ≈ 1.6 feet

Thus, the radius of a table with a circumference of 10 feet is A. 1.6 ft

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Answer: y=31-5x

Step-by-step explanation:

subtract the 5x to the other side to get y.

The hypothesis is the phrase following the word if = " three points lie on a line"

The conclusion is the phrase following the word then = "they are collinear."

A specific, verifiable prediction of what the researcher(s) believe the study's results will be is known as a hypothesis (plural: hypothese). It is stated at the outset of the investigation.

Most often, this entails speculating on a potential correlation between two variables: the independent variable (what the researcher modifies) and the dependent variable (what the research measures).

The null hypothesis and the alternative hypothesis (known as the experimental hypothesis when the technique of examination is an experiment) are traditionally written as two separate forms of the hypothesis in research.

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The distance between the highest and the lowest points of elevation is 9904 meters.

In order to determine the distance between the highest and the lowest points of elevation, subtract the heights of both places from each other.

Subtraction is a mathematical operation that is used to determine the difference between two or more numbers. The sign used to denote subtraction is -.

Height of mount Everest - height of Turpan Pandi

8850 - (-154)

8850 + 154 = 9004m

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Hello,

[tex]2(x - 3) + 2x = 22[/tex]

[tex]2x - 6 + 2x = 22[/tex]

[tex]4x - 6 = 22[/tex]

[tex]4x = 22 + 6[/tex]

[tex]4x = 28[/tex]

[tex]x = \frac{28}{4} = 7[/tex]

Answer:

Step-by-step explanation:g(-3) = 3(-3) = -9

f(g(-3)) = f(-9) = 2(-9) -1 = -18 -1 = -19

Using the summation notation, the series 5+8+11+ . . . . . . +38 can be written as

[tex]\sum\limits^{12}_{n=1} {(3n+2)}[/tex]    or    [tex]24+3\sum\limits^{12}_{n=1} {n}[/tex]

Given an arithmetic series:

     5+8+11+ . . . . . . +38

The common difference (d) of each term is:

d = 8 - 5 = 3

The first term, a(1) = 5.

Hence, using the formula for the nth term of an arithmetic sequence:

a(n) = a(1) + (n-1) . d

a(n) = 5 + (n-1) . 3

a(n) = 3n + 2

Let us find n that result in a(n) = 38

a(n) = 3n + 2

38 = 3n + 2

3n = 36

n = 12

We can, then, conclude that the series  5+8+11+ . . . . . . +38 has 12 terms.

Therefore, the summation notation is:

[tex]\sum\limits^{12}_{n=1} {a(n)} = \sum\limits^{12}_{n=1} {(3n+2)}[/tex]

[tex]= \sum\limits^{12}_{n=1} {3n}+ \sum\limits^{12}_{n=1} {2}[/tex]

[tex]= 3\sum\limits^{12}_{n=1} {n}+ 2\times 12[/tex]

[tex]= 24+3\sum\limits^{12}_{n=1} {n}[/tex]

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