rationalise the denominator of \frac{26}{4+\sqrt{3}}

Answer:

8, 16, 32

Step-by-step explanation:

using the recursive formula [tex]U_{n+1}[/tex] = 2[tex]U_{n}[/tex] and U₁ = 4 , then

U₂ = 2 U₁ = 2 × 4 = 8

U₃ = 2 U₂ = 2 × 8 = 16

U₄ = 2 U₃ = 2 × 16 = 32

Answer:

15c + 19d

Step-by-step explanation:

Here to simplify we have to add like-terms

3c + 14d + c + 11c + 5d = ( 3c + c + 11c) + ( 14d + 5d) = 15c + 19d

Glad to Help

Answer:

pretty sure its (-6, -4)

Step-by-step explanation:

in the ||| quadrant so I know they are both negative.

The point is 6 units to the left and 4 units down.

Hope this helps! Good luck!

Answer:

Step-by-step explanation:

Answer:

what is your problem

If one leg is of length 5 inches then the lengths of the hypotenuse can be 2.113 inches or 4.5315 inches.

According to the question,

We have the following information:

A right triangle contains a 25° angle and length of one leg is 5 inches.

Now, the leg for which length is given can be opposite to given angle or adjacent to given angle. So, there are two possible for the length of hypotenuse (H).

Now, when it is opposite to the given angle:

Sin 25 = 5/H

H = Sin 25*5

H = 0.4226*5

H = 2.113 inches

Now, when it is adjacent to the given angle:

Cos 25 = 5/H

H = Cos 25*5

H = 0.9063*5

H = 4.5315 inches

Hence, if one leg is of length 5 inches then the lengths of the hypotenuse can be 2.113 inches or 4.5315 inches.

To know more about hypotenuse here

https://brainly.com/question/24107292

#SPJ1

Answer:

4/3

Step-by-step explanation:

gradient=

[tex] \frac{change \: in \: y}{change \: in \: x?} [/tex]

7--5=12

16-7=9

12÷9=4/3

the gradient is the same as slope

thus the answer is 4/3

The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

A linear equation or function is given as ;

y = mx + c

Here, m is the slope and is given as (y₂ - y₁)/(x₂ - x₁).

The slope of the line passing through (-4, -6) and (2, 8) will be,

m = (8 + 6)/(2 + 4)

m = 14/6

So, y = (14/6)x + c

Substitute,  (2, 8)

8 =  (14/6)2 + c

c = 8 - 14/3 = 10/3

Therefore, y = (14/6)x + 10/3

Hence "The equation of a line is the mathematical function of a line thus the equation of the line that passes through the points (-4, -6) and (2, 8) will be y = (14/6)x + 10/3".

For more about the equation,

brainly.com/question/10413253

#SPJ1

The equation of the line is, y = -3x.

What is point slope form of the line?

A line's point slope form equation is y - y1 = m(x – x1). Consequently,

y - 0 = m(x - 0), or y = mx, is the equation of a line passing through the origin with a slope of m.

Let the line passes through the point (1, -3) and having slope of -3.

Consider, the point slope form of the line,

[tex]y-y_1=m(x-x_1)[/tex]

Plug, [tex](x_1, y_1) = (1, -3), m = -3[/tex]

So, the above equation becomes

[tex]y-(-3)=-3(x-1)\\y+3=-3x+3\\y=-3x+3-3\\y=-3x[/tex]

Hence, the equation of line that passes through the point (1, -3) and having slope -3 is y = -3x.

To know more about the point slope form of the line, click on the link

https://brainly.com/question/6497976

#SPJ1

Answer:

∅

Step-by-step explanation:

set up your equation which will be [tex]\frac{-2-5}{-4+4}[/tex]  which is undefined because denominator cannot be 0

The area of hexagon is found to be 18 square units by using the giving conditions.

P = 6a, where an is the length of one of its sides, is the formula for a regular hexagon's perimeter. Here, the hexagon's interior angles are all 120 degrees.

Given: The perimeters of an equilateral triangle and a regular hexagon are equal.

We need to find the area of the hexagon.

Let,

x = side of trainagle

a = side of hexagon

3x = 6a

x = 2a

Area of equilateral triangle = ([tex]\sqrt{3}[/tex]/4)x² = 12 square units

Area of hexagon is given as follows:

= 6([tex]\sqrt{3}[/tex]/4)a²

= (6[tex]\sqrt{3}[/tex]/4)(x²/4)

= 12(6)/4

= 18 square units

Therefore, the area of hexagon is found to be 18 square units by using the giving conditions.

Learn more about perimeter of hexagon here:

https://brainly.com/question/28821374

#SPJ4

An equation in slope-intercept form that represents the situation is C(x) = -267 + 6x.

A linear equation is an equation that has a single variable that is raised to the power of one. When shown on a graph, a linear equation is a straight line that can slope either upward or downward.

The general form of a linear equation is

y = mx + b

Where:

Slope = change in the chirps / change in the temperature

Slope = (117 - 99) / (64 - 61)

Slope = 18 / 3

Slope = 6

99 = a + 6x

99 = a + 6(61)

99 = a + 366

a = 99 - 366

a = -267

C(x) = -267 + 6x

To learn more about linear functions, please check: https://brainly.com/question/26434260

#SPJ1

By using the concept of kinetic energy, it is obtained that

Kinetic energy of the  airplane when its velocity is 300 m/s is 20250 megajoule

What is Kinetic energy?

Kinetic energy is the energy possessed by the body by virtue of its motion

If m is the mass of the body and v is the velocity of the body, then kinetic energy is given by the formula

Kinetic energy = [tex]\frac{1}{2} \times m \times v^2[/tex]

Let the mass of the airplane be m kg

Velocity = 220 m/s

Kinetic energy = [tex]\frac{1}{2} \times m \times (220)^2[/tex]

By the problem,

[tex]\frac{1}{2} \times m \times (220)^2 = 10890\times 10^6[/tex]

[tex]m = \frac{10890\times 10^6\times 2}{220\times 220}[/tex]

m = [tex]0.45 \times 10^6[/tex] kg

Now,

Velocity = 300 m/s

Kinetic energy = [tex]\frac{1}{2} \times 0.45 \times 10^6 \times 300 \times 300[/tex]

                        = [tex]20250 \times 10^6[/tex] J

                        = 20250 mega joules

To learn more about Kinetic energy, refer to the link-

https://brainly.com/question/25959744

#SPJ13

Each part of Nick's and Autumn's expressions mean can be explained as follows;

Nick;

Autumn:

ler

Nick expression:

[tex] {20( \frac{1}{2} })^{w} [/tex]

Where,

the amount of substance he begins with = 20

the amount of substance left after each week = 1/2

If w = 2

[tex] {20( \frac{1}{2} })^{w} [/tex]

[tex]{20( \frac{1}{2} })^{2} [/tex]

= 20(0.25)

= 5 milligrams

Autumn's expression:

[tex] {(1 - 0.5)}^{w} [/tex]

The one outside of parentheses = the initial amount of the substance.

The one inside of parentheses = 100% of the original amount of the substance.

0.5 represents the 50% of the substance that is lost each time period

[tex] {(1 - 0.5)}^{w} [/tex]

[tex] {(1 - 0.5)}^{2} [/tex]

= (0.5)²

= 0.25 milligrams

Complete question:

Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by 1/2 each week for a number of weeks, w. He writes the expression 20(12)w to find the amount of radioactive substance remaining after w weeks. Autumn starts with 1 milligrams of a radioactive substance. The amount of the substance decreases by 50% each week for a number of weeks, w. She writes the expression (1-0.5)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.

Read more on equation:

https://brainly.com/question/11250752

#SPJ1

Answer:

I believe its the FICA and the payroll taxes

Step-by-step explanation:

The factor of the expression 32z - 48 will be 16 and (2z - 3). And the greatest common factor is 16.

Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).

The expression is given below.

⇒ 32z - 48

The expression can be rewritten as,

⇒ 32z - 48

⇒ 16 · 2z - 16 · 3

⇒ 16 (2z - 3)

The factor of the expression 32z - 48 will be 16 and (2z - 3). And the greatest common factor is 16.

More about the greatest common factor link is given below.

https://brainly.com/question/11221202

#SPJ1

Answer:

76

Step-by-step explanation:

The value of missing number is 8.

Integers come in three types:

Given:

6(-?)+1=-47

let the unknown value be x.

6(-x ) + 1= -47

Now, Subtract 1 from both side

-6x + 1 - 1= -47 - 1

-6x = -48

x= -48/(-6)

x = 8

Hence, -6(8) + 1 = -47.

Learn more about Integers here:

https://brainly.com/question/15276410

#SPJ1

Step-by-step explanation:

   a-b=10--(1)

Same side interiors(vertical) have sum 180°

   a+b=180--(2)

From both equations

2a=190

   a=95

And

  a-b=10

   b=95-10

   b=85

The probability that at most eight of ten independently selected specimens have a hardness less than 73.84 is 0.2639.

Probability:

The chance that a particular event (or set of events) will occur is expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics.

Here we have to find the probability:

The probability that each specimen has a hardness less than 73.84 is:

p =Ф( Z< 973.84 - 70)/ 3)

= Ф(Z<1.28 ) = 0.899

P(X<=8) = 1 - P(X=9) - P (X=10)

= 0.2639

So out of 10 specimens, the probability that 8 or fewer have a hardness less than 73.84 is 0.2639

To know more about the probability refer to the link given below:

https://brainly.com/question/13604758

#SPJ4

A source of money that allows individuals to pay for goods and services later is called consumer credit and an advantage of this source of money is that there are no interest charges.

Consumer credit, also known as consumer debt, enables the consumers to incur debt or borrow money and to defer repayment of that money over time. It allows consumers to buy goods without having to pay for them in cash at the time of purchase. Examples of consumer credit include credit cards, student loans, etc. Among the advantages of using consumer credit is that there is no interest charge to borrow the money for a certain period of time until the due date.

Learn more about Consumer credit:

https://brainly.com/question/17237024

#SPJ4

Using the exterior angle theorem, the measure of angle WXY is calculated as: 20°.

Given the triangle in the image below has the following:

According to the exterior angles theorem, the sum of the two remote angles would be equal to the measure of the exterior angles, therefore:

10x - 5 = 3x + 2 + 3x + 17

Combine like terms

10x - 5 = 6x + 19

10x - 6x = 5 + 19

4x = 24

4x/4 = 24/4

x = 6

m∠WXY = 3x + 2 = 3(6) + 2

m∠WXY = 18 + 2

m∠WXY = 20°

Learn more about the exterior angle theorem on:

https://brainly.com/question/24756010

#SPJ1

The distance of PR is 21

Given,

The points P, Q, R and S all lie on the same line segment.

The ratios;

PQ:QR:RS = 1:3:1.

Distance of PS = 35

We have to find the distance of PR.

A line segment is a piece of a straight line that has all of the points on the line contained within and is bounded by two distinct endpoints. A line segment's length is determined by the Euclidean distance that separates its two ends.

Here,

PQ : QR : RS = 1 : 3 : 1.

Now let PQ = x, QR = 3x and RS = x.

Therefore,

PQ + PR + RS = PS.

x + 3x + x = 35

5x = 35

x = 7

Therefore,

PR = 3x

PR = 3 × 7

PR = 21

The distance of PR is 21

Learn more about line segment here;

https://brainly.com/question/28793582

#SPJ1

Answer:

  Barlow School has 178 more boys

Step-by-step explanation:

At Barlow School, 4/9 of 873 students are boys. At Willow School, 2/3 of 630 students are girls. You want to know which school has more boys, and by how many.

The number of boys is ...

  4/9 × 873 = 388

The 1/3 of students that are not girls are presumed to be boys. That number is ...

  1/3 × 630 = 210

The difference in the number of boys is ...

  388 -210 = 178

Barlow School has 178 more boys.

Answer:

Step-by-step explanation:

Yes it does

10 and 15

Answer:

A. the independent and dependent variables are the number of miles and total fee (y = 2.8 + 3.5x)

B. the domain is 0 <= x <= 20 and  range is 2.8≤x≤20

Step-by-step explanation:

A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a prospective study.

Individuals are tracked over time in prospective studies, and information is gathered about them as their characteristics or circumstances change. Prospective studies include things like birth cohort studies. In retrospective research, people are sampled, and details about their past are gathered. Always after a predetermined number of incidents, the analysis takes place. The fact that individuals were enrolled and baseline data was obtained before any subjects experienced an outcome of interest identifies a study as prospective.

Given,

A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a ...

Prospective study

To learn more about prospective study, visit:

https://brainly.com/question/28565073

#SPJ4

Answer:

-1,4

Step-by-step explanation:

move the point to the left 7 times

The quotation for division of 7/4 that is 1 3/4 divided by 3 will be 7/12 by the rule of division that is a/b÷c/d=a/b*d/c.

A number is divided in division, which is a straightforward operation. The simplest way to conceptualize it is as a set of objects being distributed among a set of individuals, as in the example given above. A division is the division of a given sum into equal parts. For instance, we could split a group of 20 people into four groups of 5, five groups of 4, and so on. Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. To determine how many equal groups are created or how many people are in each group, division is the primary objective.

Here,

1 3/4=7/4

7/4÷3/1,

a/b÷c/d=a/b*d/c

7/4*1/3=7/12

According to the division rule a/b÷c/d=a/b*d/c, the quotation for 7/4, which is 1 3/4 divided by 3, will be 7/12.

To know more about division,

https://brainly.com/question/21416852?referrer=searchResults

#SPJ13

The value of the expression −2(42−7)+(−5) is -75.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, we want to calculate the value of the expression:

−2(42−7)+(−5)

= -2(35) + (-5)

= -70 - 5

= -75

The value is -75.

Learn more about expressions on:

brainly.com/question/723406

#SPJ1