Here are two similar pentagons which make up a badge.
width - 3x cm & length - 27cm - large badge
width - x cm & length - (x+3)cm - small badge
Work out the width of the badge.

Answer:

3;m=-6

Step-by-step explanation:

3;m=-6

The magnitude of vector →RS is 3√2

And the direction of vector →RS is given by an angle 315°

Let R(1,0) = (x1, y1) and

S(-2,3) = (x2, y2)

By distance formula, the magnitude of vector is

[tex]|\vec {RS}| = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\|\vec {RS}| =\sqrt{(-2-1)^2+(3-0)^2} \\\\|\vec {RS}| =\sqrt{(-3)^2+3^2} \\\\|\vec {RS}| =\sqrt{9+9}\\\\ |\vec {RS}| =3\sqrt{2}[/tex]

To find the direction of the vector RS :

[tex]tan(\theta)=\frac{y_2-y_1}{x_2-x_1} \\\\tan(\theta)=\frac{3-0}{-2-1}\\\\tan(\theta)=\frac{3}{-3}\\\\ tan(\theta)=-1\\\\ \theta=tan^{-1}(-1)\\\\\theta=45^{\circ}[/tex]

However, the angle is in the fourth quadrant, so we add  360°  to obtain a positive angle.

Thus,  −45° + 360° = 315° .

Therefore, the magnitude of vector →RS is 3√2

And the direction of vector →RS is given by an angle 315°

Learn more about the magnitude and direction of vector here:

https://brainly.com/question/10151539

#SPJ4

According to the given data the m ∠1+m ∠2=m∠6+m∠ 7 proofed by symmetric property:

The symmetric property of equality is significant in mathematics because that tells us that both sides of either an equal sign are equal regardless of which side of the section they are on.

But it wasn't until the nineteenth century that mathematicians like Evariste Galois, an unhappy French genius, uncovered symmetries hidden in mathematical equation solutions.

Given: ∠3 ≅ ∠5

Prove: m ∠1+m ∠2=m∠6+m∠ 7

Now ,

m ∠1+m ∠2=m∠6+m∠ 7..........(1)

m∠6+m∠ 7 = ∠3 + m∠4..............(2)

m ∠1+m ∠2 = ∠3 + m∠4

(subtracting)

m∠4 +m∠3  = m ∠3 + m∠4

symmetric property:

m ∠1+m ∠2=m∠6+m∠ 7

According to the given data the m ∠1+m ∠2=m∠6+m∠ 7 proofed by symmetric property:

To know more about symmetric property visit:

https://brainly.com/question/1527538

#SPJ4

Answer:

First Section:4km per hour

Second Section:0km per hour

Third Section:1.5km per hour

Step-by-step explanation:

From the first section to the second section the distance remains the same therefore he didn't travel at all that's why it is 0km. For the third section he has to travel 6 kilometers in 4 hours which is 1.5.

a. The square roots and square cancel each other so 5 × 3 = 15

b. The cube roots and cubes cancel each other so 9 × 30 = 270

For math students, especially those in class 8, the square root and cube root concepts are the most crucial. In order to get the square root of any integer, we must first identify a number that, when multiplied twice by itself, equals the original number.

Similar to this, we must locate a number that, when multiplied three times by itself, equals the original number in order to get the cube root of any number.

The cube root is represented by the sign "√," whereas the square root is represented by the symbol "∛."

Learn more about roots

https://brainly.com/question/12105008

#SPJ1

Using scientific notation and subtraction between two amounts, the difference between the payrolls is given by:

B. 2.5753 x 10¹¹ dollars.

A number in scientific notation is given by:

[tex]a \times 10^b[/tex]

With the base being [tex]a \in [1, 10)[/tex].

For any generic amounts a and b, to find how much an amount a is more than an amount b, we subtract a by b.

For this problem, the budgets are given as follows:

Hence the difference is given by:

2.6 x 10¹¹ - 2.47 x 10^9

To subtract two numbers in scientific notation, they must have the same exponent, hence:

2.47 x 10^9 = 0.247 x 10^10 = 0.0247 x 10¹¹.

Then the difference is:

2.6 x 10¹¹ - 0.0247 x 10¹¹ = 2.5753 x 10¹¹ (to subtract two numbers in scientific notation, we subtract the bases and keep the exponents).

The difference between the payrolls is given by:

B. 2.5753 x 10¹¹ dollars.

More can be learned about scientific notation at https://brainly.com/question/16394306

#SPJ1

These sites are on a line with a -5 degree slope.

The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. B is the b in the location where the y-intercept is located (0, b). For instance, the y-intercept for the equation y = 3x - 7 is (0, 7) and the slope is 3.

In response to the query, I see the points as

(x ,y)

(13, 11)

(14, 6)

(15, 1)

(16, -4)

(13, 11) , (14, 6), (15, 1), and (16, -4)

slope =  (6 - 11) / (14 - 13)

= - 5/-1

 = -5

try again:   (1 - 6)/(15 -14)

= -5/1

= -5

To know more about Slope of line visit;

https://brainly.com/question/28108658

#SPJ9

4.6 percent of the world population, to the nearest tenth, lived in the United States at this time.

What are examples of linear equations?

[tex]\frac{United States population}{world population} = \frac{301,000,000}{6,602,000,000}[/tex] × 100

                               ≈ 4.6

Learn more about  linear equations

brainly.com/question/11897796

#SPJ4

The base and height of triangle are 25 and 22 feet.

We are given the relation between base and height of triangle. Let us represent height with h and base with b. The equation relating the two quantities is as follows -

h = b - 3

Now, the area of triangle is given  by the formula -

Area = 1/2 × base × height

Keep the values in formula to find the base of triangle

275 = 1/2 × b × (b-3)

550 = b × (b-3)

b² - 3b - 550 = 0

b² + 22b - 25b - 550 = 0

b (b + 22) -25 (b + 22) = 0

(b + 22) (b - 25) = 0

b = -22 and 25

As the value of base can not be negative, so, the base of triangle is 25 feet.

Calculating height of triangle-

Height = Base - 3

Height = 25 - 3

Height = 22 feet

Hence, the base and height of triangle are 25 and 22 feet.

Learn more about calculations of triangle -brainly.com/question/17335144

#SPJ4

From the inequality given by 8x + 15 > 9x - 26, x is less than 41.

Inequality refers to the relationship between two non-equal expressions. It can be denoted by > for greater than, < for less than, >/= for greater than and equal to, and </= for less than and equal to.

Solving the inequality,

8x + 15 > 9x - 26

Combine like terms in one side and the constants in the other side.

8x - 9x > -26 - 15

-x > -41

Divide both sides by -1.

x > 41

Note that when we multiply or divide by a negative number

we must reverse the inequality.

x < 41

Therefore, x is less than 41.

To learn more about solving inequalities: https://brainly.com/question/24372553

#SPJ4

I and IV only are statements that are true out of all the statements.

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

I. -(-6)=6 and -(-4)>-4

⇒ 6 = 6 and 4 > -4

IV. 17>2 or 6<9

Learn more about  linear equations

brainly.com/question/14323743

#SPJ4

The common difference d is 6 and the first term a1 is 20.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same value.

The formula of Arithmetic progression is

a(n) = a1 + (n - 1)d

given that the two terms of arithmetic sequence,

a3 = 32 and a7 = -8.

now, find the common difference d.

a(n) = a1 + (n - 1)d

Let take a(n) = a7 and a1 = a3.

a7 = a3 + (7 - 3)d

a7 = a3 + 4d

now substitute the values of a6 and a4

-8 = 32 + 4d

-8 + 32 = 4d

d = 24/4

d = 6

so, the common difference d is 6.

then, find the term a1.

take the formula

a(n) = a1 + (n - 1)d

now, substitute a(n) = a3 and d = 6.

32 = a1 + (3-1)d

32 = a1 + 2d

32 = a1 + 2(6)

32 = a1 + 12

a1 = -12+32

a1 = 20.

so, the first term a1 is 20.

Hence, the common difference d is 6 and the first term a1 is 20.

Learn more about Arithmetic progression from here:

https://brainly.com/question/6561461

#SPJ4

The following set of numbers, 8, 15, and 17, can be the measures of the sides of a triangle, specifically a right triangle.

To know if a set of number is a valid measure of the sides of a triangle, it must follow the Triangle Inequality Theorem which states that the sum of any two sides must be greater than the third side, such that a + b > c, a + c > b, and b + c > a.

let a = 8, b = 15, and c = 17

a + b > c     8 + 15 > 17     23 > 17     True

a + c > b     8 + 17 > 15      25 > 15     True

b + c > a     15 + 17 > 8     32 > 8     True

To know what type of triangle based on the length of its side:

1. Take the sum of the squares of the two smaller sides.

8^2 + 15^2 = 289

2. Compare it to the square of the largest side.

17^2 = 289

289 = 289

If the sum of the squares of the 2 is larger than the square of the 3rd, it is an acute triangle.

if they are equal, it is a right triangle

if they are smaller, then it is an obtuse triangle.

Hence, 8, 15, and 17 can be the measure of the sides of a right triangle.

To learn more about types of triangle based on side lengths: brainly.com/question/13619935

#SPJ4

The cost of the meal is 53.

The tip percentage is x.

Percentage is a measure of frequency that is used to describe a number as a fraction out of 100. The sign that is used to represent percentages is %.

The total cost of the meal is the sum of the amount paid for the meal and the amount paid for the tip. The amount that is paid for the tip is a function of the total amount of the meal.

Total cost = cost of the meal + tip paid

Total cost = cost of the meal x (1 + tip)

53( 1 + x)

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ1

The interval notation that expresses the expression is (-∝, 3] ∩ (-∝, -1) ∩ (-1, ∝) ∪ [4, ∝)

The expression is given as:

x ≤ 3 and x ≠ -1 or 4 ≤ x

In inequality, "and" is represented with ∩, while "or" is represented with ∪

The above can be represented as:

x ≤ 3 ∩ x ≠ -1 ∪ 4 ≤ x

As an interval notation, we have (-∝, 3] ∩ (-∝, -1) ∩ (-1, ∝) ∪ [4, ∝)

Hence, the interval notation that expresses the expression is (-∝, 3] ∩ (-∝, -1) ∩ (-1, ∝) ∪ [4, ∝)

Read more about interval notation at

https://brainly.com/question/24424191

#SPJ1

The equation of the circle (x + 8)^2 + (y + 3)^2 = 121 has a radius of 11 and a center located at (-8 , -3).

The standard form of the equation of  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.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle in standard form is (x + 8)^2 + (y + 3)^2 = 121, then

h = -8

k = -3

r = √121

r = 11

Learn more about equation of a circle here: https://brainly.com/question/1559324

#SPJ4

Answer:

1 is 6 pages, 7 minutes is 24 pages, 14 minutes is 45 pages

Step-by-step explanation:

the unite rate is 3

Using the distance formula, the distance between the pair of points C(11,-12) and D(6,2) is 14.86 units

Given,

The points = C(11,-12) and D(6,2)

We know the distance formula = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]

Substitute the values in the equation

The distance = [tex]\sqrt{(6-11)^{2}+(2--12)^{2} }[/tex]

[tex]=\sqrt{(-5)^{2}+14^{2} } \\=\sqrt{25+196}\\ =\sqrt{221}[/tex]

=14.86 units

Hence, Using the distance formula, the distance between the pair of points C(11,-12) and D(6,2) is 14.86 units

Learn more about distance here

brainly.com/question/15958176

#SPJ4

Step-by-step explanation:

Lets understand the situation,

This means Each team can have 3, 4 or 5 people.And 21 people take part.

we have to find How many different possible arrangements of teams are there.

Situation 1.

situation 2.

Situation 3.

situation 4.

The arithmetic series 1+5+9+. . . . . +41+45 can be expressed in summation notation as [tex]\sum\limits^{12}_{n=1} {(4n-3)}[/tex]

The given arithmetic series:

    1+5+9+. . . . . +41+45

To write the series in summation notation:

Find the common difference (d) of the series.

d = 5 - 1 = 4

Recall the formula for the nth term in an arithmetic sequence:

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

Substitute a(1) = 1 and d = 4:

a(n) = 1 + (n-1) . 4

a(n) = 4n - 3

Find n that leads to a(n) = 45

a(n) = 4n - 3

45 = 4n - 3

4n = 48

n = 12

Thus, the lower limit of the summation is n =1, and the upper limit is n = 12

Now write in summation notation as:

[tex]\sum\limits^{12}_{n=1} {a(n)}= \sum\limits^{12}_{n=1} {(4n-3)}[/tex]

This summation notation can be further simplified using the properties of summation operator:

[tex]\sum\limits^{12}_{n=1} {(4n-3)}=\sum\limits^{12}_{n=1} {4n}-\sum\limits^{12}_{n=1} {3}[/tex]

[tex]=\sum\limits^{12}_{n=1} {4n}-12\times3[/tex]

[tex]=\sum\limits^{12}_{n=1} {4n}-36[/tex]

Learn more about summation notation here:

https://brainly.com/question/542712

#SPJ4

The  Δ FGH with base FG that is 2a unit long has been drawn below.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

Δ FGH is a isosceles triangle.

Now isosceles triangle is a triangle whose two sides are equal.

In the ΔFGH, HF = HG

Hence "The  Δ FGH with base FG that is 2a unit long has been drawn below".

For more about triangles,

https://brainly.com/question/2773823

#SPJ4

Answer: the third option

Step-by-step explanation: 0.66666666666 is it in decimal form, the line above the single six just means its the same number over and over again

Answer:

.67 (See explanation for why)

Step-by-step explanation:

2/3

in order to turn this into a whole number, we are going to multiply the bottom number until it becomes any number starting with 1 and ending with a zero. this isnt possible Because 3 is a number that cannot do that.

So instead, we will multiply the number by 333

2*333 = 666

3*333 = 999

666/999 = 2/3

999 is nearly 1000, so lets write the decimal point 3 spaces inwards

.666

which can become

.66

The longer decimal for this(when using a calculator)

would give you

.6666666667

And if we round,

7 is higher than 5, so it becomes .666666667

continue...

Until you have .67

Hope this helps! ^^

The best friend is the faster runner as his speed is 51.28 m/s while my speed is 48.78 m/s.

Speed is defined as the distance travelled by someone or something in unit time. The SI unit of speed is meters per second. The speed is calculated by dividing the distance travelled by the total time taken to travel said distance.  

Given the distance travelled by both of the friends is 400 meters.

Now The first friend travels this distance in 8.2 seconds:

Therefore speed is calculated by distance ÷ time

or, speed = 400 ÷ 8.2

or , speed = 48.7804... m/s

or, speed ≈ 48.78 meters per second

And the best friend travels this distance in 7.8 seconds:

Therefore speed is calculated by distance ÷ time

or, speed = 400 ÷ 7.8

or , speed =51.2820... m/s

or, speed ≈ 51.28 meters per second

Therefore by comparing both the speeds we can conclude that the best friend is the faster runner.

To learn more about speed visit:

https://brainly.com/question/9834403

#SPJ1

Answer:

the answer is great Britain because

Step-by-step explanation:

it is very good for this subject

Answer:

3[tex]x^{2}[/tex] + 4x + xy

Step-by-step explanation:

Basically just combining like terms

[tex] \large \bf \implies{ {3x}^{2} + xy + 4x} \\ [/tex]

Step 1) Combine the like terms

Step 2) Add/Subtract the terms

Step 3) We have got the answer

Answer: c=-0.01

Step-by-step explanation:

Answer:

7 and 27

Step-by-step explanation:

We can make an equation for this, it looks like this:

6+3x+x=34

Simple algebra can be used to solve this (x is the smaller number)

1. 6+3x+x=34

2. 6+4x=34 Combine like terms

3. 4x=28 Simplify

4. x=7 simplify

Now that we have the smaller number we can use a portion of the original equation to solve with x=7.

1. 6+3x

2. 6+3(7)

3. 6+21

4. 27

So the smaller number is 7, and the larger number is 27.

Using the absolute value function, linear functions and translations, we have that:

9. Vertex (2, 0), Range: {y | 0 ≤ y < ∞}

10. The equation is f(x) = -5x + 100.

11. The correct option is: The slope of f(x) is greater than the slope of g(x).

12. h(-5) = 10.

13. The equation is f(x) = 2x + 5.

14. The graph of y = f(x) will shift right 9 units.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0, and has vertex(turning point) at (0,0). The range is from the y-coordinate of the vertex to positive infinity.

In item 9, from the table, the turning point is at (2,0), hence:

Vertex (2, 0), Range: {y | 0 ≤ y < ∞}

A linear function is modeled by the following rule:

y = mx + b

In which:

For item 10, we have that:

Then:

The equation is f(x) = -5x + 100.

For item 11, the slope is given by change in y divided by change in x, hence:

Hence:

The correct option is: The slope of f(x) is greater than the slope of g(x).

For item 12, we have that:

h(x) = -4x - 10.

Hence, when x = -5:

h(-5) = -4(-5) - 10 = 20 - 10 = 10.

Hence:

h(-5) = 10.

For item 13, we have that when x changes by 4, y changes by 8, hence the slope is:

m = 8/4 = 2.

When x = 1, y = 7, hence, considering the slope, when x = 0, y = 5, and:

The equation is f(x) = 2x + 5.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

For this problem, the rule is given by:

y = f(x - 9).

The translation is x -> x - 9, hence:

The graph of y = f(x) will shift right 9 units.

More can be learned about functions at https://brainly.com/question/24808124

#SPJ1

Answer:

(For number 9) Range {y/0<y<infinity} Vertex (2,0)

Step-by-step explanation:

I took test

I hope I helped for that part of it.

The distance between pair of parallel lines with the given equations

x=-2 x=5 is 7 units

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The distance between parallel lines on a graph can be given as x1 - x2 as both are equidistance from y for which y has been cancelled.

here x1 =5 and x2 = -2

So, x1 - x2 = 5 -(-2)

                 = 5 + 2

                 = 7

Learn more about Parallel lines

https://brainly.com/question/4954460

#SPJ4

Answer:

-7

Assuming that "It can be any"