Work out the size of one exterior angle of a regular hexagon.

Answer:

x = 7

Step-by-step explanation:

Ok, so these angle are equal, because they are opposite angle

So we could write as x+16 = 4x - 5

Now we solve the equation:

x+16 = 4x - 5

16+5 = 4x -x

21 = 3x

7 = x

Expression as a single natural logarithm of equation ln 18-ln 10 is = 0.5877866649.

ln 18-ln 10

= [tex]ln (18/10)[/tex]

= ln 1.8

= 0.5877866649

The inverse of an exponential function, the natural log is the logarithm to the base of the number e. Natural logarithms are unique varieties of logarithms that are employed in the treatment of time and growth-related issues.

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

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For the given sides AB and BC the angle included would always be Angle B

When we form a triangle we name the vertex as A, B and C. So, the sides AB and BC will always have an Angle B regardless of the naming convention we use.

A triangle is a polygon with three vertices and three edges that has three sides. It is a basic geometric shape. The term "abc" refers to a triangle containing the vertices a, b, and c. Any three non-collinear points in Euclidean geometry combine to create a singular triangle and a singular plane.

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After solving the equation In (2m + 3) = 8, the value of m is equal to 5/2.

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.

We have been asked to find m in (2 m+3) = 8

⇒ (2 m+3) = 8

⇒ 2m + 3 = 8

⇒ 2m = 8 - 3

⇒ 2m = 5

⇒ m = 5/2

So, m is equal to 5/2 in (2 m+3) = 8

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Answer:

umber is greater than or equal to 15.

Step-by-step explanation:

Let number be x

Quotient of number and 3 =

4 more than = 4+

4+ is at least 9

4+≥9

Simplifying it ,we get

≥9-4

≥5

x ≥ 5(3)

x≥15

Number needs to be greater than or equal to 15

    Equation

(x ÷ 3) + 4 ≥ 9

___________

    Solution

x ≥ 15

Step-by-step explanation:

Solve the inequality

[tex]\left(x\div3\right)+4\ge \:9\\x\div 3+4-4\ge \:9-4\\x\div 3\ge \:5\\3x\div 3\ge \:5\cdot \:3\\x\ge \:15[/tex]

Thus, the inequality solution is x ≥ 15

Answer:

9, 11, and 19

Step-by-step explanation:

9, 11, and 19 are the only plausible answers because there were only 2 periods where the phone was at 100% (other than when the graph started) and these are the only hours that fell within those periods..

[tex]\stackrel{mixed}{-6\frac{2}{7}}\div -\cfrac{8}{21}\implies -\cfrac{6\cdot 7+2}{7}\div -\cfrac{8}{21}\implies \stackrel{improper}{-\cfrac{44}{7}}\div -\cfrac{8}{21} \\\\\\ -\cfrac{44}{7}\cdot -\cfrac{21}{8}\implies \cfrac{(-44)(-21)}{(7)(8)}\implies \cfrac{924}{56}\implies \cfrac{33}{2}\implies {\LARGE \begin{array}{llll} 16\frac{1}{2} \end{array}}[/tex]

The step 2 is incorrect angle o and angle p form supplementary angles not alternate interior angle that is :

∠o +  ∠p = 180°

What are alternate interior angle ?

An alternate interior angle is one formed on the inside side of two parallel lines and opposite on the outer side of the transversal when those two parallel lines are intersected by a transversal and they are equal.

Alternate angles between a transverse and parallel lines are equal .

Here, the step 1 is correct :

as the sum of angles of a triangle is 180 degree therefore,

∠m +∠n + ∠o = 180°.............(1)

the step 2 is incorrect :

as angle o and angle p form supplementary angles not alternate interior angle therefore it will be :

∠o +  ∠p = 180°........(2)

after that step 3 and 4 is correct to get the final result as :

step 3 : ∠m +∠n + ∠o = ∠o +  ∠p

step 4 : ∠m +∠n = ∠p

Therefore, the step 2 is incorrect angle o and angle p form supplementary angles not alternate interior angle.

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y = 3x -5 is the equation of the line parallel to the line and going through the point (4,7). The format is slope intercept.

A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.

Using the information provided,

y= 3x – 5

First, we must keep in mind that parallel lines have an equal slope.

In essence,

m1 = m2 if line 1 and 2 are parallel.

Y = mx + c is the slope-intercept form of the equation; y = 3x + 6, which already has this form.

incline of the m1 = 3.

Consequently, m1 = 3 = m2.

The slope of the parallel line, m2 = 3 and the line passes through the point (4,7).

Therefore;

3 = (y - 7)/(x-4)

By cross product;

3x - 12 = y - 7

y = 3x - 5

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Answer: at least 3 more games

Step-by-step explanation:

70% of 72 is 50.4

50.4 - 48 = 2.4

Because one can't win only a fourth of a game, you need to round up. Bringing us to at least 3 more games to win

A. Using subtraction, the distance between the two birds = |-2.5 - 2.5| = |-5| = 5 meters.

B. Using additive inverses, the distance = 2.5 + 2.5 = 5 meters

The distance between any two points on a number line is the absolute difference of the coordinates of the two points.

The additive inverse of a number is the number that is added to the number to make it zero. For example, the additive inverse of a is -a.

Part A:

Using subtraction, the distance between the two birds = |-2.5 - 2.5| = |-5| = 5 meters.

Part B:

The additive inverse of -2.5 is 2.5.

Using additive inverses, the distance = 2.5 + 2.5

Using additive inverses, the distance = 5 meters

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Answer:B

Step-by-step explanation:

5x + 8

2(5x+8)

2(5x+8) is the express of twice the sum of 5 times a number and 8

answer: 2 (5x+8) = 12

The mode  for the distribution of scores in the following frequency distribution table is 3, which is the second option.

This is a term used in statistics to refer to the number of highest occurrence. Mode refers to the value that highest the number of frequency. In finding the mode, it is better to orderly arrange the given data to help see the value that occurs more frequently as this is the mode.

For the values given in the distribution of scores in the frequency distribution table the mode is three  ( 3 ) and it is the second option

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The given expression can be simplified by using rules of exponents.

There will be two rules applied, one for negative exponent and other for multiplication of exponents.

The expression can be solved by using either of the rules first. In this case, we will solve for the negative exponent first.

The base term x has a negative exponent of -4/7.  The negative exponent rules states that the term with the negative exponent can be expressed in a reciprocal or reverse form without the negative sign.

In the general form, x^-a=1/x^a.

Applying the rule here,

(x^⁻⁴/₇)^7=(1/x^4/7)^7

Now multiplying the powers and simplifying,

(1/x^4/7)^7=1^7/x^(4/7)*7=1/x^4

The simplest form of the expression (x^⁻⁴/₇)^7 is 1/x^4

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The solution of the radical equation of x is 1.

A linear equation in one variable is an equation which can be represented in the form of ax+b where x is the variable and 'a' is the coefficient and 'b' is  the two constants.

A radical equation is defined as an equation where the variable is under a radical or root.

We know that n-th root of a variable x can be written as x to the power of (1/n). Mathematically : [tex]\sqrt[n]{x} =x^{\frac{1}{n} }[/tex]

In the given equation:

∛x-1=√x-1

adding 1 to both sides we get:

or, ∛x=√x

Cross multiplying we get:

or, ∛x/√x =1

We know that (aˣ/aⁿ)=a⁽ˣ⁻ⁿ⁾

therefore :

or, [tex]x^{\frac{1}{3}-\frac{1}{2} }=1[/tex]

or, [tex]x^{-\frac{1}{6} }=1[/tex]

or, x=1

Hence the value of x in the radical equation is 1

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Answer:

the coefficient is 5 and 7 the constant is 2

Answer:

Parallel

Step-by-step explanation:

we can state that Option D may be accurate and true.

Assuming that the function, g, it has a domain of -1 ≤ x ≤ 4 and a range of                       0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8

Then the following properties must hold

1. The value(s) of x must be between -1 and 4

2. The values of g(x) must be between 0 and 18.

3. g(-1)=2

4. g(2)=9

We consider the options and state why they are true or otherwise.

A: g(5)=12

The value of x=5. This contradicts property 1 stated above. Therefore, it is not true.

B: g(1) = -2

The value of g(x)=-2. This contradicts property 2 stated above. Therefore, it is not true.

C: g(2) = 4

The value of g(2)=4. However by property 4 stated above, g(2)=9. Therefore, it is not true.

D: g(3) = 18

Given that its domain is between -1 and 4 and its range is between 0 and 18, this claim is reasonable.

Therefore, we can say that Option D can be true.

This question is incomplete

The provided options are:

Options

(A)  g(5) = 12

(B)  g(1) = -2

(C)  g(2) = 4

(D)  g(3) = 18

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Answer:

[tex]a_1 = 1\\d = 3[/tex]

Step-by-step explanation:

The nth term of an arithmetic progression is [tex]a_n = a_1 + (n - 1)d[/tex].
You are given that [tex]a_5 = 13[/tex] and [tex]a_{11} = 31[/tex].

Therefore, we can solve the following system of equations to get the first term, as well as the difference.

[tex]-\begin{cases}a_1 + 4d = 13\\a_1 + 10d = 31\end{cases}\\\\\to 6d = 18\\\to d = 3\\\\\text{Substitute d = 3 into one of the equations to find }a_1\text{:}\\a_1 + 4 \times 3 = 13\\a_1 + 12 = 13\\\to a_1 = 1[/tex]

The number of large bins that the pieces will completely fill is 3.

Each large bin can contain only one type of colour. In order to determine the number of large bins that would be used for each color, divide the color for each piece.

Number of large bins that would be used for Brown color = 283 / 150 = 1.89.

1 large bins would be completely filled with brown glass color

Number of large bins that would be used for Green color = 116 /1 50 = 0.7

No large bin would be completely filled with the green glass color

Number of large bins that would be used for Clear color = 315 / 150 = 2.1

2 large bins would be completely filled with the clear glass color

The total number of large bins that would be completely filled = 1 + 2 = 3

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[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Y(\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad Z(\stackrel{x_2}{-2}~,~\stackrel{y_2}{8}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -2 +1}{2}~~~ ,~~~ \cfrac{ 8 -6}{2} \right) \implies \left(\cfrac{ -1 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies \stackrel{\textit{\LARGE M}}{(-0.5~~,~~1)}[/tex]

The coordinates of the midpoint M are (-1/2, 1), and the length of YZ is approximately 14.32 units.

We have,

To find the coordinates of the midpoint M of the line segment YZ, we can use the midpoint formula:

Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the endpoints Y and Z, respectively.

Given:

Y(1, -6) and Z(-2, 8)

Now, apply the midpoint formula:

Midpoint M = ((1 + (-2)) / 2, (-6 + 8) / 2)

Midpoint M = (-1 / 2, 2 / 2)

Simplify:

Midpoint M = (-1/2, 1)

To find the length of YZ, we can use the distance formula:

Length of YZ = √[(x₂ - x₁)² + (y₂ - y₁)²]

Given:

Y(1, -6) and Z(-2, 8)

Now, apply the distance formula:

Length of YZ = √[(-2 - 1)² + (8 - (-6))²]

Length of YZ = √[(-3)² + (8 + 6)²]

Length of YZ = √[9 + 196]

Length of YZ = √205

Length of YZ ≈ 14.32 (rounded to the nearest tenth)

Thus,

The coordinates of the midpoint M are (-1/2, 1), and the length of YZ is approximately 14.32 units.

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Answer:

6/11

Step-by-step explanation:

3/11 + 3/11

to add both of the fractions just add the numerators (the numbers on the top) and u dont needa add the denominators which is the numbers on the bottom

that makes the answer 6/11 and u cant rlly simplify it so try that.

If its wrong mb

Answer:

A) [tex] \sf \frac{3}{11} + \frac{3}{11} = \frac{6}{11} [/tex]

B) [tex] \sf \frac{9}{10} + \frac{3}{5} = 1 \frac{1}{2}[/tex]

Answer:

x + y = 29   equation 1 

Five more than means add 5+5 three times the smaller number:

 3x equals the larger number:  = y 3x + 5 = y    equation 2

 From equation 1x + y = 29subtract x from both sidesy = 29 - x 

We now have two things that are both equal tothe larger number y.

  They must be equal to each other. 
3x + 5 = 29 - x

 Add x to both sides 3x + x + 5 = 29 - x + x4x + 5 = 29

subtract 5 from both sides 4x + 5 - 5 = 29 - 54x = 24

divide both sides by 44x/4 = 24/4x = 6 

We now know x = 6

We also know y=29-x y = 29 - 6y = 23

 Your numbers are 6 and 23

Step-by-step explanation:

Angles ECD and ACB are congruent, since they form a pair of vertical angles. Let their measure by [tex]y[/tex].

The sum of the interior angles of any triangle is 180°. This means

• in ∆CDE, we have

[tex]x + 100^\circ + y = 180^\circ[/tex]

• in ∆ABC, we have

[tex]4x + 49^\circ + y = 180^\circ[/tex]

Solve for [tex]x[/tex] by eliminating [tex]y[/tex].

[tex](x + 100^\circ + y) - (4x + 49^\circ + y) = 180^\circ - 180^\circ[/tex]

[tex]-3x + 51^\circ = 0[/tex]

[tex]3x = 51^\circ[/tex]

[tex]\boxed{x = 17^\circ}[/tex]

Answer:

y = 2

Step-by-step explanation:

- 3x + 9y = 57 ← substitute x = - 13 into the equation

- 3(- 13) + 9y = 57

39 + 9y = 57 ( subtract 39 from both sides )

9y = 18 ( divide both sides by 9 )

y = 2

Answer: y is 2

solved it with a calculator.

There will be 2 roots of the equation 2 ( [tex]x^{2}[/tex] ) + 3 x = - 4 .

2 ( [tex]x^{2}[/tex] ) + 3 x = - 4 is a quadratic equation . This is because it has degree 2  . Degree is the power of variable which is maximum in function .

Since , x is the variable in this equation , therefore it's degree is 2 .

The no . of roots a polynomial will have is equal to the degree of polynomial .

Hence , the eq . will have 2 real roots .

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Answer:

20 Songs

Step-by-step explanation:

60 minutes / 3minutes per song =20 songs

The solution to question 8, in scientific notation is  9.563 x 10¹¹.

The solution to question 9, in scientific notation is  9.83 x 10⁸.

The solution to question 10, in scientific notation is 1.35759 x 10⁹.

The solution to question 11, in scientific notation is  8.70366 x 10⁴.

Scientific notation is a form of presenting very large numbers or very small numbers in a simpler form.

(9.5 x 10¹¹) + (6.3 x 10⁹)

= (950 x 10⁹) + (6.3 x 10⁹)

= (950 + 6.3) x 10⁹

= 956.3 x 10⁹

= 9.563 x 10¹¹

(1.03 x 10⁹) - (4.7 x 10⁷)

= (103 - 4.7) x 10⁷

= 98.3 x 10⁷

= 9.83 x 10⁸

(1.357 x 10⁹) + 590,000

= (1.357 x 10⁹) + (5.9 x 10⁵)

= (13570 x 10⁵) + (5.9 x 10⁵)

= (13570 + 5.9) x 10⁵

= 13,575.9 x 10⁵

= 1.35759 x 10⁹

87,100 - (6.34 x 10¹)

= 87,100 - 63.4

= 87,036.6

= 8.70366 x 10⁴

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