Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 14 cm.
(1) How many equilateral triangles are there? _____

(2) What is the measure of each of the three angles in the equilateral triangle? _____

(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____

(4) What is the vocabulary word for the segment a? _____

(5) What is the length of the short side of one of the 30-60-90 triangles? _____

(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____

(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____

(8) What is the height of one of the the equilateral triangles? _____

(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____

(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____

The limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² +  x³] is determined as -2.

The limit of the given expression is calculated as follows;

lim x → 0 [4eˣ/2 − 4 − 2x − 12x² +  x³]

= (4e⁰)/2 - 4 - 2(0) - 12(0) + (0)

= (4)/2 - 4

= 2 - 4

= - 2

Thus, the limit of the given expression lim x → 0 [4eˣ/2 − 4 − 2x − 12x² +  x³] is determined as -2.

Learn more about limits here: https://brainly.com/question/251701

#SPJ1

Answer:

5

Step-by-step explanation:

You just multiply the indices by the power so 1/6 x 6 = 1 and 5 to the power of 1 is just 5.

The solution set of the inequality −5 < 2x + 3 < 9 is (-4,3)

The compound inequality is given as:

−5 < 2x + 3 < 9

Expand the inequality

−5 < 2x + 3 or 2x + 3 < 9

Rewrite as:

2x + 3 > -5 or 2x + 3 < 9

Subtract 3 from both sides

2x > -8 or 2x < 6

Divide both sides by 2

x > -4 or x < 3

Rewrite as:

(-4,3)

Hence, the solution set of the inequality is (-4,3)

Read more about inequality at

https://brainly.com/question/25275758

#SPJ1

Answer:

Step-by-step explanation:

[tex]1) \dfrac{4}{5}+\dfrac{3}{8}\\\\\dfrac{4}{5} \ \text{is a rational number} \ and \ \dfrac{3}{8} \ \text{is a rational number}\\\\\dfrac{4}{5}+\dfrac{3}{8} \ \text{is also a rational number}[/tex]

[tex]b) \sqrt{100}+\sqrt{5} = 10+\sqrt{5}\\\\\sqrt{5} \ \text{is a irrational number}. \\\\ \text{Rational number added to irrational number will result in an irrational number}\\\\10 + \sqrt{5} \ is \ not \ a \ rational \ number.[/tex]

c)

[tex]7\sqrt{5}-\sqrt{245}=7\sqrt{5}-\sqrt{7*7*5}[/tex]

                   [tex]= 7\sqrt{5}-7\sqrt{5}\\\\=0\\\\\text{\bf $ 7\sqrt{5}-\sqrt{245}$ ia a rational number}[/tex]

d)

[tex](4\sqrt{7})*(2\sqrt{7})=4*2*\sqrt{7*7}\\[/tex]

                       = 4*2*7

                       = 56

[tex]4\sqrt{7}*2\sqrt{7} \ \text{\bf is a rational number}[/tex]

Answer:  [tex]7\text{Ln}\left(e^{2x}+10\right)+C[/tex]

This is the same as writing 7*Ln( e^(2x) + 10) + C

=======================================================

Explanation:

Start with the equation [tex]u = e^{2x}+10[/tex]

Apply the derivative and multiply both sides by 7 like so

[tex]u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\[/tex]

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

This way we can do the following substitutions:

[tex]\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\[/tex]

Integrating leads to

[tex]\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\[/tex]

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of [tex]\frac{14e^{2x}}{e^{2x}+10}[/tex]

Based on the calculations below, the weekly gross pay of John Pelson is $1,339.90.

Let G represents weekly gross pay. The gross pay can now be calculated as follows:

Net pay = G – FIT – SIT – CIT - Health insurance – Charity ……………….. (1)

Substitute all the relevant values into the equation (1) and solve as follows:

$972.11 = G – $185.00 – 0.05G – 0.02G – $64.00 – $25.00

$972.11 + $185.00 + $64.00 + $25.00 = G – 0.05G – 0.02G

$1,246.11 = (1 – 0.05 – 0.02)G

$1,246.11 = 0.93G

G = $1,246.11 / 0.93

G = $1,339.90

Learn more about gross pay here: https://brainly.com/question/13143081.

#SPJ1

Using the normal distribution, it is found that approximately 79.67% of the bags weigh 3.00 ounces or more​.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 3.05, \sigma = 0.06[/tex]

The proportion of the bags that weigh 3.00 ounces or more​ is one subtracted by the p-value of Z when X = 3, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3 - 3.05}{0.06}[/tex]

Z = -0.83

Z = -0.83 has a p-value of 0.2033.

1 - 0.2033 = 0.7967 = 79.67%.

79.67% of the bags weigh 3.00 ounces or more​.

More can be learned about the normal distribution at https://brainly.com/question/27643290

#SPJ1

Answer:

Step-by-step explanation:

To solve this question, we can use the formula [tex]S=\theta r[/tex], where [tex]S[/tex] is the arc length, [tex]\theta[/tex] is the central angle of the sector in radians, and [tex]r[/tex] is the radius.

In this situation, we know that [tex]S=55[/tex] and [tex]\theta=5[/tex]

This means that [tex]55=5r \longrightarrow \boxed{r=11}[/tex]

Answer:

the width is 59

Step-by-step explanation:

302/2-92=59

Answer:

-12

Step-by-step explanation:

What you have to do is plug -4  into the function as a puzzle. So, replace all x with -4.

f(-4) = 7(-4) - 4(-4) = -28 + 16 = -12

f (-4) = 7x ( 1-4 ) - 4 (-4)

       = -28 + 16

      = -12

An equation is a mathematical statement this is made from two expressions related by an equal sign. for instance, 3x – 5 = 16 is an equation. solving this equation, we get the fee of the variable x as x = 7.

A declaration of the equality of mathematical expressions. An expression representing a chemical reaction by using chemical symbols. equation.

Conclusion: There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.

Learn more about Equations here https://brainly.com/question/2972832

#SPJ2

Answer:

12 ft

Step-by-step explanation:

We assume right triangle ABC with the right angle being at B. We are given that the ratio of AB/CB = 8/7, and one leg is 10.5.  Let's call the other leg is X. We don't know which leg is which so assume both. Then

(a) assume the X leg is the longer

8 / 7 = X / 10.5

(8 * 10.5) / 7= X

X = 12

OR (b) assume the X leg is the shorter

8/7 = 10.5 / X

(8X / 7) = 10.5

8X = 10.5 * 7

8X =  73.5

X = 9.1875

(a) is the greater so (a) wins

Answer:

80 m/s

Explanation:

Given:

i) initial velocity (as starts from rest) = 0 m/s

ii) acceleration:  4 m/s²

iii) distance travelled: 800 m

Formula required:

(final velocity)² - (initial velocity)² = 2 × acceleration × distance

Now solve:

v² - 0² = 2 × 4 × 800

v² = 6400

v = √6400

v = 80 m/s

Answer: [tex]\angle A+\angle D=180^{\circ}[/tex]

Step-by-step explanation:

Adjacent angles of a parallelogram are always supplementary.

26,460 cans of soda

Step-by-step explanation:

First times 9 and 5 together then times 7 with it then times 14 then times 6 and you should end up with 26,460

Answer:

(5*10^3)*(9*10^7) = 4.5*10^11

(7*10^5) / (2*10^2) = 3.5*10^3

Step-by-step explanation:

calculate 5 multiply by 9

5*9=45

the multiple of the power in the same base of number is calculated by using addition(+)

(10^3)*(10^7) = 10^(3+7)

= 10^10

in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so

45*(10^10)

= (4.5*10^1) * (10^10)

= 4.5*10^(1+10)

= 4.5*10^11

calculate 7 divide by 2

7/2=3.5

the dividing of the power in the same base of number is calculated by using subtraction(-)

(10^5)/(10^2)

= 10^(5-2)

= 10^3

in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so

3.5*10^3

Answer:

Step-by-step explanation:

(5×10³)×(9×10⁷)

= 5×10³×9×10⁷

= 5×9×10³×10⁷      (commutative property)

= (5×9)×(10³×10⁷)  (associative property)

= 45 × 10³⁺⁷

= 45 × 10¹⁰.           (Exponent property)

= 4.5 × 10¹¹

…………………………………………

(7×10⁵) / (2×10²)

= (7/2) × (10⁵/10²)

= 3.5 × 10⁵⁻²

= 3.5 × 10³

Answer:

Circumference: 25.12m

Area: 50.24 [tex]m^{2}[/tex]

Step-by-step explanation:

Formula for circumference of a circle: C=[tex]\pi d[/tex] or C=[tex]2\pi r[/tex] since the diameter is double the radius

C=3.14*2*4=3.14*8=25.12

Formula for area of a circle: A=[tex]\pi r^{2}[/tex]

A=3.14*[tex]4^{2}[/tex]=3.14*4*4=3.14*16=50.24

The slope formula along with coordinates of points ( p,q) and (x,y) [tex]m = \dfrac{y-q}{x-p}[/tex].

A slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When the slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

This is because the more the height of the line to the amount we walk or run on the horizontal axis, the more the slope is.

The slope of a line that passes through points ( p,q) and (x,y)

Its slope would be:

[tex]m = \dfrac{y-q}{x-p}[/tex]

Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

Learn more about slopes here:

https://brainly.com/question/2503591

#SPJ1

Given the radius of the regular hexagon, its area is approximately 42in².

Hence, option B) is the correct answer.

Given that;

Since a regular hexagon can be divided into six equal triangle, we will determine the area of a single triangle and then multiply the area by 6 to get the area of the regular hexagon.

Angle of one triangle in the regular hexagon = 360°/6 = 60°.

To determine the height, we divide the triangle into two equal half, making a right angled triangle with hypotenuse 4in, Base 4in/2 = 2in.

We find the perpendicular height using Pythagoras theorem

h = √( (4)² - (2)² )

h = √( 16 - 4 )

h = √( 12 )

h = √( 2² × 3 )

h = 2√3

Now, we determine the area of a single triangle.

Area = (1/2) × base × height

Area = 0.5 × 4 × 2√3

Area = (4√3)in²

Now, to get the area of the regular hexagon, we multiply the area of the triangle by 6

Area of regular hexagon = 6 × (4√3)in²

Area of regular hexagon = 24(√3)in²

Area of regular hexagon = 41.57in² ≈ 42in²

Given the radius of the regular hexagon, its area is approximately 42in².

Hence, option B) is the correct answer.

Learn more about regular hexagons here: https://brainly.com/question/10941428

#SPJ1

Answer: b

Step-by-step explanation:

Answer:

the revenue is 280 by 190

Step-by-step explanation:

let p be the point which is at a distance of 4 units from the x-axis and at a distance of 5 units from the y axis

(i) When P lies in the first quadrant then the coordinates of P are (5,4).

(ii) When of P lies in the second quadrant then the coordinates of P are (-5,4).

(iii) When P lies in the third quadrant then the coordinates of P are (-5,-4).

(iv) When P lies in the fourth quadrant then the coordinates of P are (5,-4).

Known as periodic reports, interim reports or interim statements, these updates provide important company information between annual reporting periods. To help protect investors and keep the public informed, regulations typically require public companies to submit company performance reports more than once a year.Known as periodic reports, interim reports or interim statements, these updates provide important company information between annual reporting periods. To help protect investors and keep the public informed, regulations typically require public companies to submit company performance reports more than once a year.

8.57 liters glucose (in liters) is needed for 30 units of blood.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

For 7 units of blood = 2 l of glucose needed.

Foe 1 units of blood, glucose needed = 2/7

For, 30 units of blood , glucose needed = 8.57 liters

Hence, 8.57 liters glucose (in liters) is needed for 30 units of blood.

Learn more about unitary method here:

https://brainly.com/question/22056199

#SPJ1

Answer:

Step-by-step explanation:

Your exponential formula is in the form y = ab^x. In this form, the coefficient 'a' is the initial value, the y-intercept, the value when x=0. The value 'b' is the growth factor, which is 1 more than the growth rate per increment of x. This problem is asking for the growth rate to be expressed as a percentage.

__

Given p(x) = 78500(1.02^x), we can compare to the exponential function form to see that ...

The value of x is zero in the year 2000, so the population that year is ...

  p(0) = a = 78,500

The increase per year is the value of 'b' with 1 subtracted:

  growth rate = 2% per year

Step-by-step explanation:

See the attached pics it explains everything

Answer:

Corresponding Angles Theorem

When a straight line intersects 2 parallel lines, the angles in the same relative position are congruent (equal).

Alternate Exterior Angles Theorem

When a straight line intersects 2 parallel lines, the alternate exterior angles are congruent (equal).

Vertical Angle Theorem

When two straight lines intersect, the vertical angles are congruent (equal).

Q1.   As  s ║ c  we can apply the Corresponding Angles Theorem:

⇒ 11x - 5 = 116

⇒ 11x - 5 + 5 = 116 + 5

⇒ 11x = 121

⇒ 11x ÷ 11 = 121 ÷ 11

⇒ x = 11

Q2.   As  s ║ c  we can apply the Alternative Exterior Angles Theorem:

⇒ 12x - 4 = 148

⇒ 12x - 4 + 4 = 148 + 4

⇒ 12x = 152

⇒ 12x ÷ 12 = 152 ÷ 12

⇒ x = 38/3 = 12.7 (nearest tenth)

Q1.   As  j ⊥ r  then the sum of the angles is 90°

⇒ 4x + 6x + 10 = 90

⇒ 10x + 10 - 10 = 90 - 10

⇒ 10x = 80

⇒ 10x ÷ 10 = 80 ÷ 10

⇒ x = 8

Q2.  As  j ⊥ r   we can apply the Vertical Angles Theorem:

⇒ 5x - 10 = x + 70

⇒ 5x - 10  + 10 = x + 70 + 10

⇒ 5x = x + 80

⇒ 5x - x = x + 80 - x

⇒ 4x = 80

⇒ 4x ÷ 4 = 80 ÷ 4

⇒ x = 20

Answer:

the class earned $722059884

Step-by-step explanation:

because each person sold 444 tickets and there was 232323 students

=232323×444

=103151412

because 103151412 tickets were sold and a ticket cost $7

=103151412×7

=722059884

Answer:

x = 3

Step-by-step explanation:

Hello!

We can distribute the parenthesis and solve for x.

The value of x is 3.

We can plug it back in to check if it works.

Correct!

Answer:

[tex]\huge\boxed{\sf x = 3}[/tex]

Step-by-step explanation:

9 - 2(x - 5) = x + 10

Distribute

9 - 2x + 10 = x + 10

Subtract 10 to both sides

9 - 2x = x

Add 2x to both sides

9 = x + 2x

9 = 3x

Divide 3 to both sides

9/3 = 3x/3

3 = x

OR

[tex]\rule[225]{225}{2}[/tex]

Finding the correlation coefficient, it is found that the regression line shows a:

negative trend line with a strong relationship.

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is of -0.85, which is negative and strong.

More can be learned about correlation coefficients at https://brainly.com/question/25815006

#SPJ1

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85,

The table contains data for six students in a running club: time run in minutes, x, and the corresponding average speed in mph, y.

Finding the correlation coefficient, it is found that the regression line shows a: negative trend line with a strong relationship.

It is an index that measures the correlation between two variables, assuming values between -1 and 1.

If it is positive, the relationship is positive, that is, they are directly proportional. If it is negative, they are inversely proportional.

If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.

Inserting the values of a table, the x-values as 25, 28, 30, 31, 33, 40, and the y-values as 7.5, 6, 5.5, 5, 4.5, 4.5, the coefficient is -0.85, which is negative and strong.

To learn more can about correlation coefficients visit: brainly.com/question/25815006

#SPJ1