Find the sum of all interior angles of the following regular 20 sided polygon

Answer: 230ft

Step-by-step explanation:

The perimeter is just all 4 sides added together, so,

75+75+40+40=230

The total distance around the wall is 230ft.

The scale factor [tex]\( k \)[/tex] is [tex]\( \frac{x}{6} = \frac{10}{6} = \frac{5}{3} \)[/tex].

The scale factor between two similar triangles is the ratio of the corresponding side lengths. In this case, we can find the scale factor by comparing the corresponding sides of triangles FGH and MNO.

Let's denote the scale factor as [tex]\( k \)[/tex]:

[tex]\[ k = \frac{MN}{FG} \][/tex]

Given that NO = 15 units and FG = 6 units, and MN is denoted as [tex]\( x \)[/tex], we can substitute these values into the formula and solve for [tex]\( x \)[/tex]:

[tex]\[ k = \frac{x}{6} \][/tex]

Since [tex]\( k = \frac{NO}{FG} \)[/tex] we can set up the equation:

[tex]\[ \frac{x}{6} = \frac{15}{9} \][/tex]

Now, solve for [tex]\( x \)[/tex]:

[tex]\[ x = \frac{15}{9} \times 6 \][/tex]

[tex]\[ x = 10 \][/tex]

So, the scale factor [tex]\( k \)[/tex] is [tex]\( \frac{x}{6} = \frac{10}{6} = \frac{5}{3} \)[/tex].

The scale factor of the given figures is 5 : 3.

The value of x is 10

What is the scale factor?

Scale factor is calculated by finding the ratio of the dimensions of the new shape to the dimensions of the original shape.

15 : 9 = x : 6

15/9 = x/6

Cross product

15 × 6 = 9 × x

90 = 9x

Divide both sides by 9

x = 90/9

x = 10

Therefore, the scale factor 15 : 9

= 15/9

= 5/3

= 5 : 3

Answer:

basically you have to calculate the perimeter-

Step-by-step explanation:

4+4+0.8+0.8=8+1.6=9.6

First you need to find the parameter

P= (L x 2)+(W x 2)

P=(4km x 2)+(0.8km x 2)

P=8km+1.6km

P=9.6km

ANSWER

The missing term is 24

EXPLANATION

The given arithmetic sequence is 9,14,19,_29,34

We can observe that:

[tex]14 = 9 + 5[/tex]

[tex]19 = 14 + 5[/tex]

Let the missing term be x, then

[tex]x = 19 + 5[/tex]

[tex]x = 24[/tex]

Therefore the missing term is 24.

Answer:

5, 144°

Step-by-step explanation:

A vector with magnitude v and angle θ can be split into x and y components as:

vx = v cos θ

vy = v sin θ

Here, we're given the components and asked to find the magnitude and direction.  By matching, we can see the magnitude is 5 and the angle is 144°.

So the answer is 5, 144°.

Answer:

$3000 was invested at 11%.

Step-by-step explanation:

The total interest was $426.  This was comprised of interest earned at 8% (represented by e) and (separately) interest earned at 11% (represented by v).

Then e + v = $4200 total investment, and  

i = $426 = e(0.08)(1 year) + v(0.11)(1 year)

We eliminate the variable e as follows:  since e + v = $4200, e = $4200 - v.  Thus,

i = $426 = e(0.08)(1 year) + v(0.11)(1 year) becomes:

i = $426 = ($4200 - v)(0.08)(1 year) + v(0.11)(1 year)  

This is one equation in one unknown, the amount of $ invested at 11%.

Performing the indicated multiplications:

426 = 4200(0.08) - 0.08v + 0.11v.  Simplifying this further, we get:

426 = 336 + 0.03v.

Then 90 = 0.03v, and v = 90 / 0.03 = $3000.

$3000 was invested at 11%.

Answer: First option.

Step-by-step explanation:

Given the function f(x):

 [tex]f(x)=2x-7[/tex]

And the function g(x):

[tex]g(x)=-6x-3[/tex]

You need to add them to get [tex]f(x)+g(x)[/tex]. Then:

 [tex]f(x)+g(x)=(2x-7)+(-6x-3)[/tex]

Therefore, when you add the like terms you get that [tex]f(x)+g(x)[/tex] is:

[tex]f(x)+g(x)=2x-7-6x-3[/tex]

[tex]f(x)+g(x)=-4x-10[/tex]

Since it is a linear function, the Domain is: All real numbers.

You can observe that the result obtained matches witht the first option.

Answer:

Depending of the exact career but measurements are plentiful in the healthcare business.

First, you'll most likely deal with weight and height... since that's part of most health care consultations.

Then, if you deal with medication, you'll use grams, milligrams, milliliters, liters all the time. depending if the medication is in solid or liquid form.

Even as a nutritionist, you'll deal with grams and such for portion sizes.

There are countless of ways you'll use maths and measurements in the healthcare sector.  

Answer:

Measurement can be used in healthcare career also. Like - the doctors and nurses are well trained to give medicines accurately as per measurement of milligrams or nano-gram. High doses can prove fatal with some medicines, so the correct measurement is very necessary.

Similarly, measurement is used in syrups. Like a child can be given upto 5 mg of syrup twice daily.

700-175=525. 525/35=15

Answer:

Linear Function

[tex]y=4x+18[/tex]

Step-by-step explanation:

Let

x----> the time in hours

y----> the total inches of snow on the ground

we know that

The function that best model this situation is the linear function

so

[tex]y=mx+b[/tex]

In this problem

[tex]m=4\frac{in}{h}[/tex]

[tex]b=18\ in[/tex] ----> the y-intercept

substitute

[tex]y=4x+18[/tex]

Answer:

Linear decreasing function best model this situation and the required function is

f(x)=4x+18

Step-by-step explanation:

It is given that a ski resort has 18 inches of snow on the ground. The snow is falling at a rate of 4 inches per hour.

If a function has constant rate of change, then the it is a linear function.

It the given case the rate of change is constant so linear function best model this situation.

The slope intercept form of linear function is

[tex]f(x)=mx+b[/tex]           ... (1)

where, m is slope and b is y-intercept or initial value.

Ski resort has 18 inches of snow on the ground it means initial value is 18.

The snow is falling at a rate of 4 inches per hour. So, m=4.

Substitute m=4 and b=18 in equation (1).

[tex]f(x)=4x+18[/tex]

Therefore the required function is f(x)=4x+18.

Answer:

Final answer is 3.

Step-by-step explanation:

Given function is [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Now we need to find about what is the maximum number of relative extremes contained in the graph of the given function [tex]f\left(x\right)=3x^4-x^2+4x-2[/tex].

Degree of the given function = 4.

Because degree is the highest power of variable.

Then relative number of extremas = degree - 1 = 4 - 1 = 3

Hence final answer is 3.

Answer:

54

Step-by-step explanation:

You have to do the number of options in each category by itsself

Answer:

(-2, 0), (-3, 0), and (5, 0)

Step-by-step explanation:

The x-intercept is found when y = 0.

So, we have to find x when (x + 2)(x + 3)(x - 5) = 0

We can do that by pulling apart all parts, because if one part = 0, the whole thing will have to be too (multiplication property of identity).

1. When x + 2 = 0, x = -2

2. When x + 3 = 0, x = -3

3. When x - 5 = 0, x = 5

That gives us (-2, 0), (-3, 0), and (5, 0)

Answer:

Step-by-step explanation:

x-intercepts are for

(x + 2)(x + 3)(x - 5) = 0

The product is equal to 0 if one of the factors is equal to 0.

Therefore

x + 2 = 0 or x + 3 = 0 or x - 5 = 9

x + 2 = 0     subtract 2 from both sides

x = -2

x + 3 = 0        subtract 3 from both sides

x = -3

x - 5 = 0              add 5 to both sides

x = 5

Answer:

66°

Step-by-step explanation:

Since segments MN and MP are tangent to the circle, then

[tex]\angle MPO=\angle MNO=90^{\circ}[/tex]

The sum of the measures of all interior angles of the quadrilateral is equal to 360°, so

[tex]\angle NOP+\angle MPO+\angle MNO+\angle NMP=360^{\circ}\\ \\114^{\circ}+90^{\circ}+90^{\circ}+x^{\circ}=360^{\circ}\\ \\x^{\circ}=360^{\circ}-114^{\circ}-90^{\circ}-90^{\circ}\\ \\x^{\circ}=66^{\circ}[/tex]

Answer:

The value of x = 66°

Step-by-step explanation:

From the figure we can see that,

PM and MN are the tangent from the point M to the circle with center O

m<PON = 114°

To find the value of x

From the figure we can write,

m<PON + m<PMN = 180°

114 + x = 180

x = 180 - 114 = 66°

Therefore the value of x = 66°

Answer:

1/9

Step-by-step explanation:

Of the 36 possible sums, 4 of them are 9. The probability is 4/36 = 1/9.

_____

Comment on these dice

Interestingly, the probability of any given sum is the same as it is with "normal" dice.

For this case we have the following equations:

[tex]f (x) = \frac {1} {x}\\g (x) = x ^ 2-3x[/tex]

We must find [tex](f_ {o} g) (x):[/tex]

By definition of composition of functions we have to:

[tex](f_ {o} g) (x) = f (g (x))[/tex]

So:

[tex](f_ {o} g) (x) = \frac {1} {x ^ 2-3x}[/tex]

We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined, that is, when the denominator is nonzero.

[tex]x ^ 2-3x = 0\\x (x-3) = 0[/tex]

So, the roots are:

[tex]x_ {1} = 0\\x_ {2} = 3[/tex]

The domain is given by all real numbers except 0 and 3.

Answer:

x other than 0 and 3

ANSWER

0 and 3

EXPLANATION

The given functions are

[tex]f(x) = \frac{1}{x} [/tex]

and

[tex]g(x) = {x}^{2} - 3x[/tex]

[tex]( f \circ g)(x) = f(g(x))[/tex]

[tex]( f \circ g)(x) = f( {x}^{2} -x )[/tex]

[tex]( f \circ g)(x) = \frac{1}{ {x}^{2} - 3x} [/tex]

Factor the numerator:

[tex]( f \circ g)(x) = \frac{1}{ x(x - 3)} [/tex]

The function will be undefined if the denominator is zero.

[tex]x(x - 3) \ne0[/tex]

[tex]x \ne0 \: and \: x \ne3[/tex]

Therefore 0 and not in the domain of the composed function.

if we take 72 as the 100%, what is 27 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 72&100\\ 27&x \end{array}\implies \cfrac{72}{27}=\cfrac{100}{x}\implies \cfrac{8}{3}=\cfrac{100}{x}\implies 8x=300 \\\\\\ x=\cfrac{300}{8}\implies x=\cfrac{75}{2}\implies x=37.5[/tex]

To calculate the percentage, divide the part (27) by the whole (72) and multiply by 100, resulting in 37.5%.

Percentage is a way of expressing a portion or fraction of a whole as a value out of 100. It is commonly used to compare relative quantities, represents proportions, or express the relationship between a part and a whole.

The term "percent" comes from the Latin phrase "per centum," which means "per hundred." It signifies that percentages are calculated on a scale of 100.

In practical terms, a percentage represents a fraction of a whole, where the whole is equal to 100%. It allows us to easily compare different quantities and understand their relative sizes or proportions.

To calculate a percentage, you typically divide the part (the specific quantity you want to express as a percentage) by the whole (the total or reference quantity) and then multiply by 100 to obtain the value as a percentage.

To calculate the percentage, you can divide the given number (27) by the total number (72) and then multiply the result by 100. So, to find out what percent 27 is of 72:

(27 ÷ 72) × 100 ≈ 37.5%

Therefore, 27 is approximately 37.5% of 72.

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A 9

B 10

C 6

Hope this helps;$

Answer:

a. 3:24 = 9:72.

b.  10:18 = 5:9.

c. 6:6 = 36:36.

Step-by-step explanation:

a.  72 / 24 = 3 so we multiply 3 by 3 to give 9.

b.  18/9 = 2  so we multiply 5 by 2 = 10.

c.  The answer is 6.

Answer:

c

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

Step 1: Create an equation

(2+4+x+6) ÷ 4 = 5

Step 2: Solve the equation

(12+x) ÷ 4 = 5

(12+x) = 20

x = 8

The value of the unknown number x is 8.

The given numbers include:

The sum of the given numbers is calculated as follows;

2 + 4 + x + 6 = 12 + x

The mean of the given 4 numbers is calculated as follows;

[tex]\frac{12 + x}{4} = 5\\\\12 + x = 20\\\\x = 20 -12\\\\x = 8[/tex]

Thus, the value of the unknown number x is 8.

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[tex]\bf x^3=216\implies x=\sqrt[3]{216}\implies x=6[/tex]

Divide 216 by 3 to get your x-value

Answer:

AA similarity theorem

Step-by-step explanation:

we know that

AA (Angle-Angle) Similarity states that  In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar

In this problem we have that

∠BCA=∠ECD ----> by vertical angles

∠BAC=∠DEC ---> because AB is parallel to ED (alternate interior angles)

therefore

Triangles ABC and EDC are similar by AA similarity theorem

Answer:

a) 1.

f)6.

d)5.

c)7.

g)3.

e)4.

b)2.

Step-by-step explanation:

putting the steps for rewriting the equation of a circle below in standard form completing the square in order:

Step 1)

a. where 36 is added on both sides of the equation

as it is square of half of 12.

x^2 +12x+36 +y^2 +30y=24+36               ..........(1)

Step 2)

f. where 225 is added on both sides of equation as it is square of half of 30

x^2 +12x+36 +y^2 +30y+225=24+36+225             ............(6)

Step3)

d. adding numbers on r.h.s

x^2 +12x+36 +y^2 +30y+225=285             ............(5)

Step4)

c) Factoring the x values into binomial factors

(x+6)(x+6) +36 +y^2 +30y+225=285         .............(7)

Step5)

g) re-writing x factors as squares

(x+6)^2 +36 +y^2 +30y+225=285         ...............(3)

Step6)

e)Factoring the y values into binomial factors

(x+6)^2 +36 +(y+15)(y+15)=285             ...............(4)

Step7)

b)re-writing x factors as squares

(x+6)^2 +36 +(y+15)^2=285               ...........(2)!

Answer:

its 0.4

Step-by-step explanation:

Answer:

The answer is C) 0.4

Answer:

A) P(stars) = 1/3

B) P(odd)= 4/7

C)P(solid grays or stars or striped)= 1

D)P(1,4 or 7)= 3/7

E)P(not striped)= 2/3

Step-by-step explanation:

Given:

sample set contains 1-7 solid gray, 1-7 stars and 1-7 striped cards

Let solid gray be x

stars be y

striped be z

then sample set be

1x,2x,3x,4x,5x,6x,7x,

1y,2y,3y,4y,5y,6y,7y,

1z,2z,3z,4z,5z,6z,7z

total number of cards in sample set =21

Now

a)Finding probability of stars

Number of star cards in above sample set = 7

P(stars)= 7/21

     P(y)=1/3

b)Finding probability of odd

Number of odd cards in above sample set = 12

P(odd)= 12/21

          =4/7

c)Finding probability of solid grays or stars or striped

P(solid grays or stars or striped) = P(x or y or z)

                                                      =P(x U y U z)

As the events are mutually exclusive

P(x U y U z)= P(x)+P(y)+P(z)

now P(x)= 1/3

P(y)=1/3

P(z)=1/3

P(x U y U z) = 1/3 + 1/3 + 1/3

                   = 3/3

                   =1

d)Finding probability of 1,4 or 7

Number of 1,4 or 7 cards in above sample set = 9

P(1,4 or 7) = P(1 U 4 U 7)

As the events are mutually exclusive

P(1,4 or 7) = P(1) + P(4) + P(7)

P(1)= 3/21

     =1/7

P(4)= 3/21

     =1/7

P(7)= 3/21

     =1/7

P(1,4 or 7)= 1/7 + 1/7 + 1/7

               =3/7

e)Finding probability of not striped

Number of not striped cards in above sample set = 14

P(not striped)= 14/21

                      = 2/3 !

Answer:

A

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

given

Step-by-step explanation:

The vertically opposite angles, ∠4 and ∠2 are equals.

Vertical angles are angles opposite each other where two lines cross.

A linear pair can be defined as two adjacent angles that add up to 180° or two angles which when combined together form a line or a straight angle.

According to the given question.

On line m, we have

∠4 + ∠1 = 180 degrees ...(i)    (by linear pair)

On line n, we have

∠1 + ∠2 = 180 degrees ...(ii)   (by linear pair)

from equation (i) and (ii)

∠4 + ∠1 = ∠1 + ∠2

⇒ ∠4 = ∠2

Hence, we proved that the vertically opposite angles ∠4 and ∠2 are equals.

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Answer:

The missing angle has a measure of 2 degrees.

Step-by-step explanation:

Every triangle's inner angles can be added and will always equal 180. Therefore, use subtraction to find any missing angle. In this case,

180 - 91 = 89

89 - 87 = 2

So, your answer is 2.

If the two angles of the triangle are 91° and 87°. Then the measure of the third angle of the triangle will be 2°.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The two angles of the triangle are 91° and 87°.

Then the measure of the third angle of the triangle will be

Let x be the third angle. Then we have

91° + 87° + x = 180

                 x = 180° - 87° - 91°

                 x = 2°

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Answer:

The answer is 3,589,234

Step-by-step explanation:

Because it basically means addition meaning you just have to add it 3,489,234 + 100,000 gives you the answer

Answer:

11

Step-by-step explanation:

The x-value -4 is less than 3, so use the first formula for f:  x^2 - 5.

Then f(-4) = (-4)^2 - 5 = 11