A cone 4.5 centimeters high with a radius of 3 centimeters. Label B is pointing to the circular base of the cone.

Answer: Side lengths: 7.2, 7.2[tex]\sqrt{3}[/tex], 14.4

Step-by-step explanation:

Take sin of 60 to calculate side opposite to angle 60

sin 60=[tex]\frac{\sqrt{3} }{2}[/tex]

cos 60=1/2  

7.2 / 1/2=

7.2 * 2=14.4

[tex]\frac{\sqrt{3} }{2}[/tex]*14.4=

[tex]\frac{14.4\sqrt{3} }{2}[/tex]=7.2[tex]\sqrt{3}[/tex]

The hypotenuse:

[tex](\frac{\sqrt{3} }{2})^2[/tex]+(1/2)^2=

3/4 + 1/4 = 1

1 * 14.4 =14.4

Side lengths: 7.2, 7.2[tex]\sqrt{3}[/tex], 14.4

Step-by-step explanation:

The 30-60-90 triangle is one of the most important trigonometry concept you will learn throughout your secondary schooling.

Attached below is a triangle that you should memorize for easy practice. The way this triangle is formed can be proven trigonometrically and/or with the unit circle, but that's not what this question is asking for.

When comparing the numbers on the attachment and your question, we can generate that the side 7.2=x, because the side with the 60 degree angle and right angle contains the variable x.

Since we have x now, all we would have to do is to plug in the x values and solve the question.

The hypotenuse (longest side of the triangle) = 2x = 2(7.2) = 14.4

The side opposite to the 60 degree angle (left most side)= [tex]x\sqrt{3}[/tex] = [tex]7.2\sqrt{3}[/tex] = 12.6

I hope this helped!

The equation which describes this situation in terms of the cost of each shirt (x) and the cost of each pair of pants (y) is, 5x+3y=190

Equation: There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.

Glenn is shopping for school clothes

Number of shirts Glenn want to buy=  He plans to get one of each of the same shirt in five different colors which is equal to 5

x is the cost of each shirt

that means cost of 5 shirts = 5x

Number of pair of pants he want to buy=  three pairs of the same pant each in a different color which is equal to 3

y is the cost of each pair of pants

that means the cost of three pair of pants = 3y

The total cost for his clothes is $190

The equation which describes this situation in terms of the cost of each shirt (x) and the cost of each pair of pants (y) is, 5x+3y=190

to learn more about equations visit:

https://brainly.com/question/23752439

#SPJ1

Write an example from daily life that uses rational numbers .

To learn more about  rational numbers, refer:

https://brainly.com/question/12088221

#SPJ4

I think the answer is -2.5n + 6.5.

How to work it out:

The geometric mean can be determined by multiplying the terms from part c and the first term of the sequence from part a and taking their square root.

The first term of the sequence from part a is 2 and the term from part c is 512.

Geometric mean of a sequence is the average value of a set of numbers, determined by multiplying the terms together and taking their root.

In general form, the geometric mean for a n number of terms is n√x1*x2*x3*…*xn

Since there are two terms 2 and 512, we will take the square root of the product.

Geometric mean=√2*512=√1024=32

For the geometric sequence as it is the mean, the term will be the 2nd term of the sequence

Hence, the geometric mean of the two chosen positive number 2 and 512 is 32 which is the 2nd term.

Learn more about geometric mean:

https://brainly.com/question/2292573

#SPJ4

Answer:

Step-by-step explanation:

so you get a better perspective of it

The student's error is that the common ratio would not be equal to 3/2.

What is Common Ratio:

The general form of representing a geometric progression is a1, (a1r), (a1r2), (a1r3), (a1r4) ,... where a1 is the first term of GP, a1r is the second term of GP, and r is the common ratio.

Common Ratio Formula:

Common ratio,

r =a n / a n−1

where,

an  is the nth term of the geometric progression.

an−1 is the (n - 1)t h term of the geometric progression.

Now,

[tex]S_{infinity} = 2a_{1} \\\\= a_{1} / 1-r\\\\2a_{1} = a_{1} / 1-r\\\\= 1-r = 1/ 2\\\\r = 1/2 - 1\\\\r = 1/2[/tex]

To know more about "Common Ratio"

Refer this link:

https://brainly.com/question/1509142

#SPJ4

Answer: 36 feet of wood

Step-by-step explanation:

P=perimeter. P=total length of wood

s= side length. A=area

A=s^2

81=s^2

s^2=9^2

s=9

P=4s

P=4(9)

P=36 feet of wood

Answer:

P = 36 ft

Step-by-step explanation:

The given length is,

→ a = ?

Formula we use,

→ A = a²

Now the length of one side is,

→ A = a²

→ a² = 81

→ a = √81

→ [ a = 9 ]

The total length of wood needed is,

→ P = 4a

→ P = 4 × 9

→ [ P = 36 ]

Hence, the total length is 36 ft.

Answer: 3

Step-by-step explanation:

The equation of a line is ax + by = c.

full co-ordinate of the point, in terms of a, b, c, d is (d,(c-ad)/b)

equation of a line is ax + by = c

x=d

put x=d in the equation of line

ad + by = c

by = c-ad

y=(c-ad)/b

full co-ordinate of the point, in terms of a, b, c, d is (d,(c-ad)/b)

The phrase equation and its cognates in other languages can also have subtly extraordinary meanings; as an example, in French an équation is described as containing one or more variables, even as in English, any well-shaped components together with two expressions related with an equals sign is an equation.

fixing an equation containing variables includes figuring out which values of the variables make the equality real.

The variables for which the equation must be solved are also referred to as unknowns, and the values of the unknowns that satisfy the equality are referred to as answers of the equation.

There are two kinds of equations: identities and conditional equations. An identity is authentic for all values of the variables. A conditional equation is simplest genuine for particular values of the variables

To learn more about equation visit , https://brainly.com/question/10413253

#SPJ9

The distance between the pair of points X(-2,5) and Y(1,11) is [tex]\sqrt{45}[/tex] units.

We can find the distance between the points X and Y by using distance formula.

The distance formula is used to find the distance between two defined points on a graph (in the absence of a scale).

Here the two points are  X(-2,5) and Y(1,11).

The distance formula for points (a,b) and (c,d) is given by :-[tex]\sqrt{(d-b)^2+(c-a)^2}[/tex]

Here,

(a,b) represents the point X(-2,5), and

(c,d) represents the point Y(1,11)

Putting the values of (a,b) and (c,d) in the distance formula, we get,

[tex]\sqrt{(11-5)^2+(1-(-2))^2}[/tex]

[tex]\sqrt{6^2+3^2} \\ \sqrt{36+9}\\ \sqrt{45}[/tex]

Hence, the distance is [tex]\sqrt{45}[/tex] units.

To learn more about distance formula, here:-

https://brainly.com/question/8283882

#SPJ4

A function exists described as a relation between a set of inputs containing one output each. The value of h(g(3)) is 5.

A relationship between a group of inputs and one output is referred to as a function.

In plain English, a function is an association between inputs in which each input is connected to precisely one output.

A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Where, g(3) = 0

To get h, replace g(3) with 0 in the requested equation (0).

Since h(0) = 5 according to the question, your final response is 5.

Therefore, the value of h(g(3)) is 5.

To learn more about functions, refer to;

https://brainly.com/question/11624077

#SPJ4

Answer: Hope it help

Step-by-step explanation:

The distance from the line y = -3 to the point (5,2) is 5 units.

Distance from the line ax+by+c=0 from the point (m,n) is calculated by

[tex]distance=\frac{|am+bn+c|}{\sqrt{a^{2} +b^{2} } }[/tex]

In the given question

the equation of the line is [tex]y=-3[/tex] ⇒ [tex]y+3=0[/tex]

equation of line becomes 0.x+1.y+3=0

given the point (5,2)

Substituting the values in the distance formula we get

[tex]d=\frac{0*5+1*2+3}{\sqrt{0^{2} +1^{2} } }[/tex]

[tex]=\frac{2+3}{1} \\ \\ =\frac{5}{1} \\ \\ =5[/tex]

Therefore , the distance from the line y = -3 to the point (5,2) is 5 units.

Learn more bout Distance formula here https://brainly.com/question/14348586

#SPJ4

Answer:

Dependent

18.46%

Step-by-step explanation:

All possible combinations for Sadie taking two marbles out from the hat:

[tex](6+2+2+4+2)×[(6+2+2+4+2)-1] [/tex]

[tex] = 16 \times 15[/tex]

[tex] = 240[/tex]

All the possible combinations that the first marble is brown and the second marble is not purple:

[tex]2 \times (6 + 2 + 1 + 4)[/tex]

[tex] = 2 \times 13[/tex]

[tex] = 26[/tex]

The probability:

[tex] \frac{240}{26} \times 100\%[/tex]

[tex] = \frac{240}{13} \times 50\%[/tex]

[tex] = \frac{1200}{13} \%[/tex]

[tex]≈18.46%[/tex]

Answer: M = (5, 6)

Formula for midpoint:

[tex]\sf (x_m, y_m) = \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)[/tex]

Here given:

Find midpoint M by substituting values:

[tex]\sf M = \left(\dfrac{6+4}{2}, \dfrac{7+5}{2}\right)[/tex]

[tex]\sf M = \left(\dfrac{10}{2}, \dfrac{12}{2}\right)[/tex]

[tex]\sf M = \left(5, 6\right)[/tex]

Given:-

To find:-

Answer:-

Here we are interested in finding the midpoint of a line segment whose endpoints are given to us . Say if a line segment has endpoints [tex](x_1,y_1) [/tex] and [tex](x_2,y_2)[/tex] , then the midpoint of the line is given by ,

[tex]\implies Midpoint= \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg) \\[/tex]

And here , we have;

So on substituting the respective values, we have;

[tex]\implies (x_m , y_m ) =\bigg(\dfrac{ 6+4}{2},\dfrac{7+5}{2}\bigg) \\[/tex]

[tex]\implies (x_m , y_m ) =\bigg( \dfrac{10}{2} , \dfrac{12}{2}\bigg) \\[/tex]

[tex]\implies\underline{\underline{ (x_m , y_m ) = (5,6)}}\\[/tex]

Hence the midpoint is (5,6) .

and we are done!

Considering the expression of a line and how to obtain it having 2 points, you obtain:

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

m= (y2 - y1)÷ (x2 - x1)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

In this case, you want to obtaina linear equation giving the sales y in terms of the year x. You know:

So, being (x1,y1)= (2011, 32.266) and (x2,y2)= (2012, 33.278), the slope m can be calculated as:

m= (33.278 - 32.266)÷ (2012 - 2011)

Solving:

m=1.012

Considering point 1 and the slope m, you obtain:

32.266= 1.012×2011 + b

32.266= 2035.132 + b

32.266- 2035.132= b

- 2002.866= b

Finally, the linear equation giving the sales y in terms of the year x is y=1.012x - 2002.866

You can use the equation to predict the sales for 2013 as follow:

y=1.012×2013 - 2002.866

Solving:

y=1.012×2013 - 2002.866

y= $34.29 billion

Finally, the sales in 2013 will be $34.29 billion.

Learn more about the equation of a line having 2 points:

brainly.com/question/12851029

brainly.com/question/19496333

#SPJ1

The value of the given expression will be 57 if the value of h = -7.

So, let the value of expression be 'x'.

SUbstitute h = -7 in the expression as follows:

Therefore, the value of the given expression will be 57 if the value of h = -7.

Know more about expressions here:

https://brainly.com/question/723406

#SPJ1

The complete question is given below:
If h = -7, the expression has a value of _.

39(2) + 3h = x

The sum of the 8 terms of a series 5,13,21, . . , 61 is 264

The given series is:

          5,13,21, . . . . . . , 61

Notice that this is an arithmetic series with:

first term, a(1) = 5

number of terns, n = 8

common difference, d = a(2) - a(1) = 13 - 5 = 8

last term, a(8) = 61

The sum of the first n terms in an arithmetic series is given by the formula:

S(n) = n/2 [a(1) +a(n)

Substitute n = 8, a(1) = 5, a(n) = 61:

S(8) = 8/2 (5 + 61)

       = 4 . 66

       = 264

Learn more about sum of a series here:

https://brainly.com/question/12753365

#SPJ4

Answer:

0.2, 3 out of 9, 41%, 6/13

Step-by-step explanation:

6/13 = 0.46

3 out of 9 = 3/9 = 0.33

41% = 0.41  (change percent to decimal by dividing it by 100)

0.2

Now compare:

Least to greatest:  0.2, 3 out of 9, 41%, 6/13

A reduction is a dilation from ▢PQRS to ▢WXYZ.

According to the given figure:

Therefore, a reduction is a dilation from ▢PQRS to ▢WXYZ.

Know more about a Quadrilateral here:

https://brainly.com/question/16691874

#SPJ4

Answer: x=-11

Step-by-step explanation:

5(x+5)=2x-8

5x+25=2x-8

5x+25-25=2x-8-25

5x=2x-33

3x=-33

x=-11

The value of x in the given expression is -11.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that; Five times the sum of x and 5 is 8 less than twice x.

WE are asked to Solve for x.

Then the expression form as;

5(x+5)=2x-8

Now solve for x;

5x+25=2x-8

Subtract 25 on both sides;

5x+25-25=2x-8-25

5x=2x-33

3x=-33

x=-11

Therefore, the value of x in the given expression is -11.

To know more about an expression follow;

brainly.com/question/19876186

#SPJ2

Answer:

Step-by-step explanation:

to find the y intercept of AB, first find the slope of AB: m=(1-(-1))/(2-14)=-1/6

the equation of line AB is y=-(1/6)x+b

use either of the given two points to find out b: 1=(-1/6)*2+b => b=4/3

BC is perpendicular to AB, so the slope of BC is the negative reciprocal of the slope of AB, therefore, the slope of BC is 6

Equation of BC is y=6x+b

find out b by using the coordinates of point B: 1=6*2+b => b=-11

the equation of BC is: y=6x-11

the x coordinate of point C: 13=6*x -11 =>x=4

An infinite geometric series is the outcome of an unlimited geometric sequence.

The infinite geometric series be 2/5 +4/25 + 8/125 + . . . . then the sum of the infinite geometric series is 2/3.

An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.

Given:

a(first term) = 2/5

r(common difference) = 2/5

Since, |r| < 1 the infinite series converges.

[tex]S_\infty[/tex] = a/1-r ; -1 < r < 1

[tex]S_\infty[/tex] = (2/5)/(1-2/5)

simplifying the above equation, we get

[tex]S_\infty[/tex] = (2/5)/(3/5) = 2/3

The sum of the infinite geometric series is 2/3.

To learn more about infinite geometric series, refer to:

brainly.com/question/27350852

#SPJ4

Answer:

all real x other than 2

Step-by-step explanation:

[tex]\frac{3x-6}{x-2}=3 \\ \\ 3x-6=3x-6[/tex]

Thus, the equation is true for all x in its domain, which is all real x other than 2.

Answer:

15+3b

6f+10

Step-by-step explanation:

Those are your answers

Answer:

15 + 3b

6f + 10

Step-by-step explanation:

  Multiply 3 with 5 and multiply 3 with b and then add the results of the multiplication.

3*(5 + b) = (3*5) + (3*b)

              = 15 + 3b

2*(3f + 5) = (2*3f) + (2*5)

               = 6f + 10

The Salesman's salary is modeled by the linear equation:

y = $1000 + $500*x

We know that the businessman earns a basic salary of $1000 (it does not depend on how many items he sells) and $500 for each item he sells as a commission.

Then, if we define x as the number of items he sells, the amount he gets in commissions is: x*$500

Then the equation for his total salary, y, in terms of x which is defined above is:

y = $1000 + $500*x

That is the linear equation we wanted to write.

If you want to learn more about linear equations:

https://brainly.com/question/1884491

#SPJ1

Answer:

Not a function; D: {2, 9}; R: {8, 4, 7}