A right pyramid with a square base has a base edge length of 12 meters and slant height of 6 meters.

The apothem is meters.

The hypotenuse of ΔABC is the .

The height is meters.

The volume of the pyramid is cubic meters.

The sum of the length of all the ten movies is [tex]\fbox{\begin\\\ 780\text{ minutes}\\\end{minispace}}[/tex].

Step-by-step explanation:

It is given that a new movie is released each year for [tex]10[/tex] consecutive years so there are total number of [tex]10[/tex] movies released in [tex]10[/tex] years.

The movie released in first year is [tex]60\text{ minutes}[/tex] long and each movie released in the successive year is [tex]4\text{ minutes}[/tex] longer than the movie released in the last year.

So, as per the above statement movie released in first year is [tex]60[/tex] minutes long, movie released in second year is [tex]64[/tex] minutes long, movie released in third year is [tex]68[/tex] minutes long and so on.

The sequence of the length of the movie formed is as follows:

[tex]\fbox{\begin\\\ 60,64,68,72...\\\end{minispace}}[/tex]

The sequence formed above is an arithmetic sequence.

An arithmetic sequence is a sequence in which the difference between the each successive term and the previous term is always constant or fixed throughout the sequence.

The general term of an arithmetic sequence is given as

[tex]\fbox{\begin\\\math{a_{n} =a+(n-1)d}\\\end{minispace}}[/tex]

The sequence formed for the length of the movie is an arithmetic sequence in which the first term is [tex]60[/tex] and the common difference is [tex]4[/tex].

The arithmetic series corresponding to the arithmetic sequence of length of the movie is as follows:

[tex]\fbox{\begin\\\ 60+64+68+72+...\\\end{minispace}}[/tex]

The arithmetic series formula to obtain the sum of the above series is as follows:

[tex]\fbox{\begin\\\math{S_{n} =(n/2)(2a+(n-1)d)}\\\end{minispace}}[/tex]

In the above equation  [tex]n[/tex] denotes the total number of terms, a denotes the first term, d denotes the common difference and Sn denotes the sum of n terms of the series.

Substitute [tex]\fbox{\begin\\\math{a}=60\\\end{minispace}}[/tex],[tex]\fbox{\begin\\\math{n}=10\\\end{minispace}}[/tex] and [tex]\fbox{\begin\\\math{d}=4\\\end{minispace}}[/tex] in the equation [tex]\fbox{\begin\\\math{S_{n} =(n/2)(2a+(n-1)d)}\\\end{minispace}}[/tex]

[tex]S_{10} =(10/2)(120+36) \\S_{10} =780[/tex]

Therefore, the length of the all [tex]10[/tex] movies as calculated above is [tex]\fbox{\begin\\\ 780\text{ minutes}\\\end{minispace}}[/tex]

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Answer details

Grade: Middle school

Subject: Mathematics  

Chapter: Arithemetic preogression  

Keywords: Sequence, series, arithmetic , arithmetic sequence, arithmetic series, common difference, sum of series, pattern, arithmetic pattern, progression, arithmetic progression, successive terms.

Answer:  

The total length of all 10 movies is 780 minutes.  

Further Explanation:  

Arithmetic Sequence: A sequence of numbers in which difference of two successive numbers is constant.  

The sum of n terms of an arithmetic sequence is given by the formula,  

[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]

Where,  

The first movie is 60 minutes long. This would be the first term of the sequence.  

Thus, First term, a= 60 minutes

A new movie is released each year for 10 years. In 10 years total 10 movies will released.  

Thus, Number of terms, n=10

Each movie is 4 minutes longer than the last released movie. It means the difference of length of two successive movie is 4 minutes.

Thus, Common difference, d=4

Using the sum of arithmetic sequence formula, the total length of all 10 movies is,

[tex]S_{10}=\dfrac{10}{2}[2\cdot 60+(10-1)\cdot 4][/tex]

[tex]S_{10}=\dfrac{10}{2}[2\cdot 60+9\cdot 4][/tex]                          [tex][\because 10-1=9][/tex]

[tex]S_{10}=\dfrac{10}{2}[120+36][/tex]                                  [tex][\because 2\cdot 60=120\text{ and }9\cdot 4=36][/tex]

[tex]S_{10}=\dfrac{10}{2}\times 156[/tex]                                      [tex][\because 120+36=156][/tex]

[tex]S_{10}=5\times 156[/tex]                                         [tex][\because 10\div 2=5][/tex]

[tex]S_{10}=780[/tex]                                                  [tex][\because 5\times 156=780][/tex]

Therefore, The total length of all 10 movies is 780 minutes

Learn more:  

Find nth term of series: https://brainly.com/question/11705914

Find sum: https://brainly.com/question/11741302

Find sum of series: https://brainly.com/question/12327525

Keywords:  

Arithmetic sequence, Arithmetic Series, Common difference, First term, AP progression, successive number, sum of natural number.

Answer:

the required answer is 125/24.

Answer:

The cost price of one calculator is Rs.750.

The cost price of other calculator is Rs.500.        

Step-by-step explanation:

Cost price of 1'st calculator = x

Cost price of 2'nd calculator = 1250-x

He sold one at a profit of 2%.

The selling price of one calculator is

[tex]SP_1=CP(1+\frac{P\%}{100})[/tex]

[tex]SP_1=x(1+\frac{2}{100})[/tex]          

[tex]SP_1=x(1+0.02)[/tex]      

[tex]SP_1=1.02x[/tex]    

He sold other at a loss of 3%.

The selling price of other calculator is

[tex]SP_2=CP(1-\frac{L\%}{100})[/tex]

[tex]SP_2=(1250-x)(1-\frac{3}{100})[/tex]          

[tex]SP_2=(1250-x)(1-0.03)[/tex]      

[tex]SP_2=(1250-x)(0.97)[/tex]

[tex]SP_2=1212.5-0.97x[/tex]  

According to given condition,

[tex]SP_1+SP_2=1250[/tex]

[tex]1.02x+1212.5-0.97x=1250[/tex]

[tex]0.05x=1250-1212.5[/tex]

[tex]0.05x=37.5[/tex]

[tex]x=\frac{37.5}{0.05}[/tex]

[tex]x=750[/tex]

The cost price of one calculator is Rs.750.

The cost price of other calculator is 1250-750=Rs.500.

Answer:

slope = 0

Step-by-step explanation:

The line with equation x = - 3 is a vertical line parallel to the y- axis

A perpendicular line is therefore a horizontal line parallel to the x- axis

The slope of the x- axis is zero, hence the slope of the horizontal line is

slope = 0

Answer: C.( 0,-21)

Step-by-step explanation: Use the slope-intercept form to find the slope and y-intercept.

Final answer:

The y-intercept of the given line y = 5x - 21 is -21, which means the line crosses the y-axis at the point (0, -21), corresponding to option C.

Explanation:

The y-intercept of a line represented by the equation y = mx + b is the value at which the line crosses the y-axis. To find the y-intercept, one must look at the value of b, which is the constant in the equation. Given the equation y = 5x - 21, the y-intercept would be -21.

Therefore, when x is 0, the value of y would be -21, meaning that the line crosses the y-axis at the point (0, -21). This corresponds to the option C: (0, -21).

Answer: C≈50.27cm

if u want the solution then here u go

C=2πr=2·π·8≈50.26548cm

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables, and then solve for "y".

[tex]\bf y = 4x^2-8\implies \stackrel{\textit{quick switcheroo}}{\underline{x} = 4\underline{y}^2-8}\implies x+8=4y^2\implies \cfrac{x+8}{4}=y^2 \\\\\\ \sqrt{\cfrac{x+8}{4}}=y\implies \cfrac{\sqrt{x+8}}{\sqrt{4}}=y\implies \cfrac{\sqrt{x+8}}{2}=\stackrel{f^{-1}(x)}{y}[/tex]

Answer:

fff

Step-by-step explanation:

By pythagorean theorum we calculate the height:

[tex]\sqrt{5^2-1^2}[/tex]

=[tex]\sqrt{24}[/tex] = height of triangle

area of triangle = base * height

area = [tex]2*\sqrt{24}[/tex]

There are two triangles so:

[tex]2*2*\sqrt{24}=4\sqrt{24}[/tex]

Multiply this by 13.25 to get total cost:

=$259.65

Answer:

$ 129.82 because it is to the nearest cent

Answer:

B. 19

Step-by-step explanation:

g(x) = x^2+3

Let x=4

g(4) = 4^2 +3

       = 16+3

       =19

Answer:

b

Step-by-step explanation:

all work is shown and pictured

For this case we have that by definition, the point-slope equation of a line is given by:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

We have as data that:

[tex](x_ {0}, y_ {0}): (- 6, -3)\\m = 4[/tex]

Substituting in the equation we have:

[tex]y - (- 3) = 4 (x - (- 6))\\y + 3 = 4 (x + 6)[/tex]

Finally, the equation is: [tex]y + 3 = 4 (x + 6)[/tex]

Answer:

[tex]y + 3 = 4 (x + 6)[/tex]

[tex]\huge{\boxed{y+3=4(x+6)}}[/tex]

Point-slope form is [tex]y-y_1=m(x-x_1)[/tex], where [tex]m[/tex] is the slope and [tex](x_1, y_1)[/tex] is a known point on the line.

Substitute in the values. [tex]y-(-3)=4(x-(-6))[/tex]

Simplify the negative subtraction. [tex]\boxed{y+3=4(x+6)}[/tex]

Answer:

13.7

Step-by-step explanation:

We know that sin(thetha) = BC/AB

In this case, thetha = 41, BC = 9in

→ AB = BC/sin(thetha)

→ AB = 9in/sin(41)

→ AB = 13.7

Therefore, the result is 13.7

Answer:

The correct answer is third option

13.8 in

Step-by-step explanation:

From the figure we can see a right angled triangle ABC, right angled at C,

m<A = 41°, and BC = 9 in

Points to remember

Sin θ = Opposite side/Hypotenuse

To find the value of AB

Sin 41 =  Opposite side/Hypotenuse

 = BC/AB

 = 9/AB

AB = 9/Sin(41)

 =13.8 in

The correct answer is third option

13.8 in

Answer:

There are 80 marks in total.

Step-by-step explanation:

Let the number of total marks be [tex]x[/tex].

The percentage score of the student can be written as the ratio

[tex]\displaystyle \frac{68}{x} = 85\%[/tex].

However,

[tex]\displaystyle 85\% = \frac{85}{100}[/tex].

Equating the two:

[tex]\displaystyle \frac{68}{x} = \frac{85}{100}[/tex].

Cross-multiply (that is: multiple both sides by [tex]100x[/tex], the product of the two denominators) to get

[tex]85x = 68\times 100[/tex].

[tex]\displaystyle x = \frac{68\times 100}{85} = 80[/tex].

In other words, there are 80 marks in total.

In the given scenario regarding a toy sinking in a pool, the constraints related to the depth of the pool and the rate of sinking of the toy could be part of the scenario, which illustrates a system of inequality related to the depth of the toy in the pool over time.

The question requires understanding of the constraints in a scenario that involve a system of inequalities related to the depth of a toy in a pool over time. In this case, the toy is falling, or sinking, into the pool. Therefore, the scenario will involve the depth of the pool and the rate at which the toy is falling.

Firstly, The depth of the pool is important because the toy cannot sink deeper than the pool is. Therefore, both constraints A) The pool is 1 meter deep and B) The pool is 2 meters deep could both be part of the scenario, depending on the actual depth of the pool involved.

Secondly, The rate at which the toy is falling (sinking) is also important. Both constraints C) The toy falls at a rate of at least a 1/2 meter per second and D) The toy sinks at a rate of no more than a 1/2 meter per second could be part of the scenario, depending on the actual sinking rate of the toy.

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The constraint that could be part of the scenario is that the D) toy sinks at a rate of no more than a 1/2 meter per second.

A system of inequalities is a set of two or more inequalities involving the same variables. The solution to the system is the set of values that satisfy all the inequalities simultaneously. Graphically, the solution represents the overlapping region of the individual inequalities on a coordinate plane.

The constraint that could be part of the scenario is that the toy sinks at a rate of no more than a 1/2 meter per second. This constraint ensures that the depth of the toy in the pool does not change too rapidly. If the toy sank at a faster rate than 1/2 meter per second, it would quickly reach the bottom of the pool.

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The expression equivalent to 6(2y - 4) + p is p + 12y - 24, according to the distributive property of multiplication over subtraction.

The task is to find which of the following is equivalent to 6(2y - 4) + p. The first step is to apply the distributive property of multiplication over subtraction to the term 6(2y - 4). This gives us 12y - 24. If we add p to this term, we get our equivalent expression: p + 12y - 24. So, option A. p+ 12y - 24 is equivalent to 6(2y - 4) + p.

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Answer:

5.

Step-by-step explanation:

There are a total of  21 items so the median is the mean of the 10th and 11th .

This lies on the highest column so the median is  5.

Answer:

There is no scatter plot provided, but I can tell you how to solve this. You will look at the plot. It should be numbered somewhere 0-10 and tell you that is the point system, the other side should be the students. So, now you will look at the points on the plot and determine where most of them are. If they are low, you would say that she thinks that they are bad. If it's mostly middle, you would say they need improvement, but aren't terrible. If they are high, you would say she thinks that they are very good.

Answer:

[tex]\left ( 3\sqrt{2},135^{\circ} \right )\,,\,\left ( 3\sqrt{2},315^{\circ} \right )[/tex]

Step-by-step explanation:

Let (x,y) be the rectangular coordinates of the point.

Here, [tex](x,y)=(3,-3)[/tex]

Let polar coordinates be [tex](r,\theta )[/tex] such that [tex]r=\sqrt{x^2+y^2}\,,\,\theta =\arctan \left ( \frac{y}{x} \right )[/tex]

[tex]r=\sqrt{3^2+(-3)^2}=\sqrt{18}=3\sqrt{2}[/tex]

[tex]\theta =\arctan \left ( \frac{-3}{3} \right )= \arctan (-1)[/tex]

We know that tan is negative in first and fourth quadrant, we get

[tex]\theta =\pi-\frac{\pi}{4}=\frac{3\pi}{4}=135^{\circ}\\\theta =2\pi-\frac{\pi}{4}=\frac{7\pi}{4}=315^{\circ}[/tex]

So, polar coordinates are [tex]\left ( 3\sqrt{2},135^{\circ} \right )\,,\,\left ( 3\sqrt{2},315^{\circ} \right )[/tex]

Answer:

Step-by-step explanation:

The sum of the interior angles of an n gon is found by using the following formula.

(n-2)*180 = sum of the interior angles.

(n - 2) * 180 = 3960                     Divide by 180

(n - 2) 180/180 = 3960/180         Show the division

n - 2 = 22                                     Add 2 to both sides.

n -2+2=22+2                               Combine

n = 24

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

To find the size of each angle, use

(n - 2)*180/n

(24 - 2)*180/24

22 * 180/24

3960/24 = 165

===========

another way

===========

You already know there are 24 sides. You are given the sum of the interior angles as 3960

All you really need to do is 3960/24 = 165

We have the following function:

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

The graph of this function has been plotted below. So lets analyze each statement:

As you can see x increases from -∞ to 0 and decreases from 0 to +∞

The function is undefined for [tex]x=0[/tex] since x is in the denominator.

Statement is unclear but the range is the set of all real numbers except zero.

The function is a reflection in the x axis of the function [tex]g(x)=\frac{3}{x}[/tex]

This is false since:

[tex]f(3)=-1\neq -27[/tex]

Note. As you can see those statements are false, so any of them is true, except item 3 that is unclear.

Answer:

its b and d

Step-by-step explanation:

i know

Answer:

See explanation

Step-by-step explanation:

a) To prove that DEFG is a rhombus, it is sufficient to prove that:

Using the distance formula; [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]|DG|=\sqrt{(0-(-a-b))^2+(0-c)^2}[/tex]

[tex]\implies |DG|=\sqrt{a^2+b^2+c^2+2ab}[/tex]

[tex]|GF|=\sqrt{((a+b)-0)^2+(c-0)^2}[/tex]

[tex]\implies |GF|=\sqrt{a^2+b^2+c^2+2ab}[/tex]

[tex]|EF|=\sqrt{((a+b)-0)^2+(c-2c)^2}[/tex]

[tex]\implies |EF|=\sqrt{a^2+b^2+c^2+2ab}[/tex]

[tex]|DE|=\sqrt{(0-(-a-b))^2+(2c-c)^2}[/tex]

[tex]\implies |DE|=\sqrt{a^2+b^2+c^2+2ab}[/tex]

Using the slope formula; [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

The slope of EG is [tex]m_{EG}=\frac{2c-0}{0-0}[/tex]

[tex]\implies m_{EG}=\frac{2c}{0}[/tex]

The slope of EG is undefined hence it is a vertical line.

The slope of  DF is [tex]m_{DF}=\frac{c-c}{a+b-(-a-b)}[/tex]

[tex]\implies m_{DF}=\frac{0}{2a+2b)}=0[/tex]

The slope of DF is zero, hence it is a horizontal line.

A horizontal line meets a vertical line at 90 degrees.

Conclusion:

Since [tex]|DG|\cong |GF| \cong |EF| \cong |DE|[/tex] and [tex]DF \perp FG[/tex] , DEFG is a rhombus

b) Using the slope formula:

The slope of DE is [tex]m_{DE}=\frac{2c-c}{0-(-a-b)}[/tex]

[tex]m_{DE}=\frac{c}{a+b)}[/tex]

The slope of FG is [tex]m_{FG}=\frac{c-0}{a+b-0}[/tex]

[tex]\implies m_{FG}=\frac{c}{a+b}[/tex]

Answer:

Part A) [tex]x=6[/tex]

Part B) ∠3=29°

Part C) ∠1=29°

Part D) ∠2=151°

Step-by-step explanation:

Part A) If ∠3=5x-1 and ∠5=3x+11, then x=?

we know that

∠3=∠5 ----> by alternate interior angles

so

substitute and solve for x

[tex]5x-1=3x+11[/tex]

[tex]5x-3x=11+1[/tex]

[tex]2x=12[/tex]

[tex]x=6[/tex]

Part B) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠3=?

we know that

∠3=5x-1

The value of x is

[tex]x=6[/tex]

substitute

∠3=5(6)-1=29°

Part C) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠1=?

we know that

∠1=∠3 ----> by vertical angles

we have

∠3=29°

therefore

∠1=29°

Part D) If ∠3=5x-1 and ∠5=3x+11, then the measure of ∠2=?

we know that

∠1+∠2=180° ----> by supplementary angles

we have

∠1=29°

substitute

29°+∠2=180°

∠2=180°-29°

∠2=151°

Answer:

V = 500 pi in^3

or approximately 1570 in ^3

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h  where r is  the radius and h is the height

The diameter is 10. so the radius is d/2 = 10/2 =5

V = pi (5)^2 * 20

V = pi *25*20

V = 500 pi in^3

We can approximate pi by 3.14

V = 3.14 * 500

V = 1570 in ^3

Answer:

V=1570.8

Step-by-step explanation:

The volume of a cylinder with a diameter of 10 inches and height of 20 inches is 1570.8 inches.

I changed the diameter to radius to make it easier. The radius is half the diameter, making the radius 5 inches.

Formula: V=πr^2h

V=πr^2h=π·5^2·20≈1570.79633

Answer:

$11,700

Step-by-step explanation:

If Cary earns $975 each month on his part-time job, he would earn $11,700 in a year.

1 year = 12 months

$975 per month

975 x 12 = 11700

In this question, we're going to need to find out how much Cary earns in a year.

To do this, we need to go back to the problem to see if we can get some valuable information.

We know that Cary earns $975 each month.

With the information above, we can solve the problem.

There are 12 months in a year, so that means we're going to multiply 975 by 12 in order to find out how much Cary earns in a year.

975 × 12 = 11,700

When you multiply, you would end up with the answer "11,700"

This means that Cary earns $11,700 in a year

Answer:

$102.29 is the original price of the suit.

Explanation:

$x ------- 100% price (full price)

$35.80 --------------- 35% of the original price (100%-65%=35%).

To find x, use cross-products.

x=(35.80×100)/35 =3580/35 = approximately $102.29.

Answer:

The original price of the suit was $102.29.

Step-by-step explanation:

Alex purchased a new suit discounted by 65%.

He paid $35.80 for the suit.

Let the original price (100% price) be x.

After discount the price is given = 100% - 65% = 35%

35% of x = 35.80

0.35x = 35.80

x = [tex]\frac{35.80}{0.35}[/tex]

x = 102.2857 rounded to $102.29

The original price of the suit was $102.29.

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &\$75000\\ P=\textit{original amount deposited}\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\dotfill &10 \end{cases} \\\\\\ 75000=Pe^{0.035\cdot 10}\implies 75000=Pe^{0.35}\implies \cfrac{75000}{e^{0.35}}=P \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 52851.61\approx P~\hfill[/tex]

Answer:

D. ABC = DBC

Step-by-step explanation:

They are the same length and congruent.

Answer:

d) ABC ≅ DBC

Step-by-step explanation:

∠B in ΔABC and ∠B in ΔDBC is 90°. BC is a common side in both triangles which mean that both triangles have one side of the same length. Side AC in ΔABC is the same length as side DC in ΔDBC. Therefore ∠C in both ΔABC and ΔDBC are the same size. Therefore ΔDBC is a mirror image of ΔABC, which is a form of congruent triangles.

Answer:

$0.19.

Step-by-step explanation:

Unit rate / ounce = 2.66 / 14

= $0.19.

since we know the endpoints of the circle, we know then that distance from one to another is really the diameter, and half of that is its radius.

we can also find the midpoint of those two endpoints and we'll be landing right on the center of the circle.

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[-2-(-4)]^2+[-5-(-7)]^2}\implies d=\sqrt{(-2+4)^2+(-5+7)^2} \\\\\\ d=\sqrt{2^2+2^2}\implies d=\sqrt{2\cdot 2^2}\implies d=2\sqrt{2}~\hfill \stackrel{~\hfill radius}{\cfrac{2\sqrt{2}}{2}\implies\boxed{ \sqrt{2}}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-5})\qquad \qquad \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{-2-4}{2}~~,~~\cfrac{-5-7}{2} \right)\implies \left( \cfrac{-6}{2}~,~\cfrac{-12}{2} \right)\implies \stackrel{center}{\boxed{(-3,-6)}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-3}{ h},\stackrel{-6}{ k})\qquad \qquad radius=\stackrel{\sqrt{2}}{ r} \\[2em] [x-(-3)]^2+[y-(-6)]^2=(\sqrt{2})^2\implies (x+3)^2+(y+6)^2=2[/tex]

Answer:

FIRST OPTION: [tex](x+3)^2+ (y+6)^2 =2[/tex]

Step-by-step explanation:

The equation of the circle in center-radius form is:

[tex](x- h)^2 + (y- k)^2 = r^2[/tex]

Where the center is at the point (h, k) and the radius is "r".

We know that the endpoints of the diameter of this circle are (-4, -7) and (-2, -5), so we can find the radius and the center of the circle.

In order to find the radius, we need to find the diameter. To do this, we need to use the formula for calculate the distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Then, substituting the coordinates of the endpoints of the diameter into this formula, we get:

[tex]d=\sqrt{(-4-(-2))^2+(-7-(-5))^2}=2\sqrt{2}[/tex]

Since the radius is half the diameter, this is:

[tex]r=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex]

To find the center, given the endpoints of the diameter, we need to find the midpoint with this formula:

[tex]M=(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2})[/tex]

This is:

[tex]M=(\frac{-4-2}{2},\frac{-7-5}{2})=(-3,-6)[/tex]

Then:

[tex]h=-3\\k=-6[/tex]

Finally, substituting values  into  [tex](x- h)^2 + (y- k)^2 = r^2[/tex], we get the following equation:

 [tex](x- (-3))^2 + (y- (-6))^2 = (\sqrt{2})^2[/tex]

[tex](x+3)^2+ (y+6)^2 =2[/tex]

Answer:

a = 12

b = 22

c = 25.96186

Angle A = 27.417°

Angle B = 57.583°

Angle C = 95°

Area = 131.4977

Perimeter = 59.96186

a = 12,b = 22,c = 25.96186

∠A = 27.417°,∠B = 57.583°,∠C = 95°

Law of sine states that the ratio sine of an angle and its opposite side in a triangle is same for all 3 angles and their corresponding sides.

sinA/a=sinB/b=sinC/c

Law of cosine is the generalized Pythagoras theorem is applied. It is applied for measuring one side where the opposite angle and other two sides are given.

c²=a²+b²-2abcosC

here given,

a = 12

b = 22

∠C = 95°

Applying law of cosine,

c²=a²+b²-2abcosC

=12²+22²-2.12.22.cos95°

=674.018

⇒c=√674.018

⇒c=25.96

Applying law of sine

sinA/a=sinC/c

⇒sinA=(a/c)sinC

⇒sinA=(12/25.96)sin95°=0.46

⇒A=sin⁻¹(0.46)

⇒A=27.417°

As we know sum of the 3 angles in a triangles are 180°.

∠B=180°-(∠A+∠C)=180°-(27.417°+95°)=180°-(122.42)

⇒∠B=57.583°

Therefore a = 12,b = 22,c = 25.96186

∠A = 27.417°,∠B = 57.583°,∠C = 95°

Learn more about law of sine

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Answer:

y = 3x - 10

Step-by-step explanation:

Assuming you require the equation of the parallel line through (2, - 4)

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 24 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes, hence

y = 3x + c ← is the partial equation of the parallel line

To find c substitute (2, - 4) into the partial equation

- 4 = 6 + c ⇒ c = - 4 - 6 = - 10

y = 3x - 10 ← equation of parallel line

Answer:

[tex]h \circ m \circ n \text{ where } h(x)=\sqrt{x} \text{ and } m(x)=1+\frac{15}{n} \text{ and } n(x)=x^3-9[/tex]

Step-by-step explanation:

Ok so I see a square root is on the whole thing.

I'm going to let the very outside function by [tex]h(x)=sqrt(x)[/tex].

Now I'm can't just let the inside function by one function [tex]g(x)=\frac{x^3+6}{x^3-9}[/tex] because we need three functions.

So I'm going to play with [tex]g(x)=\frac{x^3+6}{x^3-9}[/tex] a little to simplify it.

You could do long division. I'm just going to rewrite the top as

[tex]x^3+6=x^3-9+15[/tex].

[tex]g(x)=\frac{x^3-9+15}{x^3-9}=1+\frac{15}{x^3-9}[/tex].

So I'm going to let the next inside function after h be [tex]m(x)=1 + \frac{15}{x}[/tex].

Now my last function will be [tex]n(x)=x^3-9[/tex].

So my order is h(m(n(x))).

Let's check it:

[tex]h(m(x^3-9))[/tex]

[tex]h(1+\frac{15}{x^3-9})[/tex]

[tex]h(\frac{x^3-9+15}{x^3-9})[/tex]

[tex]h(\frac{x^3+6}{x^3-9})[/tex]

[tex]\sqrt{ \frac{x^3+6}{x^3-9}}[/tex]

To express the function √(x^3+6)/√(x^3-9) as a composition of non-identity functions, we can rewrite it in terms of exponential and logarithmic functions.

To express the function √(x^3+6)/√(x^3-9) as a composition of three or more non-identity functions, we can start by rewriting √(x^3+6) and √(x^3-9) as powers:

√(x^3+6) = (x^3+6)^(1/2)

√(x^3-9) = (x^3-9)^(1/2)

Next, we can express (x^3+6)^(1/2) and (x^3-9)^(1/2) in terms of powers of its components. Let's denote a = x^3+6 and b = x^3-9:

(x^3+6)^(1/2) = (a)^(1/2)

(x^3-9)^(1/2) = (b)^(1/2)

Finally, we can express these in terms of exponential and logarithmic functions:

(a)^(1/2) = e^(0.5⁢ln(a))

(b)^(1/2) = e^(0.5⁢ln(b))

Therefore, the function √(x^3+6)/√(x^3-9) can be expressed as a composition of three non-identity functions:

√(x^3+6)/√(x^3-9) = e^(0.5⁢ln(a))/e^(0.5⁢ln(b))