Is the length of the hypotenuse of a right triangle with legs that mea-
sure 5 cm and 6 cm a rational number or an irrational number? Justify
your answer. Answer in complete sentences and indude all relevant calculations

Answer:

[tex]403.06 cm^2; 100.77cm^2[/tex]

Step-by-step explanation:

Ok, step 1. What's the measure of the internal angle of a dodecagon? After some splitting in triangles you get that's [tex](n-2)\pi = 10\pi[/tex]. That makes each angle measure [tex]\frac{10}{12}\pi[/tex].

That allows us to split the whole figure in 12 isosceles triangles with (congruent) angles of [tex]\frac5{12}\pi[/tex]. Consider just one, red in my picture. The height of that triangle - orange "vertical" line -  can be found with some trigonometry as [tex]3tan \frac5{12}\pi \approx 11.2 cm[/tex]

At this point one triangle has area [tex]\frac12 \cdot 6\cdot 11.2 = 33.6 cm^2[/tex] and the whole cookie has area as 12 triangles [tex]403.06 cm^2[/tex].

After her eating spree, you're left with 3 triangles, for a grand total of [tex]100.77 cm^2[/tex]

Answer:

x= -1 and x= -5

Explanation

y=(x+1)(x+5)

set both equations equal to 0

x+1=0 and x+5=0

subtract each constant from the appropriate  side

x= -1             x=-5

Answer:

Graph the exponential function.

[tex]y=-3(8)^{x}[/tex]

Step-by-step explanation:

to make a sketch of this graph. We're gonna make a table of values. I think that's probably our best route. So we'll do a couple negative values, but I'm gonna actually start at 08 to 0. Power zero. And I'm sorry. 80 parts one and one times negative. Three is negative. Three eight to the first. Power is eight and eight times negative. Three is negative. 24 8 X squared is 64 64 times negative. Three is on negative. 192. Okay, I think that's plenty. E to the negative. First power is 18 and 1/8 times negative. Three is negative. 3/8 and eight to the negative. To power is 1 64th times negative. Three is negative. 3 60 force. Okay, I think we can see where that's going. Is getting really close to zero. So as faras my graph here, I'm gonna focus on the fourth quadrant, I think. All right. So we got our X and y axis here. We're starting at 01 and to and we'll also do negative one. And negative two aren't horizontally, vertically. I do. I want to scale this whole the way to 1 92 I guess I will. Um, so whatever it is scaled by, maybe twenties. Yeah, let's do that. 20 40 60 8120 40 60 8200. So there's negative. 200? Um, negative. 1 80 Negative 1 60? Nope. That's not right. Because I scaled by twenties didn't. So this is actually negative. 1 60 This one's negative. 1 20 This one's negative. 80. And this is negative. 40. There we go. All right now a plot. These points to negative 1 92 is practically to 200 one. Negative. 24 is all the way over here. Zero negative three is practically on the X axis The way I have this, and same with those fractional values. They're practically on the X axis. So let's start almost parallel to the X axis because it's never actually touch step than its we don't ever. Slowly and then it starts going down rapidly, decreasing in value to the point where it's almost vertical, but it never will get vertical, so there's a decent sketch of y equals negative three times eight to the power of acts

Answer:

Base=8.4 inches

Step-by-step explanation:

Area of triangular bandana is 38sq inches

Height of triangle is 9 inches

Area of ∆ =½×b×h

38=½×b×9

38×2=b×9

76/9=b

b=8.4 inches

Answer:

Yes.

Step-by-step explanation:

18 gal = 288 cups.

(1 gal = 16 cups)

If 240 students purchase 1 cup each, there will be 48 cups left over.

So,yes, there will be enough punch for everyone.

Please mark as brainliest!

Thanks!

Answer:

-18

Step-by-step explanation:

= -8 - (-2 +7) x 2

= -8 - 5 x 2

= -8 - 10

= -18

The parabolic motion is an illustration of a quadratic function

The equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31

Given that:

x stands for time and y stands for height in feet

So, we have the following coordinate points

(x,y) = (5,0), (11,0) and (10,80)

A parabolic motion is represented as:

y =ax^2 + bx + c

At (5,0), we have:

25a + 5b + c = 0

c= -25a - 5b

At (11,0), we have:

121a + 11b + c = 0

Substitute c= -25a - 5b

121a + 11b -25a - 5b = 0

Simpify

96a + 6b = 0

At (10,80), we have:

100a + 10b + c = 80

Substitute c= -25a - 5b

100a + 10b - 25a -5b = 80

75a -5b = 80

Divide through by 5

15a -b = 16

Make b the subject

b = 15a + 16

Substitute b = 15a + 16 in 96a + 6b = 0

96a + 6(15a + 16) = 0

Expand

96a + 90a + 96 = 0

This gives

186a = -96

Solve for a

a = -16/31

Recall that:

b = 15a + 16

So, we have:

b = -15 * 16/31 + 16

b =-240/31 + 16

Take LCM

b =(-240 + 31 * 16)/31

[tex]b =256/31

Also, we have:

c= -25a - 5b

This gives

c= 25*16/31 - 5 * 256/31

Take LCM

c= -880/31

Recall that:

y =ax^2 + bx + c

This gives

y = -16/31x^2 + 256/31x - 880/31

Hence, the equation that models that path of the rocket is y = -16/31x^2 + 256/31x - 880/31

Read more about parabolic motion at:

https://brainly.com/question/1130127

Answer:

  $102

Step-by-step explanation:

The pay for the day of work is the total of morning hours worked and afternoon hours worked. In each case, the hours worked is the difference between the "Out" time and the "In" time.

  morning hours = 12:15 -8:15 = 4:00

  afternoon hours = 17:30 -13:00 = 4:30

  total hours worked = morning hours + afternoon hours

  total hours worked = 4:00 +4:30 = 8:30

This notation tells you (hours):(minutes). You know that 30 minutes is 1/2 hour, so the total time worked is 8 1/2 hours.

The pay is the product of the hours worked and the pay per hour:

  pay = (8 1/2 hours) × ($12 /hour) = $102

Answer: 2

Step-by-step explanation:

Answer:

The first two

Step-by-step explanation:

graph the parabola to see

Answer:

  17.34 years

Step-by-step explanation:

The equation you wrote in the first part of the problem can be solved for the value of t that makes the population be 5000.

  [tex]P(t)=\dfrac{10000}{1+11.5e^{-0.1408614477t}}[/tex]

Setting this equal to 5000 and multiplying by the denominator, we have ...

  [tex]5000=\dfrac{10000}{1+11.5e^{-0.1408614477t}}\\\\5000+57500e^{-0.1408614477t}=10000\\\\e^{-0.1408614477t}=\dfrac{5000}{57500}\qquad\text{subtract 5000, divide by 57500}\\\\-0.1408614477t = \ln{\dfrac{1}{11.5}}=-\ln(11.5)\qquad\text{take logs}\\\\t=\dfrac{\ln(11.5)}{0.1408614477}\approx17.3386[/tex]

For the population to reach 5000, it will take about 17.34 years.

_____

Additional comment

The value -0.14086... is the natural log of the ratio 1818/2093. This means the "exact answer" is ln(11.5)/(ln(2093) -ln(1818)), an irrational number.

A graphing calculator can answer the question easily.

Answer:

Let y = '?'

6(x + y) = 6x + 30

6x +6y = 6x + 30

6x + 6y - 6x = 6x + 30 - 6x

6y = 30

6y / 6 = 30 / 6

y = 5

[tex]81c {}^{2} - 4 = (9c - 2)(9c + 2)[/tex]

since it is in the form of:

[tex]x {}^{2} - y {}^{2} = (x - y)(x + y)[/tex]

2)

[tex]75x {}^{2} - 27y {}^{2} = (5 \sqrt{3} x - 3 \sqrt{3} y)(5 \sqrt{3} x + 3 \sqrt{3} y)[/tex]

3)

[tex]z {}^{2} + 12z + 36[/tex]

[tex]z {}^{2} + 6z + 6z + 36[/tex]

[tex]z(z + 6) + 6(z + 6)[/tex]

[tex](z + 6)(z + 6)[/tex]

[tex](z + 6) {}^{2} [/tex]

4)

[tex]4f {}^{2} + 18f + 18f + 81[/tex]

[tex]2f(2f + 9) + 9(2f + 9)[/tex]

[tex](2f + 9)(2f + 9)[/tex]

[tex](2f + 9) {}^{2} [/tex]

5)

[tex]49a {}^{2} - 14a + 1[/tex]

[tex](7a - 1) {}^{2} [/tex]

6)

[tex]x {}^{4} - 16[/tex]

[tex](x {}^{2} - 4)(x {}^{2} + 4)[/tex]

Answer:

Simplify the radical by breaking the radicand up into a product of known factors.

Exact Form:

3

√

75

5

Decimal Form:

0.84343266

…

Answer:

[tex]\frac{27}{125}[/tex]

Step-by-step explanation:

[tex](\frac{3}{5})^{3}[/tex] is [tex]\frac{3^{3}}{5^{3}}[/tex]

[tex]3^{3} = 27[/tex] and [tex]5^{3} = 125[/tex]

[tex]\frac{27}{125}[/tex]

Answer: n = 3

Step-by-step explanation:

divide 3.5n by 3.5n then divide 10.5 by 3.5 which is

n = 3

Answer:

[tex]\boxed{\sf{n=3}}[/tex]

Step-by-step explanation:

To find the value of n, you have to isolate it on one side of the equation.

3.5n=10.5

First, multiply by 10 from both sides.

[tex]\sf{3.5n*10=10.5*10}[/tex]

Solve.

35n=105

Divide by 35 from both sides.

35n/35=105/35

Solve.

105/35=3

n=3

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

C. 6.

Step-by-step explanation:

3/7 of 14

= 3*14/7= 42/7

= 6.

Answer:

A) 1.7

B) 4.5

C) 7.8

Answer:

3x+45=180

3x=180-45

x=135/3

x=45

(y-4)=45

y=45+4

y=49

Answer:

x=45° and y=49° (180°in a straight line, co-interior angles add up to 180°)

Step-by-step explanation:

There are 180° in a straight line so 180°-45=135, 135=3x

135 divided by 3= 45, so x=45°, then because co-interior angles always add up to 180°, 45+ the missing angle=180, 180-45=135, so the angle next to angle (y-4) is 135°.

Then, solving the equation u have 135+(y-4)=180 because there are 180° in a straight line.

The equation ends up as y=49°

Answer:

1/7^4

Step-by-step explanation:

negative exponents flip to opposite side of the fraction and add to like-base terms.

Hello!

This is a one-step equation, meaning that we can solve it in just 1 step.

This is the step:

3x=9

x=3

That's the answer; we can easily check it:

3*3=9

Hope everything is clear.

Let me know if you have any questions!

Always Remember: Knowledge Is Power!

Answer:

A

Step-by-step explanation:

how long is the ball in the air ?

that is the same as asking : after how many seconds will the ball hit the ground (= reach the height of 0) ?

so, that means we need to find the zero solution of h(t).

at what t is h(t) = 0 ?

when at least one of the factors is 0 :

2(-2 - 4t)(2t - 5)

we have 3 factors

2 : can never be 0.

(-2 -4t) : can only be 0 for negative t, which does not make sense in our scenario (we cannot go back in time, only forward).

(2t - 5) : is 0 when 2t = 5 or t = 2.5

so, A is the right answer.

FYI : the starting height (on the hill) is given by t = 0 :

2(-2 - 0)(0 - 5) = 2×-2×-5 = 20 ft

Answer:

$5

10 Dimes = $1 so If we have 50 dimes that = 5$

Please mark brainliest trying to level up :)

Answer:

-1

Step-by-step explanation:

Follow the example below and Good Luck!!!

Answer:

  -6/5

Step-by-step explanation:

The slope of the line is the ratio of "rise" to "run". That is, it is the ratio of the vertical change between two points to the horizontal change between those points.

__

Here, two points are marked, (-1, 2) and (4, -4). Either by counting grid squares or by subtracting coordinates, we find the vertical change (rise) from the first point to the second to be (-4 -2) = -6 units. The horizontal change (run) from the first point to the second is (4 -(-1)) = 5.

The slope is the ratio of these values:

  slope = rise/run = -6/5

Answer:

V≈2144.66cm³

Step-by-step explanation:

Answer:

[tex]V = 9878.44 in^3[/tex]

Step-by-step explanation:

The volume of a cylinder, is essentially base multiplied by height. Think of it like this, you are taking a flat 2D circle and extending it in 3rd dimension by a length 'h'.

[tex]V = base * h[/tex]

The base here is the circle area, and the height is the amount you extended that 2d circle in the 3rd dimension.

The area of a circle is [tex]\pi r^2[/tex]. If we put that into our equation we get the volume of a cylinder.

[tex]V = \pi r^2 *h[/tex]

Now applying that to the question; Firstly, we are given the diameter, which is 22 inches. We need radius, to actually put it in the equation. The diameter is essentially 2 multiplied by the radius. That means to get the radius we divide the diameter by 2, giving us 11 inches. Next we are given how tall it is, 26 inches; that is the height.

[tex]r = 11in\\h = 26in[/tex]

Plug these values into the equation.

[tex]V = 3.14(11in)^2 * 26in[/tex]

Calculate this, and you get [tex]V = 9878.44 in^3[/tex]

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=250(1 + 0.16)^{t}\implies A=250(1.16)^t \\\\[-0.35em] ~\dotfill[/tex]

[tex]A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &1000\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ 1000=250(1.16)^t\implies \cfrac{1000}{250}=1.16^t\implies 4=1.16^t \\\\\\ \log(4)=\log(1.16^t)\implies \log(4)=t\log(1.16) \\\\\\ \cfrac{\log(4)}{\log(1.16)}=t\implies \stackrel{\textit{about 9 years and 4 months}}{9.34\approx t}[/tex]

Answer:

6

Step-by-step explanation:

Prime factorization of 18 = 2 × 3 × 3

Prime factorization of 24 = 2 × 2 × 2 × 3

Common factors of 18 and 24 = 2 × 3 = 6

HCF (18,24) = 6

On factoring, the value of t is 1. This shows that the car will land on the ground after 1 sec.

Quadratic functions are functions having a leading degree of 2.

Given the function height in feet of the car after t seconds expressed as

h = -16t^2 +10t +6

The height of the car on the ground is zero, hence:

16t^2 -10t -6 = 0

8t^2 - 5t - 3 = 0

Factorize the quadratic function

8t^2 - 5t - 3 = 0

On factoring, the value of t is 1. This shows that the car will land on the ground after 1 sec.

Leearn more on functions here: https://brainly.com/question/10439235