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BaLLatris [955]
3 years ago
9

Combine like terms (4x^2+6x+7)−(−8x^2−2x+6)

Mathematics
1 answer:
ANEK [815]3 years ago
3 0

Answer:

12x^2+8x+1

Step-by-step explanation:

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Aye plz help. Im abt to die. Find the perimiter of the shape below.
Law Incorporation [45]

Answer:

40

Step-by-step explanation:

Add all the sides together which is 40

4 0
3 years ago
Solve for x in the equation 2x^2+3x-7 = x^2+ 5 x + 39
AnnyKZ [126]

Answer:

X=1+\sqrt{47}

Step-by-step explanation:

Hope this helps

Mark me as brainiest

8 0
3 years ago
Read 2 more answers
A Ferris wheel is 20 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position
pantera1 [17]

Answer:

233.48s  

3.84 min

Step-by-step explanation:

In order to solve this problem, we can start by drawing what the situation looks like. See attached picture.

We can model this situation by making use of a trigonometric function. Trigonometric functions have the following shape:

y=A cos(\omega t+\phi)+C

where:

A= amplitude =-20m because the model starts at the lowest point of the trajectory.

f= the function to use, in this case we'll use cos, since it starts at the lowest point of the trajectory.

t= time

\omega= angular speed.

in this case:

\omega=\frac{2\pi}{T}

where T is the period, in this case 6 min or

6min(\frac{60s}{1min})=360s

so:

\omega=\frac{2\pi}{360}

\omega = \frac{\pi}{160}

and

\phi= phase angle

C= vertical shift

in this case our vertical shift will be:

2m+20m=22m

in this case the phase angle is 0 because we are starting at the lowest point of the trajectory. So the equation for the ferris wheel will be:

y=-20 cos(\frac{\pi}{180}t)+22

Once we got this equation, we can figure out on what times the passenger will be higher than 13 m, so we build the following inequality:

-20 cos(\frac{\pi}{180}t)+22>13

so we can solve this inequality, we can start by turning it into an equation we can solve for t:

-20 cos(\frac{\pi}{180}t)+22=13

and solve it:

-20 cos(\frac{\pi}{180}t)=13-22

-20 cos(\frac{\pi}{180}t)=-9

cos(\frac{\pi}{180}t)=\frac{9}{20}

and we can take the inverse of cos to get:

\frac{\pi}{180}t=cos^{-1}(\frac{9}{20})

which yields two possible answers: (see attached picture)

so

\frac{\pi}{180}t=1.104 or \frac{\pi}{180}t=5.179

so we can solve the two equations. Let's start with the first one:

\frac{\pi}{180}t=1.104

t =1.104(\frac{180}{\pi})

t=63.25s

and the second one:

\frac{\pi}{180}t=5.179

t=5.179(\frac{180}{\pi})

t=296.73s

so now we can build our possible intervals we can use to test the inequality:

[0, 63.25]  for a test value of 1

[63.25,296.73] for a test value of 70

[296.73, 360] for a test value of 300

let's test the first interval:

[0, 63.25]  for a test value of 1

-20 cos(\frac{\pi}{180}(1))+22>13

2>13 this is false

let's now test the second interval:

[63.25,296.73] for a test value of 70

-20 cos(\frac{\pi}{180}(70))+22>13

15.16>13 this is true

and finally the third interval:

[296.73, 360] for a test value of 300

-20 cos(\frac{\pi}{180}(300))+22>13

12>13 this is false.

We only got one true outcome which belonged to the second interval:

[63.25,296.73]

so the total time spent above a height of 13m will be:

196.73-63.25=233.48s

which is the same as:

233.48(\frac{1min}{60s})=3.84 min

see attached picture for the graph of the situation. The shaded region represents the region where the passenger will be higher than 13 m.

3 0
3 years ago
Mrs.Steffen’s third grade class has 30 students in it. The students are divided into three groups(numbered 1, 2,and 3),each havin
qaws [65]

Answer:

a. \\ 10! = 3628800;

b. \\ 10!*10!*10! = 47784725839872000000 = 4.7784725839872*10^{19}

Step-by-step explanation:

We need here to apply the <em>Multiplication Principle </em>or the <em>Fundamental Principle of Counting</em> for each answer. Answer <em>b</em> needs an extra reasoning for being completed.

The <em>Multiplication Principle</em> states that if there are <em>n</em> ways of doing something and <em>m</em> ways of doing another thing, then there are <em>n</em> x <em>m</em> ways of doing both (<em>Rule of product</em> (2020), in Wikipedia).

<h3>In how many ways can ten students line up? </h3>

There are <em>ten</em> students. When one is selected, there is no other way to select it again. So, <em>no repetition</em> is allowed.

Then, in the beginning, there are 10 possibilities for 10 students; when one is selected, there are nine possibilities left. When another is selected, eight possibilities are left to form the file, and so on.

Thus, we need to multiply the possibilities after each selection: that is <em>why</em> the <em>Multiplication Principle</em> is important here.

This could be expressed mathematically using n!:

\\ n! = n * (n-1)! * (n-2)! *...* 2*1.

For instance, \\ 5! = 5 * (5-1)! * (5-2)! *...*2*1 = 5 * 4 * 3 * 2 * 1 = 120.

So, for the case in question, the <em>ten</em> students can line up in:

\\ 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3628800 ways to line up in a single file.

<h3>Second Question</h3>

For this question, we need to consider the former reasoning with extra consideration in mind.

The members of Group 1 can occupy <em>only</em> the following places in forming the file:

\\ G1 = \{ 1, 4, 7, 10, 13, 16, 19, 22, 25, 28\}^{th} <em>places</em>.

The members of Group 2 <em>only</em>:

\\ G2 = \{ 2, 5, 8, 11, 14, 17, 20, 23, 26, 29\}^{th} <em>places</em>.

And the members of Group 3, the following <em>only</em> ones:

\\ G3 = \{ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30\}^{th} <em>places.</em>

Well, having into account these possible places for each member of G1, G2 and G3, there are: <em>10! ways</em> for lining up members of G1; <em>10! ways</em> for lining up members of G2 and, also, <em>10! ways</em> for lining up members of G3.

After using the <em>Multiplication Principle</em>, we have, thus:

\\ 10! * 10! * 10! = 47784725839872000000 = 4.7784725839872 *10^{19} <em>ways the students can line up to come in from recess</em>.

3 0
3 years ago
PLZ HELP !!!! WILL MARK BRAINLIEST, THIS IS DUE IN 15 MINUTIES !!!ANYONE PLEASEPLZ HELP !!!! WILL MARK BRAINLIEST, THIS IS DUE I
gogolik [260]

Answer:

The answer is G

Step-by-step explanation:

So what I did was I went on a website that it wont let me name and typed in each equation and then the ordered pair and checked to see if (8,-1) was a solution and it was for G.

6 0
3 years ago
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