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maw [93]
2 years ago
13

Which expression is equivalent to 60 Σ n=1 (2n − 1)2 ? Check all that apply.

Mathematics
2 answers:
Hunter-Best [27]2 years ago
7 0

9514 1404 393

Answer:

  B, D

Step-by-step explanation:

The quadratic expands to ...

  (2n -1)² = (2n)² +2(2n)(-1) +(-1)² = 4n² -4n +1

The coefficients can be factored out of the sum, so ...

  ∑(4n²) = 4∑n² for example

The sum of 60 ones is 60:

  \displaystyle\sum_{n=1}^{60}{1}=1+1+1+\dots+1=60

So, the sum can be written as ...

  \displaystyle\sum_{n=1}^{60}{(2n-1)^2}\\\\=\boxed{4\sum_{n=1}^{60}{n^2}-4\sum_{n=1}^{60}{n}+\sum_{n=1}^{60}{1}}\\\\=\boxed{4\sum_{n=1}^{60}{n^2}-4\sum_{n=1}^{60}{n}+60}

_____

It appears that the key to choosing the correct answers is paying attention to signs.

kolezko [41]2 years ago
3 0

Answer: Step number 2 is 287,980

Step-by-step explanation:

Just did the assignment.

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Executive Limousine rentals charges an initial fee of $200 and $40 per hour that the limousine is in service. Jet Limousine rent
zavuch27 [327]

At 8 hours of service, the two limousine rental companies charge the same amount.

Step-by-step explanation:

Given,

Initial fee of Executive Limousine rental = $200

Per hour charges of service = $40

Let,

x be the number of hours.

E(x) = 40x+200

Initial fee of Jet Limousine rental = $120

Per hour charges of service = $50

J(x) = 50x + 120

For the charges to be same;

E(x) = J(x)

40x+200=50x+120\\200-120=50x-40x\\80=10x\\10x=80

Dividing both sides by 10

\frac{10x}{10}=\frac{80}{10}\\x=8

At 8 hours of service, the two limousine rental companies charge the same amount.

Keywords: function, addition

Learn more about functions at:

  • brainly.com/question/10688256
  • brainly.com/question/10708697

#LearnwithBrainly

5 0
3 years ago
The cost of 3 tacos and 1 soda is $7. The costof 4 tacos and two sodas is $10. What is the cost of one taco
statuscvo [17]

Answer:

cost of tacos=$2

cost of soda=$1

Step-by-step explanation:

x=price of tacos

y=price of soda

3x+y=7 --> y=7-3x

4x+2y=10 --> y=5-2x

5-2x=7-3x

x=2

y=5-2(2)=1

4 0
3 years ago
A roller coaster starts with the cars being pulled up a ramp. The mass of the cars is estimated by the function m(p) = 175p + 1,
KiRa [710]

Answer:

E(p)=51,450p+346,920

Step-by-step explanation:

The function

m(p) = 175p + 1,180

gives the mass of the car as a function of the number of passengers in it.

And the function

E(m) = 9.8m*h

gives the potential energy of the car as a function of the car's mass.

Now if the height of the ramp is 30 meters, we have

E(m) =9.8m*(30)

E(m) =294m

And to find the potential energy as a function of the number of passengers, we just substitute m(p) into E(m) to get:

E(m(p))=294(175p+1180)

\boxed{ E(p)=51,450p+346,920}

which gives the potential energy as a function of the number of passengers.

7 0
3 years ago
PLEASE HELP WILL GIVE POINTS AND MARK BRAINLIEST PLEASE!!!!!!!!!!!!!
Usimov [2.4K]

Answer:

The point must be between 5 and 6, accurately in 5,4

Step-by-step explanation:

SQT[29] = 5,38

Best regards

4 0
3 years ago
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Bicycles have 2 wheels an tricycles have 3. There are a total of 7 bicycles and tricycle. If there are 17 wheels in all how many
Anika [276]
There are 7 bicycles and 1 tricycle
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