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Galina-37 [17]
3 years ago
11

Please help lots of points rewarded

Mathematics
2 answers:
castortr0y [4]3 years ago
8 0

Answer:

  • tₙ =  2n² - 3

Step-by-step explanation:

<u>Standard form of a quadratic equation:</u>

  • y = ax² + bx + c

<u>Apply same for the quadratic sequence:</u>

  • tₙ = an² + bn + c

<u>Substitute n with 1, 2 and 3 to get the system:</u>

  • -1 = a*1² + b*1 + c  ⇒ a + b + c = -1
  • 5 = a*2² + b*2 + c  ⇒ 4a + 2b + c = 5
  • 5 = a*3² + b*3 + c  ⇒ 9a + 3b + c = 15

<u>Subtract the first equation from the second and subtract the second equation from the third to get:</u>

  • 3a + b = 6
  • 5a + b = 10

<u>Again subtract the equations to find a:</u>

  • 2a = 4
  • a = 2

<u>Then find b and c:</u>

  • b = 3a - 6 = 6 - 6 = 0
  • c = -1 - a - b = -1 - 2 - 0 = -3

<u>Substitute the coefficients back into the equation of the quadratic sequence:</u>

  • tₙ = 2n² + 0n + (-3) = 2n² - 3
ololo11 [35]3 years ago
6 0
A of n = 2n^2 - 3
the nth term = 2 times n to the power of 2 minus 3
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The distance between the two points (4,1) and (9,1) is​
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Answer:

5 units. Since they have the same y coordinate the x coordinate determines the distance from each other. In the case 9-4=5.

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3 years ago
When Devon cashed a $450 check at the bank, the teller gave him 18 bills, all $20 bills and $50 bills. Which system of equations
Ymorist [56]
You have two totals: total # of bills and total amount of $. Using x as #of 20s, and y as # of 50s, you can use the system
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4 0
3 years ago
Read 2 more answers
URGENT! PLEASE HELP.
uysha [10]

Answer: a) BC = 1386.8 ft

b) CD = 565.8 ft

Step-by-step explanation:

Looking at the triangle,

AD = BD + 7600

BD = AD - 7600

Considering triangle BCD, we would apply the the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan 24 = CD/BD = CD/(AD - 700)

0.445 = CD/(AD - 700)

CD = 0.445(AD - 700)

CD = 0.445AD - 311.5 - - - - - - - -1

Considering triangle ADC,

Tan 16 = CD/AD

CD = ADtan16 = 0.287AD

Substituting CD = 0.287AD into equation 1, it becomes

CD = 0.445AD - 311.5

0.287AD = 0.445AD - 311.5

0.445AD - 0.287AD = 311.5

0.158AD = 311.5

AD = 311.5/0.158

AD = 1971.52

CD = 0.287AD = 0.287 × 1971.52

CD = 565.8 ft

To determine BC, we would apply the Sine trigonometric ratio which is expressed as

Sin θ = opposite side/hypotenuse

Sin 24 = CD/BC

BC = CD/Sin24 = 565.8/0.408

BC = 1386.8 ft

4 0
3 years ago
4.20. According to a report released by the National Center for Health Statistics, 51% of U.S. households has only cell phones (
Sergeu [11.5K]

Answer:

The probability that the household has only cell phones and has high-speed Internet is 0.408

Step-by-step explanation:

Let A be the event that represents U.S. households has only cell phones

Let B be the event that represents U.S. households have high-speed Internet.

We are given that 51% of U.S. households has only cell phones

P(A)=0.51

We are given that 70% of the U.S. households have high-speed Internet.

P(B)=0.7

We are given that U.S. households having only cell phones, 80% have high-speed Internet. A U.S household is randomly selected.

P(B|A)=0.8

\frac{P(A\capB)}{P(A)}=0.8\\P(A\capB)=0.8 \times P(A)\\P(A\capB)=0.8 \times 0.51\\P(A\capB)=0.408

Hence the probability that the household has only cell phones and has high-speed Internet is 0.408

7 0
3 years ago
If you help me I'll make as brilliant​
MissTica

The answer is A) 3/100.

5 0
3 years ago
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