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stellarik [79]
4 years ago
12

(w^2 – 6w)^2– 2(w^2 – 6w) – 35 = 0​

Mathematics
1 answer:
muminat4 years ago
4 0

Step-by-step explanation:

( {w}^{2}  - 6w {)}^{2}  - 2( {w}^{2}  - 6w) - 35 = 0 \\  =  {w}^{4} - 6 {w}^{2}   - 2 {w}^{2}  - 12w  =  35  \\  =  {w}^{4}   - 4 {w}^{2}  - 12w = 35

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Isabella save 2 nickels today, if she doubles the number of Nicole, she saves every day, how many days, including today, will it
Elden [556K]

Answer:

  8 days

Step-by-step explanation:

On day 8, Isabella will save 256 nickels, bringing her total to 510.

_____

The number of nickels saved on day n is 2^n. The total is 2^(n+1)-2.

_____

The above can be written down from your knowledge of binary sequences. If you want a more formal development, read on.

__

The number of nickels saved on day n is a geometric sequence with first term 2 and common ratio 2. The n-th term of the sequence is ...

  an = a1·r^(n-1) = 2·2^(n-1) = 2^n

The sum of n terms of the sequence is ...

  S = a1(r^n -1)/(r -1) = 2(2^n -1)/(2-1)

  S = 2^(n+1) -2

__

We want S > 500, so ...

  500 < 2^(n+1) -2

  502 < 2^(n+1)

  251 < 2^n

  log(251) < n·log(2)

  n > log(251)/log(2)

  n > 7.97 . . . . . . . . 8 days or more to save more than 500 nickels

3 0
3 years ago
How far from an airport can an airplane fly and return in 8 hours, if it's outgoing speed is 160 km per hour and it's returning
PilotLPTM [1.2K]
<span>speed = distance/time
total time is 8 hours

outgoing speed is 160 km per hour, 
so time = d/160

</span><span>returning speed is 240 km per hour,
so time = d/240

 d/160 + d/240 = 8

3d/480 + 2d/480 = 8
5d/480 = 8
5d =480 (8)
5d = 3840
d=3840/5
d=768

answer: so the distance is 768 km</span>
4 0
3 years ago
Read 2 more answers
Quadrilateral JKLM is a rhombus. The diagonals intersect at N. If angle JNK equals 5x - 15, find the value of x.
VLD [36.1K]
One property of a rhombus is that the diagonals are perpendicular. This means that the diagonals intersect at 90 degree angles (right angles).

So we know that angle JNK is 90 degrees

angle JNK = 90 degrees
5x - 15 = 90
5x - 15 + 15 = 90+15
5x = 105
5x/5 = 105/5
x = 21

Answer: x = 21
3 0
3 years ago
Tina is attempting to factor the expression 10x^2-13-3. In her first step, she rewrites the expression as 10x^2-10x-3x-3. Which
Setler79 [48]

ANSWER

B. The two middle coefficients add to the correct number but do not multiply to the correct number.

EXPLANATION

The given quadratic trinomial that Tina tries to factor is

10 {x}^{2}  - 13x - 3

Comparing to

a{x}^{2}  + bx  + c

we have a=10, b=-13 and c=-3

ac=-3×10=-30

We split the middle term so that their sum is -13.

Tina use

-10,-3

to get

-10x-3x

The sum is -13x alright but the product is not -30.

B is correct.

8 0
3 years ago
9 is the difference between two numbers, and their sum is 31. Find the numbers.
algol [13]

Answer:

The first number is 20, the second one is 11

Step-by-step explanation:

Let the first number be x and the second number be y

Since it says "9 is the difference between two numbers", the first equation will be x-y=9

It also says that "their sum is 31". That means the second equation will be x+y=31

here are the two equations:

x-y=9

x+y=31

You can solve this any way you like, but I'll show elimination

add the two equations

x-y=9

x+y=31

2x=40

divide by 2

x=20

Substitute 20 as x in one of the equations

20+y=31

subtract 20 from both sides

y=11

That means the two numbers are 20 and 11

Hope this helps!

4 0
3 years ago
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