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4 years ago

Find the next 4 terms of this Fibonacci sequence -x, x+y, y

Mathematics

1 answer:

Vaselesa [24]4 years ago

3 0

Answer:

see explanation

Step-by-step explanation:

Any term in a Fibonacci sequence is the sum of the previous 2 terms.

Given the first 3 terms then

a₄ = a₂ + a₃ = x + y + y = x + 2y

a₅ = a₃ + a₄ = y + x + 2y = x + 3y

a₆ = a₄ + a₅ = x + 2y + x + 3y = 2x + 5y

a₇ = a₅ + a₆ = x + 3y + 2x + 5y = 3x + 8y

Thus the next four terms are

x + 2y, x + 3y, 2x + 5y, 3x + 8y

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A family eats at a restaurant. The bill is $56.75. They are pleased with service so they leave 22% tip. What is their total afte

nika2105 [10]

$69.24 is the correct answer because 56.75 multiplied by 1.22 is 69.24

7 0

3 years ago

Use the Pythagorean identity on page 10 with x = 4 and y= 3 to generate a Pythagorean triple

Dmitry [639]

Answer:

c. 7, 24, 25

Step-by-step explanation:

For the formulas ...

a=x^2-y^2
b=2xy
c=x^2+y^2

we can use the given values of x and y to find the corresponding Pythagorean triple:

a = 4^2 -3^2 = 16 -9 = 7

b = 2·4·3 = 24

c = 4^2 +3^2 = 16 +9 = 25

The generated Pythagorean triple is (7, 24, 25), matching answer C.

6 0

3 years ago

The smallest integer that can be added to -2m3 − m + m2 + 1 to make it completely divisible by m + 1 is

QveST [7]

Hello,

-2m^3+m²-m+1=(m+1)(-2m²+3m-4) +5

We must add -5 ; the remainder will be 5-5=0.

3 0

3 years ago

Find the range, median, and mode of the following dot plot.

Aloiza [94]

Answer:

Range: 0.07

Median: 0.145

Mode: none

Step-by-step explanation:

Range: largest #- smallest #

Median: middle number (when numbers are in order least to greatest) or when two are middle number you add them, and divide by two

Mode: most occurring number(s) (if there aren't any, no mode)—but if there are multiples such as 2 zeros and 2 ones then 0 and 1 would be the mode

5 0

3 years ago

Which value is NOT a solution of 8x3 – 1 = 0?

Tpy6a [65]

Note: As you may have unintentionally missed to add the value choices. But, I would make sure to explain the concept so that you may improve your understanding in terms of solving these type of questions.

Answer:

Any value other than the values $x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4}$ will not be a solution of $8x^3\:-\:1\:=\:0$ .

Step-by-step explanation:

Considering the equation

$8x^3\:-\:1\:=\:0$

Steps to solve the equation

$8x^3-1=0$

$\mathrm{Add\:}1\mathrm{\:to\:both\:sides}$

$8x^3-1+1=0+1$

$\mathrm{Simplify}$

$x^3=\frac{1}{8}$

$\mathrm{Divide\:both\:sides\:by\:}8$

$\frac{8x^3}{8}=\frac{1}{8}$

$\mathrm{Simplify}$

$x^3=\frac{1}{8}$

$\mathrm{For\:}x^3=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}$

$x=\sqrt[3]{\frac{1}{8}},\:x=\sqrt[3]{\frac{1}{8}}\frac{-1+\sqrt{3}i}{2},\:x=\sqrt[3]{\frac{1}{8}}\frac{-1-\sqrt{3}i}{2}$

So,

$x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4}$

Therefore,

Any value other than the values $x=\frac{1}{2},\:x=-\frac{1}{4}+i\frac{\sqrt{3}}{4},\:x=-\frac{1}{4}-i\frac{\sqrt{3}}{4}$ will not be a solution of $8x^3\:-\:1\:=\:0$ .

Keywords: solution, value

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7 0

3 years ago