make a sequence of integers that starts with 43. each new term is the sum of the squares of the digits of the previous term. the sequence would be a₁= 43, a₂= 4²+3² =25, and so on. keep going until you find the first integer that appears twice in the sequence
Answers
a₁ = 43
a₂ = 4² + 3² = 16 + 9 = 25
a₃ = 2² + 5² = 4 + 25 = 29
a₄ = 2² + 9² = 4 + 81 = 85
a₅ = 8² + 5² = 64 + 25 = 89
a₆ = 8² + 9² = 64 + 81 = 145
a₇ = 1² + 4² + 5² = 1 + 16 + 25 = 42
a₈ = 4² + 2² = 16 + 4 = 20
a₉ = 2² + 0² = 4 + 0 = 4
a₁₀ = 4² = 16
a₁₁ = 1² + 6² = 1 + 36 = 37
a₁₂ = 3² + 7² = 9 + 49 = 58
a₁₃ = 5² + 8² = 25 + 64 = 89
As we can see, the first integer that appears twice in the sequence is 89.
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The sum of two numbers is 55 and the difference is 13 . What are the numbers?
Can someone help me out 10 points
Answers
B. h(x) + 41 = 31x2 + 77x
C. y = 31x2 + 77x − 41
D. y + 41 = 31x2 + 77x
Answers
Answer:
I think the answer is A. y= 31x2 + 77x + 41
Step-by-step explanation:
Final answer:
The function h(x) = 31x2 + 77x + 41 can also be written as y = 31x2 + 77x + 41, as y is often used interchangeably with f(x) or h(x) in mathematical functions. The remaining options do not accurately reformulate the original equation.
Explanation:
The function
h(x) = 31x2 + 77x + 41
can also be written as
y = 31x2 + 77x + 41
. This is because in mathematical functions, y is often used interchangeably with f(x) or h(x), representing the output or dependent variable. It's important to note that, the other options do not correctly represent the original equation. In Option B, the constant term is incorrectly added to the function on the left side; in Option C, the constant term is incorrectly subtracted; and in Option D, the constant term is incorrectly added to 'y' on the left side.
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Answers
3x3 + 9x2 - 12x
Answers
x = -1
x = 0
Equation at the end of step 1 :
((3 • (x3)) - 32x2) - 12x = 0
Step 2 :
Equation at the end of step 2 :
(3x3 - 32x2) - 12x = 0
Step 3 :
Step 4 :
Pulling out like terms :
4.1 Pull out like factors :
3x3 - 9x2 - 12x = 3x • (x2 - 3x - 4)
Trying to factor by splitting the middle term
4.2 Factoring x2 - 3x - 4
The first term is, x2 its coefficient is 1 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -4
Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4
Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -3 .
-4 + 1 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 1
x2 - 4x + 1x - 4
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-4)
Add up the last 2 terms, pulling out common factors :
1 • (x-4)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-4)
Which is the desired factorization
If you factor 3x from the expression, you have
So, we have
We easily have
So, one solution is x=0.
The other solutions depend on the quadratic equation:
So, the solutions are
Answers
X=$35.00
μ=$29.60
σ=$10.50
Z= (X−μ / σ)
^^ This formula is actually wrong though... the correct way to write it is:
Z= (X−μ) / σ
Z=(35.00-29.60)/10.50
Z=5.4/10.50
Z=0.51
Answers
pi times radius^2 times height
diameter=2 times radius
diameter times 1/2=radius
6.19/2=radius=3.095
pi times 3.095^2 times 6=177.077
so volume of cylinder=177.08
volume of gold=360
so
x cylinders=1 solid block
diviide both sdies by cylinder
x=block/cylinder
block=360
cylinder=177.08
360/177.08=2.03
so aprox 2.03 cylinders will make one block
round down since 0.03 is nigligible
the answer is 2