At noon, the minute and the hour hands of a clock overlap. In how long will they again overlap?

65 - 14 = 65-5-______

Fed [463]

Answer: 60? to be hostens i have no clue sorry i hope this help...

Step-by-step explanation:

7 0

2 years ago

What's the equivalent

olga2289 [7]

9 1/2 = 19/2

(29/5) / (19/2)

When changing division to multiplication, flip the number (right hand side).

(29/5) * (2/19)

58/95

7 0

3 years ago

5 < 4x = 2> 3x PLEASE HELP

Galina-37 [17]

Looks fishy to me, the way this problem combines <, = and > symbols.

But anyway. Subtract 3x from both sides. You'll get

5 < x = 2 > 0 2 > 0 is true, but that's a different type of math problem (true or false). If you decide to substitute '1' for 2 > 0, then the "1" says "TRUE."

Then 5 < x = true, so you must find x values that are larger than 5.

That would be (5, infinity)

Please go back and ensure that you have copied down the original problem exactly as it appears.

8 0

3 years ago

Use the intersect method to solve the equation. 14x^3-53x^2+41x-4=-4x^3-x^2+1x+4

UNO [17]

Answer:

x = (68 2^(1/3) + (27 i sqrt(591) + 445)^(2/3))/(27 (1/2 (27 i sqrt(591) + 445))^(1/3)) + 26/27 or x = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 26/27 or x = 1/27 ((-2)/(27 i sqrt(591) + 445))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3)) + 26/27

Step-by-step explanation:

Solve for x over the real numbers:

14 x^3 - 53 x^2 + 41 x - 4 = -4 x^3 - x^2 + x + 4

Subtract -4 x^3 - x^2 + x + 4 from both sides:

18 x^3 - 52 x^2 + 40 x - 8 = 0

Factor constant terms from the left hand side:

2 (9 x^3 - 26 x^2 + 20 x - 4) = 0

Divide both sides by 2:

9 x^3 - 26 x^2 + 20 x - 4 = 0

Eliminate the quadratic term by substituting y = x - 26/27:

-4 + 20 (y + 26/27) - 26 (y + 26/27)^2 + 9 (y + 26/27)^3 = 0

Expand out terms of the left hand side:

9 y^3 - (136 y)/27 - 1780/2187 = 0

Divide both sides by 9:

y^3 - (136 y)/243 - 1780/19683 = 0

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

-1780/19683 - 136/243 (z + λ/z) + (z + λ/z)^3 = 0

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ - 136/243) - (1780 z^3)/19683 + z^2 (3 λ^2 - (136 λ)/243) + λ^3 = 0

Substitute λ = 136/729 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 - (1780 u)/19683 + 2515456/387420489 = 0

Find the positive solution to the quadratic equation:

u = (2 (445 + 27 i sqrt(591)))/19683

Substitute back for u = z^3:

z^3 = (2 (445 + 27 i sqrt(591)))/19683

Taking cube roots gives 1/27 2^(1/3) (445 + 27 i sqrt(591))^(1/3) times the third roots of unity:

z = 1/27 2^(1/3) (445 + 27 i sqrt(591))^(1/3) or z = -1/27 (-2)^(1/3) (445 + 27 i sqrt(591))^(1/3) or z = 1/27 (-1)^(2/3) 2^(1/3) (445 + 27 i sqrt(591))^(1/3)

Substitute each value of z into y = z + 136/(729 z):

y = (68 2^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 1/27 (2 (27 i sqrt(591) + 445))^(1/3) or y = (68 (-2)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) - 1/27 (-2)^(1/3) (27 i sqrt(591) + 445)^(1/3) or y = 1/27 (-1)^(2/3) (2 (27 i sqrt(591) + 445))^(1/3) - (68 (-1)^(1/3) 2^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3))

Bring each solution to a common denominator and simplify:

y = (2^(1/3) ((27 i sqrt(591) + 445)^(2/3) + 68 2^(1/3)))/(27 (445 + 27 i sqrt(591))^(1/3)) or y = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (445 + 27 i sqrt(591))^(1/3)) or y = 1/27 2^(1/3) (-1/(445 + 27 i sqrt(591)))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3))

Substitute back for x = y + 26/27:

Answer: x = (68 2^(1/3) + (27 i sqrt(591) + 445)^(2/3))/(27 (1/2 (27 i sqrt(591) + 445))^(1/3)) + 26/27 or x = (68 (-2)^(2/3) - (-2)^(1/3) (27 i sqrt(591) + 445)^(2/3))/(27 (27 i sqrt(591) + 445)^(1/3)) + 26/27 or x = 1/27 ((-2)/(27 i sqrt(591) + 445))^(1/3) ((-1)^(1/3) (27 i sqrt(591) + 445)^(2/3) - 68 2^(1/3)) + 26/27

5 0

2 years ago

Write all factor pairs for the number 64

sladkih [1.3K]

A factor pair is two numbers that can be multiplied to get a number.
With any number, we know that 1*itself is a factor pair. So
1*64
The number in the ones place, 4, is even, so we know that 64 is a multiple of 2. Half of 64 is 32, so
2*32
To find out if 3 is a factor of 64, we can add 6+4. If the answer is a multiple of 3, then we know that the number itself is a multiple of 3. Because 6+4=10, and 10 is not a multiple of 3, we know that 64 is not a multiple of 3.
If 2 is not a factor of a number, then we know that 4 (2*2) cannot be a factor. Because 2 is a factor of 64, then 4 might be as well. To discover whether or not 4 is a factor of 64, we can look at the number above multiplied by 2 to equal 64 (32) and see if it divides by 2 evenly, or we can half 64 and then half it again. If either answer is a whole number, then we know that the answer*4 equals 64, and that 64 is a multiple of 4. Because half of 32 is 16, a whole number, we know that
4*16=64
Because 64 does not have a 0 or 5 in the one's place, we know that it cannot be a multiple of 5.
Because 64 is not a multiple of 3, we know it cannot be a multiple of 6, because 6 is 2*3.
I happen to be familiar with my times tables, so I can tell that the multiples of 7 are 63 and 70, but not 64.
I don't know if 64 is a multiple of 8 off the top of my head, but I can count by 8s and see if 64 comes up: 8, 16, 24, 32, 40, 48, 56, 64, 72 - I can go on, but we can already see that 64 is a multiple of 8, so 8 is a factor of 64. If we count the number of 8s I can see that there are 8 of them when we get to 64. In other words,
8*8=64
Because we have gotten to a factor pair that is the same 2 number multiplied by each other (the square root) we know that we have found all factor pairs of 64.

8 0

3 years ago

Read 2 more answers