Mathematics : asked on pobruce53

27.08.2021

Solve for x 64^x^2 = 256^x

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Step-by-step answer

09.07.2023, solved by verified expert

Mathematics, DAV Post Graduate College

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x = 0, 1.333333...

Step-by-step explanation:

1) Convert both sides to the same base.

2) Cancel the base of 16 on both sides.

3) Move all terms to one side.

4) Factor out the common term x.

5) Solve for x.

1 - Ask: When will x(1.5x-2) equal zero?

When x = 0 or 1.5x - 2 = 0
2 - Solve each of the 2 equations above.

x = 0, 1.333333...

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Mathematics

Solve for x 64^x^2 = 256^x

Step-by-step answer

P Answered by Specialist

x = 0, 1.333333...

Step-by-step explanation:

1) Convert both sides to the same base.

$16^{1.5x^{2} } =16^{2x}$

2) Cancel the base of 16 on both sides.

$1.5x^{2} =2x$

3) Move all terms to one side.

$1.5x^{2} -2x=0$

4) Factor out the common term x.

x(1.5x-2)=0

5) Solve for x.

1 - Ask: When will x(1.5x-2) equal zero?

When x = 0 or 1.5x - 2 = 0
2 - Solve each of the 2 equations above.

x = 0, 1.333333...

Mathematics

Solve for x 64^x-2=256^2x

Step-by-step answer

P Answered by PhD

6

$64^{x-2}=256^{2x}\\ \\(4^3)^{x-2}=(4^4)^{2x}\\ \\4^{3x-6}=4^{8x}\ \ \ \ \Leftrightarrow\ \ \ \ 3x-6=8x\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 3x-8x=6\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -5x=6\ \ \ \ \Leftrightarrow\ \ \ \ x=- \frac{6}{5}$

Mathematics

Which value must be added to the expression x^2 +16x to make it perfect-square trinomial? a-8 b-32 c-64 d-256 edit: it’s not a

Step-by-step answer

P Answered by PhD

2

X^2 + 16x + ?
a^2 + 2ab + b
(a + b)^2 which is a perfect square.

To find b to determine the last value, you divide 16x by 2x.
so:
b = 8
the last value would be 8^2 which is 64.

Hence answer is C - 64

Mathematics

Which value must be added to the expression x^2 +16x to make it perfect-square trinomial? a-8 b-32 c-64 d-256 edit: it’s not a

Step-by-step answer

P Answered by PhD

2

X^2 + 16x + ?
a^2 + 2ab + b
(a + b)^2 which is a perfect square.

To find b to determine the last value, you divide 16x by 2x.
so:
b = 8
the last value would be 8^2 which is 64.

Hence answer is C - 64

Mathematics

50 points: a chess competition has eliminations each round. the table below shows the number of players in each of the first 5 rounds of the tournament: round (x) 1 2 3 4 5 players f(x) 256 128 64 32 16 compute the average rate of change of f(x) from x = 1 to x = 5 and identify the meaning of that rate. −60; on average, there was a loss of 60 each round −240; on average, there was a loss of 240 each round 4; there were 4 rounds between rounds 1 and 5 240; there were 240 fewer players between rounds 1 and 5

Step-by-step answer

P Answered by PhD

Round (x)1 2 3 4 5
Players f(x)256 128 64 32 16

16-256 / 5 - 1 = -240/4 = -60

A.) −60; on average, there was a loss of 60 each round.

Mathematics

Achess competition has eliminations each round. the table below shows the number of players in each of the first 5 rounds of the tournament: round (x) 1 2 3 4 5 players f(x) 256 128 64 32 16 compute the average rate of change of f(x) from x = 1 to x = 5 and identify the meaning of that rate. −60; on average, there was a loss of 60 each round −240; on average, there was a loss of 240 each round 4; there were 4 rounds between rounds 1 and 5 240; there were 240 fewer players between rounds 1 and 5

Step-by-step answer

P Answered by Specialist

42

The average rate of change of f(x) from x =1 to x = 5 is
(16 - 256) / (5 -1) = -60
This means that on average, there was a loss of 60 each round

So, the answer is the first option.

Mathematics

50 points: a chess competition has eliminations each round. the table below shows the number of players in each of the first 5 rounds of the tournament: round (x) 1 2 3 4 5 players f(x) 256 128 64 32 16 compute the average rate of change of f(x) from x = 1 to x = 5 and identify the meaning of that rate. −60; on average, there was a loss of 60 each round −240; on average, there was a loss of 240 each round 4; there were 4 rounds between rounds 1 and 5 240; there were 240 fewer players between rounds 1 and 5

Step-by-step answer

P Answered by PhD

Round (x)1 2 3 4 5
Players f(x)256 128 64 32 16

16-256 / 5 - 1 = -240/4 = -60

A.) −60; on average, there was a loss of 60 each round.

Mathematics

What values of c makes the polynomial below a perfect square? x^2+16x+c c= a. 64 b. 32 c. 4 d. 256

Step-by-step answer

P Answered by Specialist

19

To find the perfect square of an equation, you just take your "middle" term (in this case, 16), divide it by 2, then square it.

16/2 = 8
8^2 = 64

your perfect square is 64. you can check it really quick by trying to factor x^2 + 16x + 64 and seeing that it breaks down perfectly into (x + 8)(x + 8), which can be written as (x + 8)^2, showing that you have a binomial with a perfect square!!

Mathematics

99 point question, plus ! ( answer genuinely, and do not answer just for points, if you do, your answer will be deleted, and those points will be taken this is calculus not basic 4.) find the area of the region bounded by the graphs of the equations. f(x) = (16x)/((x^2)+1), y=0, 0 ≤ x ≤ 8 a • a = 8 ln (65) b • a = 8 ln (63) c • a = 65 ln (8) d • a = 63 ln (8) 6.) find the area of the region bounded by the graphs of the algebraic functions. f (x) = x^2 + 12x + 36 g(x) = 8(x + 6) a • a = 364/3 b • a = 128/3 c • a = 256/3 d • a = 512/3 ** show all

Step-by-step answer

P Answered by PhD

3

The first solution:
$\int\limits^8_0 {\frac{16x}{1+x^2}} \, dx=8log(65)$

The second solution:
$\int\limits^2_{-6}{(-36-12x-x^2+8(6+x))} \, dx=\frac{256}{3}$

Mathematics

99 point question, plus ! ( answer genuinely, and do not answer just for points, if you do, your answer will be deleted, and those points will be taken this is calculus not basic 4.) find the area of the region bounded by the graphs of the equations. f(x) = (16x)/((x^2)+1), y=0, 0 ≤ x ≤ 8 a • a = 8 ln (65) b • a = 8 ln (63) c • a = 65 ln (8) d • a = 63 ln (8) 6.) find the area of the region bounded by the graphs of the algebraic functions. f (x) = x^2 + 12x + 36 g(x) = 8(x + 6) a • a = 364/3 b • a = 128/3 c • a = 256/3 d • a = 512/3 ** show all

Step-by-step answer

P Answered by PhD

3

The first solution:
$\int\limits^8_0 {\frac{16x}{1+x^2}} \, dx=8log(65)$

The second solution:
$\int\limits^2_{-6}{(-36-12x-x^2+8(6+x))} \, dx=\frac{256}{3}$

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