How do you multiply 5/12 times 2/9?

Answers

Answer 1
Answer: (5)/(12)\cdot(2)/(9)=(5)/(6)\cdot(1)/(9)=(5)/(54)

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If f(x) = x^3 – 2x^2, which expression is equivalent to f(i)?

Answers

f(x) = x³ - 2x².

f(i) = i³ - 2i².

i = √-1.

i³ = (√-1)³ = √-1 * √-1 *√-1 = -1*√-1 = -√-1 = -i

i² = (√-1)² = √-1 * √-1  = -1

f(i) = i³ - 2i²  = -i - 2(-1) = -i + 2

f(i) = 2 - i
i=√-1 and all the steps are there

Exponential Form3.log 1/4 1=0
4.log 1/2 32= -5
Evaluate the logarithm
6. log27 3=
8. log 1/4 256=
9. log 10 .001=
10. log 64 2=

Answers

6. 1/3
8. -4
9. -3
10. 1/6
loga n=z  ⇔a^z=n

Therefore:
3)log 1/4  1=0    ⇔(1/4)⁰=1
4)log 1/2  32 -5  ⇔(1/2)⁻⁵=2⁵=32

6)
log 27  3=n  ⇔ 27^n=3 
27=3³
(3³)^n=3  ⇒n=1/3    (3³)¹/³=3³/³=3¹=3

Answer: log 27  3=1/3

7)
log1/4 256=n  ⇔(1/4)^n=256
256=2⁸=4⁴
(1/4)^n=4⁴  ⇒n=-4       [ (1/4)⁻⁴=4⁴=256  ]

Answer: log1/4 256=-4

9)
log 10  0.001=n  ⇔  10^n=0.001
0.001=10⁻³
10^n=10⁻³  ⇒n=-3

answer: log 10    0.001=-3

10)
log 64  2=n  ⇔64^n=2
64=2⁶
(2⁶)^n=2    ⇒2(⁶n)=2¹ ⇒  6n=1  ⇒  n=1/6

answer: log 64    2= 1/6

What is -a^-2 if a=-5

Answers

Answer:

the answer is 25

Step-by-step explanation:

cause -5 times -5 is 25 cause negative times negative is positive, and 5 times 5 is 25.

Well, -2 times -2 is 4 and 4 times -2 is -8 times -2 is 16 and 16 times -2 is -32 and -32 times -2 is 64 and -64 times -2 is 128

So 128

in an over-fished area, the catch of a certain type of fish is decreasing at an average rate of 8% per year. If this decline persists, how long will it take for the catch to reach half of the amount before the decline???

Answers

n = n0(1 - 0.08)^t 
= n0(0.92)^t 

Putting n = n0 / 2: 
1 / 2 = 0.92^t 
t = log(1 / 2) / log(0.92) 
= 8.31 yr.

Use the given graph to determine the limit, if it exists. A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point 3, 1, a closed point at 3, 7, and a horizontal line starting at the open point 3, 3. Find limit as x approaches three from the right of f of x..

Answers

Answer:

The limit as x approaches three from the right of f(x) is:

                                   3

Step-by-step explanation:

We are given a coordinate graph such that:

  • The left limit of three approaches to 1 .

( Since  A coordinate graph is shown with an upward sloped line crossing the y axis at the origin that ends at the open point (3, 1) )

  • The value of the graph at x=3 is:  7

( Since a closed point at (3, 7)  )

  • Also the right limit at x=3 is:  3

(  Since there is  a horizontal line starting at the open point (3, 3)  )

right hand limit is 3 left hand limit is 1.

Hope this helps X

9.8 < 20 – 9.8t < 20

Answers

Answer:

0 < t < 1.04 or  t ∈ (0, 1.04)

Step-by-step explanation:

Solving in steps:

  • 9.8 < 20 – 9.8t < 20                  
  • 9.8 - 20 < -9.8t < 20 - 20         ⇒ subtract 20 from all sides
  • -10.2 < -9.8t < 0                        ⇒ divide all sides by -9.8, this changes  inequality signs to reverse
  • 0< t < 10.2/9.8
  • 0 < t < 1.04 or t ∈ (0, 1.04)