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1 year ago

Evaluate log4 0.25 ?

Mathematics

1 answer:

Vsevolod [243]1 year ago

8 0

Answer:

-1

Step-by-step explanation:

Recall that 0.25 = 1/4, and that 1/4 = 1/[4^(-1) Notice that 4 is the base of this log system.

Then log4 0.25 = log4(1/4) = log4(4^(-1) ) = -1 (answer)

Check: Does 4^(-1) = 0.25? Yes

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Evaluate 4(a2 + 2b) - 2b

iogann1982 [59]

<span>4(a^2 + 2b) - 2b
= 4a^2 + 8b - 2b
=</span> 4a^2 + 6b

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1 year ago

PI-3.

Fudgin [204]

Answer:

A. $301

B. $721

Step-by-step explanation:

Let $x be the amount of money they raised.

Rowena tried to put the $1 bills into two equal piles and found one left over at the end, then

$x=2q_1+1$

Polly tried to put the $1 bills into three equal piles and found one left over at the end, then

$x=3q_2+1$

Frustrated, they tried 4, 5, and 6 equal piles and each time had $1 left over, then

$x=4q_3+1\\ \\x=5q_4+1\\ \\x=6q_5+1$

Finally Rowena put all the bills evenly into 7 equal piles, and none were left over, then

$x=7q_6$

This means $x-1$ is divisible by 2, 3, 4, 5 and 6 without remainder, so

$x-1=2\cdot 3\cdot 2\cdot 5n=60n$

Hence,

$x=60n+1, \ n\in N$

The smallest amount of money they could have raised is $301, because

$x=60\cdot 5+1=301$ is divisible by 7.

Now, the number $x=60n+1$ should be divisible by 7 and must be greater than 500.

So,

$60n+1>500\\ \\60n>499\\ \\n>8$

When n = 9,

$x=60\cdot 9+1=541$ is not divisible by 7.

When n = 10,

$x=60\cdot 10+1=601$ is not divisible by 7.

When n = 11,

$x=60\cdot 11+1=661$ is not divisible by 7.

When n = 12,

$x=60\cdot 12+1=721$ is divisible by 7.

B. The least amount of money they could have raised is $721

7 0

1 year ago

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Rewrite the expression (3a^2b^3c^5)/(8x^4y^3z)so that it has no denominator. (note: do not use a fraction line in your answer. a

Gemiola [76]

Use:

$\dfrac{1}{a}=a^{-1}\\\\\dfrac{1}{a^n}=a^{-n}$

$\dfrac{3a^2b^3c^5}{8x^4y^3z}=3a^2b^3c^5\cdot8^{-1}x^{-4}y^{-3}z^{-1}$

Answer: 3"8^-1a^2b^3c^5x^-4y^-3z^-1

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1 year ago

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Tyler has a rectangular garden measuring 12m by 20m that he wants to split diagonally from corner to corner using a fence. How l

VARVARA [1.3K]

Answer:

Length of diagonal of the rectangle=

√( length) ²+( breadth) ²

=√(20) ²+(12) ²

=√400+144

√544 m

. '. Length of fence= √544 m

Perimeter of the triangle formed by the diagonal of the rectangle =(12+20+√544)

=(32+√544) m

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1 year ago

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Denzel earned money after school delivering newspapers and doing yardwork. He put - of this month's earnings into his savings. H

Inessa05 [86]

<h3><u>Question:</u></h3>

Denzel earned money after school. He put 1/2 of this month's earnings into savings. He took the rest to spend at the amusement park. He spent 1/5 of this amount on popcorn and 3/4 of it on rides. What fraction of his earnings did he take to the park but not spend on rides or popcorn.

<h3><u>Answer:</u></h3>

$\frac{1}{40}$ fraction of money not spend in amusement park