Which expression is equivalent? Thank you:)

The required expression in terms of logarithm of prim numbers are;

[tex]log_4405=log_4(3^4\times 5)=log_43^3+log_45[/tex]

[tex]log_7(\frac{8}{81} )=log_7(\frac{2^3}{3^4} )=log_72^3-log_73^4[/tex]

Prime numbers are numbers that can only be divisible by 1 and itself.

From the given logarithmic expression, we will need to write 405, 8, and 81 as the product of prime numbers

405 = 3 * 3 * 3 * 3 * 5

405 = 3^4 * 5

8= 2* 2 * 2

8 = 2^3

81 = 3 * 3 * 3 * 3

81 = 3^4

The logarithm expression [tex]log_4405 \ and \ log_7(\frac{8}{81} )[/tex] can be expressed in terms of prime numbers as;

[tex]log_4405=log_4(3^4\times 5)=log_43^3+log_45[/tex]

Similarly;

[tex]log_7(\frac{8}{81} )=log_7(\frac{2^3}{3^4} )=log_72^3-log_73^4[/tex]

Learn more here: https://brainly.com/question/23004769

Answer:

911

Step-by-step explanation:

The expression  5k+m3  is a sum. The term 5k is an addend, but it is also a product. The term m3  is an addend, but it is also a quotient.

Answer:

E

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let the diagonal ( hypotenuse ) be d , then

d² = 5² + 5² = 25 + 25 = 50 ( take square root of both sides )

d = [tex]\sqrt{50}[/tex] = [tex]\sqrt{25(2)}[/tex] = [tex]\sqrt{25}[/tex] × [tex]\sqrt{2}[/tex] = 5[tex]\sqrt{2}[/tex] → E

Answer:

The value of y is 46.715

Step-by-step explanation:

4y-10+3.14 = 180

4y = 180 + 10 - 3.14

4y = 186.86

4y ÷ 4 = 186.86 ÷ 4

y = 46.715

Answer:

b)

Step-by-step explanation:

Answer:

Step-by-step explanation:

9/50 // 12 / 1     You have a 4 tier fraction here.  You must invert the denominator (12/1) and multiply

9/50 * 1/12          Cancel 3 in the 9 and 3 in the 12

3/50 * 1 / 4         Multiply the numerators together and the denominators together.

3 / 200  each bottle with have 3/200 L or 1.5 / 100 L syrup in it.

1.5 / 100 L = 1.5 * 10 / 100 * 10 = 15 mL of medication in each bottle.      

Answer:  p=6 and r=8

Step-by-step explanation:

A)  Add exponents when multiplying:  [tex]x^{4}[/tex] *  [tex]x^{2}[/tex] = [tex]x^{6}[/tex] p = 6

B)  Multiply exponents when raised to a power:   r = 8

Answer:

$2.00

Step-by-step explanation

To solve this problem, divide $6 by 3 bars which is $2 a bar

Answer:

One bar= $2

Step-by-step explanation:

6 is the amount paid, 3 is the amount of bars he got. so to find the amount for one bar you divide, 6÷3= 2

Answer:

B

Step-by-step explanation:

n is a number. 4 less then that number translates to n-4, so the answer is B:

n-4=12

Hope that helps! :)

Answer:

C: n-4= 12

Step-by-step explanation:

To understand why this answer is correct, lets break down the sentence.

Revised Answer: n-4=12 is actually the answer as n can be any quantity, and n -4 =12 literally means n + (-4) = 12.

Answer:

Either B. 'The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him' or A. 'He did not trust the woman not to trust him. And he did not want to be mistrusted now.'.

Step-by-step explanation:

The passages from the story "Thank You, Ma'am" that support the theme that respectful treatment encourages mutual respect are: "The woman did not ask the boy anything about where he lived, or his folks, or anything else that would embarrass him." "The water dripping from his face, the boy looked at her. There was a long pause. A very long pause. After he had dried his face and not knowing what else to do dried it again, the boy turned around, wondering what next." and "Then, Roger, you go to that sink and wash your face,” said the woman, whereupon she turned him loose—at last. Roger looked at the door—looked at the woman—looked at the door—and went to the sink." Correct options are 2, 3 and 4.

These passages highlight how the woman treats the boy, Roger, with kindness and respect despite his attempt to steal her purse. Her understanding and respectful treatment lead Roger to reflect on his actions and ultimately decide to follow her guidance. This illustrates how respectful treatment encourages mutual respect between the characters.

To know more about respectful treatment :

https://brainly.com/question/28730771

#SPJ3

The expressions that can be used to derive the quadratic inequality for the

situation are;

Reasons:

The parameters of the restaurant are;

The charge per buffet = $10

Number of customers that choose the buffet every hour = 16 customers

For an increase in $1 in the cost of the buffet, the customers decrease by 2 per each hour.

The required minimum revenue per hour = $130

Required:

The situation is to be modelled as a quadratic inequality.

Two expressions for the situation, one for the cost and one for the

customers.

Assumption: x = The number of $1 increases in the cost of the buffet

Solution:

The expressions are;

Which gives;

Cost × Customers = Revenue

The inequality that models the situation is therefore;

(10 + x) × (16 - 2·x) ≥ 130

Which gives;

160 - 20·x + 16·x - 2·x² ≥ 130

160 - 4·x - 2·x² ≥ 130

Learn more about inequalities here:

https://brainly.com/question/10081223

Answer:

Cost: 10 + x

Customers: 16 - 2·x

Step-by-step explanation:

I got it right. Hope this helps.

Answer: cos(76°) ---> sin(14°)

Answer:

the answer is -2

Step-by-step explanation:

-2........

Answer:

69

Step-by-step explanation:

420

the standard form of this expression is

(72+3)(-i)

Answer:

XDDDDDDDDDDDDDDDDDDDDDDDDDD

Step-by-step explanation:

LOL

Answer:

See below for answer

Step-by-step explanation:

A.  y = 0.85x + 15     when x = 30

     y = 0.85(30) + 15

     y = 40.5

     y = 0.85x + 15        when x = 100

     y = 0.85(100) +15

     y = 100

B.    y = 0.85x + 15          when y = 185

      185 = 0.85x + 15

        185 - 15 = 0.85x

          170 = 0.85x

           170/0.85 = x

               200 = x  

C  (30, 40.5)

     (100, 100)

     (200, 185)

Answer:

see explanation

Step-by-step explanation:

A recursive formula allows the next term in a sequence by adding the common difference d to the previous term.

d = a₂ - a₁ = - 13 - (- 1) = - 13 + 1 = - 12 , then

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 12 with a₁ = - 1

Answer:

I'm past that level of math. Here's the answer:Letter B

Step-by-step explanation:

Answer:

Well, the answer is: it depends on what was printed in the problem. The principal square root symbol never has a negative output, so if the test maker printed that symbol, it’s restrictions have to be respected: all square roots then are positive.

Step-by-step explanation:

a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16. Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √(x), where the symbol √( ) is called the radical sign or radix.

Answer/Step-by-step explanation:

The square root could be positive or negative because multiplying two negative numbers gives a positive number. The principal square root is the nonnegative number that when multiplied by itself equals a. The square root obtained using a calculator is the principal square root.

Answer:

1,23,098

Step-by-step explanation:

............

Answer:

125

Step-by-step explanation:

75 + 50

Answer:

the answers you chose are correct.

Step-by-step explanation

b and d

Measure the distance between the two end points, and divide the result by 2. This distance from either end is the midpoint of that line. Alternatively, add the two x coordinates of the endpoints and divide by 2. Do the same for the y coordinates.

Answer:

C, just use the formula.

Step-by-step explanation:

Answer:

y = 1/3

Step-by-step explanation:

[tex]2x-9y=11\\\\2(7)-9y=11\\\\14-9y=11\\\\-9y=-3\\\\y=\frac{1}{3}[/tex]

2 1/5

Step-by-step explanation:

2(7)-9y=11

14-9y=11

Divide both sides by the difference of 14 and 9y

11/5y ; y=2 1/5

Answer:

The radius is 4.7 units.

Step-by-step explanation:

To answer this we need only find the square root of 22.09:  4.7

The radius is 4.7 units.

Answer:

0.375 is 37.5 % of 1

Step-by-step explanation:

Answer:one way is to simply use slope intercept form or point slope form

point slope: y-y1=m(x-x1) where m=slope and you are given a point (x1,y1)

slope intercept: y=mx+b where m=slope and b=yintercept

slope=(y2-y1)/(x2-x1) when given points (x1,y1) and (x2,y2)

we are given

(3.5,8.2) and (2,7.3)

slope=(7.3-8.2)/(2-3.5)=-0.9/-1.5=0.6

slope=0.6 or 6/10

point slope

use any point

y-y1=m(x-x1)

y-7.3=0.6(x-2) or

y-8.2=0.6(x-3.5)

slope intercept wouold be point slope but solve for y by distributing m and adding y1 to both sides

take first one

y-7.3=0.6(x-2)

y-7.3=0.6x-1.2

add 7.3 both sides

y=0.6x+6.1

equation is

POINT SLOPE FORM:

y-7.3=0.6(x-2) or

y-8.2=0.6(x-3.5)

SLOPE INTERCEPT FORM:

y=0.6x-6.1

Step-by-step explanation: