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The solution to the logarithmic equation [tex]\mathbf{log_2(x-6) = 4}[/tex] is x =24

The logarithmic equation is given as:

[tex]\mathbf{log_2(x-6) = 4}[/tex]

Apply exponential law of logarithm

[tex]\mathbf{(x-6) = 2^4}[/tex]

Remove the brackets

[tex]\mathbf{x-6 = 2^4}[/tex]

Add 6 to both sides

[tex]\mathbf{x-6 +6= 6+ 2^4}[/tex]

Express 2^4 as 16

[tex]\mathbf{x-6 +6= 6+ 16}[/tex]

Add -6 and 6

[tex]\mathbf{x= 6+ 16}[/tex]

Add 6 and 16

[tex]\mathbf{x= 24}[/tex]

Hence, the solution to the logarithmic equation [tex]\mathbf{log_2(x-6) = 4}[/tex] is x =24

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Answer:   0.53846153846154

Step-by-step explanation:   you do

= 14/26

= 14 ÷ 26

= 0.53846153846154

Answer:

2x =3

The hanger image given in the figure represents balanced equation.

Then we have to write an equation to represent the image.

In balanced form left side = right side

x + x = 1 + 1 + 1

2x = 3

The value v is 9.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that is a structure showing a balanced hanger we need to find the value,

So we can say since the hanger is balanced therefore the weight both sides will be equal,

Therefore,

v + v + v = 27

3v = 27

v = 27

Hence the value v is 9.

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Answer:

5 + (-5) and 8 + (-8)

Step-by-step explanation:

Sum of zero means when you add them you get 0

so the others are wrong

-5 + (-5) = -10 because you have -5 and you add another -5

-12 + (-12) = -24 you start with -12 and you add another -12

Think of positive and negative numbers like floors in a building. Positive numbers are the stories and the negative numbers are the basement and sub-basement, zero is the ground level. So for 5 + (-5) you go up 5 floors, then you go down 5 floors. you end up on the ground level, 0.

A student must answer at least 35 of the 40 homework assignments correctly to get an A.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

To determine the fewest number of problems a student could answer correctly and still get an A, we need to set up an inequality that represents the condition for getting an A.

If Mr. Discrete determines the score by doubling the number of correct problems out of 50 and then adding the bonus, then the score for each student can be represented by the equation:

2x + 4% × 50 = 100, where x is the number of correct problems.

If the student needs to get an A, then the score must be at least 90. Therefore, we can set up the inequality:

2x + 4% × 50 ≥ 90

Substituting 4% for 0.04, we get:

2x + 0.0450 ≥ 90

Solving for x, we find:

x ≥ 35

Therefore, to receive an A, a student must complete at least 35 out of the 40 homework assignments.

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Answer:2

Step-by-step explanation: 4 times 3 equals 12 and 12 divided by 6 is 2

There are 1(1/6) pound of vegetables in each bowl.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of bowls = 6

Number of carrot sticks = 4 pounds

Number of celery sticks = 3 pounds

The number of carrots in each bowl.

= 4/6

= 2/3 pounds

The number of celery sticks in each bowl.

= 3/6

= 1/2 pounds

The number of pounds of vegetables in each bowl.

= 2/3 + 1/2

= (4 + 3)/6

= 7/6

= 1(1/6) pounds

Thus,

There are 1(1/6) pound of vegetables in each bowl.

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Answer:

7/n would be a algebraic express

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

use half the x coefficent and square it

x^2 − 6x + (-3)^2 = 10 + (-3)^2

x^2 - 6x + 9 = 10 + 9

(x - 3)^2 = 19

Answer:

1.8

Step-by-step explanation:

0.21 : 6.3 = 0.06 : m

=> 0.21/6.3 = 0.06/m

=> m = 0.06 x 6.3 / 0.21

m = 1.8

Hope this helps!!

Answer:

The three prizes can be awarded in 6 different ways

Step-by-step explanation:

1. P1 - Book; P2 - Calc; P3 - Card

2. P1 - Book; P2 - Card; P3 - Calc

3. P1 - Calc; P2 - Card; P3 - Book

4. P1 - Calc; P2 - Book; P3 - Card

5. P1 - Card; P2 - Book; P3 - Calc

6. P1 - Card; P2 - Calc; P3 - Book

Answer:

To calculate the gradient of a straight line we choose two points on the line itself. The difference in height (y co-ordinates) ÷ The difference in width (x co-ordinates).

so it is 0.2

Answer:

3.9% is the rounded version

Step-by-step explanation:

Answer:

37.0%

Step-by-step explanation:

thanks pi sa points uwu (^^)

godblesss

Answer:

2

Step-by-step explanation:

When the input is -1  ( the x value is -1)  what is the the output ( what is the value of y)

Using the graph, we got to x =-1 and go up and find y =2

When the input is -1 the output is 2

Answer:

X: input

Y: output

so if we input -1 we look at the graph to see the y value

2

Hope This Helps!!!

Answer:  X =  2 2/3

Step-by-step explanation:

4 5/9 is the same as the sum of 2 1/3 and 5/6 times a number.

Let X be the "number."  Translate the sentence:

(4 5/9) = ((2 1/3) + (5/6))*X

"4 5/9 is the same":  (4 5/9) =

"as the sum of 2 1/3 and 5/6":  ((2 1/3) + (5/6))

"times a number": *X

Put them all together:

(4 5/9) = ((2 1/3) + (5/6))*X

(41/9)-(7/3) = (5/6)X

(41/9)-(21/9) = (5/6)X

(20/9) = (5/6)X

X = (20/9)*(6/5)

X = 120/45

X = 2 30/45 or 2 2/3

Answer:

2i

Step-by-step explanation:

Distribute:

(5y + 2)(y - 3)

5y^2-15y+2y-6

Which can be simplified into 5y^2-13y-6

Now the equation now looks like this: 5y^2-13y-6=-13(2+y)

For -13(2+y) multiply -13 with 2+y

Which is -26-13y

5y^2-13y-6=-26-13y

Simplify:

5y^2+20

Which can be simplified into 5(y^2+4)

y^2+4=0

y^2=-4

y=2i

Hope this helps!

Answer:

A = 27 cm²

Step-by-step explanation:

let 'w' = width

let '3w' = length

P = 2l + 2w

24 = 2(3w) + 2w

24 = 6w + 2w

24 = 8w

w = 3

l = 3(3) or 0

A = lw

A = 3(9)

A = 27

Answer:

676.09

Step-by-step explanation:

550.87 + 75.98 = 626.85

626.85 - 34.88 = 591.97

591.97 + 84.12 = 676.09 therefore that's the amount at the end of the month

Answer:

5x

Step-by-step explanation:

The natural log of 5x is the exponent to give e to get 5x as a result.  You are simply applying the definition of logarithm

The expression [tex]e^{ln(5x)[/tex] evaluates to 5x after simplification.

Option: A is correct.

Here, we have,

The expression [tex]e^{ln(5x)[/tex] involves two important mathematical properties:

[tex]e^{ln(x)} = x[/tex]:

This is a fundamental property of the natural logarithm and the base of the natural exponential function, e.

When the natural logarithm (ln) and the natural exponential function [tex](e^x)[/tex] are composed, they "cancel out," and the result is the argument inside the ln function (x).

[tex]e^0 = 1[/tex]:

The natural exponential function raised to the power of 0 is equal to 1.

Now, let's simplify the expression step by step:

[tex]e^{ln(5x)[/tex]

Using property 1,[tex]e^{ln(5x)[/tex] simplifies to:

5x

Therefore, the correct option is "5x."

The expression [tex]e^{ln(5x)[/tex] evaluates to 5x after simplification.

Option: A is correct.

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Answer:

1 gal = ____ pt

lelz XD

Answer:

x-12

Step-by-step explanation:

let us say that the other number is n. then we have n+12=x or n=12-x

Answer:

slope: 2/3

y intercept: -1

Step-by-step explanation:

slope: rise/run

Answer:

An odd integer is denoted by 2n+1 where n is an integer.

First odd integer = 2n+1

Next odd integer = 2n+3

8 ≦ (2n+1)+(2n+3) < 24

8 ≦ 2n+1+2n+3 < 24

8 ≦ 4n+4 < 24

Divide through by 4

2 ≦ n+1 < 6

Subtract 1 for all three sides:

1 ≦ n < 5

n ∈ {1,2,3,4}  

Answer:  {2n+1, 2n+3}  {1,3}, {3,5}, {5,7

Step-by-step explanation:

Answer:

im sorry i dont know but you can try

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

-64/8 = -8................ .......

mark me brainliest plz if you are helped

Answer:

so you divide -64/8 like you would 64/8 and once you get your answer you just put a negative in front because a negative divided by a positive is a negative so your answer is -8

Step-by-step explanation:

Answer:

The answer is 144 feet and it will be in the air for 6 sec

Step-by-step explanation:

Answer:

92

Step-by-step explanation:

Like and give 5 star rating

Answer:

Yep, they are all correct

Both the answers are correct

Answer:

I think the answer is c

Step-by-step explanation:

please give me brainlist

Answer:

[tex]\frac{1}{32}[/tex]

Step-by-step explanation:

Using the rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] , then

[tex]2^{-5}[/tex] = [tex]\frac{1}{2^{5} }[/tex] = [tex]\frac{1}{32}[/tex]

Answer:

100 + 100 + 40 + 40 + 40 + 40 = 360 yd^3