Plz answer quickly, I need to get this done soon. I will mark Brainliest.

Justify each step in solving the equation 4x=7(x-3) by writing a reason for each statement.


Statement Reason
1. 4x=7(x-3) 1. Given
2. 4x=7x-21 2.?
3. -3x=-21 3.?
4. x=7 4. ?

Fill in the blanks.

−1/8*(1/8) =

-(1/8)² =

-1/64

The correct expressions are as follows:

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]343[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}[/tex]

[tex]\texttt{ }[/tex]

Let's recall following formula about Exponents and Surds:

[tex]\boxed { \sqrt { x } = x ^ { \frac{1}{2} } }[/tex]

[tex]\boxed { (a ^ b) ^ c = a ^ { b . c } } [/tex]

[tex]\boxed {a ^ b \div a ^ c = a ^ { b - c } }[/tex]

[tex]\boxed {\log a + \log b = \log (a \times b) }[/tex]

[tex]\boxed {\log a - \log b = \log (a \div b) }[/tex]

Let us tackle the problem!

[tex]\texttt{ }[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7^2)^{\frac{7}{5}}[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5}} \cdot (7)^{2\times \frac{7}{5}}[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}}[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{1}{5} + \frac{14}{5}}[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{\frac{15}{5}}[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = 7^{3}[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}} = \boxed{343}[/tex]

[tex]\texttt{ }[/tex]

From the results above, it can be concluded that the correct statements are:

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]343[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Equivalent [tex]7^{\frac{1}{5}} \cdot 7^{\frac{14}{5}}[/tex]

[tex]7^{\frac{1}{5}} \cdot 49^{\frac{7}{5}}[/tex] Not Equivalent [tex]49^{\frac{2}{10}} \cdot 7^{\frac{1}{5}}[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Mathematics

Chapter: Exponents and Surds

Keywords: Power , Multiplication , Division , Exponent , Surd , Negative , Postive , Value , Equivalent , Perfect , Square , Factor.

Answer:

equivalent

not equivalent

equivalent

not equivalent

-step explanation:

0.214285714

Hope this helps! :)

P.S- can you help me with my problem? LOL it's just that no one will help me! It's on planets. Hopefully, you know those stuff. :(

Standard deviation is the square root of the variance.

To  find the variance from the standard deviation, raise it to the 2nd power:

Standard deviation = 4

Variance = 4^2 = 4x4 = 16.

the answer is a add -19w and dont forget to do it on each side

You should put brainliest to the other person that answered this question.

Correct answer is option(2).

Isaac can add the ordered pair (1, 3) to the set to keep it a function.

A function is a relation where each input (or domain element) is associated with exactly one output (or range element).

This means that in the set of ordered pairs representing a function, no two pairs can have the same first element (input) but different second elements (outputs).

Given the function defined as : {(0,1),(2,3),(5,8),(7,2)},

we need to add one more ordered pair without violating the property that each input maps to exactly one output.

Let's examine each option:

1.) (0, 2) : This pair has the same first element as (0, 1). Adding (0, 2) would imply that the input 0 maps to both 1 and 2, which is not allowed in a function because each input must map to exactly one output.

2.) (1, 3) : This pair has a first element of 1, which is not present in the original set of ordered pairs. Therefore, adding (1, 3) does not create any conflicts. The input 1 is not repeated, so each input still maps to exactly one output. This maintains the function property.

3.) (5, 3) : This pair has the same first element as (5, 8). Adding (5, 3) would imply that the input 5 maps to both 8 and 3, which violates the definition of a function.

4.) (7, 0) : This pair has the same first element as (7, 2). Adding (7, 0) would imply that the input 7 maps to both 2 and 0, which also violates the definition of a function.

Therfore , Only the pair (1,3) can be added to the set without violating the function property. This pair introduces a new input that does not conflict with the existing inputs in the set.

Answer: 2/9

Step-by-step explanation:

lt

2

7

×

7

9

=

2 × 7

7 × 9

=

14

63

=

14 ÷ 7

63 ÷ 7

=

2/9

Answer:

Consider two adjacent rectangular rooms having Length=L, and, Breadth = B

Now Suppose the wall which is in between two rooms has a height or length =H.

Breadth of wall = B [ if the wall doesn't exceed the breadth of room]

Considering two rooms to be identical,

Area of each room= L × B square unit

Area of each tile = 1×1=1 square unit

Number of tiles required= L B ÷ 1= LB tiles( product of length and breadth of room is number of tiles required)

Suppose if,LB= N

B= N/L  .................(1)

Area of wall(W) = B×H= B H square unit

B =W/H ......................(2)

Equating (1) and (2)

⇒N/L = W/ H

⇒H =[tex]\frac{WL}{N}[/tex]

⇒H =[tex]\frac{WL}{LB}[/tex]

⇒H = W/B

 ⇒  H =[tex]\frac {\text{ Area of Wall}}{\text{Breadth of room or wall}}[/tex]

The original number is 3.

I actually began with the guess-and-check method, but seeing as that won't always work, let's go over the formal way. To get the original number, you first need to determine how many times the number was squared.

To make it simple, let's use x to focus on the exponents. The number was squared 3 times, so x^2, x^2, x^2. Basically, you need to multiply. 2 * 2 * 2 = 8. So, now find the 8th root of 6561 (depending on the calculator, you can just input it). You should come up with 3. Let me know if this part confuses you.

To find the next 2 numbers, you just need to continue the pattern.

6561^2 = 43,046,721

43,046,721^2 = 1,853,020,188,851,841

To my knowledge, which means this could be wrong, they're both perfect squares. Since the number to get them both were whole numbers, they should both have a square root that equals a whole number.

Original number (3): Not a perfect square (3 is not the square of any integer). First intermediate number (9): A perfect square (9 is the square of 3). Final number (6561): A perfect square (6561 is the square of 81). So, the only perfect square in the sequence is the first intermediate number, 9.

Here's why:

Original number: Starting with an unknown number, let's call it x. Squaring it gives us x^2.

First intermediate number: Squaring x^2 again, we get (x^2)^2 = x^4.

Final number: Finally, squaring x^4 one last time, we reach the given number, 6561: (x^4)^2 = x^8 = 6561.

Now, let's backtrack to find the original number x:

Since 6561 is the square of 81, and 81 is the square of 9, we can conclude that the original number x must be the square root of 9, which is 3.

Therefore, the sequence of numbers you provided is indeed correct:

Original number: 3 (squared to get 9)

First intermediate number: 9 (squared to get 81)

Final number: 81 (squared to get 6561)

No equation is given .

24 cans in total is your answer

6 times 4

6 · 4 = 24

24 cans in total

(a) Lily: 5 * 2 - 12 + 3 = 1 pt

(b) Rose: -3 * 2 -1 + 6 + 7 = 6 pts

(c) Rose

we are given

[tex]\frac{17}{40}[/tex]

we can use long division method

Firstly, we will try to make denominator either 10 , 100 , 1000 , 10000 form

and then we can put decimal accordingly

Here , we are given 40 in the denominator

[tex]40 \times 25=1000[/tex]

so, we will multiply both top and bottom by 25

[tex]\frac{17}{40}=\frac{25\times 17}{25\times 40}[/tex]

[tex]\frac{17}{40}=\frac{425}{1000}[/tex]

now, we can put decimal to three places because we have 1000 in bottom

so, we get

[tex]\frac{17}{40}=0.425[/tex]...............Answer

Let me know if you cant read anything

Hope it helps ❤️

The lines will keep going forever ❤️

1: Thirty subtracted from four times a number is greater than the opposite of ten.

Let the number be x, so equation becomes : [tex]30-4x>-10[/tex]

2: Given equation is  [tex]27-2b\leq-6[/tex] this states that the result of 27-2b is less than equal to opposite of six.

Given that a student works no more than 25 hours per week, and that work is performed every day of a 7-day week, the maximum number of hours they can work per day is approximately 3.57, making it fair to say they can work up to 3 hours each day. This scenario can be represented by the inequality h ≤ 3.

To answer your question, we need to find an inequality that represents how many hours the student can work each day given they work no more than 25 hours every week.
If we assume a typical week encompasses 7 days, and the student works every day of the week, then we should distribute the maximum hours worked per week over these seven days.
This results in 25 hours ÷ 7 days ≈ 3.57 hours/day. However, since you can't work a fraction of an hour, the student can work up to 3 hours a day.
The inequality representing this scenario would be h ≤ 3, where 'h' represents the number of hours the student can work each day.

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To convert 1.8499 × 10^9 by moving the decimal nine places to the right, you get 1,849,900,000. This is achieved by shifting the decimal point and adding zeros as needed.

To move the decimal nine places to the right for the number 1.8499 × 10^9, you follow these steps:

Thus, 1.8499 × 10^9 in standard notation becomes 1,849,900,000.

Let the nuber be x

According to question

3(x +4) = 18+ x

3x+ 12=18+x

3x-x=18-12

2x = 6

x =6/2

x = 3

given 4y = 2x - 10 and y = 6, then

2x - 10 = 24 ( add 10 to both sides )

2x = 34 ( divide both sides by 2 )

x = [tex]\frac{34}{2}[/tex] = 17

You can draw a triangle or a quadrilateral since they have at least three angles. For the second part, any angle can be named with three letters. After naming each corner/angle of the figure, name an angle so that the actual angle letter is the middle letter, surrounded by the letters of the corners that is just next to it.

There are Infinite number of figure , that contains at least three angles and requires three letters to name each angle

1.Any of the Triangle, either Acute, Obtuse, Right, Scalene, Isosceles, or Equilateral.

2. Any of the Quadrilateral, Parallelogram,Rectangle, Square, Trapezoid, and Kite.

→Or In General

Any of the Polygon whether it is Regular or Irregular.

→Because, A polygon is defined as ,a simple closed figure made up of three or more line segment.

The answer would be 108 because you multiply the 9 and the 12 together and get 108. I hope this helps.

The answer is X is greater than -2! <3

Answer:

[tex]408\frac{miles}{hour}[/tex]

Step-by-step explanation:

we know that

To find the speed divide the total distance by the time

so

[tex]\frac{34}{(1/12)}=34*12=408\frac{miles}{hour}[/tex]

To round 39,189 to the nearest thousand, we need to look at the digit in the hundreds place. If the digit in the hundreds place is 5 or greater, we round up, if it is less than 5, we round down. In this case, 1 is less than 5, so we round 39,189 down to 39,000.

To round 39,189 to the nearest thousand, we need to look at the digit in the hundreds place. In this case, it is 1. If the digit in the hundreds place is 5 or greater, we round up to the next thousand. If it is less than 5, we round down to the current thousand. Since 1 is less than 5, we round 39,189 down to 39,000.

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[tex]|x-2|-5 <-2 \\\\|x-2|<3\\\\x-2<3 \wedge x-2>-3\\\\x<5 \wedge x>-1\\\\x\in(-1,5)[/tex]

To answer this question, we know that 1km equals 1000m

and 1 hour is equal to 60 minutes. In the same way 1 minute equals 60 sec onds

So we have to change the units of elephant speed to km per hour.

For this we do the following procedure:

1) we multiply 6.9 m / s by the conversion factor from meters to kilometers (1 km / 1000m)

[tex]6.9 \frac{m}{s} *\frac{1 km}{1000 m}=0.0069\frac{km}{s} \\[/tex]

2) The result obtained is multiplied by the conversion factor from seconds to minutes (60s / 1min)

[tex]0.0069 \frac{km}{s} *\frac{60 s}{1 min}=0.414 \frac{km}{min}\\[/tex]

3) The result obtained is multiplied by the conversion factor from minutes to hours (60min / 1hr)

[tex]0.414\frac{km}{min}*\frac{60 min}{1 h}= 24.84\frac{km}{h} \\[/tex]

The answer is 24.84 km / h

 You can skip step 2) multiplying 0.0069 km / s by the conversion factor from seconds to hours (3600 s / 1h)