The rule which allows us to change the sign of an exponent is called the ____ rule.

Nope!

They cannot be equal if they have the same numerator but different denominators. they need to be able to reduce into the same number

No, two fractions with the same numerator and different denominators can not be equal.

The numerator simply means the number that's on top of a fraction. The denominator simply means the number that's under the fraction.

Two fractions with the same numerator and different denominators can not be equal. An example is 1/4 and 1/6 aren't equal.

Read related link on:

https://brainly.com/question/13674561

Answer:

33 Students

Step-by-step explanation:

4+7=11 so the number of students in the class must be a multiple of 11. The only multiple of 11 between 24 and 40 is 33.

Answer:

33

Step-by-step explanation:

Let's take the constant of proportionality to be X

4x+7x=between 24 to 40

11x= 24 to 40

X should be a natural number therefore the number of students should be multiple of 11

Only multiple of 11 between 24 and 40 is 33

The area of the rectangle with dimensions (3x + 5) by (x - 2) is represented by the algebraic expression 3x² - x - 10.

The area of a rectangle is found by multiplying its length by its width. Given a rectangle with length (3x + 5) and width (x - 2), we can find its area by using the formula for the area of a rectangle, which is length × width.

Area = (3x + 5)(x - 2)
By expanding this, we use the distributive property:
Area = 3x(x) + 3x(-2) + 5(x) + 5(-2)
Area = 3x² - 6x + 5x - 10
By combining like terms, we get:
Area = 3x² - x - 10

Answer:

5 numbers of stamp packs and 7 number of envelop packs that Alex has to buy.

Step-by-step explanation:

Alex wants to buy the same number of stamps and envelops.

Stamps are sold in packs of 14 and envelop are sold in the packs of 10.

Now, we have to find the least number of stamp packs and envelop packs that Alex should buy to get an equal number of stamps and envelops.

The least common multiple of 14 and 10 will give the result.

14 has multiples 14, 28, 42, 56, 70, .......

And 10 has multiples 10, 20, 30, 40, 50, 60, 70, ........

Therefore, 70 is the least common multiple.  

In that case 5 numbers of stamp packs and 7 number of envelop packs that Alex has to buy to get 70 stamps and 70 envelop. (Answer)

The least number of stamps and envelopes Alex can buy to have the same number is 70 of each, which he can get by purchasing five packs of each.

Alex wants to buy the same number of stamps and envelopes. To find the least number of each he could buy to have the same number, we need to find the least common multiple (LCM) of the two pack sizes, 14 (stamps) and 10 (envelopes).

The multiples of 14 are 14, 28, 42, 56, 70, etc., and the multiples of 10 are 10, 20, 30, 40, 50, 60, 70, etc. The first common multiple they share is 70.

Therefore, Alex can buy five packs of envelopes (5 x 10 = 50 envelopes) and five packs of stamps (5 x 14 = 70 stamps) to have the same number of each, which is 70.

Answer:

560mph

Step-by-step explanation:

11,760÷21=560

label- 560mph

Answer:

560 MILES

Step-by-step explanation:

11760/21=560

Answer:  9

====================================

Explanation:

The intersection of the two sets is the list of all values that are in both sets at the same time.

Let's convert set A into roster notation. Roster notation means we just list out all the members (use ellipses if there are a lot of values you don't want to write out; luckily these sets are small). Plug n = 2 into x = 3n and you'll find that x = 6. Repeat for n = 3, and you get x = 9. Repeat for n = 4 and you get x = 12.

Set A looks like this: {6, 9, 12}

-------

Repeat the same basic steps for set B. We'll plug m = 1 into x = 4m-3 to get x = 1. Plug m = 2 into that same equation to get x = 5. Finally m = 3 leads to x = 9

Set B = {1, 5, 9}

-------

In summary,

A = {6, 9, 12}

B = {1, 5, 9}

We see that only 9 is in both sets at the same time.

Therefore, [tex]A \cap B = \left\{ 9 \right\}[/tex] which says "the intersection of set A and set B is the set { 9 } ".

The Venn Diagram shown below has the single element 9 in the overlapping region of the two circles. The other values are in their proper respective circles, but not inside the overlapping region. Set U is the universal set.

Answer:

A subordinate clause—also called a dependent clause—will begin with a subordinate conjunction or a relative pronoun and will contain both a subject and a verb. This combination of words will not form a complete sentence. It will instead make a reader want additional information to finish the thought.

Answer:

y = 5

Step-by-step explanation:

Divide each side by 8 to get (y-9) = -4.

Add 9 to each side to isolate the variable y. This leaves you with y = 5

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}[/tex]

[tex]8(y-9)=-32\qquad\text{divide both sides by 8}\\\\\dfrac{8\!\!\!\!\diagup(y-9)}{8\!\!\!\!\diagup}=\dfrac{-32\!\!\!\!\!\diagup^4}{8\!\!\!\!\diagup_1}\\\\y-9=-4\qquad\text{add 9 to both sides}\\\\y-9+9=-4+9\\\\y=5[/tex]

[tex]\bold{METHOD\ 2:}[/tex]

[tex]8(y-9)=-32\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(8)(y)+(8)(-9)=-32\\\\8y-72=-32\qquad\text{add 72 to both sides}\\\\8y-72+72=-32+72\\\\8y=40\qquad\text{divide both sides by 8}\\\\\dfrac{8y}{8}=\dfrac{40}{8}\\\\y=5[/tex]

The expression is ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )

Given that, we have to use the numbers 4.3 , - 1.07 and – 2.971 such that the value of the expression with the given numbers and the either addition or subtraction operation between them to be negative value.

So, now take the numbers.

If we add the negative numbers and subtract the positive number from it, we will always get a negative number  

So, expression will be ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )  

- 1.07 – 2.971 – 4.3  

- 8.341

Here the result is negative value.

Hence, the expression is ( – 1.07 ) + ( - 2.971 ) – ( 4.3 )

Final answer:

To simplify the expression (6rs - 7bc )-( 9rs - 7bc), distribute the negative sign, combine like terms, and simplify to get -3rs.

Explanation:

To simplify the expression (6rs - 7bc )-( 9rs - 7bc), you can start by distributing the negative sign to the terms inside the second set of parentheses. This will change the signs of both terms inside it, making the expression become 6rs - 7bc - 9rs + 7bc. You can then combine like terms. Notice that -7bc and +7bc are like terms and cancel each other out, as do 6rs and -9rs. Simplifying these terms, you get -3rs.

Here is the step-by-step process:

Distribute the negative sign: 6rs - 7bc - 9rs + 7bc.

Combine like terms: (6rs - 9rs) + (-7bc + 7bc).

Simplify the expression: -3rs + 0.

Final answer: -3rs.

It's often helpful to eliminate terms wherever possible to simplify the algebra and then check the answer to ensure it is reasonable.

Answer:

a. $18.36 for 3 pizzas  :  k  = 6.12

b. $4.17 for 3 pounds of bananas .   k  = 1.39

c. $16.48 for 4 pounds of potatoes .  k  = 4.12

d. 2 cups of flour to make 24 cookie .  k  = 12

Step-by-step explanation:

PROPORTIONALITY:

Two quantities x and y are said to proportional to each other

if for x ∝ y , x = y k.

Here, k is called the PROPORTIONALITY CONSTANT.

⇒  [tex]x\propto y \implies  k = \frac{x}{y}[/tex]

Now, for the given quantities:

a.  $18.36 for 3 pizzas [box]    

Here, [tex]k = \frac{18.36}{3}  = 6.12[/tex]

So, the proportionality constant is 6.12.

b. $4.17 for 3 pounds of bananas [box]

Here, [tex]k = \frac{4.17}{3}  = 1.39[/tex]

So, the proportionality constant is 1.39.

c. $16.48 for 4 pounds of potatoes [box]

Here, [tex]k = \frac{16.48}{4}  = 4.12[/tex]

So, the proportionality constant is 4.12.

d. 2 cups of flour to make 24 cookies

Here,  [tex]k = \frac{24}{2}  = 12[/tex]

So, the proportionality constant is 12

Answer:

Initial value (y-intercept) of each function.

Rate of change (slope) of each function.

Initial value to compare starting points.

Slope to compare rise or fall. (Answer)

Step-by-step explanation:

Sample Response: Linear relationships can be compared using their initial values, or y-intercepts, and their rates of change, or slopes. Initial values can tell you which relationship started with a greater value. Comparing slopes can tell you which relationship is rising or falling faster.

Therefore, I included in the response  

Initial value (y-intercept) of each function.

Rate of change (slope) of each function.

Initial value to compare starting points.

Slope to compare rise or fall. (Answer)

Answer:

D. All answers are correct

Step-by-step explanation:

The film The Birth of a Nation promoted the KKK.

There was pseudo-scientific racism also going on.

From these two facts, we know that the answer definitely is D. Also, generally when there is "All of the above" as an answer, "All of the above" is correct.

Answer:

[tex]-\frac{1}{3} < x < 2[/tex] and -3 < x < 3

Step-by-step explanation:

The inequality equation is  

3x² - 5x - 2 < 0

⇒ 3x² - 6x + x - 2 < 0

⇒ (x - 2)(3x + 1) < 0

Therefore, either (x - 2) > 0 and (3x + 1) < 0

⇒ x > 2 and [tex]x < -\frac{1}{3}[/tex] which is not possible for any particular value of x.

or, (x - 2) < 0 and (3x + 1) > 0

⇒ x < 2 and [tex]x > -\frac{1}{3}[/tex] which is valid.

So, the solution is [tex]-\frac{1}{3} < x < 2[/tex] (Answer)

Now, another inequality is  

x² - 9 < 0

⇒ x² < 9

Therefore, -3 < x < 3 is the solution. (Answer)

Answer:

3.98/16= 0.24875 round up to make 0.25

5.98/32= 0.186875 round up to make 0.19

34.99/128= 0.273359375 = 0.27

Step-by-step explanation:

3.98/16= 0.24875 round up to make 0.25

5.98/32= 0.186875 round up to make 0.19

34.99/128= 0.273359375

The correct equation for the booster club aiming to earn $200 per match from student and adult tickets priced at $4 and $8, respectively, is 4x + 8y = 200. This represents the sum of $4 per student ticket (x) and $8 per adult ticket (y) sold to reach the goal.

To solve the problem presented by the high school soccer booster club, we need to formulate a linear equation that represents their goal for ticket sales revenue from students and adults. The tickets are priced at $4 for students and $8 for adults. If we let x represent the number of student tickets sold and y the number of adult tickets sold, the total revenue T would be expressed as the sum of $4 per student ticket and $8 per adult ticket.

The booster club aims to earn $200 per match, which gives us the equation for their goal: 4x + 8y = 200. Here, the 4 and 8 are the prices of the tickets for students and adults, respectively, and x and y are the numbers of tickets sold. This clearly aligns with option b from the choices you've provided.

To illustrate with an example similar to your situation, a tutoring school equation of y = 3000x + 500  combines a one-time enrollment fee of $500 with a tuition of $3000 per year. In this case, y represents the total cost of attendance and x the number of years a student is enrolled.

Answer:

Step-by-step explanation:

Yeah it right thank sweetheart

The original width of the rectangle is 8 cm and the original length is 18 cm. These dimensions are found by setting up an equation based on the change in area when both dimensions are reduced by 2 cm.

Finding Original Dimensions of a Rectangle

Let's denote the width of the rectangle as w, and the length will then be w + 10 cm. The area of the original rectangle is w(w + 10) square centimeters. Now, by decreasing each dimension by 2 cm, the new width becomes w - 2 cm and the new length becomes (w - 2) + 10 cm = w + 8 cm. The area of the new rectangle is (w - 2)(w + 8) square centimeters.

The problem states that the area of the rectangle is decreased by 48 cm2 when the dimensions are reduced. This gives us the equation:

w(w + 10) - (w - 2)(w + 8) = 48

Expanding the terms and solving for w will provide us with the width of the original rectangle. After finding w, we can calculate the original length by adding 10 cm to the width. To solve for w, we proceed with the calculation:

[tex]w_2 + 10w - (w_2[/tex] + 6w - 16) = 48

w2 + 10w - w2 - 6w + 16 = 48

4w + 16 = 48

4w = 32

w = 8 cm.

Therefore, the original width is 8 cm and the original length is 18 cm (that is, 8 cm + 10 cm).

Answer:

D. 158/6

Step-by-step explanation:

If you divide 158/6 you get 26.3333333333 which is a repeating decimal, and makes it a rational number.

Answer: 1/6

Step-by-step explanation: To multiply fractions, first multiply across the numerators, then multiply across the denominators.

So here, we have 1 × 2 which is 2 and 4 × 3 which is 12. So now we have the fraction 2/12.

Notice however that 2/12 is not in lowest terms so we need to divide the numerator and the denominator by the greatest common factor of 2 and 12 which is 2.

So if we divide the numerator and the denominator by 2, we get 1/6.

Therefore, 1/4 × 2/3 = 1/6.

Answer:

1/6

Step-by-step explanation:

For fraction multiplication, multiply the numerators and then multiply the denominators to get

1 x 2           2

-------    = --------

4 x 3          12

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 2 and 12. GCF(2,12) = 2

2 divided by 2           1

------------------------   =  ----  

12 divided by 2         6

So...

1/4 x 2/3 = 1/6

Answer:

draw a square

Step-by-step explanation:

draw a square then write 32mm on all sides

draw a triangle  with a wide bottom a small side a medium side

Answer:

1+3i

Step-by-step explanation:

(6+4i)-(5+i)

6+4i-5-i

1+4i-i

1+3i

Answer: 1+3i

Step-by-step explanation:

(6 + 4i) − (5 + i)

Before solving further, note that :

Minus × Minus = Plus

Plus × Minus = Minus

Plus × Plus = Plus

(6 + 4i) − (5 + i)

Open the bracket

= 6 + 4i - 5 - i

Collect like terms

= 6 - 5 + 4i - I

= 1 + 3i

Answer:

The correct answer is D. 15 squared centimeters.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Base one = 10 centimeters

Base two = 5 centimeters

Height = 2 centimeters

2. Let's find out the area of the trapezoid, using the following formula:

Area = 1/2 (Base one + Base two) * Height

Replacing with real values:

Area = 1/2 (10 + 5) * 2

Area = 1/2 (15 * 2) = 1/2 (30)

Area = 15 centimeters ²

The correct answer is D. 15 squared centimeters.

Answer:

A

Step-by-step explanation:

An ordered pair is a point on a coordinate graph that represents data. The x represents an independent variable and the y a dependent. Your y is your vertical axis. Each square on this graph represents 50 feet. The line on your graph hits the intersection between 2 minutes and 100 feet. Therefore (2,100) Is an ordered pair

Answer:

$8950.37

Step-by-step explanation:

Use the compound amount formula A = P(1 + r/n)^(nt), in which P is the initial amount of money (the principal), r is the interest rate as a decimal fraction, n is the number of times per year that interest is compounded, and t is the number of years.

Here we have A = $11,000, n = 2, r = 0.07 and t = 3, and so:

$11,000 = P(1 + 0.07/2)^(2*3), or

$11,000 = P (1.035)^6

                                           $11,000        $11,000

Solving for P, we get P = ---------------- = ------------- = $8950.37

                                            1.035^6          1.229

Depositing $8950.37 with terms as follows will result in an accumulation of $11,000 after 3 years.

To determine how much money should be deposited today in an account that earns 7% compounded semiannually to accumulate to $11,000 in three years, one needs to apply the formula for compounded interest and solve for the principle amount.

The subject in question pertains to compounded interest under the domain of financial mathematics. In this context, the student wants to determine how much money needs to be deposited today to accumulate a given amount, in this case, $11,000, in an account that earns 7% compounded semiannually in three years. It's important to note that when interest is compounded, it's added to the principal, and future interest calculations are based on this adjusted amount.

Applying the formula for compounded interest: A = P(1 + r/n)^(nt)

Where:

our aim is to find P (the principal amount or the amount to be deposited today), which can be mathematically rearranged from the formula above as follows:

**P = A / [(1 + r/n)^(nt)]**

Substituting A = $11,000, r = 7% (or 0.07 in decimal form), n = 2 (since the interest is compounded semiannually), and t = 3, we calculate P (the amount to be deposited today).

https://brainly.com/question/14295570

#SPJ2

Answer:

The quantity of large frames is 7

The quantity of small frames is 13

Step-by-step explanation:

Given as :

The price of each large frames = $ 10

The price of each small frames = $ 5

The total number of both frames bought = 20

The price for both the frames = $ 135

Now,

Let the quantity of large frames = L

And The quantity of small frames = S

So , According to question

The total number of both frames bought = 20

Or, The quantity of large frames + the quantity of small frame = 135

Or, L + S = 20         ......A

And $ 10 L + $ 5 S = $ 135                         ................B

Or, $ 10× ( L + S ) = $ 10× 20

Or, $ 10 L + $ 10 S = $ 200

(  $ 10 L + $ 10 S ) - ( $ 10 L + $ 5 S ) = $ 200 - $ 135

Or , ( $ 10 L - $ 10 L ) + ( $ 10 S - $ 5 S ) = $ 65

Or, 0 + 5 S = 65

∴  S = [tex]\frac{65}{5}[/tex]

I.e S = 13

So, The quantity of small frames = S = 13

Put the Value of S in eq A

So , L + S = 20

Or, L = 20 - S

Or, L = 20 - 13

∴   L = 7

So, The quantity of large frames = L = 7

Hence The quantity of large frames is 7

And   The quantity of small frames is 13   Answer

Answer:

Step-by-step explanation:

[tex]9c-7=7c-11\qquad\text{add 7 to both sides}\\\\9c-7+7=7c-11+7\\\\9c=7c-4\qquad\text{subtract}\ 7c\ \text{from both sides}\\\\9c-7c=7c-7c-4\\\\2c=-4\qquad\text{divide both sides by 2}\\\\\dfrac{2c}{2}=\dfrac{-4}{2}\\\\c=-2[/tex]

Answer:

2

Step-by-step explanation:

Simplifying

9c + -7 = 7c + -11

Reorder the terms:

-7 + 9c = 7c + -11

Reorder the terms:

-7 + 9c = -11 + 7c

Solving

-7 + 9c = -11 + 7c

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-7c' to each side of the equation.

-7 + 9c + -7c = -11 + 7c + -7c

Combine like terms: 9c + -7c = 2c

-7 + 2c = -11 + 7c + -7c

Combine like terms: 7c + -7c = 0

-7 + 2c = -11 + 0

-7 + 2c = -11

Add '7' to each side of the equation.

-7 + 7 + 2c = -11 + 7

Combine like terms: -7 + 7 = 0

0 + 2c = -11 + 7

2c = -11 + 7

Combine like terms: -11 + 7 = -4

2c = -4

Divide each side by '2'.

c = -2

Simplifying

c = -2

Answer:

6 lunch tables

Step-by-step explanation:

Since one lunch table can hold 10 students and 60 students are needed to hold,

60 ÷ 10 = 6 lunch tables

Answer:

6

Step-by-step explanation:

1 table is 10

60 divided by 10= 6

Answer:

x= 10

Step-by-step explanation:

45-15=30

30/3=10