Mrs. Smith needed to split 28 students into 4 equal groups for the race. Which step could help her to work 30 divided by 3?
(A) (27 divided by 9) + (9 divided by 3)
(B) (24 divided by 4) + (4 divided by 4)
(C) (21 divided by 3) + (9 divided by 3)
(D) (20 divided by 4) + (10 divided by 4)

The first step in solving the expression 9(12-3)+4 is to perform the operation within the parentheses, subtracting 3 from 12. This operation adheres to the Order of Operations (PEMDAS) and simplifies the expression for further steps.

The first step in solving the problem 9(12-3)+4 involves using the Order of Operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, according to PEMDAS, we start with the operation within the parentheses. So, we subtract 3 from 12, resulting in 9 times 9, plus 4. The operation within the parentheses simplifies the problem and sets the stage for the subsequent multiplication and addition.

After simplifying the operation within the parentheses, we multiply the result by 9 and then add 4 to get the final answer. This step-by-step approach helps in solving the problem accurately.

Step One: Identify the unknown in the problem. In this case, the unknown is the result of the expression 9(12-3)+4.

Step Two: The first step in solving this problem is to simplify the expression inside the parentheses using the order of operations (PEMDAS/BODMAS).

Step Three: Perform the operations within the parentheses first, then multiply the result by 9 and finally add 4. This will give you the solution to the given expression.

Well, first find out what 20% of $15 is.

20% x $15 = $3

Take that from the original price.

$15-$3=$12

Answer:

1)  x =  15, y =  30 is the solution of the given system of equation.

2) x = 0.5 , y = 12.5   is the solution of the given system of equation.

Step-by-step explanation:

First QUESTION:

Here the given set if equation are:

y =  x + 15

y = 2 x

Substituting the value of y = 2 x in the first equation, we get:

y =  x + 15  ⇒   2 x = x + 15

or, 2 x - x = 15

⇒ x  = 15

⇒ y = 2 x  = 2 (  15) =  30, or y = 30

Hence, x =  15, y =  30 is the SOLUTION of the given system of equation.

Second QUESTION:

Here the given set if equation are:

y  = x +12

4 x + 2 y = 27​

Substituting the value of y = x + 12 in the second  equation, we get:

4 x + 2 y = 27​   ⇒ 4 x + 2 (x + 12)  = 27​

or, 4 x + 2(x) + 2 (12) = 27

⇒ 6 x  = 27 - 24 = 3

⇒ x = 3 /6  = 0.5

Now, y = x +  12  = 0.5 +  12 = 12.5 or y = 12.5

Hence, x = 0.5 , y = 12.5  is the SOLUTION of the given system of equation.

Answer:

f^-1 (x)=(x/2)^(1/3)

Step-by-step explanation:

y=2x^3

x=2y^3

2y^3=x

y^3=x/2

y=(x/2)^(1/3)

Answer:

Let's solve!

Step-by-step explanation:

[tex]logx^{\frac{1}{8} } = -\frac{3}{2}[/tex]

[tex]then[/tex]

[tex]10^{-\frac{3}{2}} = x^{\frac{1}{8} }[/tex]

[tex](10^{-\frac{3}{2} })^{8} = (x^{\frac{1}{8} })^{8}[/tex]

[tex]x = 10^{3*4} = 10^{-12}[/tex]

[tex]x= 10^{-12}[/tex]

If the equation looks like this, then it has the solution

[tex]x= 10^{-12}[/tex]

Another answer is

√x = 2 or x = 4

I hope this helps!

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Answer:24.5

=

2.45

×

10

=

2.45

×

10

1

⇒

24.5

×

10

−

5

=

2.45

×

10

1

×

10

−

5

=

2.45

×

10

−

4

Step-by-step explanation:

Answer:

[tex]2.45*10^1[/tex]

Step-by-step explanation:

You move the decimal point of a number until the new form is a number from 1 up to 10 (N), and then record the exponent (a) as the number of places the decimal point was moved. Whether the power of 10 is positive or negative depends on whether you move the decimal to the right or to the left. Moving the decimal to the right makes the exponent negative; moving it to the left gives you a positive exponent.

Step-by-step explanation:

Step 1: Distribute the 3 to (x-4)

    ⇒ 3(x)-3(4) = 12

Step 2: Calculate the left side!!

   ⇒ 3x-12= 12

Step 3: Add 12 to both sides!

   ⇒ 3x= 24

Step 4: Divide 3 by both sides!

⇒ 3x/3= 24/3

Step 5: YOUR ANSWER!!

  ⇒ 8

ANSWER: 8

Answers:

110

95

80

65

75

Yay

Final Answer:

The equation of the image after a dilation with a scale factor of 4, centered at the origin, is y = 8x + 8.

Explanation:

When a function undergoes dilation centered at the origin, each coordinate (x, y) is transformed to (kx, ky), where k is the scale factor. In this case, the original equation y = 2x + 2 is dilated by a factor of 4. Therefore, the new equation becomes y' = 4(2x + 2), which simplifies to y' = 8x + 8. The scale factor of 4 multiplies both the coefficient of x and the y-intercept, resulting in a steeper slope and a vertical shift.

In the original equation, the coefficient of x was 2, indicating a slope of 2. After the dilation, the coefficient becomes 8, indicating a steeper slope of 8. Additionally, the y-intercept of 2 is multiplied by 4, yielding a new y-intercept of 8. This transformation preserves the line's direction while magnifying its steepness and shifting it vertically. The equation y' = 8x + 8 represents the dilated image of the original line.

To summarize, the process involves multiplying both the coefficient of x and the y-intercept by the scale factor. This scaling maintains the line's direction while adjusting its steepness and vertical position. The resulting equation, y' = 8x + 8, accurately describes the image of the original line after dilation by a factor of 4 centered at the origin.

Answer:

Part a) [tex]x+y < 400[/tex]

Part b) The graph in the attached figure

Part c) see the explanation

Part d) The number of seat tickets sold must be less than 300 tickets

Step-by-step explanation:

Part a) write an inequality to describe the constraints. specify what each variable represents

Let

x ----> number of lawn tickets sold

y ----> number of seat tickets sold

we know that

The sum of the number of lawn tickets sold plus the  number of seat tickets sold must be less than 400 tickets

so

The linear inequality that represent this situation is

[tex]x+y < 400[/tex]

Part b) use graphing technology to graph the inequality. sketch the region on the coordinate plane

we have

[tex]x+y < 400[/tex]

using a graphing tool

The solution is the triangular shaded area of positive integers (whole numbers) of x and y

see the attached figure

Remember that the values of x and y cannot be a negative number

Part c) name one solution to the inequality and explain what it represents in that situation

we know that

If a ordered pair lie on the solution of the inequality, then the ordered pair is a solution of the inequality (the ordered pair must satisfy the inequality)

I take the point (200,100)

The point (200,100) lie on the triangular shaded area of the solution

Verify

Substitute the value of x and the value of y in the inequality and compare the result

For x=200,y=100

[tex]x+y < 400[/tex]

[tex]200+100 < 400[/tex]

[tex]300 < 400[/tex] --> is true

so

The ordered pair satisfy the inequality

therefore

The ordered pair is a solution of the inequality

That means ----> The number of lawn tickets sold was 200 and the number of seat tickets sold was 100

Part d) if you know that exactly 100 lawn tickets were sold, what can you say about the number of seat tickets?

we have that

x=100

substitute in the inequality

[tex]100+y < 400[/tex]

solve for y

subtract 100 both sides

[tex]y < 400-100[/tex]

[tex]y < 300[/tex]

therefore

The number of seat tickets sold must be less than 300 tickets

Answer:

D. y= -4x +5

Step-by-step explanation:

To find the equation that is equivalent to y + 3 = -4(x - 2), we need to simplify and rearrange the equation to the standard y = mx + b form.

To find the equation that is equivalent to y + 3 = -4(x - 2), we need to simplify and rearrange the equation to the standard y = mx + b form. Here are the steps:

Therefore, the equation that is equivalent to y + 3 = -4(x - 2) is -4x + y = 5.

Answer:

[tex]\large\boxed{\dfrac{2}{5}}[/tex]

Step-by-step explanation:

[tex]\text{The product of the number and its reciprocal gives us 1.}\\\text{Reciprocal of }\ \dfrac{5}{2}\ \text{is equal}\ \dfrac{2}{5}.\\\\\dfrac{5}{2}\times\dfrac{2}{5}=\dfrac{5\!\!\!\!\diagup}{2\!\!\!\!\diagup}\times\dfrac{2\!\!\!\!\diagup}{5\!\!\!\!\diagup}=\dfrac{1}{1}\times\dfrac{1}{1}=1\times1=1[/tex]

Answer:

(a) 65 gallons per minute

(b) 280 gallons

(c) 8080 gallons

(d) 150 minutes.

Step-by-step explanation:

Water is filled up by pumps into a tank at a constant rate.

The volume of water in the tank V, in gallons, is given by the equation  

V(t) = 65t + 280 ......... (1), where t is the time, in minutes.  

(a) The rate at which water is pumped into the tank is 65 gallons per minute. (Answer)

(b) 280 gallons of water was there in the tank when the pumps were turned on because f(0) = 65 × 0 + 280 = 280. (Answer)

(c) After 2 hours i.e. (2 × 60) = 120 minutes the volume of water in the tank will be f(120) = 65 × 120 + 280 = 8080 gallons. (Answer)

(d) The tank has a capacity of 10000 gallons of water.

So, if the tank starts to overflow after t minutes, then  

10000 = 65t + 280

⇒ 65t = 9720

⇒ t = 149.53 minutes ≈ 150 minutes (Answer)

Final answer:

The rate at which water is being pumped into the tank is 65 gallons per minute, the tank initially had 280 gallons of water, after two hours the volume will be 8,080 gallons, and the pumps will turn off after approximately 150 minutes when the volume reaches 10,000 gallons.

Explanation:

The water tank problem can be analyzed step by step based on the given linear equation v(t) = 65t + 280, which describes the volume V of water in gallons as a function of time t in minutes.

(a) Rate of Water Being Pumped

The coefficient of t in the equation represents the rate at which water is being pumped into the tank. Therefore, the water is being pumped at a constant rate of 65 gallons per minute.

(b) Initial Volume of Water

The constant term in the equation, 280, represents the volume of water that was in the tank when the pumps were turned on. This means the tank initially had 280 gallons of water.

(c) Volume After Two Hours

To convert two hours to minutes, we multiply by 60 minutes per hour, giving us 120 minutes. Plugging this value into the equation gives us v(120) = 65(120) + 280 = 7,800 + 280 = 8,080 gallons. So, after two hours, the volume of water in the tank would be 8,080 gallons.

(d) Time to Reach 10,000 Gallons

To find the time when the volume reaches 10,000 gallons, we set the equation equal to 10,000 and solve for t: 10,000 = 65t + 280. Subtracting 280 from both sides gives us 9,720 = 65t, and dividing both sides by 65 gives us t ≈ 149.54 minutes. To the nearest minute, the pumps will turn off after approximately 150 minutes.

Answer:

(2, 120° )

Step-by-step explanation:

To convert from rectangular to polar form, that is

(x, y) → (r, Θ ), use

r = [tex]\sqrt{x^2+y^2}[/tex]

Θ = [tex]tan^{-1}[/tex]( [tex]\frac{y}{x}[/tex])

here (x, y ) = (- 1, [tex]\sqrt{3}[/tex])

r = [tex]\sqrt{(-1)^2+(\sqrt{3} }[/tex] )^2

  = [tex]\sqrt{1+3}[/tex] = [tex]\sqrt{4}[/tex] = 2

Θ = [tex]tan^{-1}[/tex]([tex]\sqrt{3}[/tex]) = 60° ← related acute angle

Note (- 1, [tex]\sqrt{3}[/tex]) is in the second quadrant so Θ must be in the second quadrant.

Θ = 180° - 60° = 120°

(- 1, [tex]\sqrt{3}[/tex]) → (2, 120°)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The polar form of a Cartesian coordinates is given by (r, @) where r = √x^2 + y^2

@ = tan^-1 y/x

r = √-1^2 + √3^2

r = √4

r= 2

@ = tan ^-1 √3/-1 -tan √3/1 = -60°

@ = 180-60 = 120°

The answer you’re looking for is: simplify.

When you rewrite an expression, we are simplifying it. We first use the distributive property through any groupings symbols, then evaluate terms we exponent that are given. Lastly, we combine any like terms, weather they are constants or variables.

Hope this helps! :)

Answer:

It is simplify. It is what you do when like terms are combined in order to get your answer.

Hope this helps!

Answer:

The total number of students actually went for skiing is 0.75 times the total students .

Step-by-step explanation:

Given as :

Some Students were surveyed about their wither break plans.

The percentage of students who actually did not go for skiing = 25 %

So , The percentage of students who actually go for skiing = 100 % of students - 25 %

I.e The percentage of students who actually go for skiing = 75 %

Let The total number of students = x

So, out of x students , The The percentage of students who actually go for skiing = 75 % of the total students

I.e The The percentage of students who actually go for skiing = 75 % of x

Or, The The percentage of students who actually go for skiing = 0.75 × x

So, The number of students for skiing = 0.75 x

Hence The total number of students actually went for skiing is 0.75 times the total students . Answer

Answer:This can be checked by the following steps;

Step-by-step explanation:

The pair (1,2) is a solution to the inequality 6x - y > 3 because when these values are substituted into the inequality, the result is 4 > 3, which is a true statement.

The question is asking if the pair of numbers (1,2) is a solution to the inequality 6x - y > 3. We can evaluate this by substituting the pair of values (1, 2) into the inequality in place of x and y. This gives us 6*1 - 2 > 3, or 6 - 2 > 3, which simplifies to 4 > 3. Since 4 is indeed greater than 3, we can conclude that the pair (1,2) is a solution to the inequality 6x - y > 3.

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Final answer:

The horizontal asymptote indicates that as more pure acid is added, the concentration approaches 1, meaning the acid concentration trends towards 100% purity but never fully reaches it. (Option D)

Explanation:

The horizontal asymptote of the function f(x) = x + 60 / (x + 300) describes the behavior of the acid concentration as the volume of pure acid x becomes very large. When an increasingly larger volume of pure acid is added, the concentration of the acid in the new substance approaches a certain value. This implies that, no matter how much more acid is added past a certain point, the concentration doesn't change significantly.

The correct statement regarding the horizontal asymptote is: D. As more pure acid is added, the concentration of acid approaches 1. This means that the concentration of the acid will get closer and closer to 100%, or pure acid, but it will never actually reach that concentration because you are always adding the acid to some amount of solution.

Answer:

3, 6, 9, 12 is not geometric

Step-by-step explanation:

A geometric progression has a common ratio r between consecutive terms.

3, 6, 9 , 12

has a common difference of 3 between terms and is arithmetic

1, 5, 25, 125

r = 5 ÷ 1 = 25 ÷ 5 = 125 ÷ 25 = 5 ← geometric

4, 8, 16, 32

r = 8 ÷ 4 = 16 ÷ 8 = 32 ÷ 16 = 2 ← geometric

2, 6, 18, 54

r = 6 ÷ 2 = 18 ÷ 6 = 54 ÷ 18 = 3 ← geometric

Answer:

3, 6, 9, 12 would not be a geometric sequence.

Step-by-step explanation:

The reason for this is because, geometric sequence is multiplication or division while arithmetic is addition and subtraction.

1, 5, 25, 125 is multiplication. x5

4, 8, 16, 32 is multiplication as well. x2

2, 6, 18, 54 is multiplication as well. x3

While 3, 6, 9, 12 would be +3.

Therefore, 3,6, 9, 12 would not be a geometric sequence.

1/4 is the simplified fraction for 6/24.

Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

you can divide the numerator and denominator of [tex]\frac{6}{24}[/tex] by 6, resulting in [tex]\frac{1}{4}[/tex]

Answer:

1/24 ≈ 4.2%

Step-by-step explanation:

P(head) = 1/2

P(4) = 1/6

P(2 heads and 4) = (1/2)² (1/6) = 1/24 ≈ 4.2%.

Answer:

250 239 439for lawns he mods $25

The possible transformations that establish congruence between shapes are dilation, translation, and reflection.

The possible rules that represent a transformation mapping one shape onto another to establish congruence are:

A dilation by a scale factor of 3 about the origin stretches or shrinks the shape uniformly in all directions. A translation moves the shape without changing its size or shape. A reflection across a line is a flip of the shape over that line. These transformations can establish congruence between shapes.

Transformations that establish congruence between shapes by preserving size, shape, and orientation ensure that the transformed shape aligns with the original shape. The correct answer is option

B) A translation to the right 2 and down 6.

C) A reflection across the line y=2.

D) A counter-closckwise rotation of 90 degrees about the origin.

The rules that represent transformations mapping one shape onto another to establish congruence are:

B) A translation to the right 2 and down 6, which preserves both size and shape, simply moving the shape to a different location without changing its orientation or proportions.

C) A reflection across the line y=2, which reflects the shape across a line, maintaining its size and shape but reversing its orientation.

D) A counter-clockwise rotation of 90 degrees about the origin, which rotates the shape by a right angle, preserving its size and shape while changing its orientation.

These transformations preserve congruence by maintaining the size, shape, and orientation of the original shape.

Options B, C, and D represent transformations that map one shape onto another to establish their congruence, preserving size, shape, and orientation.

Answer:

685.50

Step-by-step explanation:

754 - 26 = 728

728 / 1.062 = 685. 50

Answer:  $685.50

Step-by-step explanation:

1.062x+26=754

1.062x=728

x=685.499

to nearest cent $685.50

Answer:

Step-by-step explanation:

P is 5 ticks to the left of 0, so it would be -5/8

Q is 5 ticks to the right of 0, so it would be at 5/8

 an absolute value turns a negative number into a positive number

 so absolute value of  P located at -5/8 = 5/8

 this is the location of point Q

Joe said that the absolute values of the numbers represented by the two points are the same. 

Answer:

Tim, because each point is fraction 3 over 8 units away from 0.

Step-by-step explanation:

That is how absolute value works.

Answer: 65%

Step-by-step explanation:

2258 glove-784 remaining = 1474 gloves used

now create part to whole relationship

1474 gloves used/2258 total gloves = 0.65 approx or 65%

Answer:

Last year: length of 4 meters  

This year: width of 10 meters and a length of 12 meters

Step-by-step explanation:

Answer:

50%

Step-by-step explanation:

To find the percentage of his correct answers, divide the amount of correct answers he got by the total number of problems.

26 out of 52 is another way to say

26/52

= 26 ÷ 52

= 0.50

0.5 is the decimal form of the answers Tristan got correct.

To convert it to a percentage, more the decimal two places to the right.

0.50 => 50%

Tristan got 50% of the problems correct.

Answer:

46.46 gallons

Step-by-step explanation:

we know that

An airplane consumes 30.25 gallons of fuel in 2.8 hours of flying

so

using proportion

Find out how many gallons will it consume in 4.3 hours of flying

[tex]\frac{30.25}{2.8}\ \frac{gal}{h}=\frac{x}{4.3}\ \frac{gal}{h}\\\\x=30.25*(4.3)/2.8\\\\x= 46.46\ gal[/tex]

Answer:

[tex]BE=15\ units[/tex]

Step-by-step explanation:

we know that

In a rhombus the diagonals are perpendicular

so

The triangle ABE is a right triangle

see the attached figure to better understand the problem

Applying the Pythagoras Theorem to the right triangle ABE

[tex]AB^2=AE^2+BE^2[/tex]

where

AB is the hypotenuse of the right triangle (greater side)

AE and BE are the legs of the right triangle

we have

[tex]AB=17\ units\\AE=8\ units[/tex]

substitute

[tex]17^2=8^2+BE^2[/tex]

solve for BE

[tex]289=64+BE^2[/tex]

[tex]BE^2=289-64[/tex]

[tex]BE^2=225[/tex]

[tex]BE=15\ units[/tex]

Answer:

C) 16

Step-by-step explanation: