By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?

Answer:

B. [tex]y=8x[/tex]

Step-by-step explanation:

A proportional relationship in 'x' and 'y' is given as:

[tex]y=kx[/tex]

Where, 'k' is called as the constant of proportionality.

So, the graph of a proportional relationship always crosses the origin.

This means that the 'x' and 'y' intercepts of a proportional relationship is always at the origin (0, 0).

From among all the options, the option that matches the definition of a proportional relationship is option B. [tex]y=8x[/tex]

Here, [tex]k=8[/tex].

Therefore, the correct option is option B.

Answer:

[tex]f^{-1}(x)=\frac{x}{6}+\frac{2}{3}[/tex]

Step-by-step explanation:

Given function.

[tex]f(x)=6x-4[/tex]

To find the inverse function [tex]f^{-1}(x)[/tex]

Step 1:

Replace [tex]f(x)[/tex] with[tex]y[/tex] in the function.

[tex]y=6x-4[/tex]

Step 2:

Interchange [tex]y[/tex] with [tex]x[/tex] in the equation.

[tex]x=6y-4[/tex]

Step 3:

Solve for [tex]y[/tex].

We have [tex]x=6y-4[/tex]

Adding 4 to both sides,

[tex]x+4=6y-4+4[/tex]

[tex]x+4=6y[/tex]

Dividing each term by 6 to isolate [tex]y[/tex]

[tex]\frac{x}{6}+\frac{4}{6}=\frac{6y}{6}[/tex]

[tex]\frac{x}{6}+\frac{4}{6}=y[/tex]

Simplifying fractions by dividing the numerator and denominator by  their GCF.

[tex]\frac{x}{6}+\frac{4\div 2}{6\div 2}=y[/tex]

[tex]\frac{x}{6}+\frac{2}{3}=y[/tex]

Thus the equation of [tex]y[/tex] is:

[tex]y=\frac{x}{6}+\frac{2}{3}[/tex]

Step 4:

Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]

[tex]f^{-1}(x)=\frac{x}{6}+\frac{2}{3}[/tex] (Answer)

Thus, we have the inverse function

Answer:

[tex]\large\boxed{16a^6x^4y^2}[/tex]

Step-by-step explanation:

[tex]\text{Use}\\\\(ab)^n=a^nb^n\\\\(a^n)^m=a^{nm}\\=====================\\\\\left(-4x^2ya^3\right)^2=\\\\=(-4)^2(x^2)^2(y)^2(a^3)^2\\\\=(-4)(-4)x^{2\cdot2}y^2a^{3\cdot2}\\\\=16x^4y^2a^6[/tex]

The expression (−4x^2ya^3)^2 written as a monomial in standard form is 16x^4y^2a^6.

To write the given expression, (−4x2ya3)2, as a monomial in standard form, we first need to calculate square ofeach part of the term inside the parentheses. The square of -4 is 16. The rule of exponents states that when raising a power to a power, you multiply the exponents. Therefore, the square of x2 is x4 (since 2*2=4), the square of y is y2, and the square of a3 is a6 (since 3*2=6). Combining these, we find that the expression in standard form is 16x4y2a6.

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The equilibrium price 'p' is found when setting the supply and demand equations equal to each other and solving for p. Doing so gives us p = 29, which is not available among the provided options, suggesting an error in the question or answer options.

In the given situation, the point of equilibrium occurs when the quantity demanded (D) is equal to the quantity supplied (S). Therefore, we can set the demand equation equal to the supply equation and solve for p.

The equations at the moment are: D = p + 22 and S = 3p - 36.

Setting them equal to each other means setting D and S to the same value, resulting in: p + 22 = 3p – 36.

To solve for p, you first combine like terms, which will give you: 22 + 36 = 3p - p, simplifying that leads to: 58 = 2p.

Finally, to isolate p, divide both sides of the equation by 2: p = 58 / 2 = 29.

However, none of the options includes p = 29, which suggests there might be a typo or error in the provided choices or the equations.

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Asa has 15 dimes and 32 quarters.

Step-by-step explanation:

Given,

Total coins = 47

Worth of coins = $9.50 = 9.50*100 = 950 cents

1 dime = 10 cents

1 quarter = 25 cents

Let,

Number of dimes = x

Number of quarters = y

According to given statement;

x+y=47      Eqn 1

10x+25y=950   Eqn 2

Multiplying Eqn 1 by 10

[tex]10(x+y=47)\\10x+10y=470\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](10x+25y)-(10x+10y)=950-470\\10x+25y-10x-10y=480\\15y=480[/tex]

Dividing both sides by 15

[tex]\frac{15y}{15}=\frac{480}{15}\\y=32[/tex]

Putting y=32 in Eqn 1

[tex]x+32=47\\x=47-32\\x=15[/tex]

Asa has 15 dimes and 32 quarters.

Keywords: linear equation, elimination method

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The question involves setting up and solving a system of linear equations based on the total number and value of the coins. It's a high school level mathematics question about algebra.

The subject of this question falls into the field of Mathematics, specifically algebra. We need to find the number of dimes (let's denote it as D) and quarters (Q) Asa has saved, knowing their total amount and value. We can set up a system of equations based on the information provided:

Solving this system of equations will give us the precise numbers of each coin that Asa has saved.

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Answer:

The zeros are:

[tex]x=-1,\:x=\frac{3}{2}[/tex]

Step-by-step explanation:

As the function is given by

[tex]F(x)=4x^4-4x^3-11x^2+6x+9[/tex]

We have to find the zeros of [tex]4x^4-4x^3-11x^2+6x+9[/tex].

So,

[tex]4x^4-4x^3-11x^2+6x+9=0[/tex]

Factor left side of equation.

[tex]\left(x+1\right)^2\left(2x-3\right)^2=0[/tex]

[tex]\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

[tex]Solving\:x+1=0[/tex]

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]

[tex]x+1-1=0-1[/tex]

[tex]x=-1[/tex]

[tex]Solving\:2x-3=0[/tex]

[tex]x=\frac{3}{2}[/tex]

So, the zeros are:

[tex]x=-1,\:x=\frac{3}{2}[/tex]

Keywords: zeros, equation

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Answer:

The first one.

Step-by-step explanation:

The third and fourth ones can't be right because at when the line takes its first curve (just before .25 hours) it doesn't keep increasing in height, and she walked during that time.

The second one can't be right because when she started out she wasn't immediately between 1.25 and 1.5 miles.

That leaves only the first one.

The graph for the given situation is required.

The correct option is the first graph.

Let us convert the minutes to hour since the graph is shown in hours.

[tex]\dfrac{13}{60}=0.2167\ \text{hours}[/tex]

[tex]\dfrac{17}{60}=0.2833\ \text{hours}[/tex]

Whenever a line in a graph has an angle with the [tex]x[/tex] axis then there is a change of the [tex]y[/tex] axis with respect to change in [tex]x[/tex] axis.

That means slope

[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

Here, the slope of an angled line will be

[tex]m=\dfrac{\text{Change in distance}}{\text{Change in time}}=\text{Speed}[/tex]

The slope here indicates constant speed.

From 0 to 0.2167 hours she ran at constant speed.

From 0.2167 to [tex]0.2167+0.2833=0.5[/tex] hours she walked

From 0.5 hours to [tex]0.5+0.2167=0.7167[/tex] hours she ran.

From 0.7167 hours to [tex]0.7167+0.2833=1[/tex] hour she sat and stretched.

The slope or angle will be more for the running sections compared to the walking sections as running is faster than walking.

And the graph will always be going up.

At the end when she is not moving the line will be a horizontal line because her position is not changing.

So, the correct option is the first graph.

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Answer:

6 minutes.

Step-by-step explanation:

She ascends at a rate of 5 feet per minute from the reef.

Once she reaches  a height of -30 feet, she must rest for 15 minutes and she then continues to the surface at the same rate.

So, she dives from - 30 feet height to water surface i.e. 0 feet height with a rate of 5 feet per minute.

Therefore, she will take [tex]\frac{30}{5} = 6[/tex] minutes to reach the surface.  

(Answer)

Answer:

6 min

Step-by-step explanation:

Answer:

x = - 0.25, x = 1.25

Step-by-step explanation:

The solutions to the equation are the values of x where the graph crosses the x- axis, that is as an estimate

x ≈ - 0.25 and x ≈ 1.25

Answer:

[tex]x=-0.4[/tex]

[tex]x=1.7[/tex]

Hopefully the answers are accepted to the nearest tenths.

Step-by-step explanation:

Since the left hand side was already graphed, we just need to graph the right hand side which is [tex]x+1[/tex].

We are going to still let [tex]y[/tex] represent the outputs of [tex]x+1[/tex].

So we want to graph the equation [tex]y=x+1[/tex] on the same graph as the parabola, the almost U shaped graph.

You could make a table to plot the equation.

[tex]y=x+1[/tex]

[tex]x[/tex]     |      [tex]y[/tex]         |     ordered pair to graph [tex](x,y)[/tex]

-------------------------------------------------------------------------------------------------------

     -2                     -2+1=-1                          (-2,-1)

     -1                       -1+1=0                           (-1,0)

      0                       0+1=1                            (0,1)

      1                         1+1=2                           (1,2)

      2                        2+1=3                          (2,3)

The purple line I made is the line formed from these points which was generated from the equation [tex]y=x+1[/tex].

Now where the blue curve touches the purple line is our solutions. I put those in orange.

The solutions are approximately, [tex]x=-0.4[/tex] or [tex]x=1.7[/tex].

Hopefully, it accepts solutions to the nearest tenths.

We are trying to approximate where those orange dots are on the number line. Please see attachment 2.      

Answer:

-$4

Step-by-step explanation:

The expected payback formula is the sum of probability multiply the value

E(x) = p(x1)*x1 + p(x2)*x2 + .....

In this case, we have two possibility of payback

1) winning

The payback is $400 -$8 = $392

x1 = 392

The probability of winning is one out of 100 (since the choices are 0 to 99)

p(x1) = 1/100

2. Losing

The payback is -$8 since the person didn't win anything is loose

x2 = -8

Since there is only one winning number, the other 99 numbers are loosing numbers

p(x2) = 99/100

Therefore expected payback is

E(x) = p(x1)*x1 + p(x2)*x2

= (1/100)*392 + (99/100)*(-8)

= -400/100

= -$4

The expected payback for a game in which you bet $8 on any number from 0 to 99, and win $400 if your number comes up, is -$4.00, indicating an average loss of $4.00 per game.

In this probability problem, you are betting $8 on a number from 0 to 99. This means there are 100 possible outcomes, each equally likely if the game is fair. Your profit if you win is $400. Since there's a 1 in 100 chance of winning, we can calculate the expected return as follows:

Expected Return = Probability of winning * Payoff when winning = (1/100) * $400 = $4.00

However, since you are always paying $8 to play the game, in expectation you are losing money in every game. The expected payback from this game is hence $4-$8=-$4.00 and not $48.00. In other words, we can anticipate losing $4.00 on average every time we play this game.

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Answer:

No

Step-by-step explanation:

The square root of 34 does not multiply by itself

Yes, the square foot of 34 is a rational number

Any fraction with non-zero denominators is a rational number. Some of the examples of rational numbers are 1/2, 1/5, 3/4, and so on.

square root, in mathematics, a factor of a number that, when multiplied by itself, gives the original number. For example √25 = 5 i.e 5 × 5 = 25

The square root of 34 is of a value

√34 = 5.381

This value can be converted into fraction

= 5381/1000

Therefore we can say that the square root of 34 is a rational number.

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Answer:

5

Step-by-step explanation:

Answer:

6 pounds.

Step-by-step explanation:

70-25.36= 44.64 (the amount of money she spent)

44.64/7.44 (per pound cost)= 6

Answer:

Rachel bought 6 pounds of coffee.

Step-by-step explanation:

First, do $70-$25.36, because that will give you the total amount of money she spent on coffee.

$70-$25.36= $44.64.

Rachel spent $44.64 on coffee.

Next, you know that every pound of coffee costs $7.44.

So, $7.44x = $44.64

x= the number of pounds of coffee Rachel purchased.

So, we have to now isolate x.

$7.44x / $7.44 = $44.64 / $7.44

x= 6

Therefore, Rachel purchased 6 pounds of coffee.

If you need anymore help on any math problems, email me at: icecreamforest7@aol.com

I also tutor.

Hope this helps:)

Answer:

124 miles

Step-by-step explanation:

Since he has a budget of $54.00, we first deduct the fixed charge of $29.2

Money for the miles will be 54-29.2=$24.8

Cost per mile is $0.2

[tex]Miles=\frac {24.8}{0.2}=124 miles[/tex]

Therefore, Mike is limited to travel 124 miles with the car on hire

Answer:

8x^2y= 8x^3 - 4x^2

y = x - 1/2

y = (2x - 1)/2

the answer is c

Answer:

[tex]S=42000*\sum_{i=0}^{n}0.02^n[/tex]

Step-by-step explanation:

The salary per year is the combination of the $42000 per year (constant) plus the 2% rise per year. So the ecuation is:

Firt year [tex]S=(42000 + 0.02*42000)[/tex]

Second year [tex]S=(42000 + 0.02*42000)+0.02*(42000 + 0.2*42000)[/tex]

Generalizing:

[tex]S=42000*\sum_{i=0}^{n}0.02^n[/tex]

Final answer:

The equation that represents Giovanna's current situation is Current Salary = $42,840.

Explanation:

The equation that represents Giovanna's current situation can be determined by using the formula for calculating annual salary with a percentage increase.

The formula is:
Current Salary = Initial Salary + (Percentage Increase * Initial Salary)

Using this formula, we can substitute the given values:
Initial Salary = $42,000
Percentage Increase = 2% (or 0.02)

Substituting these values into the formula:

Current Salary = $42,000 + (0.02 * $42,000)

Simplifying the equation:

Current Salary = $42,000 + $840

Current Salary = $42,840

Therefore, the equation that represents Giovanna's current situation is:
Current Salary = $42,840

Answer:

Step-by-step explanation:

reduced amount  = 70 - 40 = $30

Percent of reduction =  [tex]\frac{30}{70}*100\\=\frac{300}{7} \\=42\frac{6}{7}[/tex]%

0r 42.86%

Answer:

Step-by-step explanation:

percent decrease = (original number - new number) / (original number) * 100

                              = (70 - 40) / 70 * 100

                             = 30/70 * 100

                             = 0.42857 * 100

                             = 42.857 % decrease....if u need it rounded, 42.86%....or if u

                               need it rounded to the nearest whole percent, its 43%

Answer:

Step-by-step explanation:

f: y=x^2

g: y= -x^2

h: y= -x^2-5

first we transform the graph of f to the graph of g using the reflexion across y-axis .

then we transform of g to the graph of h using the translation -5( vector j )

look at the photo below for the graphics.

:)

Answer: a translation 5 units to the left

Graphing is a very useful tool to solve a system of equations but the only major disadvantage is that it is very time-consuming. So, we can solve the system of equations quickly by isolation one variable in one equation and then we get the answer by substituting the resulting expression for the variable in the other equation.

Step-by-step explanation :

Step 1:

Consider the system of equations:

5x + y =13  

3x=15 - 3y

Step 2 :  

y is the easiest variable to isolate in the first equation, because it has no coefficient:

y = 13 - 5x

Step 3 :

In the second equation, substituting for y :

3x = 15 - 3(13 - 5x)

Step 4 :

Solve the equation:

3x = 15 - 39 + 15x

3x = 15x - 24

-12x = - 24

x = 2

substituting this x-value into the "isolated equation" to find y:

y = 13 - 5x = 13 - 5(2) = 13 - 10 = 3

The solution to the system is (2, 3).  This point is used to check for solutions in both equations.

Interpreting the solution of a system of equations involves determining the type of solution (unique, infinitely many, or no solution) and understanding how it relates to the problem being solved. It allows us to find the specific values for the variables that satisfy all the equations and provides insights into the relationships between the variables.

Interpreting the solution of a system of equations is a crucial step in solving a problem. It allows us to understand the relationship between the variables and determine the values that satisfy all the equations in the system. Here's how you can interpret the solution:

1. Determine the type of solution: A system of equations can have three types of solutions: a unique solution, infinitely many solutions, or no solution. To determine the type of solution, solve the system of equations using methods such as substitution, elimination, or matrices.

2. Unique solution: If the system of equations has a unique solution, it means that there is only one set of values for the variables that satisfies all the equations. This solution represents the point where all the equations intersect. In practical terms, this means that there is a specific answer to the problem being solved.

3. Infinitely many solutions: If the system of equations has infinitely many solutions, it means that there are multiple sets of values for the variables that satisfy all the equations. This usually occurs when the equations represent the same line or planes that overlap. In practical terms, this may indicate that there are multiple valid solutions to the problem.

4. No solution: If the system of equations has no solution, it means that there are no values for the variables that satisfy all the equations simultaneously. This usually occurs when the equations represent parallel lines or planes that do not intersect. In practical terms, this may indicate that the problem being solved is not feasible or does not have a valid solution.

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Answer:

0.6

Step-by-step explanation:

The the exponent is positive , move it 3 times to the right.

If it was a negative exponent , you would move it to the left.

The greater number is 121

Step-by-step explanation:

The given is:

We need to find the greater number

Assume that the smaller number x and the greater number is y

∵ The smaller number is x and the greater number is y

∵ Their sum is 151

∴ x + y = 151 ⇒ (1)

∵ The lesser number is 19 more than the square root of the greater

   number

∴ x = 19 + √y ⇒ (2)

- Substitute x in equation (1) by equation (2)

∵ (19 + √y) + y = 151

- Subtract 151 from both sides and re-arrange the terms from

  the greatest power y

∴ y + √y - 132 = 0

Chang [tex]\sqrt{y}[/tex] to [tex]y^{\frac{1}{2}}[/tex] and substitute  [tex]y^{\frac{1}{2}}[/tex] by h

∵ [tex]y^{\frac{1}{2}}[/tex] = h

∴ y = h²

- Substitute each y by h

∴ h² + h - 132 = 0

- Factorize it into two factors

∴ (h - 11) (h + 12) = 0

- Equate each factor by 0 to find h

∵ h - 11 = 0

- Add 11 to both sides

∴ h = 11

∵ h + 12 = 0

- subtract 12 from both sides

∴ h = -12

∵ h = [tex]y^{\frac{1}{2}}[/tex]

∴ [tex]y^{\frac{1}{2}}[/tex] = 11 and -12

∵ [tex]y^{\frac{1}{2}}[/tex] = √y

∴ √y = 11

∴ √y = -12 ⇒ rejected square root can't give -ve number

∴ √y = 11 only

- To find y square the both sides

∴ y = 121

The greater number is 121

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The solution involves setting up two equations from the given information and then substituting one into the other to create a quadratic equation in terms of the greater number, x, and solving for x.

The question involves finding two positive numbers given that their sum is 151 and that the lesser number is 19 more than the square root of the greater number. To find the greater number, let's denote the greater number as x and the lesser number as y. The two conditions given are:

We can substitute the second condition into the first:

After simplifying the quadratic equation and solving for x, we will find the value for the greater number.

Answer:

c a multiple of 13

Step-by-step explanation:

The resulting number will be a multiple of 13 if 13 is added 101 times option (C) A multiple of 13 is correct.

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that:

if 13 is added 101 times:

The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

= 13 + 13 + 13 + 13 ...... 101 times

Sequence can be defined as the systematic way of representing the data that follows a certain rule of arithmetic.

= 101×(13)

Thus, the resulting number will be a multiple of 13 if 13 is added 101 times option (C) A multiple of 13 is correct.

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Answer:

y=9

Step-by-step explanation:

2+y=-7+2y

2=-7+2y-y

2=-7+y

y=2-(-7)

y=2+7

y=9

Answer:

2 + y = -7 + 2y

collect like terms

y-2y=-7-2

-y=-9

y=9

Step-by-step explanation:

The final concentration of salicylic acid in the ointment is approximately 8.70%.

To calculate the final concentration of salicylic acid in the ointment base, we need to know the total mass of the product after mixing. The final concentration of salicylic acid is expressed as a percentage, which is the mass of salicylic acid divided by the total mass of the product, multiplied by 100.

Let's assume that when you add 8 g of salicylic acid to 84 g of the ointment base, there is no change in the total volume, and the two substances mix completely.

Total mass of the product = Mass of salicylic acid + Mass of ointment base

Total mass = 8 g + 84 g = 92 g

Now, we can calculate the final concentration of salicylic acid:

Final Concentration (%) = (Mass of salicylic acid / Total mass) * 100

Final Concentration (%) = (8 g / 92 g) * 100 ≈ 8.70%

So, the final concentration of salicylic acid in the ointment is approximately 8.70%.

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Answer:

-17/10

Step-by-step explanation:

-4(1/8)-3(2/5)=-4/8-6/5=-20/40-48/40=-68/40=-17/10

Assumption:

Something is missing in question. If we see deeply it is apparent that there is some issue with option b i.e. B) 8 − 4x 10 = 4 + 2x we assume that the questioner want to type B) 8-4x^10 = 4 + 2x.

Answer:

The correct answer is B) 8-4x^10 = 4 + 2x.

Step-by-step explanation:

All equations given is the question can be solve easily to determine the value of x. However if we solve equation mentioned in option b we cannot  get single answer easily.

For example value of x in eq given in option A

15x + 123 = 5x+4

1oX = -119

 X = -119/10

Answer:

The answer is d

Step-by-step explanation:

i just did it lol

Answer:

Step-by-step explanation:

When you add the numbers of students with A's in history and math, you get  8+15 = 23. However, this counts the 3 kids who got A's in both subject two times! So, there are 23-3=20 (20 students) different students who got an A in at least one of the courses. That gives us 35-20=15 who didn't get an A in either.

So, the answer is 15!!

Hope this helped, have a great day! :D

Answer:

Step-by-step explanation:

the easiest way is to convert these fraction to decimals because as you can see on the number line the numbers are whole and decimals on the small tik mark

-3 3/4 would convert to as -3.75

1/2 would convert into 0.5

now plot those on a number line

*remember the small tiks are worth .25*