If x2 = 60, what is the value of x?

the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x - 1}{2} \).[/tex]

To find the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex], we'll switch the roles of [tex]\( x \)[/tex]  and [tex]\( y \)[/tex] and solve for [tex]\( y \)[/tex].

1. Start with the original function:

  [tex]\[ f(x) = 2x + 1 \][/tex]

2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:

  [tex]\[ x = 2y + 1 \][/tex]

3. Solve for [tex]\( y \)[/tex]:

  [tex]\[ x - 1 = 2y \][/tex]

  [tex]\[ \frac{x - 1}{2} = y \][/tex]

So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:

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

Therefore, the inverse of the function [tex]\( f(x) = 2x + 1 \)[/tex] is [tex]\( f^{-1}(x) = \frac{x - 1}{2} \).[/tex]

find volume of tray:

convert 4cm to inches 4/2.54 = 1.575 inches

volume = 10*14*1.575 = 220.47 cubic inches

 1 gallon = 231 cubic inches

231-220.47 = 10.53 more paint in a gallon

 so the paint will over fill the tray by 10.53 in3

Answer:

The answer is:

The paint will overfill the tray by 10.53 in3 (cubic inches).

Step-by-step explanation:

In order to determine the correct option, first we have to get the volume of the tray.

The volume of the tray is a solid prism, where its formula is:

width=10 in

length=14 in

deep=4 cm=[tex]\frac{4}{2.54} =1.575[/tex] in

Volume=[tex]10*14*1.57=220.5[/tex] cubic inches

The value of the deep measure was changed from cm to inches units.

We subtract the allowed volume of the gallon with the volume tray:

231-220.5=10.5 cubic inches

It means that 1 gallon of paint is enough to paint the tray, where the remaining paint is 10.5 cubic inches.

Finally, the correct option is:

The paint will overfill the tray by 10.53 in3 (cubic inches).

it answer is c ,d and f

The correct equations are [tex]y^2 = x[/tex], [tex]y^2 = 10x[/tex] and [tex]y^2 = 5x[/tex] respectively

A parabola is symmetrical open plane curve that is created by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.

In the given question, Lauren describes a parabola that has positive non zero coordinate value on

The equation of focus of a parabola is given as

[tex]y = a(x - h)^2 + k[/tex]

In the options given,

[tex]y^2 = x[/tex] is correct

[tex]y^2 = 10x[/tex]  is also correct and

[tex]y^2 = 5x[/tex] is correct

This shows that only option c, d and f are the right answers.

The correct equations are [tex]y^2 = x[/tex], [tex]y^2 = 10x[/tex] and [tex]y^2 = 5x[/tex] respectively

Learn more on focus of a parabola here;

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Answer:

All real numbers greater than 0.

Step-by-step explanation:

We have the function, [tex]f(x) = 2(\frac{1}{4})^{x}[/tex].

'Reflection over y-axis means to flip the graph over y-axis', which changes the function by f(x) becomes f(-x).

So, after reflection, the given function transforms into,

[tex]g(x)=f(-x)[/tex]

i.e. [tex]g(x)=2(\frac{1}{4})^{-x}[/tex]

According to the graph of the function g(x), we see that,

Range of [tex]g(x)=2(\frac{1}{4})^{-x}[/tex] is the 'Set of all real non-negative numbers' i.e. {x | x > 0} i.e. [tex](0,\infty)[/tex]

Answer:

An example of a data set that satisfies each of these conditions is:

[72, 75, 79, 80, 80, 81, 82, 84, 88, 94, 98]

Step-by-step explanation:

Let's start by defining the terms:

Mean: Average of all numbers

Median: Middle score in a set of given numbers

Mode: Most frequently occuring number

Range: Difference between the lowest and highest number

There are many possible data sets for these conditions, but these are the numbers I found work. I'm sure there is a simpler way to figure this out, but this way makes the most sense to me. This was my process.

We know that all of our numbers need to add up to 913. We know this because our mean is 83 and there are 11 numbers (83X11=913). We can check this by taking 913/11 (the number of scores)=83 (mean)

We know that the median needs to be 81. When the numbers are in order lowest to highest, we would need to have 5 numbers below 81 and 5 numbers above 81.  The sixth number in the set should be 81.

We know the mode is 80, so 80 has to be in our data set at least twice with all other numbers appearing less often. This is why I put two 80s and one of every other number in my data set.

I then picked the lowest number in my data set, ensuring that a range of 26 would allow me enough space on both sides of the median. Since I have my lowest number, I can add 26 and get the highest number in my data set.

Once I have the main numbers, I just need to put other numbers before and after the median that would give me a sum of 913 (see the section about the mean). These can be any numbers that go in the right order as long as they don't change any of the numbers we've already established and they total 913.

Here's work you can copy and paste:

7 cups + 3 liters = 9.8 pints

7c+3l=9.8p

5 liters - 9 cups = 6 pints

5l+9c=6p

Cups and Liters

7c+3l=9.8p

p= 7c+3l/9.8 (put in equation 2)

5l-9c= 7c+3l/9.8

49l-88.2c=7c+3l

49l-3l=7c-88.2c

46l=45.2c

1Liter = 2.1 Cups

Cups and Pints

7c+3l=9.8p

3l=9.8p-7c

l=9.8p-7c/3 (put in equation 2)

5(9.8p-7c/3)-9c=6p

(49p-35c/3)-9c=6p

49/3p-35/3c-9c=6p

49/3p-6p=35/3c+9c

31/3p=62/3c

1 Pint = 2 Cups

Pints and Liters

7c=9.8p-3l

c=9.8p-3l/7 (put in equation 2)

5l-9(9.8p-3l/7)=6p

5l-63/5p+27/7l=6p

5l+27/7l=6p+63/5p

62/7l=93/5p

​1 Liter = 2.1 Pints

Answer:

a and c

Step-by-step explanation:

Final answer:

To calculate the dog's weight from three years ago, we take the current weight and divide it by 1.50 since the weight increased by 50%. The equation 1.50 * x = 45 pounds results in x = 30 pounds, indicating the dog weighed 30 pounds three years ago.

Explanation:

The question concerns the original weight of a dog whose weight increased by 50% over a period of three years, bringing its weight to 45 pounds at the end of that period. To determine the dog's weight from three years ago, we use the following steps:

Understand that a 50% increase implies that the final weight is 150% of the original weight (100% + 50%).

Represent the original weight as 'x'.

Set up the equation: 1.50 * x = 45 pounds.

Divide both sides by 1.50 to solve for 'x': x = 45 / 1.50.

Calculate 'x' to find that 'x' equals 30 pounds.

Therefore, the dog weighed 30 pounds three years ago.

In the given problem, the square root of 1.69 is 1.3.

The square root of a non-negative real number is a value that, when multiplied by itself, results in the original number. In mathematical notation, the square root of the number "x" is represented by the symbol "√x."

The square root is an inverse operation of squaring, which means that if one squares a number and then take its square root, he or she gets back to the original value. The concept of the square root is nearly related to obtaining the side length of a square with a given area or obtaining the magnitude of a vector in mathematics.

1.69 also can be written as [tex]\dfrac{169}{100}[/tex] in fraction form.

[tex]\sqrt{\dfrac{169}{100}} = \sqrt{\dfrac{13^2}{10^2} }[/tex]

         [tex]= \sqrt{(\dfrac{13}{10} )^2}\\= \dfrac{13}{10} \\= 1.3[/tex]

Thus, 1.3 is the square root of 1.69.

Learn more about square roots here:

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The answer is (x + f) + g

area for triangle = 1/2 x h x b

so 1 triangle = 1/2 x 5.12 x 3.23 = 8.2688 since the triangles are congruent they are equal so 8.2688 x 2 = 16.5376

 round that up to 17

Answer is C 17 square inches

Answer:

30.76 [tex]ft^{2}[/tex]

Step-by-step explanation:

To calculate the circumference of a circle you just have to multiply the diameter by pi.

C= D*[tex]\pi[/tex]

And in order to calculate the value of the diameter you have to clear the formula for the area.

A= [tex]r^{2} *\pi[/tex]

r=[tex]\sqrt{\frac{24 \pi }{\pi } }[/tex]

r=[tex]\sqrt{24}[/tex]

r=4,89

Once we get the radius, we only have to calculate the diameter:

D=2r=9,79

now we just calculate the circumference:

C=D*[tex]\pi[/tex]= (9.79)(3.14)= 30.76

Answer: There is 1500 squared feet of the house.

Explanation:

Since we have given that

Dimensions of a house is given by

[tex]45\ yards\ and\ 10\ yards[/tex]

So, we need to find the square footage of the house ,

Area of house is given by

[tex]Length\times Breadth\\=45\times 10=4500\ yards^2[/tex]

Now, we'll change it into feet ,

As we know that

[tex]1\ yard=3\ feet[/tex]

So, total squared footage of the house is given by

[tex]\frac{4500}{3}=1500\ feet^2[/tex]

Hence, there is 1500 squared feet of the house.