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3 years ago

What is the domain and range of x+5

1 answer:

3 0

The domain of a function is the set of all acceptable input values (X-values). The range of a function is the set of all output values (Y-values).

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2b plus 4a minus a minus 2 plus 12b

jarptica [38.1K]

The value of the expression 2b plus 4a minus a minus 2 plus 12b is 3a + 14b - 2.

Expression:

An expression is defined as the a combination of operators, constants and variables. And it may consist of one or more operands, and zero or more operators to produce a value.

Given,

Here we have the statement "2b plus 4a minus a minus 2 plus 12b".

Now, we have to find the simplified form of this statement.

In order to find the simplified form,

First we have to convert the statement into expression form, then we get

2b plus 4a minus a minus 2 plus 12b = 2b + 4a - a - 2 + 12b

Now, we have to combine the like terms, then we get,

=> (2b + 12b) + (4a - a) - 2

Perform the appropriate arithmetic operations, then we get the simplified form of the expression as,

=> 14b + 3a - 2

Now, we have to arrange them in order then we get,

=> 3a + 14b - 2

To know more about Expression here.

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8 0

1 year ago

What’s the domain and range of:<br> log(√(2x-1) + 3 )<br> Please explain how you got it too!!

Radda [10]

Two main facts are needed here:

1. The logarithm $\log x$ , regardless of the base of the logarithm, exists for $x>0$ .

2. The square root $\sqrt x$ exists for $x\ge0$ .

(in both cases we're assuming real-valued functions only)

By (2) we know that $\sqrt{2x-1}$ exists if $2x-1\ge0$ , or $x\ge\dfrac12$ .

By (1), we know that $\log(\sqrt{2x-1}+3)$ exists if $\sqrt{2x-1}+3>0$ , or $\sqrt{2x-1}>-3$ . But as long as the square root exists, it will always be positive, so this condition will always be met.

Ultimately, then, we only require $x\ge\dfrac12$ , so the function has domain $\left[\dfrac12,\infty)$ .

To determine the range, we need to know that, in their respective domains, $\sqrt x$ and $\log x$ increase monotonically without bound. We also know that $x=\dfrac12$ at minimum, at which point the square root term vanishes, so the least value the function takes on is $\log3$ . Then its range would be $[\log3,\infty)$ .

3 0

3 years ago

Dominic invested $520 in an account in the year 1995, and the value has been growing exponentially at a constant rate. The value

Tom [10]

Answer:

I believe the answer is $936.64

Step-by-step explanation:

I hope this helps!

6 0

2 years ago

Calculate the surface area and volume of the shape below.

pav-90 [236]

Surface area

Let's calculate the surface area of the rectangular block. It has length, width and height of L = 15, W = 5, H = 8. The surface area is going to be

SA = 2*(LW+WH+LH)

SA = 2*(15*5+5*8+15*8)

SA = 470

This is without the cylinder attached to the top surface. If we account for that, then we'll have to subtract off the area of the circle covered up which is

pi*r^2 = pi*3^2 = 9pi = 28.27433 approximately

So 470-28.27433 = 441.72567 is the approximate surface area of the rectangular block after we subtract off the circular portion covered up by the cylinder.

----------

The lateral surface area of the cylinder is approximately

2*pi*r*h = 2*pi*3*4 = 24pi = 75.39822

Which adds onto the top circular area of 28.27433 to get 28.27433+75.39822 = 103.67255

Meaning that 103.67255 is the surface area for the cylinder portion. Again we don't worry about the bottom portion as it's not part of the outer surface.

---------

Overall, the total surface area of this compound 3D figure is

(surface area for rectangular portion) + (surface area cylinder portion) = 441.72567+103.67255 = 545.39822

When rounding to the nearest whole number, the total surface area is about 545 square cm

<h3>Answer: 545 square cm</h3>

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

Volume

The rectangular block has volume L*W*H = 15*5*8 = 600 cubic cm

The cylinder has volume pi*r^2*h = pi*3^2*4 = 113.0973355 approximately

Add the two volumes to get 600+113.0973355 = 713.0973355 and this rounds to 713. We don't have to do any subtraction in this section.

<h3>Answer: 713 cubic cm</h3>

4 0

3 years ago

Josh is building a sandbox for his little sister. He uses these plans, which have a scale of 2 in. : 3 ft.

skelet666 [1.2K]

Answer:

Width of 6ft and length of 9ft

Step-by-step explanation:

The sandbox has a ratio of 2:3. If you plug the numbers in with the ratio, you can find the actual dimensions.

Let x be the length

Let y be the width

(Length)

2in / 3ft = 6in / (x)ft

2in / 3ft = 6in / <u><em>9ft </em></u>

(Width)

2in / 3ft = 4in / (y)ft

2in / 3ft = 4in / <em><u>6ft</u></em>

6 0

2 years ago