What is the domain of the function f(x) = 2x^2 - 3?

1 answer:

4 0

Domain: Set of all real numbers

If you want to express the domain in set-builder notation, then you'd write something like $\left\{x|x\in\mathbb{R}\right\}$ which is fancy notation to basically say "x is any real number"

If you want to write the domain in interval notation, then you'd write $\left(-\infty, \infty\right)$ which is the interval from negative infinity to positive infinity. In other words, the entire real number line.

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The domain is the set of all real numbers because we don't have any restrictions to worry about. There are no division by zero errors. There are no cases where we have to worry about taking the square root of a negative number, or anything similar. Any number can replace x to generate an output for y.

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A rectangular prism has a volume of 144 cubic feet. The height of the prism is 6 feet. Give one possible pair of dimensions for

IrinaK [193]

You're given the volume and height of rectangular prism.
To find the possible length and width: √144/6=24;
24 is the product of length and width, so now just divide 24 by 4 or 6 or 2 or...
24/4=6.
The possible length and width is 4 and 6.
Check: 4×6×6=144ft³

6 0

3 years ago

~~~20 POINTS~~~

ASHA 777 [7]

I'm so sorry for the late answer!

(a) Rectangular container
There are 3 pairs of congruent sides. Each side's area can be solved by multiplying either 12, 8, or 3. Then because for each side, there is another side that is exactly the same, we can multiply by 2.
(2*12*8) + (2*12*3) + (2*8*3) = 312

(b) Surface Area of a cylinder is $2 \pi r^{2} +2 \pi rh$
We know that r is 2 and that the whole expression is equal to 312.
Plug 2 back into the equation and set it equal to 312.
$2 \pi *4+2 \pi *2h = 312 \\ 4 \pi *h = 312-8 \pi \\ h = \frac{312-8 \pi }{4 \pi } = 23$
The height of the cylinder has to be around 23 inches.

4 0

3 years ago

Please explain,<br> 2 (4m-5) - (6m-11) =33

zlopas [31]

Answer:

m = 16

Step-by-step explanation:

2(4m - 5) - (6m - 11) = 33 (Given)

8m - 10 - 6m + 11 = 33 (Distribute)

2m + 1 = 33 (Combine like terms)

2m = 32 (Subtract 1 on both sides)

m = 16 (Divide 2 on both sides)

You can check by substituting your answer into the equation:

2(4(16) - 5) - (6(16) - 11) = 33

2(64 - 5) - (96 - 11) = 33

2(59) - (85) = 33

118 - 85 = 33

33 = 33

7 0

3 years ago

Find the x - and y -intercepts of the graph of the linear equation -4x+8y=-16 .

Sav [38]

Answer:

x: (4, 0)
y: (0, -2)

Step-by-step explanation:

To find the x-intercept, set y=0 and solve for x. That will mean dividing by the coefficient of x:

-4x +0 = -16

x = -16/-4 = 4 . . . . the x-intercept

To find the y-intercept, set x=0 and solve for y. That will mean dividing by the coefficient of y:

0 +8y = -16

y = -16/8 = -2 . . . . the y-intercept

The x- and y-intercepts are (4, 0) and (0, -2), respectively.

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<em>Additional comment</em>

The standard form equation of a line, ax+by=c, is especially nice for finding the intercepts, as they are always (c/a, 0) and (0, c/b). Once you see this, you can do a question like this in your head.