Answer:
Domain: all real numbers
Range: all real numbers
Step-by-step explanation:
The domain is all x values, and the range is all y values.
<u><em>Domain:</em></u>
The domain is all real numbers except where the slope is undefined (a vertical line). In this case, no number makes the expression undefined, so the domain is:
all real numbers
<u><em>Interval notation:</em></u><em> </em>(-∞,∞)
all negative numbers and positive numbers (all real numbers)
<em><u>Set-Builder Notation:</u></em> {x | x ∈ R
}
<em><u>Range:</u></em>
The range is the set of all valid values. Graph the line and check. Since all values of y are valid, the range is:
all real numbers
<u><em>Interval notation:</em></u><em> </em>(-∞,∞)
all negative numbers and positive numbers (all real numbers)
<em><u>Set-Builder Notation:</u></em> {x | x ∈ R
}
:Done
Answer:
100 in²
Step-by-step explanation:
The area of the banner is equal to the area of the initial rectangle minus the area of the cutout triangle.
The rectangle has a height of 8 inches and width of 14 inches, so its area is:
A = (8 in) (14 in) = 112 in²
The triangle has a base of 8 inches and a height of 3 inches, so its area is:
A = ½ (8 in) (3 in) = 12 in²
So the area of the banner is 112 in² − 12 in² = 100 in².
1) This is a combination, so use ⁴⁰C₂.
⁴⁰C₂ = 780
There are 780 handshakes in total.
2) I got my solution by using the combinations formula. Or another way you could do this is to add up... 39 + 38 + 37 + 36 + 35 + 34 + 33 + 32 + 31... +1. You will end up with 780 (I did this to double check my work).
3) The quickest way to figure this out if Drake invited 1,000 people is to use the natural numbers formula = n(n+ 1)/2.
Plug the numbers in: 999(1000)/2 = 499,500
If Drake invited 1,000 people, there would be 499,500 handshakes.
I am guessing you want to round to the tenths, because nothing comes after the hundredths. So it would be 0.9. (But it would stay the same if you are rounding to the hundredths.)
Answer:
x = 0
Step-by-step explanation:
when y is -3, x is 0
