answer: 7. if the functions had a negative leading coefficient and is of even degree, which statement about the graph is true?
here is me explaining it:
the pizza would be delivered around 5, give or take 15 minutes. this means it could be delivered anywhere from 4: 45 to 5: 15
let's say 5: 00 is equivalent to 0 on a number line and x represents time. 4: 45 would be equal to -15x because we are 15 minutes behind our starting point, 5: 00. 5: 15 would be equal to 15x because we are 15 minutes ahead of your starting point (which means you're late on the pizza delivery! )
absolute value is very confusing. the basic definition is how far you are from your starting point. if we deliver the pizza at 4: 45 (15 minutes before the starting point) we would be -15. this means we are 15 away from our starting point, 5: 00. that's the absolute value. |-15| (absolute value of negative fifteen) is equal to 15. if you did not understand this i suggest rereading this paragraph.
the normal way you would write this scenario would be 4.75 (4 and 3 quarters, or 4: 45. you can also write as a fraction.) is less than x and x is less than 5.25 (5 and 1 quarter or 5: 15). 4.75< x< 5.25 the reason why i am using numbers is because you cannot represent typical time as values on a graph, number line, or in an equation.
another way to write this scenario is with absolute value. we can write this as |x| being less than or equal to .25 (remember, this just means 15 minutes). |x| ≤ .25.
sorry if the end was confusing. because we are talking about time this whole question is 10x harder. like i said earlier, you cannot represent time as, well, time, in a graph, equation, or number line. i set the values as follows: 1/4 or .25 for 15 minutes, and 1 for 1 hour. this is just a common way to set up graphs involving time.
|x| ≤ .25
i hope this ! : )
tell me if you need more assistance
b: ∠x = 28.6°, ∠y = 31.2°, ∠z = 120.2°
this is one of those questions where "test taking skill" is all you need. the only answer that has angles that sum to 180° is the one shown above. the remaining choices do not describe the angles of a triangle.
if you want to do more work than simply adding the offered numbers, you can also check them against the law of sines. it should be true that
x/sin(x) = y/sin(y) = z/sin(z)
and all of these ratios must be greater than 15, the longest side length.
if you want to solve the triangle from scratch, i'd suggest solving for the largest angle using the law of cosines.
z² = x² +y² -2xy·cos(z)
z = arccos((x² +y² -z²)/(2xy)) = arccos(-75.11/149.4) = 120.182°
now you can find y from the law of sines
y = arcsin(y/z·sin(z)) = 31.242°