I think the answer is 11 3
Let's try plugging in some negative numbers. Let's do x=-1. 5+-1=4. So we know that if we put in a negative number for x, then n will be positive. But what if we do a number greater than -5, because 5+-5=0. So let's try x=-6. So 5+(-6)=-1. Hmm. So here it is. We know that any number under -5 will be positive and any number above -5 will be negative.
You don't say whether this is a right triangle or not.
Assuming it is a right triangle, then we use the Pythagorean Theorem to determine the length of the hypotenuse:
(hypo) = (length of third side) = √(12^2 + 4^2) = √(144+16) = √160 = 4√10.
This is approx. 12.65 inches. Since this does not match any of the possible answer choices, we'll have to take a different approach to answering this question.
Given that 2 sides of the given triangle are 12 and 4 inches, respectively, we see that the 3rd side has to be longer than 8 inches; otherwise we'd have three line segments on the same line, not forming a triangle.
By this reasoning, 9 inches is the only possible answer that could be correct. With sides 12, 9 and 4 inches, the triangle would be obtuse and appear quite flat, but not be part of a straight line as with a third side of 8.
Answer:
a. A minimum of 300
Step-by-step explanation:
If her bill is $142 then it is a sum of the flat rate plus the money she pays for all the smses she sent. As an equation, it can be expressed this way
106 + 0.12x = 142 where x is the number of smses
0.12x = 36
x = 300 smses
So if we were told that she pays $142 per month, we'd know that she sends 300 smses. But we are told she pays AT LEAST $142 so there is a possibility that she sends even more than 300 smses
Answer: Hello mate!
Let's define the variable t as the time, and define t = 0 as the moment when the first skater starts to move:
We know that the speed of the first skater is 8 m/s, and we need to find the position as a function of time, then we need to integrate the velocity over time
if v1(t) = 8m/s
then p1(t) = (8m/s)*t
now we also know that the second skater has a velocity of 9m/s and enters in the frozen lake at t= 10s.
then the velocity of the second skater is: v2(t) = 9m/s, and the position is:
p2(t) = (9m/s)*(t - 10s)
now we want to know how many seconds after the second skater starts are needed for the second skater to overtake the first one.
this is equivalent to see when his positions will be equal.
so p1(t) = p2(t):
(8m/s)*t = (9m/s)(t - 10s) = (9m/s)*t - 90m
(8m/s)*t - (9m/s)*t = -90m
(-1m/s)*t = 90m
t = 90m/(1m/s) = 90s
Then in t = 90 seconds, the second skater will overtake the first one, and knowing that the second skater started at t = 10 seconds; there are 80 seconds after the second skater started needed to overtake the first skater.
