Becca's family has 4 gallons of milk. They drink 5/8 gallon per day. How long will their milk last? A. 2 1/2 days B. 4 days C. 4
1 answer:
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Answer:
Step-by-step explanation:
If you're looking for what the half angle of the tangent of theta is, I'm a bit confused as to why you think the angle in the 4th quadrant, x, is relevant. But maybe you don't know it isn't and it's a "trick" to throw you off. Hmm...
Anyways, the half angle identity for tangent is
There are actually 3 identities for the tangent of a half angle, but this one works just as well as either of the others do, so I'm going with this one.
If theta is in QIII, the value of -4 goes along the x axis and the hypotenuse is 5. That makes the missing side, by Pythagorean's Theorem, -3. Filling in our formula:
which simplifies a bit to
and a bit more to
Bring up the lower fraction and flip it to divide to get
which of course simplifies to
-3. Choice A.
Answer:
See attachment
Step-by-step explanation:
We want to graph the system
2x+y=8
-x+2y=6
Let us rewrite the lines in slope intercept form:
y=-2x+8
The first line has a slope of -2 and a y-intercept of 8
The second line has a slope of 1/2 and a y-intercept of 3
We can no graph the lines as shown in the attachment.
Lets say that the two unknown integers are 
and 
.
We know the following things about and :
And, we want to find
.
To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:
So, given what we know about the unknown integers, the previous can be written as:
We can easily solve for:
The answer is 168.
Another approach to solve the problem is, from the two starting equations, compute the values of and , which are 12 and 14, and directly compute their product; however, the approach described is more elegant.
We know the following things about
And, we want to find
To solve this, we'll use the expansion of the squared of the sum of any two inegers; this is expressed as:
So, given what we know about the unknown integers, the previous can be written as:
We can easily solve for
The answer is 168.
Another approach to solve the problem is, from the two starting equations, compute the values of