Answer:
1. LM < PN
2. AD < DC
3. m<CAB < m<CBA
4. m<1 = m<2
Step-by-step explanation:
Recall: an angle measure is relative to the length of the opposite side. That is, the longer the side opposite to an angle, the larger the measure of that angle and vice versa.
1. LM is opposite to <LNM,
PN is opposite to <NLP
m<LNM is less than m<NLP, therefore,
LM < PN
2. AD is opposite to <ABD
DC is opposite to <DBC
m<ABD is less than m<DBC, therefore,
AD < DC
3. m<CAB is opposite to CB
m<CBA is opposite to CA
CB is less than CA, therefore,
m<CAB < m<CBA
4. The side opposite to <1 is congruent to the side opposite to <2.
Therefore,
m<1 = m<2
<h3>
Answer: 65</h3>
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Explanation:
We'll need to compute the difference quotient. In this case, we need to find what is equal to. It's called a difference quotient because there's a subtraction in the numerator (aka "difference") and we're dividing to form the quotient.
The idea is that as h approaches 0, then that expression I wrote will approach the derivative we're after. Keep in mind that h will technically never get to 0 itself. It only gets closer and closer.
Anyways, let's compute first
Then we'll subtract off g(t)
A very important thing to notice: the terms that don't have any 'h's in them have been canceled out (eg: 5t^2 combined with -5t^2 added to 0). Why is this important? It's because we need to factor 'h' out and we'll have a pair of 'h's cancel like so
The left hand side cannot have h = 0, or else we have a division by zero error. But if we approached 0 (not actually getting there), then the expression 5h+10t+5 will approach 5(0)+10t+5 = 10t+5
---------------------
In short: The derivative of is
In terms of symbols,
Later on in calculus, you'll learn a shortcut so you won't have to compute the difference quotient every time you need a derivative. Refer to the power rule for more information.
After we find the derivative, it's as straight forward as plugging in t = 6 to compute g ' (6)
Side note: This tells us that the slope of the tangent line is m = 65 when t = 6. In other words, this line is tangent to g(t) when t = 6, and this particular tangent line has slope m = 65.
Step-by-step explanation:
To tell if JKON and JKLM are similar, compare the ratios between corresponding sides. For example:
JK / KO = 5/8
JK / KL = 5/22
The ratios aren't the same, so the shapes aren't similar.
63+82+m∠DCE=180
145+m∠DCE=180
m∠DCE=35
Answer:
160
Step-by-step explanation:
is there 240 seventh graders in total? If so all you have to do is:
240 x 2/3
which equals 160 seventh graders.