The distance between the points C(-3,1) and D(5,6) is 10.3 units.
<u>Step-by-step explanation:</u>
Let us consider CD is a line segment.
The point C is (-3,1) and D is (5,6).
The Cartesian formula for line is used to find the length between the CD.
Distance between two points = 
.
The points are (-3,1) and (5,6).
=
.
=
=
.
=
.
=
.
=10.295 ≈ 10.3.
Distance between two points 10.3 units.
Answer: Choice B
a_n = 10(1/2)^(n-2) is the nth term
average rate of change = -35/3
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Explanation:
Each time x increases by 1, y is cut in half. For instance, going from (2,10) to (3,5) shows this.
If we want to go in reverse, decreasing x by 1 will double the y value. So (1,20) is another point and (0,40) is another. We'll be using (0,40) and (3,5) because we want the average rate of change from x = 0 to x = 3. I'm using x in place of n here.
Use the slope formula to find the slope of the line through (0,40) and (3,5)
m = (y2-y1)/(x2-x1)
m = (5-40)/(3-0)
m = -35/3
The negative slope means the line goes downhill as you read it from left to right. The average rate of change from n = 0 to n = 3 is -35/3
The nth term of this geometric sequence is 20(1/2)^(n-1) since 20 is the first term (corresponds to n = 1) and 1/2 is the common ratio. Your teacher has done a bit of algebraic manipulation to change the n-1 into n-2. This means the 20 has to change to 10 to counterbalance.
In other words, 20(1/2)^(n-1) is equivalent to 10(1/2)^(n-2) when n starts at n = 1.
In analyzing the given diagram which is a combination of two right angle triangle, the value of sin∠L is 5/13.
<h3>What is the value of sin∠L?</h3>
Given that angle ONM is a right angled triangle, we can find length of OM using the Pythagorean theorem.
c = √( a² + b² )
OM = √( 4² + 3² )
OM = √( 16 + 9 )
OM = √25
OM = 5
Next, angle OML is also a right angled triangle, we can get the hypotenuse LO.
c = √( a² + b² )
LO = √( OM² + ML² )
LO = √( 5² + 12² )
LO = √( 25 + 144 )
LO = √169
LO = 13
Now, to get sin∠L, we use the mnemonic: SOHCAHTOA
sinθ = opposite / hypotenuse
sin∠L = OM / LO
sin∠L = 5/13
Therefore, in analyzing the given diagram which is a combination of two right angle triangle, the value of sin∠L is 5/13.
Learn more about Pythagorean theorem here: brainly.com/question/343682
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Hey there!
If she missed 4 problems, and that took off 20%, that means 4 is 20% of the total items.
20% is the same as 1/5 of the total amount, since there are 5 20s in 100.
So, we can simply multiply 4 by 5 to get the total amount of problems.
4 x 5 = 20
This means there were 20 problems on the test.
Hope this helps!
Option A
<em><u>Solution:</u></em>
Given expression is:
To evaluate the expression, let us make the exponent of 10 same
[ Here, decimal point is moved three times left, so add 3 ]
Therefore,
Thus Option A is correct
