Answer:
12 3/4 same slope fro both
13 DE = 5, CB = 10
14 see below
Step-by-step explanation:
12. the slopes are the same
D(0, 3) E(4, 6) slope is (change in y)/(change in x)
change in y = 3 to 6 is a change of +3
Change in x = 0 to 4 is a change of +4
slope is 3/4
13 To fine lengths you can distance formula or Pythagorean theorem (spoiler: they are related to each other)
DE² = 3² + 4²
DE² = 9 + 12
DE² = 25
√DE² = √25 = 5
DE = 5
and
CB² = 6² + 8²
CB² = 36 + 64
CB² = 100
√CB² = √100 = 10
CB = 10
14. since the slopes are the same are DE is 1/2 or CB its is the mid segment. because (taken from mathopenref.com/trianglemidsegment.html)
The midsegment is always parallel to the third side of the triangle. In the figure above, drag any point around and convince yourself that this is always true.
The midsegment is always half the length of the third side. In the figure above, drag point A around. Notice the midsegment length never changes because the side BC never changes.
A triangle has three possible midsegments, depending on which pair of sides is initially joined.
The value of the composition of functions f(g(3)) is given by (A) -1.
Here given that the functions are,
f(x) = 3x-7
g(x) = (x+1)/(x-1)
To find the value of g(3) we have to first substitute the value x = 3 in the given function g(x), doing that we get,
g(3) = (3+1)/(3-1) = 4/2 =2
Thus the value of g(3) = 2
Now in order to find the value of composition of functions f(g(3)) we have to substitute the value of x = g(3) = 2 in the given function f(x), doing that we get,
f(g(3)) = f(x = g(3)) = f(x = 2) = f(2) = 3*2-7 = 6-7 = -1
Thus the value of the required composition of functions f(g(3)) is given by -1.
Hence the correct option is given by (A).
<em>The question is incomplete. Find the full content below. </em>
Consider these functions:
f(x) = 3x-7
g(x) = (x+1)/(x-1)
What the value of f(g(3))?
(A) -1
(B) 0
(C) 3
(D) 5
Learn more about Composition of Functions here -
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Step-by-step explanation:
y= 1
when x=2
here
when x= 3
y=4
Answer:P(t) = 10t - 400
Step-by-step explanation:
Selling price of each ticket = $10
Cost of setting up the dance= $400
Profit = Revenue - cost
Revenue = price × quantity
Revenue that will maximize profit = 10t
where t= quantity of tickets that maximises profits
Cost = $400
Profit(t) = Revenue - cost
P(t)= 10t - 40
hmu if you need sumin els
The correct first step to solving the system of equations in the most efficient manner is x = -4y +19.
The given system of equations is;
<h2>What is the first step to solving an equation?</h2>
The first step would be to rearrange the variables in the second equation so we have a defined expression for x.
We would want to do this so we could then plug in the defined expression for x into the other equation and solve for the other variable.
x + 4y = 19
Rearrange this by getting the 4y to the other side.
We can get 4y on the other side by subtracting 4y from both sides
x + 4y - 4y = 19 - 4y
x = -4y + 19
Hence, the correct first step to solving the system of equations in the most efficient manner is x = -4y +19.
To know more about the System of equations click the link given below.
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