Answer:
y = 2x − 1
Step-by-step explanation:
By eliminating the parameter, first solve for t:
x = 4 + ln(t)
x − 4 = ln(t)
e^(x − 4) = t
Substitute:
y = t² + 6
y = (e^(x − 4))² + 6
y = e^(2x − 8) + 6
Taking derivative using chain rule:
dy/dx = e^(2x − 8) (2)
dy/dx = 2 e^(2x − 8)
Evaluating at x = 4:
dy/dx = 2 e^(8 − 8)
dy/dx = 2
Writing equation of line using point-slope form:
y − 7 = 2 (x − 4)
y = 2x − 1
Now, without eliminating the parameter, take derivative with respect to t:
x = 4 + ln(t)
dx/dt = 1/t
y = t² + 6
dy/dt = 2t
Finding dy/dx:
dy/dx = (dy/dt) / (dx/dt)
dy/dx = (2t) / (1/t)
dy/dx = 2t²
At the point (4, 7), t = 1. Evaluating the derivative:
dy/dx = 2(1)²
dy/dx = 2
Writing equation of line using point-slope form:
y − 7 = 2 (x − 4)
y = 2x − 1
The functions and their matching properties are:
- y = (1/4)ˣ: y-intercept at (0,1); graph approaches 0 as x increases
- y = 2(1/2)ˣ: y-intercept at (0,2); graph approaches 0 as x increases
- y = 3ˣ: y-intercept at (0,1); graph approaches positive infinity as x increases
<h3>How to match the functions with their properties?</h3>
The functions are exponential functions;
Exponential functions are represented using:
y = abˣ
Where a represents the y-intercept.
Also, when b is less than 1, the graph would approach 0 as the x value increases, otherwise it approaches positive infinity.
This means that the graphs of y = (1/4)ˣ and y = 2(1/2)ˣ would approach 0 as the x value increases
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Answer:
a = - 17
Step-by-step explanation:
5+2a = -29
2a = -29-5
2a = - 34
a = -34/2
a = -17
(-2,8) is the image point of A(8,2)
<h3>What is
Rotation ?</h3>
A rotation is a type of transformation which takes each point in a figure and rotates it a certain number of degrees around a given point.
As we know , the rule for rotation of
is given by :-
(x,y)⇒(-y,x)
In the above formula (x,y) is the point of pre-image and (-y,x) is a point of image.
Since ,given point of pre-image : A(8,2)
After the rotation of
, the image point are :-
(8,2) ⇒ (-2,8)
Therefore,
The image point of A(8,2) is (-2,8) .
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Answer:
22
Step-by-step explanation:
Missy has 156 cards in total. Since we know she has 4 times as many as them, we divide 156 by 4
156/4= 39
Ashe has 17 cards and we still don't know how many Caleb has. Since we know that they have 39 cards together, we need to subtract Ashe's cards to find how many Caleb has
39-17=22
Let's check our work
Caleb has 22 cards
Ashe has 17 cards
Together they have 39
Which is 4 times less than how many cards Missy has
Missy has 156 cards
We are correct!