An equation for the parabola would be y²=-19x.
Since we have x=4.75 for the directrix, this tells us that the parabola's axis of symmetry runs parallel to the x-axis. This means we will use the standard form
(y-k)²=4p(x-h), where (h, k) is the vertex, (h+p, k) is the focus and x=h-p is the directrix.
Beginning with the directrix:
x=h-p=4.75
h-p=4.75
Since the vertex is at (0, 0), this means h=0 and k=0:
0-p=4.75
-p=4.75
p=-4.75
Substituting this into the standard form as well as our values for h and k we have:
(y-0)²=4(-4.75)(x-0)
y²=-19x
Answer:
Given that,
The number of grams A of a certain radioactive substance present at time, in years
from the present, t is given by the formula

a) To find the initial amount of this substance
At t=0, we get


We know that e^0=1 ( anything to the power zero is 1)
we get,

The initial amount of the substance is 45 grams
b)To find thehalf-life of this substance
To find t when the substance becames half the amount.
A=45/2
Substitute this we get,


Taking natural logarithm on both sides we get,







Half-life of this substance is 154.02
c) To find the amount of substance will be present around in 2500 years
Put t=2500
we get,




The amount of substance will be present around in 2500 years is 0.000585 grams
Answer:
1) one solution
2) Infinitely many solution
3) no solution
Step-by-step explanation:
The first equation is -14-8x=-2(-3x+7)
Let us expand the right hand side to get:
-14-8x=-2*-3x+-2*7
We multiply -14-8x=6x-14
We group similar terms to get:
-8x-6x=-14+14
Combine similar terms to get:
-14x=0
Divide through by -14 to get:
x=0
2) The second equation is 3+5x=5(x+2)-7
We expand to obtain:
3+5x=5x+5*2-7
Multiply to get:
3+5x=5x+10-7
This gives us
3+5x=5x+3
5x=5x
1=1
There is infinitely many solutions
3) The third equation is: 36-7x=-7(x-5)
We expand to get:
36-7x=-7x+35
Group similar terms;
-7x+7x=35-36
0=-1
This statement is not true so there is no solution.

parallel sides measure :
Area :
height (h) = x
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Therefore, height of Trapezoid is 4 ft
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Answer:
1) √248 = ± 15.7480157
2)√63 = ± 7.93725393
Step-by-step explanation: