The focus of a parabola is (3,-7) and the directrix is y = -4.What is an equation of the parabola?
Answers
Answer:
(a) (x -3)^2 = -6(y +5.5)
Step-by-step explanation:
The equation of a parabola can be written as ...
(x -h)^2 = 4p(y -k)
where (h, k) is the vertex, and p is the distance from the focus to the vertex.
The vertex is half-way between the focus and directrix, so is ...
(h, k) = (1/2)((3, -7) +(3, -4)) = (3, -5.5)
The focus is at y=-7, and the vertex is at y=-5.5, so the distance between them is ...
-7 -(-5.5) = -1.5
Then the equation for the parabola is ...
(x -3)^2 = 4(-1.5)(y -(-5.5))
(x -3)^2 = -6(y +5.5) . . . . matches the first choice
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Find the distance between the two points in simplest radical form. (4,3) and (−2,0)
A.
2.4 feet
B.
7.0 feet
C.
13.0 feet
D.
10.9 feet
i think B not i'm not 100% sure plz help me and would u plz explain how u got the answer thank u :)
Answers
One of the legs is 5 feet.
We need to find the height.
a^2 + 5^2 = 12^2
a^2 + 25 = 144
a^2 = 144 - 25
a^2 = 119
a = √119
a ≈ 10.9 feet
The ladder reaches up 10.9 feet.
Answer:
that is correct i took the test 10.9
Step-by-step explanation:
Answers
Answers
The quantity of pure water is 64 gallons which are to be evaporated.
What is an expression?
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The total amount of salt must be equal before and after evaporation.
Multiply the percent of salt in the solution before evaporation by the total gallons of solution
= 12% x 160 gallons convert 12% to decimal form (12% ÷ 100)
= 0.12 * 60
Subtract the number of gallons of pure water that should be evaporated from the total number of gallons of the solution and multiply by the percent of salt in the solution after evaporation
= 20% * (160 - x)convert 20% to decimal form (20% ÷ 100)
= 0.20(160 - x)
Set the before & after evaporation equations equal to one another to solve for x.
0.12 x 160 = 0.20(160 - x)
19.2 = (0.20 * 160) + (0.20 * -x)
19.2 = 32 - 0.20x
-12.8 = -0.20x
64 gallons = x
Therefore, the quantity of pure water is 64 gallons which are to be evaporated.
To know more about an expression follow
#SPJ2
The total amount of salt must be equal before and after evaporation.
STEP 1
BEFORE EVAPORATION: multiply the percent of salt in the solution before evaporation by the total gallons of solution
= 12% * 160 gallonsconvert 12% to decimal form (12% ÷ 100)
= 0.12 * 60
STEP 2
AFTER EVAPORATION: subtract the number of gallons of pure water that should be evaporated from the total number of gallons of the solution and multiply by the percent of salt in the solution after evaporation
= 20% * (160 - x)convert 20% to decimal form (20% ÷ 100)
= 0.20(160 - x)
STEP 3
Set the before & after evaporation equations equal to one another to solve for x.
0.12 * 160= 0.20(160 - x)multiply 0.20 by each term in parentheses
19.2= (0.20 * 160) + (0.20 * -x)multiply in parentheses
19.2 = 32 - 0.20xsubtract 32 from both sides
-12.8= -0.20xdivide both sides by -0.20
64 gallons= x
CHECK:substitute x= 64 into the step 3 equation
0.12 * 160= 0.20(160 - x)19.2= 0.20(160 - 64)subtract in parentheses19.2= 0.20(96)19.2= 19.2
ANSWER: 64 gallons of pure water should be evaporated.
Hope this helps! :)
Answers
Answer:
Step-by-step explanation:
Let the equation of the line is y = mx + c
where m = slope = 3
and c = y-intercept
Now the equation of this line will become
y = 3x + c
Since this line passes through (2, )
so = 6 + c
c = - 6
=
So the line will be y = 3x +
y+1/2=3(x-2)
or y=3x-13/2
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∴ 70,000 ÷ 0.2 = the answer
Answers
Answer:
y=x^2
Step-by-step explanation:
if you look at it, x is constantly multiplying itself so-