Arrange the parabolas represented by the equations in increasing order with respect to the y-values of their directrixes.1: y = -x2 + 3x + 8
2: y = 2x2 + 15x + 18
3: y = -x2 + 7x + 14
4: y = -2x2 + 9x + 7
5: y = x2 + 13x + 5
6: y = -x2 + 8x + 5
7: y = -2x2 + 4x + 8
Answers
P is distance from vertex to directix
remember to subtract P from the y value of the vertex (p-k) and that y value is the directix, y=p-k
nut
ok so one way is to just graph them on a graphing utility
remember if the graph opens up, then the directix is below that
or we can convert to 4P(y-k)=(x-h)^2 form where P is distance from directix
I will only convert the 1st one fully, you should be able to do the rest
1. y=-x^2+3x+8
multiply both sides by -1 since we don't like the x^2 term negative
-y=x^2-3x-8
add8 to both sides
-y+8=x^2-3x
take 1/2 of linear coeficient and square it and add to both sides
-3/2=-1.5
(-1.5)^2=2.25
-y+10.25=x^2-3x+2.25
factor perfect square
-y+10.25=(x-1.5)^2
force undistribute -1 in left side
(-1)(y-10.25)=something, we don't care anymore for now
factor out a 4 in -1
4(-1/4)(y-10.25)
k=10.25
p=-1/4=-0.25
directix=k-p=10.25-(-0.25)=10.5
directix is y=10.5
basically completee the square with x and find P by force factoring a 4 out
2. directix: y=-1.75
3. directix: y=1.5
4. directix: y=17.25
5. d: -37.5
6. d: 9.25
7. d=2.625
order them yourself
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An electronics company is planning to introduce a new line of computers. For the 1st year, the fixed costs for setting up the production line are $200,000. The variable costs for producing each computer are $40. the revenue from each computer is $65. find the total profit P(x) from the production and sale of x computers and break-even point.
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Write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b is the y-intercept:Part A) Passes through (2, 5) and m = 3/4 Part B) Passes through (−3, 2) and (1, −3) Part C)m=2/5 and y-intercept =-6 Part D) x-Intercept = 4 and y-intercept = −2 Part E) Passes through (−2, 2) and parallel to 4x − 3y − 7 = 0
Answers
Answer:
129.032258064516129
Step-by-step explanation:
Final answer:
To convert 3.1 miles into laps on a 400m track, we first convert miles to meters, getting approximately 4988.954 meters. Dividing by 400 meters per lap, we find the distance is approximately 12.5 laps.
Explanation:
The first step is to convert miles into meters, because the laps are measured in meters. There are approximately 1609.34 meters in a mile. So, 3.1 miles would be approximately 4988.954 meters (3.1 x 1609.34 = 4988.954).
As each lap is 400m, we can determine the number of laps by dividing the total distance in meters by the length of one lap. So, 4988.954 meters divided by 400 meters per lap gives us approximately 12.5 laps. Since we need to round to the nearest tenth, our final answer becomes 12.5 laps.
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Answers
Answer:
Step-by-step explanation:
to find increased percent
increase amount = $70 - $40
=$30
increase percent = increase amount /original amount *100%
=30/40 *100%
=3000/40
=75%
to find decrease percent
decrease amount = $70 - $40
=$30
decrease percent = decrease amount /original amount *100%
=30/70 *100%
=3000/70
=42.85 %
A.8√35
B.12√7
C.10V7
D.9V35
Answers
The square root of 80 p to the 3rd
Answers
You know the square roots of 16 and p , so you can take them out of the radical.
= (4p) x √(5p)
You should start by factoring the number inside the cube root/radical sign, which in this case is 80. If you remember how to do factor trees, just do that with the number 80. The p is already prime, so you don't need to worry about it at first. (see picture 1)
Now see if there are any triplets of prime numbers. In this case, there is a triplet of twos (see picture 2), so you bring down one 2 to your answer (see picture 3). If there had been two triplets, you would have brought both numbers down and multiplied them.
There should be three prime numbers left: 2, 5, and p. (see picture 4) Go back down to your answer, put a cube root/radical sign next to the 2, and put your prime numbers in the cube root/radical. You should have 2∛2·5p. 2·5 can be simplified to 10, so your final answer will be 2∛10p (see picture 5).
Answers
Answer:
x = 7 and x = -3
Step-by-step explanation:
x^2-4x-21=0
you can factor to get
(x-7)(x+3)=0
then set each equal to 0
x - 7 = 0 and x + 3 = 0
then just solve for x!
x = 7 and x = -3
A. 100 - 20
B. 100 + 20
C. 100/20
D. 100 x 20
Answers
This is because the formula to finding speed is distance divided by time.
Answer:
100/20
Step-by-step explanation: