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Rom4ik [11]
3 years ago
9

Write the equation of the parabola that has the vertex at point (1.5,0) and passes through the point (3,3).

Mathematics
1 answer:
astra-53 [7]3 years ago
4 0

<u>Answer</u>:

3y = 4(x - 1.5)²

<u>Step-by-step explanation:</u>

The equation of the parabola in the vertex form is:

y = a (x-h)² + k

Where: (h,k) the coordinates of the vertex & a is a multiplier

The parabola has a vertex at ( 1.5 , 0 )

So, h = 1.5 , k = 0

∴ y = a (x - 1.5)² + 0

∴ y = a (x - 1.5)²

The parabola passes through points ( 3 , 3 )

∴ 3 = a (3 - 1.5)²

∴ 1.5² a = 3  ⇒ a = 3/1.5² = 3/2.25 = 4/3

∴ y = (4/3) (x - 1.5)²

mukitbly both sides by 3

∴ 3y = 4(x - 1.5)²

So, the equation of a parabola that has a vertex at ( 1.5 , 0 ) and passes through points ( 3 , 3 ) is 3y = 4(x - 1.5)²

See the attached figure.

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14x-y=42 what is the slope
igomit [66]

Answer:

14


Step-by-step explanation:

14x-y=42

14x=42+y

y=14x-42

8 0
3 years ago
What is the shortest board a man must buy in order to cut 3 sections from it, each 4 feet 8 inches long?
kakasveta [241]

Convert the mixed number to inches. 3 feet 8 inches = 44 inches (12 inches per foot x 3 feet= 36 inches + 8 inches= 44 inches). 44 inches (length each section needs to be) x 4 (number of sections needed)=176 inches (total molding needed). To determine the amount of molding needed in feet, convert 176 inches into feet by dividing 176 inches by 12 inches. You get 14 2/3 feet, so the shortest board length is 15 feet.

7 0
3 years ago
The angle of elevation to the sun is 24°. What is the length of the shadow cast by a person 1.82 m tall? A. 0.81 m B. 1.99 m C.
Zanzabum

Answer:

C. 4.09 m

Step-by-step explanation:

Let the length of the shadow cast by a person be x m.

\tan \: 24 \degree =  \frac{height \: of \: person}{length \: of \: the \: shadow}  \\  \\ 0.4452286853 =  \frac{1.82}{x}  \\  \\ x =  \frac{1.82}{0.4452286853}  \\  \\ x = 4.08778693 \: m \\ x = 4.09 \: m

7 0
3 years ago
Stan has made a $125.30 monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years. He would now
MissTica
The future value of a monthly deposit A=125.30 at annual interest i=0.015 per annum for n=35 years compounded monthly is given by
FV=A((1+i/12)^(12*n)-1)/(i/12)
=125.30(1+0.015/12)^(12*35)/(0.015/12)
=$69156.05

The annuity formula is given by
Payment = r(PV)/(1-(1+r)^(-n))
where
r=interest rate per period = 0.015/12
PV= $69156.05
n=20*12=240
so
Payment = (0.015/12)<span>69156.05/(1-(1+0.015/12)^(-240))
= $333.71  per month.</span>
7 0
3 years ago
Read 2 more answers
10x + 1 = 2(3× + 5) - 1
MArishka [77]

Answer:

x = 2

Step-by-step explanation:

10x + 1 = 2(3x + 5) - 1

  1. mutlipy the 2 to the 3x and the 5
  2. you should get 10x + 1 = 6x + 10 - 1
  3. now you have to add the combine terms
  4. so it will now be 10x + 1 = 6x + 9
  5. now you.have to get the x's on one side and the constants (numbers alone) on the other side
  6. so you can subtract the 6x on both sides
  7. once you do that you wil get 4x + 1 = 9
  8. After you get this equation you will have to subtract the one from both sides.
  9. you will get 4x = 8
  10. All you have to do it divide 4 on both sides. Your final answer is x = 2.
7 0
3 years ago
Read 2 more answers
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