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Softa [21]
3 years ago
15

The equation of a parabola is (y−3)2=20(x+1) .

Mathematics
2 answers:
gavmur [86]3 years ago
8 0

Answer:

The equation of the directrix of the parabola is x=-6.

Step-by-step explanation:

The given equation is

(y-3)^2=20(x+1)            .... (1)

If a parabola is defined as

(y-k)^2=4p(x-h)              .... (2)

Where, (h,k) is vertex and the directix of the parabola is x=h-p.

From (1) and (2), we get

h=-1,k=3

4p=20

p=5

The value of p is 5.

The equation of directix is

x=h-p

x=-1-5

x=-6

Therefore the equation of the directrix of the parabola is x=-6.

True [87]3 years ago
6 0

ANSWER

x =  - 6

EXPLANATION

The given parabola has equation:

{(y - 3)}^{2}  = 20 {(x + 1)}^{2}

This parabola opens in the direction of the positive x-axis.

This can be rewritten as:

{(y - 3)}^{2}  = 4(5) {(x + 1)}^{2}

The vertex is (-1,3)

The directrix of this parabola is

x =  - 1 - 5

x =  - 6

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It is both because 8^{2} is 64 and 4^{3} is 64.

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Lana has $15 for dinner her meal is $13.90 she wants to leave a 18% tip does she have enough explain your answer
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Start off by finding 18% of 13.90.

18%=18/100=0.18

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An 18% tip would be $2.50.


Now, to find out if Lana has enough money, add $2.50 to $13.90 to find out the total amount she would leave.  You get $16.40.  Since $16.40>$15, the answer is no because the total cost including the 18% tip is greater than $15.

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50 Points: Name the similar triangles &amp; Prove the similarity with details
Leno4ka [110]

<u>Let's consider the facts at hand</u>:

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  • Sides BE = DF

<u>Based on the diagram, triangles BCE and triangles DCF are similar</u>

   ⇒ based on the Angle-Angle theorem

      ⇒ since ∠BCE = ∠DCF and ∠BEC = ∠DFC

         ⇒ the two triangles are similar

Hope that helps!

<em>Definitions of Theorem I used:</em>

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8 0
2 years ago
AM is a median in △ABC (M∈ BC ). A line drawn through point M intersects AB at its midpoint P. Find areas of △APC and △PMC, if A
Snowcat [4.5K]

Answer:

The area of APC is 70m². The area of triangle PMC is 35m².

Step-by-step explanation:

Let the area of triangle ABC be x.

It is given that AM is median, it means AM divides the area of triangle in two equal parts.

\text{Area of }\triangle ACM=\text{Area of }\triangle ABM=\frac{x}{2}    .....(1)

The point P is the midpoint of AB, therefore the area of APC and BPC are equal.

\text{Area of }\triangle APC=\text{Area of }\triangle BPC=\frac{x}{2}          ......(2)

The point P is midpoint of AB therefore the line PM divide the area of triangle ABM in two equal parts. The area of triangle APM and BPM are equal.

\text{Area of }\triangle APM=\text{Area of }\triangle BPM=\frac{x}{4}        .....(3)

The area of triangle APM is 35m².

\text{Area of }\triangle APM=\frac{x}{4}

35=\frac{x}{4}

x=140

Therefore the area of triangle ABC is 140m².

Using equation (2).

\text{Area of }\triangle APC=\frac{x}{2}

\text{Area of }\triangle APC=\frac{140}{2}

\text{Area of }\triangle APC=70

Therefore the area of triangle APC is 70m².

Using equation (3), we can say that the area of triangle BPM is 35m² and by using equation (2), we can say that the area of triangle BPC is 70m².

\triangle BPC=\triangle BPM+\triangle PMC

70=35+\triangle PMC

35=\triangle PMC

Therefore the area of triangle PMC is 35m².

8 0
3 years ago
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