MATHEMATICS HIGH SCHOOL

What is an equation of the parabola with vertex at the origin and focus (-6, 0)?

Answers

Answer 1

Answer:

Answer:

$y^(2)=-24x$

Step-by-step explanation:

According to analytic geometry, a parabola is define as

$y^(2)=4px$

Where $p$ is the coordinate of the focus.

So, the equation for this parabola is

$y^(2)=4(-6)x$

$y^(2)=-24x$

The negative sign indicates that the parabola opens leftward. The image attached shows the graph.

Answer 2

Answer: Hello,

p is the parameter of the parabola
y²=2px is his equation.
Focus F=(p/2,0)
Directrice x=-p/2

Here p/2=-6==>p=-12
Equation is y²=-24x

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I need help with this question!

Answers

2. Jayden ran a whole mile in one hour

Answer:

1: 3 miles

2: 1 mile

Step-by-step explanation:

Esther starts at one corner of a square field and walks 90 feet along one side to another corner of the field. She turns 90° and walks 70 feet, and then walks straight back to where she started. What is the area of the part of the field she walked around?a. 3150 ft²
b. 4900 ft²
c. 6300 ft²
d. 8100 ft²

Answers

Since it is a square field and she walked from one corner to another, each side of the square filed is 90 feet.
Since she walked 70 feet and then straight back to where she started, she has formed a triangle, the legs are 90 and 70 and the hypotenuse (the distance back to the start) is not needed to solve this problem.
So we have a triangle whose length is 90 and whose height is 70
A = $(1)/(2)$ bh or in this case $(1)/(2)$ (90) x (70) or 1/2 of 6300. Answer a. 3150 ft² is half of 6300 and is the correct answer

How can I factorise (2x cubed - 5x + 3) ?

Answers

$2x^3-5x+3=2x^3-2x-3x+3\n\n=2x(x^2-1)-3(x-1)\n\n=2x\underbrace{(x^2-1^2)}_(use\ (*))-3(x-1)\ \ \ |(*)\ a^2-b^2=(a-b)(a+b)\n\n=2x\underbrace{(x-1)}_((**))(x+1)-3\underbrace{(x-1)}_((**))\n\n=(x-1)[2x(x+1)-3]\n\n=(x-1)\underbrace{(2x^2+2x-3)}_((***))\n\n(***)\ 2x^2+2x-3\to a=2;\ b=2;\ c=-3\n\nx=(b^2\pm√(b^2-4ac))/(2a)$

$therefore\nx=(-2\pm√(2^2-4(2)(-3)))/(2(2))=(-2\pm√(4+24))/(4)=(-2\pm√(28))/(4)=(-2\pm√(4\cdot7))/(4)=(-2\pm2\sqrt7)/(4)\n\n=(-1\pm\sqrt7)/(2)\n\nso,\ the\ answer:\n\n(x-1)\cdot2\left(x-(-1-\sqrt7)/(2)\right)\left(x-(-1+\sqrt7)/(2)\right)\n\n=\boxed{(x-1)(2x+1+\sqrt7)\left(x+(1-\sqrt7)/(2)\right)}=\boxed{(1)/(2)(x-1)(2x+1+\sqrt7)(2x+1-\sqrt7)}$

2x³ - 5x +3

P = Finding the divisors of the constant 3 : 1 and 3
Q = Finding the divisors of the master coefficient 2 : 1 and 2

Now verify the probably roots: +- p/q
+- 1/1 , +-1/2 , +-3/1 , +-3/2

+-1 , +-1/2 , +-3    , +- 3/2

x=1 is root: 2x³-5x+3 = 2(1)³-5(1)+3 = 0

If x=1 is root, so x-1=0

Divinding by (x-1)

2x³+0x²-5x+3 | x-1
-2x³+2x² 2x² +2x-3
  0 +2x²-5x
-2x²+2x
0 -3x +3
3x - 3
0 0

So,
2x³-5x+3 = (x-1)(2x²+2x-3)

(x-1)(2x²+2x-3)

A rope.Measure 60cm was divided into 2 groups . 1 was used to make a rectangle of length 12cm and breadth 6cm. And the other was used to make a hexagon . What is the size of the hexagon in each side

Answers

Answer:

4cm

Step-by-step explanation:

Firstly, we need to know the perimeter of the rectangle so as to know the length used to make the rectangle. This is 2(l + b)

P = 2(12 + 6) = 2(18) = 36cm

The length remaining to make the hexagon would be 60 - 36 = 24cm

Now since the hexagon is regular, the length of each side would be 24/6 = 4cm

Note: hexagon is a polygon with 6 sides

In the function f(x) = 4(x2 − 6x + ____) + 20, what number belongs in the blank to complete the square?

Answers

The right answer for the question that is being asked and shown above is that: In the function f(x) = 4(x2 − 6x + ____) + 20, what number belongs in the blank to complete the square?

x2 - 6x + 9

So the answer on the blank space is 9. It should be a perfect square.
= 6/2
= 3^2
= 9

Write 130% as a fraction in lowest terms.

Answers

By lowest terms i'm guessing you mean the most simplified:

Firstly right the fraction in tenths (or one you know),
13/10

The answer is 13/10 and it can't be simplified anymore

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