MATHEMATICS HIGH SCHOOL

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2?a) (x-3)^2 = 20(y-1)
b) (y-1)^2 = 20(x-3)
c) (y-1)^2 = -20(x-3)
d) (x-3)^2 = 20(y-1)

Answers

Answer 1

Answer:

Answer with Step-by-step explanation:

We have to find:

the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2

General form of Parabola that opens left or right:

(y−k)²=4p(x−h)

Vertex =(h,k)

Directrix: x=h−p

Here, h=3,k=1 and h-p=-2 i.e. p=h+2=5

Hence, equation of parabola in this case equals

(y-1)²=4×5(x-3)

i.e. (y-1)²=20(x-3)

Hence, correct option is:

b) (y-1)²=20(x-3)

Answer 2

Answer: Hello,

Remenber:
if S=(0,0) y²=2px then F=(p/2,0 and d:x=-p/2

Let's pose
x'=x-3
y'=y-1 axes passing by the point (3,0) in base (x,y) and (0,0) in base (x',y')

y'²=2p'x'
d': x'=-5=-p'/2 ==> p'=10 and y²=20x'
Returning in base (x,y) : (y-1)²=20(x-3)

Answer B

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HELP I HAVE 5 MIN TO TURN THIS IN!!!!!!!!!!!!!!!!!!!!!!!!!!!!What are the simplified versions of the expressions shown below??

WILL MARK BRAINLIEST!!!!!!!!!!!!
(11, 15, and 18 don't count)

Answers

Answer:

hi....see the pic...that's the answer....my name is Sayan....my account dp pic is my mom .. please follow me....

Decide whether this statement is always true, never true, or sometimes true, and explain why: In a quadratic equation of the form 0 = ax2 + bx + c, there will be two real solutions if a and c are of opposite signs

Answers

Answer:

Always true

Step-by-step explanation:

Here, we want to evaluate if the given statement is true

The discriminant D can be calculated using the formula;

b^2 - 4ac

if D is greater than 0, then we will have only real roots

In a case where a and c are of opposite signs;

then -4ac will always give a positive value which can be added to b^2

This positive value will ensure that D is greater than zero and hence we can have only real roots

So this assertion is always true if a and c are of opposite signs

Which of the following statements is always true? A. Acute triangles are scalene. B. Scalene triangles are acute. C. Acute triangles are equilateral. D. Equilateral triangles are acute.

Answers

D.) equilateral triangles are acute.
- In an equilateral triangle, the 3 angles are always 60 degrees.

Final answer:

None of the given options in the question are true. Not all acute, scalene or equilateral triangles are the other types. They have distinct characteristic which defines them.

Explanation:

The subject matter of this question is about the different types of triangles, namely acute triangles, scalene triangles, and equilateral triangles.

An acute triangle is a triangle in which all three angles are less than 90 degrees. A scalene triangle is a triangle where all sides and angles are different. An equilateral triangle is a triangle where all sides and angles are equal, with each angle being 60 degrees.

Looking at these definitions, we can see that none of the given options are true. Not all acute triangles are scalene (they can be isosceles or equilateral), not all scalene triangles are acute (they can be obtuse or right), not all acute triangles are equilateral (they can be scalene or isosceles), and not all equilateral triangles are acute (they are, by definition, always acute).

Learn more about Triangles here:

brainly.com/question/34963952

#SPJ6

kirby often forgets to switch the inequity sign when dividing a negative. when solving 3x-10≥x, should kirby collect the variables on the left or the right? why?

Answers

You should collect the variable on the left side since you can't have two variables of the same letter on each side.so you would take the variable from the right side and subtract it from the left. So subtract x on both sides. Your new problem is 2x-10 is greater than or equal to 0. Now you add 10 on both sides. Your new problem is 2x is greater than or equal to 10. Now divide by 2 on both sides. Your answer would be x is greater than or equal to 5

Write the equivalent expression to (5x - 3x^2) - (5x -2)

Answers

Answer:

-3x^2+2

Step-by-step explanation:

(5x - 3x^2) - (5x -2)

Distribute the minus signs

(5x - 3x^2) - 5x +2

Combine like terms

-3x^2 +5x-5x+2

-3x^2+2

PLZ HELP! MATH >__<What is the lateral area of the rectangular prism with a base length of 14 m, a base width of 9 m, and a height of 6 m?
A. 264 m2
B. 276 m2
C. 528 m2
D. 756 m2

Answers

Lateral area = surface area not including the bases.

To find this area we just need to add up the area of all of those sides.

The 2 bases are the same area and defined by the length and width.

That leaves the 2 sides defined by length and height,
plus the 2 defined by width and height.

Of course, to find the area of a rectangle, we just multiply together its two dimensions.
length × height = 14 × 6 = 84
width × height = 9 × 6 = 54

2 × 84 + 2 × 54 = 276 m²

My answer would be 276m2
k12

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