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melisa1 [442]
2 years ago
14

Find a and k so that the given points lie on the parabola (An algebraic solution is required)

Mathematics
2 answers:
Ad libitum [116K]2 years ago
6 0

The value of a is -3 and the value of k is 10

A parabola is a U-shaped plane curve where any point is equidistant from a fixed point (known as the focus) and from a fixed line known as the directrix. The parabola is an integral part of the conic section topic

The section of a right circular cone by a plane parallel to the generator of the cone is a parabola. It is the location of a point that moves so that the distance from the fixed point (the focus) is equal to the distance from the fixed line (the directrix).

The fixed point is called the focus

A fixed line is called a directrix

Solving an algebraic equation is the process of finding a number or set of numbers that, when substituted for the variables in the equation, reduce them to an identity. Such a number is called the root of the equation

Here the equation y = a(x -2)^2 + k...........(1)

and two points A(1,7) and B(4, -2) is given

We need to find the value of a and k

Put A(1,7) in equation (1) , we get,

7 = a + k ,therefore k = 7 - a......(2)

Put B(4, -2) in equation (1), we get,

-2 = 4a + k........(3)

Put k= 7-a in (3)

-2 = 4a+7 -a

3a = -9

a= -3

From equation (2) , we get k = 7-(-3)= 10

Hence the value of k is 10 and the value of a is -3

<u>Learn more about algebraic </u><u>equation</u><u> </u><u>here:</u>

brainly.com/question/28082787

#SPJ1

Aleks [24]2 years ago
4 0

For the given points to lie on the parabola,

a = -3 and k = 10.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix).

According to the question,

Equation of parabola : y = a(x-2)^{2} + k

Points A(1,7) and B(4,-2)

For the points to lie on the parabola,

7 = a(1-2)^{2}+k

7 = a + k

Similarly,

-2 = a(4-2)^{2} + k

-2 = 4a + k

On solving the two equations simultaneously, we get,

a = -3

k = 10

Learn more about parabolas here:

brainly.com/question/4061870

#SPJ1

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Geometry help please how do I do these?
trapecia [35]

Answer:

Question 7:

∠L = 124°

∠M = 124°

∠J = 118°

Question 8:

∠Q = 98°

∠T = 98°

∠R = 82°

Question 15:

m∠G = 110°

Question 16:

∠G = 60°

Question 17:

∠G = 80°

Question 18:

∠G = 70°

Step-by-step explanation:

The angles can be solving using Symmetry.

Question 7.

The sum of interior angles in an isosceles trapezoid is 360°, and because it is an  isosceles trapezoid

∠K = ∠J  = 118°

∠L = ∠M

∠K+∠J+∠L +∠M = 360°

236° + 2 ∠L = 360°

Therefore,

∠L = 124°

∠M = 124°

∠J = 118°

Question 8.

In a similar fashion,

∠Q+∠T+∠S +∠R = 360°

and

∠R = ∠S = 82°

∠Q = ∠T

∠Q+∠T + 164° = 360°

2∠Q + 164° = 360°

2∠Q = 196°

∠Q = ∠T  =98°.

Therefore,

∠Q = 98°

∠T = 98°

∠R = 82°

Question 15.

The sum of interior angles of a kite is 360°.

∠E + ∠G + ∠H + ∠F = 360°

Because the kite is symmetrical

∠E  = ∠G.

And since all the angles sum to 360°, we have

∠E +∠G + 100° +40° = 360°

2∠E = 140° = 360°

∠E  = 110° = ∠G.

Therefore,

m∠G = 110°

Question 16.

The angles

∠E = ∠G,

and since all the interior angles sum to 360°,

∠E + ∠G + ∠F +∠H = 360°

∠E + ∠G  + 150 + 90 = 360°

∠E + ∠G   = 120 °

∠E = 60° = ∠G

therefore,

∠G = 60°

Question 17.

The shape is a kite; therefore,

∠H = ∠F = 110°

and

∠H + ∠F + ∠E +∠G = 360°

220° + 60° + ∠G = 360°,

therefore,

∠G = 80°

Question 18.

The shape is a kite; therefore,

∠F = ∠H  = 90°

and

∠F +∠H + ∠E + ∠G = 360°

180° + 110° + ∠G  = 360°

therefore,

∠G = 70°.

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3 years ago
A family has 2 cars. the first car has a fuel efficiency of 15 miles per gallon of gas and the second has a fuel efficiency of 2
lora16 [44]

Car 1: 15x

Car 2: 20y

15x+20y=1300

x+y=75

So y=75-x

15x+20(75-x)=1300

-5x+1500=1300

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x=40.

y=75-40

y=35

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How many solutions does the equation - 8x + 5 = - 8x + 4 have
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we don't have solutions !!

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klemol [59]
No.

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The radius goes from the center of the circle (which is not on the circumference) to one point of the circumference.

The diameter is a chord (the largest chord possible); but not the radius.
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