All categories

3 years ago

When you ARE NOT given the vertex from a graph, how do you find the k value?

Mathematics

1 answer:

Simora [160]3 years ago

5 0

Answer:

$f( - \frac{b}{2a} )$

Step-by-step explanation:

When you not given the vertex form, the you are given the standard form:

$f(x) = a {x}^{2} + bx + c$

The value of k, is the y-value of the vertex of the function.

To find the value of k, you plug in

$x = - \frac{b}{2a}$

In order works, you evaluate

$f( - \frac{b}{2a} )$

This will give you the k-value

You might be interested in

Helpppp!! right answer only pleaseee

hodyreva [135]

Answer:

linear equation

Step-by-step explanation:

it's the only one that matches the description :)

5 0

3 years ago

Read 2 more answers

Calculate area and perimeter

mina [271]

Answer:

area ≈ 12.505

perimeter ≈ 16.1684

Step-by-step explanation:

We are given

- the radius of the circle (and therefore area of the circle)

- the area of the triangle

We want to find

- angle AOB/AOT. We want to find this because 360/the angle gives us how many OABs fit into the circle. For example, if AOT was 30 degrees, 360/30 = 12 (there are 360 degrees in a circle, so that's where 360 comes from). The area of the circle is equal to πr² = π6² = 36π, and because AOT is 30 degrees, there are 12 equal parts of sector OAB in the circle, so 36π/12=3π would be the area of the sector. A similar conclusion can be reached from the circumference instead of the area to find the distance between A and B along the circle, and OA + AB + BO = the perimeter of the minor sector.

First, we can say that OAT is a right triangle because a tangent line is perpendicular to the line from the center to the point on the circle, so AT is perpendicular to OA. This forms two right angles, one of which is OAT

One thing that we can start to solve is AT. We know that the area of a triangle is equal to base * height /2, and the height of this triangle is AO, with the base being AT. Therefore, we can say

15 = AO * AT / 2

15 = 6 * AT / 2

15 = 3 * AT

divide both sides by 3 to isolate AT

AT = 5

Because OAT is a right triangle, we can say that the hypotenuse ² = the sum of the squares of the two other lengths. The hypotenuse is opposite of the largest angle (in this case, the right angle, as in a right triangle, the right angle is always the largest), so it is OT in this case. The other two sides are OA and AT, so we can say that

OA² + AT² = OT²

5²+6² = OT²

25+36=61=OT²

square root both sides

OT = √61

Next, the Law of Sines states that

sinA/a = sinB/b = sinC/c with angles A, B, and C with sides a, b, and c. Corresponding sides are opposite their corresponding angles, so in this case, AT corresponds to angle AOT, OT corresponds to angle OAT, and AO corresponds to angle ATO.

We want to find angle AOT, as stated earlier, so we have

sin(OAT)/OT = sin(ATO)/OA = sin(AOT)/AT

We know the side lengths as well as OAT/sin(OAT) and want to figure out AOT/sin(AOT), so one equation that helps us get there is

sin(OAT)/OT = sin(AOT)/AT, encompassing our 3 known values and isolating the one unknown. We thus have

sin(90)/√61 = sin(AOT) /5

plug in sin(90) = 1

1/√61 = sin(AOT)/5

multiply both sides by 5 to isolate sin(AOT)

5/√61 = sin(AOT)

we can thus say that

arcsin(5/√61) = AOT ≈39.80557

As stated previously, given ∠AOT, we can find the area and perimeter of the sector. There are 360/39.80557 ≈ 9.04396 equal parts of sector OAB in the circle. The area of the circle is πr² = 36π, so 36π / 9.04396 ≈ 12.505 as the area. The circumference is equal to π * diameter = π * 2 * radius = 12 * π, and there are 9.04396 equal parts of arc AB in the circumference, so the length of arc is 12π / 9.04396 ≈ 4.1684. Add that to OA and OB (both are equal to the radius of 6, as any point from the center to a point on the circle is equal to the radius) to get 6+6 + 4.1684 = 16.1684 as the perimeter of the sector

5 0

3 years ago

A rock is thrown upward at a speed of 69 mph when the rock reaches its peak how fast is it going and what is the magnitude and a

aleksandrvk [35]

At it's peak the rock is going 0mph the acceleration is .0000038 m/s^2 if on earth

6 0

3 years ago

What happens to the distance between each billiard ball during this rigid transformation?

Delicious77 [7]

The question is incomplete. Here is the complete question.

To set up a game of billiards, the first player moves the balls contained within a triangular rack as shown. What happens to the distance between each billiard during this rigid transformation?

A. The distance remains constant throughout the transformation.

B. The distance decreases at the start and increases after all motion stops.

C. The distance stays the same at the start but decreasesexactly when motion ends.

D. The distance increases at the start and then decreases as the rack gets further from the player.

Answer: A. The distance remains constant throughout the transformation.

Step-by-step explanation: In a rigid motion, all moving points in the plane are moving in way such tha:

1) relative distance between them stays the same and

2) relative position of the points stays the same

There are four types of rigid motions: translation, rotation, reflexion and glide reflection.

Translation: every point or object is moved by the same amount and in the same direction;

Rotation: the object rotates by the same amount around a fixed point;

Reflexion: the object exchange points from one side of a line with points on the other side of the line at the same distance from the line;

Glide Reflection: is a mirror reflection followed by a translation parallel to the mirror.

In the game of billiards, because all the balls are inside the triangular rack, the distance, and also the position, between them stays the same, limited by the rack. Since they are moving by the same amount in the same direction, the rigid transformation is a translation.

Therefore, the distance of the balls in the triangular rack remains constant throughout the transformation.

6 0

2 years ago

Possible answers: A) 336cm B) 110m C) 588m D) 1,029m

kozerog [31]

Answer: The area of the enclosure is 1,029 square meters

Step-by-step explanation: The first thing is to use the unit of measurement required by the question, and to do this we need to convert what we have to what is required.

If the scale of the diagram is given as every 4cm represents 7m, that means, every unit of the actual measurement would be given as

(X/4) x 7

For the length of the enclosure, we can determine that as follows;

Length = (28/4) x 7

Length = 7 x 7

Length = 49m

And for the width,

Width = (12/4) x 7

Width = 3 x 7

Width = 21m

Therefore, the area is calculated as,

Area = L x W

Area = 49 x 21

Area = 1029 m²

5 0

2 years ago

Read 2 more answers