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3 years ago

Please answer quickly, I need to get this done. I'll mark brainliest.

Mathematics

1 answer:

worty [1.4K]3 years ago

7 0

J (-4, 1), K (-4, -2), L (-3, -1)

(a) To rotate a point 90° counterclockwise about the origin, multiply the y-coordinate by -1 and then interchange the z- and y- coordinates.

(x, y)'' = (-y, x)

Substitute all of J (-4, 1), K (-4, -2), L (-3, -1) for (x, y)

Solution:

J'' = J (-4, 1) × (x, -1) = (-4, -1)

K'' = K (-4, -2) × (x, -1) = (-4, 2)

L'' = L (-3, -1) × (x, -1) = (-3, 1)

J'' (-1, -4), K'' (2, -4), L'' (1, -3)

Image ▲J"K"L": Look at the first attached picture.

(b) To reflect a point in the y-axis, we multiply its x-coordinate by -1.

Substitute all of J (-4, 1), K (-4, -2), L (-3, -1) for (x, y)

Multiplying by -1:

J'' = J (-4, 1) × (-1, y) = (4, 1)

K'' = K (-4, -2) × (-1, y) = (4, -2)

L'' = L (-3, -1) × (-1, y) = (3, -1)

J'' (4, 1), K'' (4, -2), L'' (3, -1)

Image ▲J"K"L": Look at the second attached picture.

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Write the equation of the conic section below.

tangare [24]

Answer:

$(x-3)^2=8(y+1)$

Step-by-step explanation:

Standard form of a parabola with a vertical axis of symmetry:

$(x-h)^2=4p(y-k) \quad \textsf{where}\:p\neq 0$

$\textsf{Vertex}=(h, k)$

$\textsf{Focus}=(h,k+p)$

$\textsf{Directrix}:y=(k-p)$

$\textsf{Axis of symmetry}:h=k$

If p > 0, the parabola opens upwards, and if p < 0, the parabola opens downwards.

From inspection of the graph:

Vertex = (3, -1)
Directrix = y = -3

Therefore:

h = 3
k = -1
k - p = -3

Use the Directrix equation to find p

⇒ y = (k - p)

⇒ -3 = -1 - p

⇒ p = 2

Therefore the equation of the conic section is:

$\implies (x-3)^2=4\cdot 2(y-(-1))$

$\implies (x-3)^2=8(y+1)$

Rearranging in standard form $ax^2+bx+c$ :

$\implies (x-3)^2=8y+8$

$\implies x^2-6x+9-8=8y$

$\implies x^2-6x+1=8y$

$\implies y=\dfrac{1}{8}x^2-\dfrac{3}{4}x+\dfrac{1}{8}$

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2 years ago

In the jone school library,10/20 of the computers have scanners.in simplest form, which fraction of the computers have scanners?

n200080 [17]

Answer:

1/2

Step-by-step explanation:

5 0

3 years ago

What is the name of the following net?

Burka [1]

The answer is square pyramid

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3 years ago

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At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least

Lapatulllka [165]

Answer:

4 is the maximum number of ride tickets she can buy

Step-by-step explanation:

Here, r represents the number of ride tickets and f represents number of food tickets.

The system of inequalities is given as:

r+f\geq 16 ....[1]

4r+2f\leq 40 .....[2]

To solve Mathematically:

Multiply equation [1] by -2 we have;

-2r-2f \leq -32 .....[3]

Add equation [2] and [3] we have;

2r \leq 8

Divide both sides by 2 we have;

r \leq 4

Since r must be less than or equal to 4.

You can also see the graph of the given system of inequalities as shown below.

The intersection point is, (4, 12)

Therefore, the maximum number of ride tickets she can buy is, 4

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3 years ago

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irina1246 [14]

Answer:

360/12 = 30 degrees

Step-by-step explanation:

To find any exterior angle, you need to divide 360 degrees by the total number of sides from the polygon.

Since the polygon in question is a dodecagon (with 12 sides), all you need to do is divide 360 degrees by 12, thus, the size of the exterior angle is 30.

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