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DENIUS [597]
3 years ago
5

Triangle ABC has vertices at A(−3, 4), B(4, −2), C(8, 3). The triangle is translated 4 units down and 3 units left. Which rule r

epresents the translation? After the translation, what are the coordinates of vertex C?
A) (x, y) → ( x + 3, y + 4); (11, 7)
B) (x, y) → (x − 4, y + 3); −6, 7)
C) (x, y) → ( x − 3, y − 4); (5, −1)
D) (x, y) → (x − 2, y − 1); (−5, 7)
Mathematics
1 answer:
Anarel [89]3 years ago
5 0
4 units down => y - 4
3 units left => x - 3
=> C
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Parabolas. Please help me
olganol [36]
  1. x² = 16 y
  2. x = 0
  3. (x + 4)² = 2/3 (y - 2)
  4. Gayle identifies that the vertex of the parabola is <u>(3, -1)</u> . The parabola opens <u>right</u>, and the focus is <u>3 </u>units away from the vertex. The directrix is <u>6 </u>units from the focus. The focus is the point <u>(6, -1)</u>. The directrix of the equation is <u>x = 0.</u>
  5. (y - 6)² = 4p (x - 3)

Step-by-step explanation:

1. First figure

We plot the parabola as given in the attached diagram.

As it is facing upwards, the equation goes as x² = 4py

where, p = 4 (refer the attached diagram)

x² = 4py

x² = 4 (4) y

∴, standard form of parabola is x² = 16 y

2. Second figure

(y + 3)² = 4 (x - 1)

Comparing the given equation with the standard form

(y - k)² = 4p (x - h)

Now from this equation we get to know that

h = 1

p = 1

Directrix is x = (h - p)

So, x = 0

3. Third figure

3x² + 24x - 2y + 52 = 0

3x² + 24x = 2y - 52

3 (x² + 8x) = 2 (y - 26)

(x² + 8x) = 2 (y - 26) / 3

Adding 16 on both sides,

x² + 8x + 16 = 2 (y - 26) / 3 + 16

(x + 4)² = 2/3 y - 52/3 + 16

(x + 4)² = 2/3 y - 4/3

(x + 4)² = 2/3 (y - 2)

4. Fourth figure

(y + 1)² = 12 (x - 3)

Comparing the given equation with the standard form

(y - k)² = 4p (x - h)

Now from this equation we get to know that

k = -1

h = 3

p = 3

Gayle identifies that the vertex of the parabola is <u>(3, -1)</u> . The parabola opens <u>right</u>, and the focus is <u>3 </u>units away from the vertex. The directrix is <u>6 </u>units from the focus. The focus is the point <u>(6, -1)</u>. The directrix of the equation is <u>x = 0.</u>

5. Fifth figure

Focus = (2, 6)

Directrix is x = 4

Therefore, it follows the standard form

(y - k)² = 4p (x - h)

Directrix is given by x = h-p = 4

Focus is given by (h + p, k) = (2, 6)

Solving for (h - p) = 4, (h + p) = 2

2 - p - p = 4

-2p = 2

p = -1

Hence, h = 3

Therefore, the standard form can be written as

(y - 6)² = 4p (x - 3)

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Use the spinner to identify the probability to the nearest hundredth of the pointer
Blizzard [7]
The answer is 0.60 because the sum of the shaded angles equals 145°, divided by 360° equals 0.60
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Find 62(9) . Express your answer as a fraction in simplest form
Bas_tet [7]

Answer:

558/1

Step-by-step explanation:

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Divide. Round your answer to the nearest hundredth 1÷3
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Well your going to get 0.3333333333(the 3's are infinite) :D
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What is y={-\dfrac{1}{3}}x-9y=− 3 1 ​ x−9y, equals, minus, start fraction, 1, divided by, 3, end fraction, x, minus, 9 written i
Kobotan [32]

Answer:

x+3y=-27

Step-by-step explanation:

We are given that

y=(-\frac{1}{3})x-9

We have to find the  standard form of given equation

y=\frac{-x-27}{3}

3y=-x-27

By using multiplication property of equality

x+3y=-27

We know that

Standard form of equation

ax+by=c

Therefore, the standard form of given equation  is given by

x+3y=-27

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4 years ago
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