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3 years ago

Triangle ABC is translated six units to the right in one unit at what are the coordinates of C?

Mathematics

1 answer:

WINSTONCH [101]3 years ago

7 0

The answer is A (The First Answer Choice)

The reason is that the coordinates of C is (-2, -3). When it was shifted 6 units to the right and one up it means that -2 is added with 6 which is 4. Furthermore -3 plus 1 is -2 which makes the new coordinates at (4, -2).

Hope This Helps

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Part 2: Identify the vertex, focus, and directrix of each. Then sketch the graph.

Andre45 [30]

Answer: $\bold{1.\quad \text{Vertex}}:(-3,-6)\qquad \text{Focus}:\bigg(-3,-\dfrac{17}{4}\bigg)\qquad \text{Directrix}:y=-\dfrac{19}{4}$

2. Vertex: (-5, 4) Focus: (-6, 4) Directrix: x = -4

Step-by-step explanation:

The vertex form of a parabola is y = a(x - h)² + k or x = a(y - k)² + h

(h, k) is the vertex
p is the distance from the vertex to the focus
-p is the distance from the vertex to the directrix

$\bullet \quad a=\dfrac{1}{4p}$

1) y = (x + 3)² - 6 → a = 1 (h, k) = (-3, -6)

$a=\dfrac{1}{4p}\qquad \rightarrow \qquad 1=\dfrac{1}{4p} \qquad \rightarrow \qquad p=\dfrac{1}{4}\\\\\text{Focus = Vertex + p}\\\\.\qquad =\dfrac{-18}{4}+\dfrac{1}{4}\\\\.\qquad = -\dfrac{17}{4}\qquad \rightarrow \qquad \text{Focus}=\bigg(-3,-\dfrac{17}{4}\bigg)\\\\\\\text{Directrix: y = Vertex - p}\\\\.\qquad \quad y=\dfrac{-18}{4}-\dfrac{1}{4}\\\\.\qquad \quad y= -\dfrac{19}{4}$

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$2.\quad x=-\dfrac{1}{4}(y-4)^2-5\qquad \rightarrow \quad a=\dfrac{1}{4}\qquad (h, k)=(-5,4)$

$a=\dfrac{1}{4p}\qquad \rightarrow \qquad -\dfrac{1}{4}=\dfrac{1}{4p} \qquad \rightarrow \qquad p=-1\\\\\text{Focus = Vertex + p}\\\\.\qquad =-5+\ -1\\\\.\qquad = -6\qquad \rightarrow \qquad \text{Focus}=(-6,4)\\\\\\\text{Directrix: y = Vertex - p}\\\\.\qquad \quad y=-5+\ -1\\\\.\qquad \quad y= -4$

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4 years ago

Jason earns $8 per hour mowing lawns.At the end of the week he earned $224.How many hours did he work?

Taya2010 [7]

28 hours is the answer

6 0

3 years ago

Read 2 more answers

A particular prism has ten faces. How many edges does it have?

vova2212 [387]

Answer:

I think the answer is .........

Step-by-step explanation:

24 edges,

8 0

3 years ago

Order the group of quadratic functions from widest to narrowest graph y=3^2, y=5^2, y=7^2

Sedbober [7]

Y = 7^2
y = 5^2
y = 3^2

if wide is the greatest and narrow means smallest then i hope its right

Ur Welcome and if its wrong plz let me know and i will fix it,
xXharleyquinn04Xx

7 0

3 years ago

In a fund-raising committee of 45 people, the ratio of men to women is 7 : 2. Find the number of women required to join the exis

bagirrra123 [75]

Answer:

18 women

Step-by-step explanation:

Sum the parts of the ratio, 7 + 2 = 9 parts

Divide 45 by 9 to find the value of one part of the ratio.

45 ÷ 9 = 5 ← value of 1 part, thus

7 parts = 7 × 5 = 35 ← number of men

2 parts = 2 × 5 = 10 ← number of women

We require to change the ratio to 5 : 4

The 5 part of the ratio represents the number of men, thus

35 ÷ 5 = 7 ← value of 1 part of the ratio, thus

4 × 7 = 28 ← number of women

Number of women required to join existing committee = 28 - 10 = 18

3 0

4 years ago