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1 year ago

Write an equation for a parabola opening upward, shifted 6 units right, and three units down

Mathematics

1 answer:

jolli1 [7]1 year ago

5 0

y = (x-6)²-3

1) Let's write a transformation described as it is, algebraically speaking.

• opening upward, (a >0)

• shifted 6 units right, (-6)

• and three units down -3

2) Starting from the parent function y=x², then we can write:

y = (x-6)²-3

Notice that the horizontal shift is within the parentheses with a swapped sign. And outside that -3 indicating the vertical shift.

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What are the types of roots of the equation below? x^4 - 81 = 0

natali 33 [55]

Answer:

x^4 - 81 = 0

(x² - 9)(x² + 9) = 0

Notice that the first of these is itself a difference of two squares:

(x - 3)(x + 3)(x² + 9) = 0

So the solutions are x = 3, x = -3, x = 3i, x = -3i

4 0

3 years ago

Which equation can be used to solve for b? B 5 cm 10 cm 30°

kati45 [8]

The Question is Incomplete The complete question with figure is below.

Answer:

Therefore the equation to solve for b is

$\tan 30 = \dfrac{5}{b}$

Step-by-step explanation:

Given:

In Right Angle Triangle ABC

∠C = 90°

BC = 5 cm

AB = 10 cm

∠A = 30°

To Find:

b = ?

Solution:

In Right Angle Triangle ABC Tangent identity we have

$\tan A = \dfrac{\textrm{side opposite to angle A}}{\textrm{side adjacent to angle A}}$

Substituting the values we get

$\tan 30 = \dfrac{BC}{AC}\\\\\tan 30 = \dfrac{5}{b}$

Therefore the equation to solve for b is

$\tan 30 = \dfrac{5}{b}$

6 0

3 years ago

julie grows apples. the first year she planted 6 seeds. the second year she planted 18 seeds. the third year she planted 54 seed

luda_lava [24]

Answer:

90-96

Step-by-step explanation:

7 0

3 years ago

A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 24 ft long and 14 ft wide.

expeople1 [14]

rounded part is a semicircle so the area for that is the area of a circle ÷ 2

area of the rectangle + (area of the circle ÷ 2) = answer

24 * 14 = 336 = area of the rectangle

14 ÷ 2 = r

(pi * 7^2) ÷ 2

(pi * 49) ÷ 2 = 153.86 ÷ 2 = 76.93 = area of semicircle

336 + 76.93 = 412.93 ft^2 = answer

6 0

3 years ago

What is the formed of the fact family for 6,7,13 what is the answer

Keith_Richards [23]

Answer:

7 + 6 = 13

13 = 7 + 6

13 – 6 = 7

7 = 13 – 6

Step-by-step explanation:

7 + 13 = 20

13 + 7 = 20

13 – 13 = 0

13 – 0 = 13

7 + 0 = 7

6 + 0 = 6

13 – 0 = 13

13 – 13 = 0

7 + 0 = 7

6 + 0 = 6

13 – 0 = 13

13 – 13 = 0

7 + 6 = 13

13 = 7 + 6

13 – 6 = 7

7 = 13 – 6

5 0

2 years ago