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Leno4ka [110]
3 years ago
9

Identify the vertex for (x-3)2 – 1.

Mathematics
2 answers:
Natasha_Volkova [10]3 years ago
7 0

Answer: Last Option

(3, -1)

Step-by-step explanation:

We have the following quadratic function:

f(x) =(x-3)^2 - 1

By definition for a quadratic function in the form:

f (x) = a (x-h) ^ 2 + k

the vertex of the function is always the point (h, k)

Note that for this case the values of h, a, and k are:

a = 1\\h = 3\\k = -1

Therefore the vertex of the function f(x) =(x-3)^2 - 1 is the point

(3, -1)

nalin [4]3 years ago
3 0

Answer:

D.  (3, -1).

Step-by-step explanation:

The vertex for ( x - a)^2 + b  is (a, b).

Comparing (x - 3)^2 - 1 with this we get:

a = 3 and b = -1.

You might be interested in
Eric Tangler prism with the value of 10 cubic units is filled with cubes the side lengths of 1/2 unit how many 1/2 unit cubes do
lawyer [7]

Complete Question

Rectangular prism with the value of 10 cubic units is filled with cubes the side lengths of 1/2 unit how many 1/2 unit cubes does it take to fill the prism?

Answer:

80 cubes

Step-by-step explanation:

Step 1

The volume of a cube = (side length)³

From the above question, the side length of the cube = 1/2 unit

Hence, the volume of the cube = (1/2 unit)³

= 1/8 cubic units

Step 2

Rectangular prism with the value of 10 cubic units.

The number of 1/2 unit cubes that it takes to fill the prism is calculated as:

10 cubic units ÷ Volume of 1/2 unit cubes

= 10 cubic units ÷ 1/8 cubic units

= 10 × 8/1

= 80 cubes.

Therefore, number of 1/2 unit cubes that it takes to fill the prism is 80 (1/2 units) cubes

4 0
3 years ago
Write the square roots of 49 i in ascending order of the angle.
Troyanec [42]

Answer:

The square roots of 49·i in ascending order are;

1) -7·(cos(45°) + i·sin(45°))

2) 7·(cos(45°) + i·sin(45°))

Step-by-step explanation:

The square root of complex numbers 49·i is found as follows;

x + y·i = r·(cosθ + i·sinθ)

Where;

r = √(x² + y²)

θ = arctan(y/x)

Therefore;

49·i = 0 + 49·i

Therefore, we have;

r = √(0² + 49²) = 49

θ = arctan(49/0) → 90°

Therefore, we have;

49·i = 49·(cos(90°) + i·sin(90°)

By De Moivre's formula, we have;

r \cdot (cos(\theta) + i \cdot sin(\theta) )^{\dfrac{1}{2}}  =  \pm \sqrt{r} \cdot \left (cos\left (\dfrac{\theta}{2} \right ) + i \cdot sin\left (\dfrac{\theta}{2} \right ) \right )

Therefore;

√(49·i) = √(49·(cos(90°) + i·sin(90°)) = ± √49·(cos(90°/2) + i·sin(90°/2))

∴ √(49·i) = ± √49·(cos(90°/2) + i·sin(90°/2)) = ± 7·(cos(45°) + i·sin(45°))

√(49·i) = ± 7·(cos(45°) + i·sin(45°))

The square roots of 49·i in ascending order are;

√(49·i) = - 7·(cos(45°) + i·sin(45°))  and  7·(cos(45°) + i·sin(45°))

8 0
3 years ago
Pls help me for brainliest
olga2289 [7]

Answer:

middle one- is the answer :D

Step-by-step explanation:

5 0
3 years ago
HELP ASAP PLZ!!!!!
liberstina [14]
14 - 6.2 * (-3 -7)
According to PEMDAS, we do the parentheses first.
-3-7=-10
Next we do what is outside the parentheses
14-6.2=7.8
Then we multiply both answers together.
7.8*-10 = -78

A.-78
5 0
4 years ago
A container holds 4 gallons of lemonade. A large lemonade contains 16 ounces. How many large lemonades could the restaurant sell
Natali [406]

Answer:

They could sell 32 large lemonades before they run out

Step-by-step explanation:

4 gallons is equivalent to 512 oz

When you divide 512 oz buy 16oz you get 32

Hope this helps!

7 0
3 years ago
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