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2 years ago

A graph in the form y = ax2 will have a vertex at __

Mathematics

2 answers:

alex41 [277]2 years ago

6 0

Answer: For a given quadratic y = ax2 + bx + c, the vertex (h, k)

Step-by-step explanation:

pychu [463]2 years ago

3 0

A graph in the form y = ax2 will have a vertex at h, k.

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baherus [9]

Answer: see proof below

<u>Step-by-step explanation:</u>

Given: cos 330 = $\frac{\sqrt3}{2}$

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

$\text{Scratchwork:}\quad \bigg(\dfrac{\sqrt3 + 2}{2\sqrt2}\bigg)^2 = \dfrac{2\sqrt3 + 4}{8}$

Proof LHS → RHS:

LHS cos 165

Double-Angle: cos (2 · 165) = 2 cos² 165 - 1

⇒ cos 330 = 2 cos² 165 - 1

⇒ 2 cos² 165 = cos 330 + 1

Given: $2 \cos^2 165 = \dfrac{\sqrt3}{2} + 1$

$\rightarrow 2 \cos^2 165 = \dfrac{\sqrt3}{2} + \dfrac{2}{2}$

Divide by 2: $\cos^2 165 = \dfrac{\sqrt3+2}{4}$

$\rightarrow \cos^2 165 = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}$

$\rightarrow \cos^2 165 = \dfrac{2\sqrt3+4}{8}$

Square root: $\sqrt{\cos^2 165} = \sqrt{\dfrac{4+2\sqrt3}{8}}$

Scratchwork: $\cos^2 165 = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2$

$\rightarrow \cos 165 = \pm \dfrac{\sqrt3+1}{2\sqrt2}$

Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

$\rightarrow \cos 165 = - \dfrac{\sqrt3+1}{2\sqrt2}$

LHS = RHS $\checkmark$

4 0

2 years ago

9 packages of grape cost $24 how many packages of grapes can you buy for $8

Leto [7]

Ok. First you have to find the unit rate. Since you can buy 9 packages of grapes for $24, then you can get 1 grape package for $2.6667. If you have $8, you can buy 3 packages of grapes.

8 0

2 years ago

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13 in scientific notation

boyakko [2]

13 in SciNote is 13x10^1

8 0

2 years ago

Write the equation for the perpendicular bisector of a segment that has endpoints (–1, 10) and (3, 6).

andrezito [222]

PLEAE ADD THE PICTURE TOO

7 0

2 years ago

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The value of a collector's item is expected to increase exponentially each year. The item is purchased for $500 and its value in

slava [35]

Answer:

$607.75

Step-by-step explanation:

As a first approximation, compound interest will be slightly higher than simple interest for a relatively short time period. Here simple interest at 5% for 4 years will add 4×5% = 20% to the value, adding about $100 to the initial $500 value. That is, we expect the value in 4 years to be slightly more than $600.

The appropriate answer choice is $607.75.

_____

The actual amount can be calculated using the multiplier 1.05 for each of the 4 years, or 1.05^4 ≈ 1.21550625 for the entire period. Then the predicted item value is ...

$500 × 1.21550625 = $607.753125 ≈ $607.75

3 0

2 years ago

Read 2 more answers