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3 years ago

What is the theoretical probability that Marco will choose a card with a heart on it?

1 answer:

6 0

Considering that there is no real question content here, we can't be for sure, so I am just going to say 100% probability since it seems like that is the only card he can pick from ; ~ ;

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What is the vertex of the absolute value function defined by ƒ(x) = |x + 5| + 7?

Temka [501]

To answer this, you need to know the general form of an absolute value function. the equation for this is f(x) = a|x - h| + k, and in this equation, the vertex is (h, k).

with that information, you can see that your vertex will be (-5, 7). you must take the negative for 5 because the general equation states that your h value is usually subtracted from x. to check your vertex, try plugging it into your general equation:
f(x) = a|x - (-5)| + 7
f(x) = a|x + 5| + 7 ... you see that this matches your given equation. this last part here was just to show why your 5 must be negative; your answer is bolded.

7 0

2 years ago

Find f'(x) and state the domain of f': f(x) = In (2x^2+1)

-Dominant- [34]

Answer:

$f'(x) = \frac{4x}{2x^2+1}$

Domain: All Real Numbers

General Formulas and Concepts:

Algebra I

Domain is the set of x-values that can be inputted into function f(x)

Calculus

The derivative of a constant is equal to 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Chain Rule: $\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Derivative: $\frac{d}{dx} [ln(u)] = \frac{u'}{u}$

Step-by-step explanation:

Step 1: Define

f(x) = ln(2x² + 1)

Step 2: Differentiate

Derivative ln(u) [Chain Rule/Basic Power]: $f'(x) = \frac{1}{2x^2+1} \cdot 2 \cdot 2x^{2-1}$
Simplify: $f'(x) = \frac{1}{2x^2+1} \cdot 4x$
Multiply: $f'(x) = \frac{4x}{2x^2+1}$

Step 3: Domain

We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.

Therefore, our domain would be all real numbers.

We can also graph the differential function to analyze the domain.

5 0

2 years ago

A circle has a radius of 3. An arc in this circle has a central angle of 20 degrees.

TiliK225 [7]

Answer:

π/3 units

Step-by-step explanation:

arc length = 2πr(°/360)

= 2π*3(20/360)

= π/3 units

4 0

2 years ago

Why can it help to line up the decimal points before comparing and ordering numbers with decimals

aliina [53]

So you don't loose your place

5 0

2 years ago

Read 2 more answers

I did it wrong the first time

kvv77 [185]

Answer:

4.6

Step-by-step explanation:

For this question, we need the opposite side and have the opposite

with that said, out of SOH, CAH, TOA it's fastest to use TOA

tan(75)=17/x

17/(tan(75))=x

x= 4.555136271

which rounds to

4.6

4 0

3 years ago

Read 2 more answers