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3 years ago

PLEASE PLEASE PLEASE HELP TRANSLATING SENTENCES INTO EQUATIONS

Mathematics

2 answers:

pickupchik [31]3 years ago

8 0

Answer:

5(w + 7) = 4

Step-by-step explanation:

Do one part of the sentence at a time until you write the entire sentence as an equation.

"Five times the sum of a number and 7 is 4."

The problem tells us to use w for the number, so we write w below.

"Five times the sum of a number and 7 is 4."

Now we move on to the part dealing with the sum of the number and 7. A sum is an addition, so we add 7 to the number w.

w + 7

"Five times the sum of a number and 7 is 4."

Now we take care of the part dealing with product of 5 and the sum.

5(w + 7)

"Five times the sum of a number and 7 is 4."

The last part is dealing with the part "is 4". The word "is" very often means "equals", so the entire expression we wrote is equal to 4.

5(w + 7) = 4

Answer: 5(w + 7) = 4

adell [148]3 years ago

6 0

Answer:

5×(w + 7) = 4

Step-by-step explanation:

w is the unknown number.

5 times something means multiply something 5 times.

a sum means adding things

so, the sum of a number and 7 is

w + 7

5 times that sum is then

5×(w + 7)

and that while thing is (equals) 4

5×(w + 7) = 4

by the way, solving that means

5w + 35 = 4

5w = -31

w = -31/5

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The equation of a circle centered at the origin is x^2+y^2=16. what is the radius of the circle?

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The center is (0,0) and the radius is 4

Step-by-step explanation:

x^2+y^2=16.

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According to the graph, which range value corresponds to a domain value of 2?

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Answer:

Step-by-step explanation:

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3 years ago

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Find the 2nd Derivative: f(x) = 3x⁴ + 2x² - 8x + 4

ad-work [718]

Answer:

$f''(x)=36x^2+4$

Step-by-step explanation:

Let's start by finding the first derivative of $f(x)= 3x^4+2x^2-8x+4$ . We can do so by using the power rule for derivatives.

The power rule states that:

$\frac{d}{dx} (x^n) = n \times x^n^-^1$

This means that if you are taking the derivative of a function with powers, you can bring the power down and multiply it with the coefficient, then reduce the power by 1.

Another rule that we need to note is that the derivative of a constant is 0.

Let's apply the power rule to the function f(x).

$\frac{d}{dx} (3x^4+2x^2-8x+4)$

Bring the exponent down and multiply it with the coefficient. Then, reduce the power by 1.

$\frac{d}{dx} (3x^4+2x^2-8x+4) = ((4)3x^4^-^1+(2)2x^2^-^1-(1)8x^1^-^1+(0)4)$

Simplify the equation.

$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x^1-8x^0+0)$
$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8(1)+0)$

$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8)$
$f'(x)=12x^3+4x-8$

Now, this is only the first derivative of the function f(x). Let's find the second derivative by applying the power rule once again, but this time to the first derivative, f'(x).

$\frac{d}{d} (f'x) = \frac{d}{dx} (12x^3+4x-8)$

$\frac{d}{dx} (12x^3+4x-8) = ((3)12x^3^-^1 + (1)4x^1^-^1 - (0)8)$

Simplify the equation.

$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4x^0 - 0)$
$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4(1) - 0)$
$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4 )$

Therefore, this is the 2nd derivative of the function f(x).

We can say that: $f''(x)=36x^2+4$

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2 years ago

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