Samira ran around a park loop that was 1/3 mile long. She ran around the loop 9 times. Samira says she ran 9/3 miles. Her brother Amal says she ran 3 miles. Who is correct? Use words and drawings to explain how you know.

Answers

Answer 1
Answer: They are both correct because 9/3 is equal to 3
Answer 2
Answer: The brother is correct by convention but technically they are the exact same number, I'd just say the brother because he simplied it to be a more usable number.

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Solve the equation 3x + 6y = 18 for y

Answers

y= -x/2 + 3 Move all terms that don't have "y" to the right side to solve it

What is the equation of the line of symmetry for g(x) = 5x2 – 10x + 24?
x = _________

Answers

x = -b/2a
so substitute the numbers inside the it gives
x = -(-10)/2*5
x = 10/10
x = 1
so line of symmetry is 1

3902.00 divided by 3

Answers

So,

3902/3 = x

1300\overline{6} = x

Fraction: 1300 2/3
The answer for your question is 1300.66667

Determine the domain of the function.f as a function of x is equal to the square root of eleven minus x.

Answer Choices:
All real numbers except 11
x > 11
All real numbers
x ≤ 11

Answers

Answer:

Option D, x ≤ 11

Step-by-step explanation:

We have to determine the domain of the function.

f(x) = √(11-x)

This function is defined for the positive values of ( 11 - x ) because under root of negative terms is not defined.

Therefore, domain of the given function will be ( 11 - x ) ≥ 0

x ≤ 11

Option D, x ≤ 11 is the answer.

What is the first derivative of r with respect to t (i.e., differentiate r with respect to t)? r = 5/(t2)Note: Use ^ to show exponents in your answer, so for example x2 = x^2. Also, type your equation answer without additional spaces.

Answers

Answer:

The first derivative of r(t) = 5\cdot t^(-2) (r(t)=5*t^{-2}) with respect to t is r'(t) = -10\cdot t^(-3) (r'(t) = -10*t^{-3}).

Step-by-step explanation:

Let be r(t) = (5)/(t^(2)), which can be rewritten as r(t) = 5\cdot t^(-2). The rule of differentiation for a potential function multiplied by a constant is:

(d)/(dt)(c \cdot t^(n)) = n\cdot c \cdot t^(n-1), \forall \,n\neq 0

Then,

r'(t) = (-2)\cdot 5\cdot t^(-3)

r'(t) = -10\cdot t^(-3) (r'(t) = -10*t^{-3})

The first derivative of r(t) = 5\cdot t^(-2) (r(t)=5*t^{-2}) with respect to t is r'(t) = -10\cdot t^(-3) (r'(t) = -10*t^{-3}).

Which point on the number line represents 0.059?

Answers

It is in the thousandths place

Final answer:

The point on the number line that represents 0.059 is very close to 0. Specifically, it is located a bit over halfway along the sixth segment of the section between 0 and 1, if this section is divided into 100 equal segments.

Explanation:

The point on the number line that represents 0.059 would be very close to 0. On a number line, which sequences numbers from left to right in increasing order, the number 0.059 is more than 0 but less than 1, so it appears somewhere between these two points. However, because 0.059 is substantially less than 1, its exact position would be much nearer to the 0 mark than the 1.

For example, if we consider a number line stretching from 0 to 1 and divide it into 100 equal segments, each representing 0.01, the point 0.059 would be located just a little over halfway along the sixth segment from the 0 point. This is because the decimal 0.059 rounds to 0.06, which is specifically represented by the position at the end of the sixth segment.

This process allows us to graphically represent decimals on the number line, and provides context for understanding the size and relative value of this decimal number.

Learn more about Position of Decimals on Number Line here:

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