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3 years ago

How many ways can you write 5^8 as a quotient of two exponential terms? Explain your reasoning.

1 answer:

6 0

Exponents can be expressed in terms of quotient or fraction.
For example: x^6 can be expressed as x^8 / x^2 = x^8-2 = x^6.

From the question, 5^8 can be expressed as
5^10/5^2 = 5^8
(5^2)(5^8) / (5^2) = 5^8

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Solve with solution...no spam answers pls

Agata [3.3K]

Let's analyze Hannah's work, step-by-step, to see if she made any mistakes.

In Step 1, Hannah wrote $\dfrac{d}{dx} (-3+8x)$ as the sum of two separate derivatives $\dfrac{d}{dx}(-3)+ \dfrac{d}{dx} (8x)$ using the sum rule.

This step is perfectly fine.

In Step 2, $\dfrac{d}{dx}(8x)$ was kept as it is, and $\dfrac{d}{dx}(-3)$ was rewritten as $0$ using the constant rule.Indeed, according to the constant rule, the derivative of a constant number is equal to zero.

This step is perfectly fine.

In Step 3, $\dfrac{d}{dx} (8x)$ was rewritten as $\dfrac{d}{dx}(8) \dfrac{d}{dx}(x)$ supposedly using the constant multiple rule.

The problem is that according to the constant multiple rule, $\dfrac{d}{dx}(8x)
$ should be rewritten as $8 \dfrac{d}{dx}(x)$ and not as $\dfrac{d}{dx}(8)\dfrac{d}{dx}(x)$ .

Therefore, Hannah made a mistake in this step.

6 0

4 years ago

Read 2 more answers

Kasey needs 1.5 cups of milk and 4 cups of sugar to make 12 muffins. She plans to make 36 muffins . How many fl oz of sugar does

Masja [62]

Answer:

12 cups of milk

Step-by-step explanation:

36/12= 3

4 x 3= 12

So the Answer is 12 cups of milk

4 0

3 years ago

Rani is making rice pudding. She uses

Goryan [66]

Rani will use 3/2 cups of white rice for 3 cups of milk.

<h3>What is termed as unitary method?</h3>

"It is a method in which we obtain the value of a single unit by subtracting the value of multiple units and thus the value of multiple units by subtracting the value of a single unit."

The value of several things is given in the unitary method, and we must either figure out the significance of more or lesser things.
To do so, we must first determine the value of one item by division and then determine the value of ever more or fewer items by multiplication.

Now, for the given question;

1 cup of white rice is required for every 2 cups of milk by Rani.

Thus,

2 cups of milk ------> 1 cup of white rice.

So, using unitary method. Divide both side by 2.

1 cups of milk ------> 1/2 cup of white rice.

Now, calculate for the 3 cups of milk.

multiplying both side by 3.

3 cups of milk ------> 3/2 cup of white rice.

Therefore, the 3/2 cups of white rice required for the 3 cups of milk.

To know more about unitary method, here

brainly.com/question/28540270

#SPJ9

6 0

1 year ago

Austin bought 5 pairs of jeans and 2 shirts for $166. Travis bought 3 pairs of jeans and 4 shirts for $164 at the same store. Ho

OLEGan [10]

Answer:

pair of jeans = 21

shirt = 30.5

Step-by-step explanation:

Let the cost of each pair of jeans be $ x, and the cost of each shirt be $ y.

Since, cost of each pair of jeans is $ x, the cost of 5 pair of jeans will be $ 5x and cost of 2 shirts will be $ 2x.

Likewise, the cost of each pair of jeans is $ x, so the cost of 3 pair of jeans will be $ 3x and cost of 4 shirts will be $ 4y.

5 pair of jeans and 2 shirts for $166. This means:

Equation 1: 5x + 2y = 166

3 pair of jeans and 4 shirts for $164. This means:

2x + 4y = 164

Dividing both sides by 2, we get:

Equation 2: x + 2y = 82

Subtracting Equation 2 from Equation 1, we get:

5x + 2y - (x + 2y) = 166 - 82

5x + 2y - x - 2y = 84

4x = 84

y = 30.5

Using the value of x, in Equation 2, we get:

21 + 2y = 82

2y = 61

y = 30.5

Since, x represents the cost of pair of jeans, the cost of each shirt is $ 16.

y represents the cost of sweater, so the cost of each sweater is $ 33.

4 0

3 years ago

Which conditions will result in the construction of a unique triangle?

Arlecino [84]

Answer:

A unique triangle will be produced if you are given: all three sides (Side-Side-Side) two sides and the included angle (Side-Angle-Side) two angles and the included side (Angle-Side-Angle)

Step-by-step explanation:

oof sorry I barely realized that I was supposed to select a number....sorry, but hope this helps :)

3 0

3 years ago