X^{4} - 5x^(2) + 2x + 3

Regan's New Year's resolution is to exercise more. Today, she plans to run 1.5 miles on the track around her school's football f

Contact [7]

Answer:

6 laps

Step-by-step explanation:

According to the scenario, calculation of the data are as follows:

Each lap = 0.25 miles

Regan's plan to run= 1.5 miles

So, we can calculate number of laps by using following formula,

Number of laps = Total miles to run ÷ each lap miles

By putting the value, we get

Number of laps = 1.5 miles ÷ 0.25 miles

= 6 laps

So, she should run 6 laps.

7 0

3 years ago

Why is it called point-slope formula?

bogdanovich [222]

Yeah what they said

5 0

3 years ago

Odette plants basil from seed and each day measures the height of the plants compared to the soil line. She records her measurem

Leno4ka [110]

Answer: are there any options

Step-by-step explanation:

6 0

3 years ago

What is the 3rd equivalent fraction to 2/3

olga_2 [115]

Answer:

What do you mean by third equivilent fraction? One equivalent fraction is 4/6.

Step-by-step explanation:

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B3x%5E%7B8%7D%2A7x%5E%7B3%7D%20%7D%7B3x%5E%7B6%7D%2A7%20%7D" id="TexFormula1" title="

denis23 [38]

Answer:

$a = \dfrac{x^2}{3} \quad \textsf{and} \quad b = \dfrac{x^3}{7}$

Step-by-step explanation:

Given expression:

$\dfrac{3x^{8} \cdot 7x^{3} }{3x^{6} \cdot 7 }$

There are several ways this problem can be approached, and therefore many different answers. The goal is to reduce the given expression to a simple product of two terms in x, set that to the given form 3a⋅7b then solve for a and b.

$\implies \dfrac{3x^{8} \cdot 7x^{3} }{3x^{6} \cdot 7}$

Cancel the common factors 3 and 7:

$\implies \dfrac{\diagup\!\!\!\!3x^{8} \cdot \diagup\!\!\!\!7x^{3} }{\diagup\!\!\!\!3x^{6} \cdot \diagup\!\!\!\!7}$

$\implies \dfrac{x^8 \cdot x^3}{x^6}$

Separate the fraction:

$\implies \dfrac{x^8}{x^6} \cdot x^3$

$\textsf{Apply the quotient rule of exponents} \quad \dfrac{a^b}{a^c}=a^{b-c}:$

$\implies x^{8-6} \cdot x^3$

$\implies x^{2} \cdot x^3$

Now equate the simplified expression to the given form:

$\implies x^{2} \cdot x^3=3a \cdot 7b$

Therefore:

$\begin{aligned}x^{2} &=3a \:\: &\textsf{ and }\:\: \quad x^3 &=7b\\ \Rightarrow a & = \dfrac{x^2}{3} & \Rightarrow b & = \dfrac{x^3}{7}\end{aligned}$

However, we could also separate them as:

$\begin{aligned}x^{3} &=3a \:\: &\textsf{ and }\:\: \quad x^2 &=7b\\ \Rightarrow a & = \dfrac{x^3}{3} & \Rightarrow b & = \dfrac{x^2}{7}\end{aligned}$

Another way of writing them would be to go back a few steps and separate the fraction in x terms differently:

$\implies \dfrac{x^8 \cdot x^3}{x^6}=x^8 \cdot \dfrac{x^3}{x^6}=x^8 \cdot x^{-3}$

Therefore, this would give us:

$\begin{aligned}x^{8} &=3a \:\: &\textsf{ and }\:\: \quad x^{-3} &=7b\\ \Rightarrow a & = \dfrac{x^8}{3} & \Rightarrow b & = \dfrac{1}{7x^3}\end{aligned}$

As the given expression reduces to x⁵, we can separate the x term in any way we like, so long as the coefficient of a is ¹/₃ and the coefficient of b is ¹/₇. Therefore, there are many possible answers.

7 0

2 years ago

Read 2 more answers

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