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ioda
2 years ago
9

Zach can run 7 1/2 miles in 1 1/2 hours find the average speed in miles per hour

Mathematics
1 answer:
PtichkaEL [24]2 years ago
8 0

Zach is running 5 miles an hour.

Using division we can do 7 1/2 / 1 1/2 we would get 5.

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(x + x² + 4x) 3

3(x) + 3(x²) + 3(4x)

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3 years ago
Someone help me out please
uysha [10]

1 step (B): raise both sides of the equation to the power of 2.

(\sqrt{x+3}-\sqrt{2x-1})^2=(-2)^2,\\   (x+3)-2\sqrt{x+3}\cdot \sqrt{2x-1}+(2x-1)=4,\\ 3x+2-2\sqrt{x+3}\cdot \sqrt{2x-1}=4.

2 step (A): simplify to obtain the final radical term on one side of the equation.

-2\sqrt{x+3}\cdot \sqrt{2x-1}=4-3x-2,\\ -2\sqrt{x+3}\cdot \sqrt{2x-1}=2-3x,\\ 2\sqrt{x+3}\cdot \sqrt{2x-1}=3x-2.

3 step (F): raise both sides of the equation to the power of 2 again.

(2\sqrt{x+3}\cdot \sqrt{2x-1})^2=(3x-2)^2,\\ 4(x+3)(2x-1)=(3x-2)^2.

4 step (E): simplify to get a quadratic equation.

4(2x^2-x+6x-3)=(3x)^2-2\cdot 3x\cdot 2+2^2,\\ 8x^2+20x-12=9x^2-12x+4,\\ x^2-32x+16=0.

5 step (D): use the quadratic formula to find the values of x.

D=(-32)^2-4\cdot 16=1024-64=960, \\ \sqrt{D} =8\sqrt{5} ,\\ x_{1,2}=\dfrac{32\pm 8\sqrt{5}}{2} =16\pm 4\sqrt{5}.

6 step (C): apply the zero product rule.

x^2-32x+16=(x-16-4\sqrt{5}) (x-16+4\sqrt{5}) ,\\ (x-16-4\sqrt{5}) (x-16+4\sqrt{5}) =0,\\ x_1=16+4\sqrt{5} ,x_2=16-4\sqrt{5}.

Additional 7 step: check these solutions, substituting into the initial equation.

3 0
3 years ago
Hey, can someone help me?
mel-nik [20]
I would go with 115 is the answer you 
7 0
3 years ago
Read 2 more answers
Which graph best represents the relationship between time and the number of teams registered?
alexdok [17]
<h2>Explanation:</h2><h2></h2>

The complete question is in the attached file. So we have to choose between two graphs. On of them is a linear model while the other is an exponential model. From the statements, we have a relationship between time and the number of teams registered. So we can establishes variables in the following form:

x:\text{Time} \\ \\ y:\text{Number of teams registered}

We also know that each week 6 teams register to participate, so:

\bullet \ \text{For week 0:} \rightarrow \text{0 teams registered} \\ \\ \bullet \ \text{For week 1:} \rightarrow \text{6 teams registered} \\ \\ \bullet \ \text{For week 2:} \rightarrow \text{12 teams registered (Because 6+12)} \\ \\ \bullet \ \text{For week 3:} \rightarrow \text{18 teams registered (Because 12+6)}

As you can see, as x increases one week, y increases at a constant ratio of 6. Therefore, this can be modeled by a linear function given by the form:

y=6x

In conclusion, <em>the linear model (first graph below) is the one that bests represents  the relationship between time and the number of teams registered.</em>

7 0
3 years ago
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