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3 years ago

Kevin can travel 22 1/2 miles in 1/3 hour .What is the average speed in miles per hour?

1 answer:

8 0

You can choose to answer this with fractions or decimals. I'll choose fractions because we won't need calculators. 22 1/2 miles "in" 1/3 hour, means 22 1/2 mi divided by 1/3 hour.
22 1/2 = [(22×2) + 1] ÷ 2 = 45/2
So (45/2)mi ÷ (1/3)hr is the same as (45/2) × (3/1), or (45×3)/2 = 135/2, which is 67 1/2, or 67.5 mi/hr (mph).

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2x = 70

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Solve the system of equations by any method. 5x+9y =16 x+2y =4

Alisiya [41]

Answer:

The system of equations has one solution at (-4, 4).

Step-by-step explanation:

We are given the system of equations:

$\displaystyle\left \{ {{5x+9y=16} \atop {x+2y=4}} \right.$

We can use elimination to solve this system. We need to multiply the second equation by -5 so we can cancel out our x-terms.

$-5\times(x+2y=4) \rightarrow -5x - 10y = -20$

Therefore, our system now becomes:

$\displaystyle\left \{ {{5x+9y=16} \atop {-5x-10y=-20}} \right.$

Now, we can add these two equations together and solve for y.

$\displaystyle(5x + 9y) + (-5x - 10y) = 0 - y\\\\16 + (-20) = -4\\\\-y = -4\\\\\frac{-y}{-1}=\frac{-4}{-1}\\\\y = 4$

Now, we can substitute our value for y into one of the equations and solve for x.

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3 years ago

Which expression is equivalent to log w (x2-6)4

natka813 [3]

Log w (x^2-6)^4

Using log a b = log a + log b, with a=w and b=(x^-6)^4:
log w (x^2-6)^4 = log w + log (x^2-6)^4

Using in the second term log a^b = b log a, with a=x^2-6 and b=4
log w (x^2-6)^4 = log w + log (x^2-6)^4 = log w + 4 log (x^2-6)

Then, the answer is:
log w (x^2-6)^4 = log w + 4 log (x^2-6)

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