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4 years ago

What is the unit rate of 115miles in 2hours

Mathematics

2 answers:

maksim [4K]4 years ago

5 0

You would divide miles to hours amd get 57.5

Dimas [21]4 years ago

5 0

115 miles in 2 hours is what we call a rate: a comparison of two numbers with very different units. This rate is 115 miles / 2 hours. It's almost like a fraction! The numerator is 115 miles, and the denominator is 2 hours.

So, what is a unit rate? A unit rate is a rate (comparison of two numbers) with a denominator of 1. So we need our rate, 115 miles / 2 hours, to have a denominator of 1. We need to make the bottom number of our rate 1 hour. How do we do that? Well, we need to divide both the numerator (115 miles) and the denominator (2 hours) by 2!

115/2=57.5. 2/2=1. So, this rate is equal to 57.5 miles / 1 hour. Since the denominator is 1, THAT's a unit rate!!

Answer: 57.5 miles / 1 hour

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What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1? PLs HELP!!

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ANSWER
$f(x)= \frac{1}{4} {(x - 1)}^{2}$

EXPLANATION

Since the directrix is
$y = - 1$

the axis of symmetry of the parabola is parallel to the y-axis.

Again, the focus being,

$(1,1)$

also means that the parabola will open upwards.

The equation of parabola with such properties is given by,

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where
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The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.

This implies that,
$h = \frac{1 + 1}{2} = 1$

and
$k = \frac{ - 1 + 1}{2} = 0$

The equation of the parabola now becomes,

$(x - 1) ^{2} = 4p(y - 0)$

$|p| = 1$

Thus, the distance between the vertex and the directrix.

This means that,

$p = - 1 \: or \: 1$

Since the parabola opens up, we choose
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${(x - 1)}^{2} = 4(1)(y - 0)$

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or

$y = \frac{1}{4} {(x - 1)}^{2}$

This is the same as,

$f(x)= \frac{1}{4} {(x - 1)}^{2}$

The correct answer is D .

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3 years ago

Read 2 more answers