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Pachacha [2.7K]

3 years ago

13

Lia has a goal of walking at least 20 miles. She walks at a rate of 5 miles per hour. Which inequality can Lia use to find h, th

e number of hours she should walk in order to meet or exceed her goal? A. 5h ≥ 20 B. 5h ≤ 20 C. H+5 ≥ 20 D. H+5 ≤ 20

1 answer:

mars1129 [50]3 years ago

7 0

Answer:

5h ≤ 20 or h ≤ 4

Step-by-step explanation:

Lia walks at a rate of 5 miles per hour.

Lia has a goal of walking at least 20 miles

Let h be the number of hours she should walk in order to meet or exceed her goal.

At least in inequality means ≤. ATQ,

5h ≤ 20

Dividing both sides by 5.

h ≤ 4

So, she should walk atleast 4 hours. Hence, the correct option is (b).

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Multiply output number by 4.

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<em>The applicable theorem is the mid-point theorem </em>
<em>The appropriate formula for area is the Heron's formula </em>
<em>The ratio of ABC to DEF is 1 : 9</em>

<u>(a) The length of IJ</u>

The given parameter are:

$\mathbf{EF = 9m}$

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The above highlight means that

$\mathbf{IJ= \frac 12 \times EF}$ --- midpoint theorem

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In (a), the midpoint theorem is used to calculate IJ

GH and IJ are corresponding sides of similar triangles,

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For the given triangles, the lengths of the sides are known.

When side lengths are known, the formula to use for finding the triangle's area is the Heron's formula.

The Heron's formula is:

$\mathbf{Area = \sqrt{s \times (s -a) \times (s - b) \times (s - c)}}$

Where:

$\mathbf{s = a + b + c}\\\mathbf{a,b,c \to sides\ of\ the\ triangle}$

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For the small triangle, we have:

$\mathbf{a= 3.8,\ b = 4,\ c = 3}$

So, we have:

$\mathbf{s = 3.8 + 4 + 3 = 10.8}$

So, the area is:

$\mathbf{Area = \sqrt{s \times (s -a) \times (s - b) \times (s - c)}}$

$\mathbf{A_{small} = \sqrt{10.8 \times (10.8 -3.8) \times (10.8 - 4) \times (10.8 - 3)}}$

$\mathbf{A_{small} = \sqrt{4009.824}}$

For the big triangle, we have:

$\mathbf{a= 11.4,\ b = 12,\ c = 9}$

So, we have:

$\mathbf{s = 11.4 + 12 + 9 = 32.4}$

So, the area is:

$\mathbf{Area = \sqrt{s \times (s -a) \times (s - b) \times (s - c)}}$

$\mathbf{A_{big} = \sqrt{32.4 \times (32.4 -11.4) \times (32.4 - 12) \times (32.4 - 9)}}$

$\mathbf{A_{big} = \sqrt{324795.744}}$

The ratio of the small triangle to the big triangle is:

$\mathbf{Ratio = A_{small} : A_{big}}$

$\mathbf{Ratio = \sqrt{4009.824}:\sqrt{324795.744}}$

Divide by 4009.824

$\mathbf{Ratio = \sqrt{1}:\sqrt{81}}$

Take square roots

$\mathbf{Ratio = 1 : 9}$

Hence, the ratio of ABC to DEF is 1 : 9

Read more about similar triangles at:

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The cost per can will be:

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How about Food Lion?

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Total cost: $2.75

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Answer: Three-fourths divided by one-half is <u><em>one and a half.</em></u>

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<em> </em>

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3 years ago