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polet [3.4K]
3 years ago
15

Given segments AB and CD intersect at E.

Mathematics
1 answer:
nata0808 [166]3 years ago
7 0

The length of a segment is the distance between its endpoints.

  • \mathbf{AB = 3\sqrt{2}}
  • AB and CD are not congruent
  • AB does not bisect CD
  • CD does not bisect AB

<u>(a) Length of AB</u>

We have:

\mathbf{A = (1,2)}

\mathbf{B = (4,5)}

The length of AB is calculated using the following distance formula

\mathbf{AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}

So, we have:

\mathbf{AB = \sqrt{(1 - 4)^2 + (2 - 5)^2}}

\mathbf{AB = \sqrt{18}}

Simplify

\mathbf{AB = 3\sqrt{2}}

<u>(b) Are AB and CD congruent</u>

First, we calculate the length of CD using:

\mathbf{CD = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}

Where:

\mathbf{C = (2, 4)}

\mathbf{D = (2, 1)}

So, we have:

\mathbf{CD = \sqrt{(2 -2)^2 + (4 - 1)^2}}

\mathbf{CD = \sqrt{9}}

\mathbf{CD = 3}

By comparison

\mathbf{CD \ne AB}

Hence, AB and CD are not congruent

<u>(c) AB bisects CD or not?</u>

If AB bisects CD, then:

\mathbf{AB = \frac 12 \times CD}

The above equation is not true, because:

\mathbf{3\sqrt 2 \ne \frac 12 \times 3}

Hence, AB does not bisect CD

<u>(d) CD bisects AB or not?</u>

If CD bisects AB, then:

\mathbf{CD = \frac 12 \times AB}

The above equation is not true, because:

\mathbf{3 \ne \frac 12 \times 3\sqrt 2}

Hence, CD does not bisect AB

Read more about lengths and bisections at:

brainly.com/question/20837270

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A bicycle tire has a radius of 11 inches. To the nearest inch, how far does the tire travel when it makes 7 revolutions?
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Answer:

d = 483.56 inches

Step-by-step explanation:

We have,

Radius of a bicycle tire is 11 inches. It is required to find the distance traveled by the distance covered by the tire when it makes 7 revolutions. One revolution means the circumference of circle. So,

C=2\pi r\\\\C=2\times 3.14\times 11\\\\C=69.08\ \text{inches}

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C=69.08\times 7\\\\C=483.56\ \text{inches}

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8 0
3 years ago
In 1985, the cost of clothing for a certain familiy was $620. In 1995, 10 years later, the cost of clothing for this famility wa
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Answer:

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Calculation for the cost of this familiy's clothing in 1991

First step is to calculate the amount that is increase per year

Increase per year= ($1000-$620)/(1995-1985)

Increase per year= 380/10

Increase per year= $38

Now let y be :38*x + $620 and let x be 6 years (1991-1985)

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Using ratios we will be able to find how many free throws she will make if she attempts 60.

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42:60

Basically we kept multiply the right side of the ratio which is 10 by 2 until we were at 60 free throws.

Erin will make 42 free throws if she attempts 60 free throws.

6 0
3 years ago
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