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TEA [102]
2 years ago
4

Jolene is creating a model of a pyramid. The model created will need to be scaled up from the blueprint. triangle ACB, point D i

s on segment AC between points A and C, point E is on segment BC between points B and C If segments DE and AB are parallel, which of the following expressions will help Jolene determine the length of segment AC? AC equals CB times CD all over CE AC = AB AC equals CB times AC all over CE AC = BC

Mathematics
1 answer:
NeTakaya2 years ago
3 0

Answer:

AC equals CB times CD all over CE (option A)

Step-by-step explanation:

To determine length of segment AC, we would draw the diagram obtained from the given information.

Find attached the diagram.

The diagram gives two similar triangles: ∆ACB and ∆DCE

Using similar triangles theorem, ratio of corresponding sides are equal.

There are two ways to get AC using the theorem

1st: AC/AB = DC/DE

AC = AB × (DC/DE)

2nd: AC/CB = DC/CE

AC = CB × DC/CE

Let's compare with the options to find out which one was used.

a) AC equals CB times CD all over CE b) AC = AB

c) AC equals CB times AC all over CE d) AC = BC

The correct option from the workings  we derived is AC equals CB times CD all over CE (option A)

It is same as: AC = CB × DC/CE

CD = DC

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Describe a triangle for which the centroid, circumcenter, incenter, and orthocenter are the same point. What features of this tr
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Answer:

An equilateral triangle

Step-by-step explanation:

Because an equilateral has a feature that all sides have the same length and all angles are of the same, it does not matter from which side and peak the centroid, circumcenter, incenter and orthocenter is created, they would always end up at the same point.

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2 years ago
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In triangle ABC, m∠ABC = (4x – 12)° and m∠ACB = (2x + 26)°. Yin says that if x = 19, the triangle must be equilateral. Is he cor
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He is not correct.  If this is to be an equilateral triangle then all the angles must be the same measure.  That means that 180/3 = 60°.  They all have to equal 60°.  If one of the angles measures 4x-12, then 4x-12=60.  Solving for x, we will add 12 to both sides to get 4x=72.  x here is 18.  For the other angle measuring 2x+26, we would do the same.  2x+26=60.  Subtract 26 from both sides to get 2x= 34 and x = 17.  He was way off.
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2 years ago
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Sofia is working two summer jobs, making $12 per hour babysitting and making $8 per hour clearing tables. In a given week, she c
Mamont248 [21]

The possible values for the number of whole hours clearing tables that she must work to meet her requirements is 2, 3 hours

<em><u>Solution:</u></em>

Amount earned in babysitting = $ 12 per hour

Amount earned in clearing tables = $ 8 per hour

In a given week, she can work a maximum of 17 total hours and must earn a minimum of $180

Sofia worked 14 hours babysitting

Therefore,

Amount earned at babysitting = 14 x 12 = 168

Thus, Sofia earned $ 168 at babysitting

Sofia must earn a minimum of $ 180

Remaining amount to be earned = 180 - 168 = 12

Thus, Sofia must earn $ 12 from clearing tables

Amount earned in clearing tables = $ 8 per hour

So, she must work for atleast 1.5 hours to get $ 12 from clearing tables

She can work a maximum of 17 total hours and Sofia worked 14 hours babysitting

Remaining is 17 - 14 = 3 hours

Thus possible values for the number of whole hours clearing tables that she must work to meet her requirements is 2 hours or 3 hours

3 0
2 years ago
Zucchini weights are approximately normally distributed with mean 08 pound and standard deviation 0.25 pound. Which of the follo
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Answer:

The correct option is  A

Step-by-step explanation:

From the question we are told that

   The  mean is  \mu  =  0.8 \ pounds

    The standard deviation is  \sigma =  0.25  \  pounds

Generally the the probability that a  randomly selected zucchini will weigh between 0 55 pound and 13 pounds is mathematically represented as

       P(0.55 <  X  <  1.3)  =  P(\frac{0.55 - 0.8}{ 0.25} <  \frac{X -  \mu}{\sigma }  <  \frac{1.3 - 0.8}{0.25})

=>    P(0.55 <  X  <  1.3)  =  P( -1 <  Z  <  2 )

So looking the option of normal curves given in the question we see that it is option A that matches our interval  

8 0
2 years ago
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