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kumpel [21]
2 years ago
7

ABC and ∆PQR are similar. ∆ABC is dilated by a scale factor of 1.25 and rotated 45° counterclockwise about point B to form ∆PQR.

The side lengths of ∆ABC are , 5 units; , 4.2 units; and , 4 units. Match each side of ∆PQR to its length.
Mathematics
1 answer:
loris [4]2 years ago
8 0
This is the concept of transformation of figures, given that ΔABC is similar to ΔPQR, the sides of ABC are 5 units, 4.2 units and 4 units. Since the two triangles are similar and PQR is the image of ABC under the dilation 1.25, the sides of PQR will be:
(5*1.25),(4.2*1.25),(4*1.25)
this will give us:
6.25, 5.25, 5
The length of the sides of PQR are 6.25 units, 5.25 units and 5 units
Hope you get a good grade
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bogdanovich [222]
8 dollars is the answer
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Simplify to create an equivalent expression. 8−4(−x+5)
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Read 2 more answers
In triangle RST, U is the midpoint of RS, V is the midpoint of ST, and W is the midpoint of TR. Use the triangle diagram to answ
Zolol [24]

(1)

we are given

U is the midpoint of RS

and we have

RU=12

so, we can use formula

RS=2RU

we can plug values

RS=2\times 12

RS=24............Answer

(2)

V is the midpoint of ST

so, we get

SV=VT

now, we can plug values

2x=11

divide both sides by 2

x=5.5.........Answer

(3)

now, we can find y

W is the midpoint of TR

so, we get

RW=WT

we can plug value

15.9=3y

divide both sides by 3

y=5.3

(4)

we can see that

triangles URW and RST are similar

so, their sides ratios must be equal

so, we get

\frac{RW}{RT} =\frac{UW}{ST}

we can plug values

\frac{15.9}{2\times 15.9} =\frac{UW}{2VT}

\frac{15.9}{2\times 15.9} =\frac{UW}{2\times 11}

UW=22\times \frac{15.9}{2\times 15.9}

UW=11...........Answer

(5)

we can see that

triangles SUV and RST are similar

so, their sides ratios must be equal

so, we get

\frac{SU}{SR} =\frac{UV}{RT}

now, we can plug values

\frac{12}{2\times 12} =\frac{UV}{2\times 15.9}

UV=2\times 15.9\times \frac{12}{2\times 12}

UV=15.9.............Answer

4 0
2 years ago
An experienced carpenter can frame a house twice as fast as an apprentice. Working together, it takes the carpenters 2 days. How
AleksAgata [21]

Answer:

<em>6 days</em>

<em></em>

Step-by-step explanation:

Let the time taken by Carpenter working alone = C days

Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2C days

Time taken working together = 2 days

Work done in one day working together = \frac{1}{2}

Work done in one day by Carpenter working alone = \frac{1}{C}

Work done in one day by apprentice working alone = \frac{1}{2C}

Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone =  \frac{1}{C}+\frac{1}{2C} = Work done in one day working together = \frac{1}{2}

\dfrac{1}{C}+\dfrac{1}{2C}=\dfrac{1}{2}\\\Rightarrow \dfrac{2+1}{2C}=\dfrac{1}{2}\\\Rightarrow C = 3\ days

Time taken by Carpenter alone to complete the work = 3 days

Time taken by Apprentice alone to complete the work = 3 \times 2= <em>6 days</em>

4 0
2 years ago
in a random sample of 200 people, 154 said that they watched educational television. fine the 90% confidence interval of the tru
melisa1 [442]

Answer:

[0.7210,0.8189] = [72.10%, 81.89%]

Step-by-step explanation:

The sample size is  

n = 200

the proportion is

p = 154/200 = 0.77

<em>Since both np ≥ 10 and n(1-p) ≥ 10 </em>

<em>We can approximate this discrete binomial distribution with the continuous Normal distribution. As the sample size is large enough, not applying the continuity correction factor makes no significant  difference. </em>

The approximation would be to a Normal curve with this parameters:

<em>Mean </em>

p = 0.77

<em>Standard deviation </em>

\bf s=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.77*0.23}{200}}=0.0298

The 90% confidence interval for the proportion would be then  

\bf  [0.77-z^*0.0298, 0.77+z^*0.0298]

where \bf z^* is the 10% critical value for the Normal N(0,1) distribution , this is a value such that the area under the N(0,1) curve outside the interval \bf [-z^*,z^*] is 10%=0.1

We can either use a table, a calculator or a spreadsheet to get this value.

In Excel or OpenOffice Calc we use the function

<em>NORMSINV(0.95) and we get a value of 1.645 </em>

The 90% confidence interval for the proportion is then

\bf  [0.77-1.645^*0.0298, 0.77+1.645^*0.0298]=[0.7210,0.8189]

This means there is a 90% probability that the proportion of people who watch educational television is between 72.10% and 81.89%

If the television company wanted to publicize the proportion of viewers, do you think it should use the 90% confidence interval?

Yes, I do.

5 0
2 years ago
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