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ser-zykov [4K]
3 years ago
14

HELP GEOMETRY PLZ!!!

Mathematics
1 answer:
meriva3 years ago
3 0

Answer:

Statement 2.: QK/KL=16/40; PK/MK=26/65

Statement 3.: QK/KL=2/5=PK/MK

Reason 4: Vertical angles

Reason 5: SAS

Step-by-step explanation:

Statement 2:

The smaller of the sides adjacent to <PKQ (QK=16) in triangle PKQ is corresponding with the smaller of the sides adjacent to <MKL (KL=40) in triangle MKL.

The larger of the sides adjacent to <PKQ (PK=26) in triangle PKQ is corresponding with the larger of the sides adjacent to <MKL (MK=65) in triangle MKL.

Ratio of the corresponding sides:

\frac{QK}{KL}=\frac{16}{40}

\frac{PK}{MK}=\frac{26}{65}


Statement 3. Simplifying ratios:

Dividing the numerator and denominator by 8:

\frac{QK}{KL}=\frac{\frac{16}{8}}{\frac{40}{8}}\\ \frac{QK}{KL}=\frac{2}{5}

Dividing the numerator and denominator by 13:

\frac{PK}{MK}=\frac{\frac{26}{13}}{\frac{65}{13}}\\ \frac{PK}{MK}=\frac{2}{5}


Reason 4: <MKL is conguent with <PKQ because they are vertical angles (angles opposite by the vertex)


Reason 5: The two triangles (∆QPK y ∆LMK) have a congruent angle (<MKL with <PKQ) and the corresponding sides including this angle proportionals (QK/KL=2/5=PK/MK), then the two triangles (∆QPK y ∆LMK) are similar. This case is SAS.

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Online jewelry sales have increased steadily over the last 10 years. In 2003, sales were approximately 2 billion dollars, and in
KiRa [710]

Answer:   <em>(i)  The unit rate at which online jewelry sales have been increasing is 1.33 billion dollars per year. </em>

<em>(ii)  The online jewelry sales in 2019 will be 191.7 billion dollars.</em>

Step-by-step explanation:

In 2003, sales were approximately 2 billion dollars and in 2010, they were approximately 14.8 billion dollars.

(i)  If x is the number of years after 2003 and y is the amount of sales....

then the equation will be:   y= ab^x , where a is the initial amount and b is the growth rate.

for 2003,  x=0 and for 2010,  x=7

So, the two points in form of (x, y) will be:   (0,2) and (7,14.8)

Now plugging these two points int the above equation....

2= ab^0\\ \\ a= 2\\ \\ and\\ \\ 14.8=ab^7\\ \\ 14.8=2*b^7\\ \\ b^7=7.4\\ \\b= \sqrt[7]{7.4}=1.3309.... \approx 1.33

Thus, the online jewelry sales have been increasing at a rate of 1.33 billion dollars per year.

(ii)   As we got a=2 and b=1.33, so the equation will be now:  y= 2(1.33)^x

<u>For the year 2019, the value of</u>  x will be: (2019-2003) = 16

So plugging x=16 into the above equation, we will get.....

y=2(1.33)^16\\ \\ y=191.7150... \approx 191.7

<em>(Rounded to the nearest tenth)</em>

Thus, the online jewelry sales in 2019 will be 191.7 billion dollars.


6 0
3 years ago
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alisha [4.7K]
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3 0
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