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2 years ago

Find the missing length. The triangles in each pair are similar?

Mathematics

1 answer:

larisa [96]2 years ago

7 0

Answer:

The length of the missing side is 117 :)

Step-by-step explanation:

I set up a proportion using sides NM, LD, LN, and DC :

182/28 = x/18

182(18) = 28x

3276 = 28x

3276/28 = 28x/28

x = 117

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In the figure, triangle CAE is an enlargement of triangle CBD with scale factor of 4/3. The area of the smaller triangle is 9cm2

balandron [24]

Answer:

16 cm^2

Step-by-step explanation:

Given

$\triangle CAE$ -- Bigger Triangle

$\triangle CBD$ -- Smaller Triangle

$k = \frac{4}{3}$ --- Scale factor

Area of CBD = 9

Required

Determine the area of CAE

The area of triangle CBD is:

$A_1 = \frac{1}{2}bh$

$\frac{1}{2}bh = 9$

The area of CAE is:

$A_2 = \frac{1}{2}BH$

Where:

$B = \frac{4}{3}b$ and

$H = \frac{4}{3}h$

The above values is the dimension of the larger triangle (after dilation).

So, we have:

$A_2 = \frac{1}{2}*\frac{4}{3}b * \frac{4}{3} * h$

$A_2 = \frac{1}{2}*\frac{4}{3} * \frac{4}{3} *b* h$

$A_2 = \frac{1}{2}*\frac{16}{9} *b* h$

Re-order

$A_2 = \frac{16}{9}*\frac{1}{2}* b* h$

$A_2 = \frac{16}{9}*\frac{1}{2}bh$

Recall that:

$\frac{1}{2}bh = 9$

$A_2 = \frac{16}{9}*9$

$A_2 = 16$

Hence, the area is 16 cm^2

3 0

3 years ago

The city of Anvil is currently home to 21000 people, and the population has been growing at a continuous rate of 4% per year. Th

Yanka [14]

Answer:

They'll reach the same population in approximately 113.24 years.

Step-by-step explanation:

Since both population grows at an exponential rate, then their population over the years can be found as:

$\text{population}(t) = \text{population}(0)*(1 + \frac{r}{100})^t$

For the city of Anvil:

$\text{population anvil}(t) = 21000*(1.04)^t$

For the city of Brinker:

$\text{population brinker}(t) = 7000*(1.05)^t$

We need to find the value of "t" that satisfies:

$\text{population brinker}(t) = \text{population anvil}(t)\\21000*(1.04)^t = 7000*(1.05)^t\\ln[21000*(1.04)^t] = ln[7000*(1.05)^t]\\ln(21000) + t*ln(1.04) = ln(7000) + t*ln(1.05)\\9.952 + t*0.039 = 8.8536 + t*0.0487\\t*0.0487 - t*0.039 = 9.952 - 8.8536\\t*0.0097 = 1.0984\\t = \frac{1.0984}{0.0097}\\t = 113.24$

They'll reach the same population in approximately 113.24 years.

4 0

3 years ago

7. The scale on a map of Florida is 1 ⅛ inches to 25 miles. The distance on the map from Gainesville to Ocala is 1 ⅝ inches. Bas

sergij07 [2.7K]

Answer:

Since I figure you don't need this answer anymore, I'm just using it for free pts

Step-by-step explanation:

8 0

3 years ago

What are the real and complex solutions of the polynomial equation? X4-41x2=-400

stich3 [128]

For the answer to the question above, I'll provide a solution for my answer below.
x^4 - 41x^2 = - 400
=> x^4 - 41x^2 + 400 = 0 
=> x^2 = (1/2) [41 ±√(1681 - 100)] 
=> x^2 = (1/2) (41 ± 9) 
=> x^2 = 16 or 25

So, therefore, the answers for your problem are
=> x = ± 4 or ± 5.

I hope my answer helped you.

8 0

3 years ago

a paper factory makes 8415 sheets of paper and 45 minutes how many sheets of paper does the factory make in one minute

lesantik [10]

Do 8415 divided by 45 which is 187

4 0

3 years ago

Read 2 more answers