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Alika [10]
3 years ago
15

The diagram shows corresponding lengths in two similar figures. Find the area of the smaller figure.

Mathematics
2 answers:
nikitadnepr [17]3 years ago
7 0

Answer:

Correct choice is D

Step-by-step explanation:

If two similar figures have the coefficient of similarity k, then the ratio between the area of these figures is equal to k^2.

You are given corresponding lengths in two similar figures, then

k=\dfrac{15}{20}=\dfrac{3}{4}.

Therefore,

\dfrac{A_{small}}{A_{large}}=\left(\dfrac{3}{4}\right)^2=\dfrac{9}{16}

and

A_{small}=\dfrac{9}{16}\cdot A_{large}=\dfrac{9}{16}\cdot 64=9\cdot 4=36\ cm^2.

butalik [34]3 years ago
5 0

The area are in the ratio of the squares of corresponding sides.

That is  15^2 : 20^2  = 225:400

so the area of the smaller figure = (225/400) * 64

= 0.5625 * 64

= 36 cm^2  (answer)

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3 years ago
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Answer:

See the explanation.

Step-by-step explanation:

We are given the function f(x) = x² + 2x - 5

Zeros :

If f(x) = 0 i.e. x² + 2x - 5 = 0

The left hand side can not be factorized. Hence, use Sridhar Acharya formula and  

x= \frac{-2+\sqrt{2^{2}-4\times(-5)\times1 } }{2} and  

x= \frac{-2-\sqrt{2^{2}-4\times(-5)\times1 } }{2}

⇒ x = -3.45 and 1.45

Y- intercept :

Putting x = 0, we get, f(x) = - 5, Hence, y-intercept is -5.

Maximum point :

Not defined

Minimum point:  

The equation can be expressed as (x + 1)² = (y + 5)

This is an equation of parabola having the vertex at (-1,-5) and axis parallel to + y-axis

Therefore, the minimum point is (-1,-5)

Domain :  

x can be any real number

Range:  

f(x) ≥ - 6

Interval of increase:

Since this is a parabola having the vertex at (-1,-5) and axis parallel to + y-axis.

Therefore, interval of increase is +∞ > x > -1

Interval of decrease:

-∞ < x < -1

End behavior :  

f(x) = x^{2} +2x-5 =x^{2}  (1+\frac{2}{x} -\frac{5}{x^{2} } )

So, as x tends to +∞ , then f(x) tends to +∞

And as x tends to -∞, then f(x) tends to +∞. (Answer)

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3 years ago
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6 0
2 years ago
Based on this equation, estimate the price of a car that had been driven 56 thousand kilometers.
OLEGan [10]

Answer:

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Step-by-step explanation:

7 0
2 years ago
A local petting zoo had a total of 98,464 visitors last year. The zoo was open every day except thanksgiving, Christmas, and New
riadik2000 [5.3K]

Answer:

The average number of visitors per day is 272.

Step-by-step explanation:

Total number of visitors in the zoo in a year =  98,464

Now,we know that  1 YEAR = 365 DAYS

Also, the zoo was closed on thanksgiving, Christmas, and New Year's Eve

So, the Number of days zoo was open = Total Days in  year -  3 days

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So, \textrm{Number of visitor per day} =  \frac{\textrm{Total number of visitors in 352 days}}{\textrm{352 days}}

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or, the number of people visiting per day is 272.

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