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3 years ago

I need help with this if you get it right I will mark you

Mathematics

1 answer:

Arlecino [84]3 years ago

4 0

9514 1404 393

Answer:

D 9/DF = 18/16

Step-by-step explanation:

Corresponding sides are proportional. The proportions based on a given similarity statement can be written 4 ways.

For these isosceles triangles, the similarity statement could be written either of two ways:

ΔDEF ~ ΔABC or ΔDEF ~ ΔCBA

Corresponding sides will depend on the similarity statement you use. Using the first one, they are ...

DF and AC (short sides)

DE and AB (long sides)

EF and BC (long sides)

For each (short side, long side) pair, we can write the proportion 4 ways:

DF/DE = AC/AB ⇒ DF/9 = 16/18
DF/AC = DE/AB ⇒ DF/16 = 9/18
DE/DF = AB/AC ⇒ 9/DF = 18/16 . . . . . matches choice D
AC/DF = AB/DE ⇒ 16/DF = 18/9

Using the other pair of long sides, or using the other similarity statement, the numerical proportions are the same as the ones listed above.

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Carl ran around the track 3 more times than Daria and 2 fewer times than Erin. When they were done they added up the number of l

Paul [167]

Answer:

Total laps = 10d

Step-by-step explanation:

Let c = Carl's laps

d = Daria's laps

e = Erin's laps

c = 3d

c = e/2

c + d + e = totals laps

We can insert 3d in place of c in the third equation

3d + d + e = total laps

Also, e/2 equals 3d

e/2 = 3d

Multiply both sides by 2

(e/2 = 3d)2

e = 6d

Insert the new e

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2 years ago

Solve each inequality below. Represent the solutions on number lines. 7x − 2 < 3 + 2x

LekaFEV [45]

Hi, I would be glad to help you here.

<span>7x − 2 < 3 + 2x

Move terms

7x - 2x - 2 < 3

Collect the like terms

(7x - 2x) = 5x (<3 + 2 stays the same)

Calculate

5x (<3 + 2 = 5)

5x <5

Divide both sides of the inequality by (5) giving you,

x < 1

So, finally in a total the correct answer here is (x < 1)

</span>

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3 years ago

Find the domain and range of the following function f(x) = 3lx+7l-2

Vesna [10]

Answer:

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Step-by-step explanation:

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3 years ago

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Pachacha [2.7K]

Answer:

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If f(x)=x is your normal function, then flipping it across the y-axis would look like f(x)=-x.

Step-by-step explanation:

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3 years ago

<img src="https://tex.z-dn.net/?f=%20%20%5Crm%20%20%5Clim_%7Bk%20%5Cto%20%5Cinfty%20%7D%20%5Csqrt%5B%20%20k%5D%7B%20%5CGamma%20%

Naddik [55]

We have

$\sqrt[k]{\Gamma\left(\dfrac1k\right) \Gamma\left(\dfrac2k\right) \cdots \Gamma\left(\dfrac kk\right)} \\\\ = \exp\left(\dfrac{\ln\left(\Gamma\left(\dfrac1k\right) \Gamma\left(\dfrac2k\right) \cdots \Gamma\left(\dfrac kk\right)\right)}k\right) \\\\ = \exp\left(\dfrac{\ln\left(\Gamma\left(\dfrac1k\right)\right)+\ln\left( \Gamma\left(\dfrac2k\right)\right)+ \cdots +\ln\left(\Gamma\left(\dfrac kk\right)\right)}k\right)$

and as k goes to ∞, the exponent converges to a definite integral. So the limit is

$\displaystyle \lim_{k\to\infty} \sqrt[k]{\Gamma\left(\dfrac1k\right) \Gamma\left(\dfrac2k\right) \cdots \Gamma\left(\dfrac kk\right)} \\\\ = \exp\left(\lim_{k\to\infty} \frac1k \sum_{i=1}^k \ln\left(\Gamma\left(\frac ik\right)\right)\right) \\\\ = \exp\left(\int_0^1 \ln\left(\Gamma(x)\right)\, dx\right) \\\\ = \exp\left(\dfrac{\ln(2\pi)}2}\right) = \boxed{\sqrt{2\pi}}$

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2 years ago