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xz_007 [3.2K]
3 years ago
9

Are triangles DEF and LNM similar if LN equals 5 MN equals 3 DE equals 10 and FE equals 6

Mathematics
1 answer:
melisa1 [442]3 years ago
4 0

Answer:

D.  Yes by SAS Similarity Postulate

Step-by-step explanation:

This is the answer because if you flip triangle LNM around to shape the DEF.  Then you will see that:

1. angle D is congruent to angle L

2. angle E is congruent to angle N

3. angle F is congruent to angle M

4. angle E and N are both 90 degrees

Because (DE and LN) and (MN and FE) are similar and (E and N) are 90 degrees, then we do not need (FD and ML) to tell if triangle DEF and triangle LNM is similar or not. They are similar.

We next need to figure out if the triangles are similar by SSS (Side-side-side) Similarity Postulate or SAS (side-angle-side) Similarity Postulate.  The SAS Similarity Postulate states that if you have 2 similar sides and 1 congruent angle, then the two shapes are similar. Right now we have 2 similar sides in (DE and LN) and (MN and FE) and 1 congruent angle that are both 90 degrees. This follows all the rules of the SAS Similarity Postulate, so that means that these two triangles are similar by SAS Similarity Postulate.

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yawa3891 [41]

Answer: 900 boxes

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3 0
3 years ago
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Ming throws a stone off a bridge into a river below.
AURORKA [14]

Answer:

1 seconds after being thrown, the stone reaches its max height

Step-by-step explanation:

The parabolic (quadratic) equation is:

h(x)=-5(x-1)^2+45

Lets expand this in the form ax^2+bx+c, so we have:

h(x)=-5(x-1)^2+45\\h(x)=-5(x^2-2x+1)+45\\h(x)=-5x^2+10x-5+45\\h(x)=-5x^2+10x+40

We can say the values of a,b, and c, now to be:

a = -5

b = 10

c = 40

The number of seconds at which the max would occur is given by the point, x, at:

x=-\frac{b}{2a}

We know a and b, let's find the seconds, x,

x=-\frac{b}{2a}=-\frac{10}{2(-5)}=-\frac{10}{-10}=--1=1

Hence,

1 seconds after being thrown, the stone reach its max height

6 0
3 years ago
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A manufacturing process makes rods that vary slightly in length but follow a normal distribution with mean length 25 cm and stan
Galina-37 [17]

Answer:

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22)  = 0.1251

Step-by-step explanation:

<u><em>Step(i):</em></u>-

Given mean of the Population = 25cm

Given standard deviation of the Population = 2.60

Let 'x' be the random variable in normal distribution

Given x=22

Z = \frac{x-mean }{S.D} = \frac{22-25}{2.60} = -1.15

<u><em>Step(ii):</em></u>-

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22) = P( Z<-1.15)

             = 1-P(Z>1.15)

             =  1-( 0.5+A(1.15)

             =  0.5 - A(1.15)

             = 0.5 - 0.3749

             = 0.1251

The probability of randomly selecting a rod that is shorter than 22 cm

P(X<22)  = 0.1251

7 0
3 years ago
What’s the answer????
BlackZzzverrR [31]

Answer:

1. 0.6

2. 0.25

Step-by-step explanation:

because math

7 0
3 years ago
Which is equivalent to 3 cube root 125
aleksklad [387]
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remember that \sqrt[n]{x^m}=x^\frac{m}{n}
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so
3 \sqrt[3]{125}=3*5=15 or \sqrt[3]{125} =5not sure which one you mean
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3 years ago
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