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3 years ago

In the diagram, KL = , LM = , and MN = . What is the perimeter of isosceles trapezoid KLMN?

Mathematics

1 answer:

slamgirl [31]3 years ago

6 0

The trapezoid is isosceles. Thus, the bases are $\overline{KL}$ and $\overline{NM}$ , while the equal sides are $\overline{LM}$ and $\overline{KN}$ .

This also means that the length of the sides $\overline{LM}$ and $\overline{KN}$ are equal.

The perimeter of the trapezoid is the sum of the lengths of the sides of the trapezoid, so the perimeter is:

$KL+LM+MN+NL=2 \sqrt{2}+ \sqrt{5}+ \sqrt{2}+\sqrt{5}=3 \sqrt{2}+2 \sqrt{5}.$

Answer: third choice

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3 years ago

Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 15 ca

Rainbow [258]

Answer:

(A) 0.006593 or 0.6593%

(B) 0.01538 or 1.538%

Step-by-step explanation:

The total number of possibilities to pick 3 parts out of 15 possible parts is given by the following combination:

$n=\frac{15!}{(15-3)!3!}=\frac{15*14*13}{3*2*1}\\n=455\ ways\\$

(A) There are only three possibilities for which the inspector finds exactly one nonconforming part (NCC, CNC, CCN). Therefore, the probability is:

$P(N=1) = \frac{3}{455}=0.006593 =0.6593\%$

(B) There are three possibilities for which the inspector finds exactly one nonconforming part, three possibilities for two nonconforming parts (NNC, CNN, NCN), and one possibility for all nonconforming parts (NNN). The probability that the inspector finds at least one nonconforming part is:

$P(N>0) =P(N=1)+P(N=2)+P(N=3) \\P(N>0) = \frac{3}{455}+ \frac{3}{455}+ \frac{1}{455}\\P(N>0) =0.01538 =1.538\%$

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3 years ago

Is (2, 2) a solution of y < 4x - 6?<br> Choose 1 answer<br> yes or no

zalisa [80]

No, (2,2) is not solution of y < 4x - 6

Step-by-step explanation:

To solve above linear problem, we use standard method of Back- Substitution.

First of all, A point (2,2) only becomes solution of equation, if it satisfies equation $y < 4x - 6$ .

Here, the $y < 4x - 6$ seems to be like a linear equation.

In this Equation, using Back- Substitution method,

Point (2,2) : first digit 2 corresponds to x- coordinate and second digit 2 corresponds to y-coordinate.

$y < 4x - 6.....(1) \\\ x= 2 .....(2) \\\ y= 2 .....(3)$

By putting value of x and y in equation (1),

Equation becomes,

$2 < 4 \times 2 - 6$

$2 < 8 - 6$

$2 < 2$ .... not true mathematically.

Finally, the result came is not true. Therefore, (2,2) is not solution for equation

$y < 4x - 6$

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3 years ago

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Naddika [18.5K]

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3 years ago

Solve. (K+1)(k-5)=0<br> Explin how to solve ???

Anna71 [15]

Alright remember, if any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
k+1=0
k-5=0
Set the first factor equal to 0 and solve
k=-1
Set the next factor equal to 0 and solve
k=5
The final solution is all the values that make (k+1)(k-5)=0 true.
k=-1, 5

Hope this helped you out :)

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3 years ago

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