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vodka [1.7K]
3 years ago
8

72 The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Fin

d the length of the segment determined by the points of intersection between the line and the other two sides of the triangle.
Mathematics
1 answer:
katrin [286]3 years ago
6 0

Answer:

  18√2

Step-by-step explanation:

The smaller triangle sharing a vertex with the larger one is similar and half the area. That means its linear dimensions are √(1/2) = (√2)/2 times those of the larger triangle.

The line segment of interest has length ...

  36 × (√2)/2 = 18√2

_____

The ratio of area of similar figures is the square of the ratio of their linear dimensions. Thus the ratio of linear dimensions is the square root of the ratio of area.

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4 years ago
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1 to 8 plz plz plz help me
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Answer:

1-8 = -7

Step-by-step explanation:

1 - 8

1 0 -1 -2 -3 -4 -5 -6 -7

4 0
2 years ago
A study of homeowners in the 5th congressional district in Maryland found that their annual household incomes are normally distr
tino4ka555 [31]

Answer:

The minimum income level for this target group is of $51,253.6.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of $41,182 and a standard deviation of $11,990

This means that \mu = 41182, \sigma = 11990

Find the minimum income level for this target group.

The 100 - 20 = 80th percentile, which is X when Z has a p-value of 0.8, so X when Z = 0.84.

Z = \frac{X - \mu}{\sigma}

0.84 = \frac{X - 41182}{11990}

X - 41182 = 0.84*11990

X = 51253.6

The minimum income level for this target group is of $51,253.6.

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3 years ago
What ordered pair is a solution of the system of equations y=x^2-x-20 and y=3x-15?
Licemer1 [7]

Hey there!!

Equations given :

y = x² - x - 20 -------- ( 1 )

y = 3x - 15 ------------ ( 2 )

Now, lets first solve for the 1st equation ...

... x² - x - 20

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... x² + 4x - 5x - 20

... x ( x + 4 ) - 5 ( x + 4 )

... ( x - 5 ) ( x + 4 )

y = ( x - 5 ) ( x - 4 )

Now, let's solve the second equation ...

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We have two equations, now getting them together..

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Divide by x-5 on both sides

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Add 4 on both sides

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Now substituting this, we get the value of y

We have,

y = 3x - 15

... y = 3(7 ) - 15

... y = 21 - 15

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Hence, the ordered pair is ( 7 , 6 )

Hope my answer helps!

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