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3 years ago

Find the value of y.

Mathematics

1 answer:

snow_tiger [21]3 years ago

4 0

Answer:

y = √55

Step-by-step explanation:

All the triangles are similar, so the ratio of short side to hypotenuse is the same for all:

5/y = y/(5+6)

y^2 = 55

y = √55

_____

Comment on the geometry

There are three "geometric mean" relationships that apply to this geometry.

the altitude BD is the geometric mean of BC and BA (√30)
the long side of the large triangle is the geometric mean of the longer segment of the hypotenuse and the whole hypotenuse (x = √66)
the short side of the large triangle is the geometric mean of the shorter segment of the hypotenuse and the whole hypotenuse (y = √55)

If you were aware of the last of these relationships, you could write down the answer without any "work."

y = √(5(5 +6)) = √55

The geometric mean is the n-th root of the product of n numbers. When there are 2 numbers, it is the square root of their product.

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3 years ago

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Which expression represents (−21−−−−√5)6 in rational exponent form? (−21)6/5 −215/6 (65)−21 (56)−21

Dennis_Churaev [7]

Answer:

$(-21)^\frac{6}{5}$

Step-by-step explanation:

Which expression represents [⁵√(−21)]⁶ in rational exponent form?

Solution:

Rational numbers are numbers which can be expressed as fractions in the form a / b, where a, b are integers and b is not equal to zero.

A rational exponent is an exponent that is a fraction. For example √2 = $2^\frac{1}{2}$ .

When expressing a number in rational exponent form, the numerator of the fractional exponent refers to a normal power, but the denominator refers to the root.

$[\sqrt[5]{(-21)}]^6 = (-21)^\frac{6}{5}$

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3 years ago

The following histogram presents the amounts of silver (in parts per million) found in a sample of rocks. One rectangle from the

gladu [14]

Answer:

The height of the missing rectangle is 0.15

Explanation:

The image attached has the mentioned histogram.

Such histogram presents the relative frequencies for the clases [0,1], [1,2],[2,3], [4,5], and [5,6] Silver in ppm.

Only the rectangle for the class [3,4] is missing.

The height of each rectangle is the relative frequency of the corresponding class.

The relative frequencies must add 1, because each relative frequency is calculated dividing the absolute class frequency by the total number in the sample; hence, the sum of all the relative frequencies is equal to the total absolute class frequencies divided by the same number, yielding 1.

In consequence, you can sum all the known relative frequencies and subtract from 1 to get the missing relative frequency, which is the height of the missing rectangle.

1. Sum of the known relative frequencies: