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2 years ago

What is 8a^3b^-2 when a=4 and b=-5

Mathematics

2 answers:

Softa [21]2 years ago

7 0

8(4)^3=512 5^-2= 1/25

tiny-mole [99]2 years ago

5 0

8a $a^{3} +3b-2$
= 8x $4^{3} -3x(-5)-2$
= 64x8+15-2
=192+13
205

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The altitude to the hypotenuse of a right triangle divides the hypotenuse into 15 inches and 30 inch segments. Explain or show h

e-lub [12.9K]

9514 1404 393

Answer:

CX = 15√2 inches

BC = 15√3 inches

AC = 15√6 inches

Step-by-step explanation:

In this geometry, all of the triangles are similar:

ΔABC ~ ΔACX ~ ΔCBX

Corresponding segments are proportional in similar triangles, so we have ...

AX/CX = CX/BX = (long leg)/(short leg)

Filling in the numbers, we get

30/CX = CX/15

CX² = 15×30

CX = 15√2 . . . . . exact length of the altitude (inches)

Similarly, we can form proportions with the legs:

AB/BC = CB/BX

BC² = (BX)(AB) = (45)(15)

BC = 15√3 . . . inches

and

AC/AB = AX/AC

AC² = (AX)(AB) = (30)(45)

AC = 15√6 . . . inches

_____

Additional comment

You may notice that each of the segments we're interested in is the root of a product involving segments of the hypotenuse. This "root of a product" is called the geometric mean. Here, the three geometric mean relations are ...

altitude = geometric mean of hypotenuse segments

short side = geometric mean of short segment and whole hypotenuse

long side = geometric mean of long segment and whole hypotenuse

Strictly speaking the geometric mean is the n-th root of the product of n items. Here, there are only 2 items, so it is the square root of their product.

8 0

2 years ago

Ralph is 3 times as old as Sara. In 6 years , Ralph will be only twice as old as Sara will be then. Find Ralph’s age now .

Delvig [45]

Answer:

Ralph's current age is 18.

Step-by-step explanation:

Let r and s represent the current ages of Ralph and Sara respectively. Our task here is to determine r, Ralph's age now.

If Ralph is 3 times as old as Sara now, then r = 3s.

Six years from now, Ralph's age will be r + 6 and Sara's will be s + 6. Ralph will be only twice as old as Sara will be then. This can be represented algebraically as

r + 6 = 2(s + 6).

We now have the following system of linear equations to solve:

r + 6 = 2s + 12, or r - 2s = 6, and r = 3s (found earlier, see above).

r - 2s = 6

r = 3s

Substituting 3s for r in r - 2s = 6, we get 3s = 2s + 6, or s = 6. Sara is 6 years old now, meaning that Ralph is 3(6 years), or 18 years old.

Ralph's current age is 18.

3 0

2 years ago

Which are vertical angles?

vichka [17]

Answer:

You should republish this question but with a picture because this doesnt really make sense

7 0

2 years ago

Read 2 more answers

The state of Georgia has roughly 10⁷ human residents. Each human has roughly 10¹³ bacteria cells in his or her digestive tract.

crimeas [40]

Answer:

10^20

Step-by-step explanation:

So in this word problem, we have to multiply 10^13 bacteria cells on a single person by the 10^7 of people.

Always remember this, when you have exponenets with the same bases, and the question asks for multiplying and dividing exponents, you just need to add and subtract the exponent.

So in this case, we will just add since it calls for multipactation.

So we need to solve:

10^13+7

This will just equal:

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Hope this helps ;)

6 0

2 years ago

Whole numbers are written on cards and then placed in a bag. Tyra selects a single card, writes down the number. and then placed

wariber [46]

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That drives to tell that the outcomes appear to be equally like.

That means that the probabilities are uniform, so the answer is:
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3 0

2 years ago