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almond37 [142]
3 years ago
13

Which expression is equivalent to 6 to the power of 6 times 6 to the power of -9

Mathematics
1 answer:
const2013 [10]3 years ago
5 0

Answer:

Sixth power of ten means 10 is raised to a power of 6. This means 6 will be in the exponent of 10 as 10⁶. So, our expression becomes: 3 x 10⁶.

Step-by-step explanation:

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10. What is the distance between (8,7) and (3,-5)?
Anarel [89]

Answer:

distance between points=13 units

Step-by-step explanation:

distance between points=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

put (x_1,x_2)=(8,7) and (y_1,y_2)=(3,-5)

distance between points=\sqrt{(3-8)^2+(-5-7)^2}

distance between points=\sqrt{(-5)^2+(-12)^2}

distance between points=\sqrt{25+144}

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distance between points=13 units answer

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3 years ago
The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer l
Licemer1 [7]

Answer:

longer leg: 20 in

shorter leg: 15 in

hypotenuse: 25 in

Formulas:

<u>Pythagorean Theorem</u>

c^2 = a^2 + b^2

c ... hypotenuse

a ... one leg

b ... another leg

Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).

Step-by-step explanation:

longer leg: x

shorter leg: x - 5

hypotenuse: x + 5

To find x (longer leg), let's use Pythagorean theorem.

c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x

Now let's factorize to get solutions for x.

0 = x(x-20)

First solution:

x = 0

Second solution:

x - 20 = 0\\x = 20

Since a side of a triangle has to be a positive number, x is equal to 20.

Now let's just substitute x back to get side lengths. From the question the lengths are in inches.

longer leg: x = 20 in

shorter leg: x - 5 = 20 - 5 = 15 in

hypotenuse: x + 5 = 20 + 5 = 25 in

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Answer:

Step-by-step explanation:

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What is the distance between points (2,3) and (-5,-3)
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They are 7 points away from each other.

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