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Maksim231197 [3]
3 years ago
6

Alicia says the expression 2(m +4)+5 is equivalent to the expression 2m+13. Identify two properties that can be used to support

Alicia's claim and justify your answer
Mathematics
1 answer:
Xelga [282]3 years ago
6 0
Associative property and distributive property
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F(x) = <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B7%7D%20-%5Csqrt%7Bx%5E2%2B2x-15%7D" id="TexFormula1" title="\sqrt{x+7} -\
elena-s [515]

Answer:

x >= -7  ................(1a)

x >= 3   ...............(2a1)

Step-by-step explanation:

f(x) =  \sqrt{x+7}-\sqrt{x^2+2x-15}  .............(0)

find the domain.

To find the (real) domain, we need to ensure that each term remains a real number.

which means the following conditions must be met

x+7 >= 0  .....................(1)

AND

x^2+2x-15 >= 0 ..........(2)

To satisfy (1),  x >= -7  .....................(1a) by transposition of (1)

To satisfy (2), we need first to find the roots of (2)

factor (2)

(x+5)(x-3) >= 0

This implis

(x+5) >= 0 AND (x-3) >= 0.....................(2a)

OR

(x+5) <= 0 AND (x-3) <= 0 ...................(2b)

(2a) is satisfied with x >= 3   ...............(2a1)

(2b) is satisfied with x <= -5 ................(2b1)

Combine the conditions (1a), (2a1), and (2b1),

x >= -7  ................(1a)

AND

(

x >= 3   ...............(2a1)

OR

x <= -5 ................(2b1)

)

which expands to

(1a) and (2a1)   OR  (1a) and (2b1)

( x >= -7 and x >= 3 )  OR ( x >= -7 and x <= -5 )

Simplifying, we have

x >= 3  OR ( -7 <= x <= -5 )

Referring to attached figure, the domain is indicated in dark (purple), the red-brown and white regions satisfiy only one of the two conditions.

3 0
3 years ago
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A circle has a radius of 4.2 cm.
patriot [66]

Step-by-step explanation:

r=4.2

cicumference of circle =2Πr=2×3.14×4.2=26.3

8 0
3 years ago
Eight less than the quotient of a number and 3 is 18
Dmitriy789 [7]
The answer is 39 
Hope this helps
8 0
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2(3 x5-8)-4x2 (8-6+2)
4vir4ik [10]

Answer:

-18

Step-by-step explanation:

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Answer:i honestly dont know just trying to get points

Step-by-step explanation:

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