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Brilliant_brown [7]
3 years ago
10

Fill in the blanks to rewrite the following statement with variables: Given any positive real number, there is a positive real n

umber that is smaller. (a) Given any positive real number r, there is s such that __________ s is __________ . (b) For any __________ , __________ such that s < r.
Mathematics
1 answer:
sveticcg [70]3 years ago
3 0

Answer:

a) there is s such that <u>r>s</u> and s is <u>positive</u>

b) For any <u>r>0</u> , <u>there exists s>0</u> such that s<r

Step-by-step explanation:

a) We are given a positive real number r. We need to wite that there is a positive real number that is smaller. Call that number s. Then r>s (this is equivalent to s<r, s is smaller than r) and s is positive (or s>0 if you prefer). We fill in the blanks using the bold words.

b) The last part claims that s<r, that is, s is smaller than r. We know that this must happen for all posirive real numbers r, that is, for any r>0, there is some positive s such that s<r. In other words, there exists s>0 such that s<r.

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If g(x) = x^2 + 6x with x ≥ -3, find g ^-1(0).
Dvinal [7]

Answer: 0

<u>Step-by-step explanation:</u>

g(x) = x² + 6x   ; x ≥ -3

To find the inverse, swap the x's and y's and solve for "y":

    x = y² + 6y

x + 9 = y² + 6y + 9   <em>add 9 to both sides to create a perfect square</em>

x + 9 = (y + 3)²

+/-\sqrt{x+9} = y + 3   <em>take square root of both sides</em>

-3 +/-\sqrt{x+9} = y    ; y ≥ -3

g⁻¹(0) = -3 +/-\sqrt{0+9}

        = -3 +/-\sqrt{9}

        = -3 ± 3

        = -3 + 3   ,   -3 - 3

        =     0      ,      -6

since the restriction is: y ≥ -3, then -6 is not valid

4 0
3 years ago
Please help<br> Quick I added the pic
Natali5045456 [20]
Exact form: 34/5

Decimal Form: 6.8

Mixed Number Form: 6 4/5

Hope this helps!
8 0
3 years ago
Select the function whose graph is shifted one unit below the graph of y=2/x-4
MAVERICK [17]
This is in the form of a slope formula where y=mx+b. B pretty much gives you the vertical shift. Meaning that y=2/x-3 would be correct.
7 0
3 years ago
I need help fast please
marta [7]

Step-by-step explanation:

(-)(-) = +

-  \frac{3}{5}  +  \frac{5}{9}

-   \frac{27}{45}  +  \frac{25}{45}

- \frac{2}{45}

8 0
3 years ago
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Arturiano [62]

Answer:

-9y = -7x + 1

y = 7/9x -1/9 is the answer

6 0
3 years ago
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