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Ad libitum [116K]
3 years ago
13

What is the minimum possible value for y in the equation y = x^2 + 12x + 5?

Mathematics
1 answer:
Dafna11 [192]3 years ago
4 0

Answer:

Step-by-step explanation:

hello :

y = x² + 12x + 5

y = ( x²+12x+36) -36+5

y= (x+6)²-31.......vertex form when the minimum possible value is : - 31

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A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times.
tatyana61 [14]

Answer:

(a)g(n)=0.05\cdot 2^n

(b)g^{-1}(n)=\log_{2}20g(n)

(c)43 times

Step-by-step explanation:

<u>Part A</u>

The paper's thickness = 0.05mm

When the paper is folded, its width doubles (increases by 100%).

The thickness of the paper grows exponentially and can be modeled by the function:

g(n)=0.05(1+100\%)^n\\\\g(n)=0.05\cdot 2^n

<u>Part B</u>

<u />g(n)=0.05\cdot 2^n\\2^n=\dfrac{g(n)}{0.05}\\ 2^n=20g(n)\\$Changing to logarithm form, we have:\\\log_{2}20g(n)=n\\$Therefore:\\g^{-1}(n)=\log_{2}20g(n)<u />

<u />

<u>Part C</u>

If the thickness of the paper, g(n)=384,472,300,000 mm

Then:

g^{-1}(n)=\log_{2}20g(n)\\g^{-1}(n)=\log_{2}20\times 384,472,300,000\\=\dfrac{\log 20\times 384,472,300,000}{\log 2} \\g^{-1}(n)=42.8 \approx 43\\n=43

You must fold the paper 43 times to make the folded paper have a thickness that is the same as the distance from the earth to the moon.

3 0
3 years ago
A butcher $32 for X pounds of beef ribs. Which expression represents the price per pound?
Lera25 [3.4K]

Answer:

The expression $32/x represents the price per pound.

Step-by-step explanation:

Given:

$32 for X pounds of beef ribs.

Now, the symbol which represents the per is this →  / .

So, $32/x shows the expression for the price per pound.

Therefore, the expression $32/x represents the price per pound.

4 0
3 years ago
Write an equation of the line that passes through a pair of points (-5, -2), (4, 5)
PIT_PIT [208]
To find the equation of a line knowing two points it passes through, we must first find the slope and then substitute the x and y values to figure out the y intercept. 

First thing is to find the slope using the formula m = Δy ÷ Δx
m = 5 - (-2) ÷ 4 - (-5)

Now we simplify 
m = 7 ÷ 9 

Our equation so far is y = 7/9x + b. Now we can substitute the values of x and y from a point to figure out the answer. The equation here uses the point (4,5)

5 = 7/9 · 4 + b

Get b on one side
5 - 28/9 = b

Simplify
b = 1 + 8/9

That makes the equation of the line y = 7/9x + (1 + 8/9)
8 0
3 years ago
Read 2 more answers
Plz answer it fast...
Sveta_85 [38]

Answer:

Rs 2163.20.

Step-by-step explanation:

The formula for this is

A = P(1 + r)^t     where P is the amount invested, r = the rate (as a decimal) and t = the number of years.

So for rs 2000 we have:

A = 2000(1 + 0.04)^2 = Rs 2163.20

4 0
3 years ago
A line has a slope of 2 and passes through the point
Goryan [66]

Answer:

y = 2x + 11

Step-by-step explanation:

The point slope formula for a line is

y - y1 = m(x - x1)

We already have the slope, 2, and we can substitute the point (-4, 3) into (x1, y1):

y - 3 = 2(x + 4)

y - 3 = 2x + 8

y = 2x + 11

5 0
2 years ago
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