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Nutka1998 [239]
3 years ago
5

The parabola with equation $y=ax^2+bx+c$ is graphed below:

Mathematics
2 answers:
sineoko [7]3 years ago
8 0

Answer:

2

Step-by-step explanation:

Source: AOPS

Mashutka [201]3 years ago
4 0

Answer:

m-n=2

Step-by-step explanation:

Instead of using the standard form, we can use the vertex form of a quadratic equation:

f(x)=a(x-h)^2+k

Where a is the leading coefficient, and (h, k) is our vertex.

Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:

f(x)=a(x-2)^2-4

Now, we need to determine a.

We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:

12=a((4)-2)^2-4

Solve for a. Subtract within the parentheses:

12=a(2)^2-4

Add 4 to both sides:

16=a(2)^2

Square:

16=4a

Solve:

a=4

Thererfore, the value of a is 4.

So, our function is:

f(x)=4(x-2)^2-4

Now, let’s find our roots. Set the equation to 0 and solve for x:

0=4(x-2)^2-4

4=4(x-2)^2\\1=(x-2)^2\\x-2=\pm1 \\ x=2\pm1 \\ x=3\text{ or } 1

So, our roots are 1 and 3.

The greater root is 3 and the lesser root is 1.

Therefore, m-n, where m>n, is 3-1 or 2.

Our final answer is 2.

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A child has 60 total coins. There are ten times as many nickels as there are quarters (q) and twelve more dimes than quarters. W
klio [65]

Answer:

10q+q+(12+q)=60

4 0
3 years ago
If s and t are integers greater than 1 and each is a factor of the integer n, which of the following must be a factor of n st ?
yulyashka [42]

Answer:

A) None

Step-by-step explanation:

1) s^t shoudnt neccesarily be a factor of nst, for example, if s = 3, t = 4, and n = 12, then both s and t are factors of n, but 3^4 = 81 is not a factor of nst = 144.

2) (st)^2 shoudnt neccesarily be a factor of nst. Let s be 4, let t be 6, and let n be 12. Then n is a factor of both s and t, but (st)^2 = 24^2 is not a factor of nst = 12*24. In fact, it is a greater number.

3) Again, s+t isnt necessarily a factor of nst, let s be 2 and t be 3. Then both s and t are factor of n = 12. However 5 = s+t is not a factor of nst = 72.

So, neither of the three options is guaranteed to be a factor of nst. In fact, for s = 4, t = 6, and n = 12, none of the three options are valid.

4 0
3 years ago
On a standard reticulocyte preparation with new methylene blue, there are 100 cells counted with blue-stained granulofilamentous
DIA [1.3K]

Answer:

0.322 × 10¹² /L

Step-by-step explanation:

Data provided in the question:

Number of cells counted with blue-stained granulofilamentous material

i.e number of RET = 100

The red blood cells count = 3.22 × 10¹² /L

Hematocrit = 30%

Now,

RET% = [ [ Number of RET ] ÷ 1000 RBCs ] × 100%

= [ 100 ÷ 1000 ] × 100%

= 0.1 × 100%

= 10%

also,

Absolute reticulocyte count = ( %RET × RBC count ) ÷ 100

= [ 10 × 3.22 × 10¹² /L ] ÷ 100

= 0.322 × 10¹² /L

8 0
3 years ago
A climatologist wants to determine the thickness of a glacier with a surface area of about 2 km². He selected 10 locations at ra
atroni [7]

Answer:

i want to help but ant

Step-by-step explanation:

I want to hep but i think i got the wrong answer

8 0
2 years ago
A box of uncooked spaghetti cost $0.1369 per ounce. how much is this cost to the nearest cent?
AlladinOne [14]
The cost to the nearest sent is 0.14

This is because you can round the .136 up to the nearest hundredths place.
3 0
3 years ago
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