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lesya692 [45]
3 years ago
12

Find the area of the square with a radius of 4

Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
5 0

Answer:

8

Step-by-step explanation:

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An initial population of 415
slamgirl [31]

Answer:

The exponential function to model the duck population is:

f(n)=415*(1.32)^n, where:

x is the duck population

n is the number of years

Step-by-step explanation:

In order to calculate the duck population you can use the formula to calculate future value:

FV=PV*(1+r)^n

FV=future value

PV=present value

r=rate

n=number of periods of time

In this case, the present value is the initial population of 415 and the rate is 32%. You can replace these values on the formula and the exponential function to model the duck population would be:

f(n)=415*(1+0.32)^n

f(n)=415*(1.32)^n, where:

x is the duck population

n is the number of years

3 0
3 years ago
What is the distance bewteen -7 and 41
Gala2k [10]
To find distance, subtract the largest number from smaller

41 - (-7)

41 + 7 = 48

the distance is 48

hope this helps
3 0
3 years ago
Dilations geometry!
iogann1982 [59]

Answer:

A' (0,20)

B' (30,-20)

C' (-10,-40)

Answered by GAUTHMATH

7 0
2 years ago
Hello, I am currently very stuck with this problem and I am unsure as to how I would solve it.
borishaifa [10]

We have the equation

20y=x^2-10-15

Let's complete the square, to do it let's add and subtract 25 on the right side

\begin{gathered} 20y=x^2-10-15+25-25 \\  \\ 20y=(x-5)^2-15-25_{} \\  \\ 20y=(x-5)^2-40 \\  \\  \end{gathered}

Now we can have y in function of x

\begin{gathered} y=\frac{1}{20}(x-5)^2-2 \\  \\  \end{gathered}

Now we can already identify the vertex because it's in the vertex form:

y=a(x-h)+k

Where the vertex is

(h,k)

As we can see, h = 5 and k = -2, then the vertex is

(5,-2)

Now we can continue and find the focus, the focus is

\mleft(h,k+\frac{1}{4a}\mright)

We have a = 1/20, therefore

\begin{gathered} \mleft(5,-2+5\mright) \\  \\ (5,3) \end{gathered}

The focus is

(5,3)

And the last one, the directrix, it's

y=k-\frac{1}{4a}

Then

\begin{gathered} y=-2-5 \\  \\ y=-7 \end{gathered}

Hence the correct answer is: vertex (5, -2); focus (5, 3); directrix y = -7

5 0
1 year ago
I don’t understand this at all
Romashka [77]

Answer:

a) the midpoint is (1.5, 2.5)

b) the line is y = -(7/3)*x + 6.

Step-by-step explanation:

a)

Suppose we have two values, A and B, the mid-value between A and B is:

(A + B)/2

Now, if we have a segment with endpoints (a, b) and (c, d), the midpoint will be in the mid-value of the x-components and the mid-value of the y-components, this means that the midpoint is:

( (c + a)/2, (b + d)/2)

a) Then if the endpoints of the segment are (-2, 1) and (5, 4), the midpoint of this segment will be:

( (-2 + 5)/2, (1 + 4)/2) = (3/2, 5/2) = (1.5, 2,5)

The midpoint of the segment is (1.5, 2.5)

b)

Now we want to find the equation of a perpendicular line to our segment, that passes through the point (1.5, 2.5).

First, if we have a line:

y = a*x + b

A perpendicular line to this one will have a slope equal to -(1/a)

So the first thing we need to do is find the slope of the graphed segment.

We know that for a line that passes through the points (a, b) and (c, d) the slope is:

slope = (c - a)/(d - b)

Then the slope of the segment is:

slope = (4 - 1)/(5 - (-2)) = 3/7

Then the slope of the perpendicular line will be:

s = -(7/3)

Then the perpendicular line will be something like:

y = -(7/3)*x + d

Now we want this line to pass through the point (1.5, 2.5), then we can replace the values of this point in the above equation, and solve for d.

2.5 = -(7/3)*1.5 + d

2.5 + (7/3)*1.5 = d = 6

Then the line is:

y = -(7/3)*x + 6

7 0
3 years ago
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