All categories

3 years ago

(07.01)

Mathematics

2 answers:

siniylev [52]3 years ago

7 0

A(t)=I(1-r)^t
A(t)=9500(1-0.15)^7
A(7)=9500(0.85)^7
A(7)=9500(0.3205770883)≈ $3,045.48

Zinaida [17]3 years ago

6 0

The answer is $3,045.48

You might be interested in

A bag contains 3 red pens 5 blue pens and 2 black pens a pen is selected at random and is not replaced what is the probability o

LUCKY_DIMON [66]

Answer: 1/6

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

what is the equation of the line that is parallel to the given line and passes through the point (2, 3) ? a. x + 2y = 4 b. x + 2

aleksandr82 [10.1K]

Answer:

see explanations

Step-by-step explanation:

The given blue line has a slope of m = -1/2.

The line parallel to the given line passing through point (x0,y0)=(2,3) is given by the point-slope form:

(y-y0)=m(x-x0)

substitute values

(y-3) = (-1/2)(x-2)

Expand and transpose

y = (-1/2)x + 1 + 3

y = (-1/2)x + 4 ....................(1)

We choose the second equation b. x+2y=8 and convert to slope-intercept form:

2y=-x+8

y = (-1/2)x + 4, which is exactly equation (1)

b. x+2y=8 is the correct answer.

3 0

3 years ago

Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

2 years ago

Find the coordinates of the center of the following circle. (x - 3)² + (y - 7)² = 49

Zepler [3.9K]

When you write the equation of a circle in the form

$(x-x_0)^2+(y-y_0)^2=r^2$

Then the center of the circle has coordinates $(x_0, y_0)$ and the radius is $r$

So, in your case, the center of the circle is $(3,7)$

7 0

3 years ago

Determine the number of bytes in 513 BM

Naddik [55]

We know,
1 MB = 1000 KB
513 MB = (1,000 * 513) KB
= 513,000 KB

Now,
1 KB = 1,000 bytes
513,000 KB = (1,000 * 513,000) bytes
= 513,000,000 bytes

∴ 513 MB is 513,000,000 bytes

3 0

3 years ago