A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. The patient currently has a bone density of 1,500 kg/mg3. The doctor writers an exponential function to represent the situation. Which values should the doctor use of a and b in a function written in the form f(x)= abx, where f(x) represents the bone density after x years?

Answers

Answer 1

Answer: If a patient is losing bone density at the rate of 3 % annually then it will rest:
100% - 3% = 97 %, or 0.97 of a bone density.
The doctor should use a function: $f(x)= 1,500 * 0.97^(x)$
a = 1,500, b = 0.97

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Which is a factor of x^2 + 8x – 48?(x – 6)

(x + 4)

(x – 16)

(x + 12)

Answers

$x^2 + 8x - 48 =\n\nx^2 -4x + 12x - 48=\n\nx(x - 4)+12(x-4)=\n\n(x-4)(x+12)$

Your answer is D. (x + 2)

Answer:

Step-by-step explanation:

What is the LCD of thw fractions 1/3 and 11/15?

Answers

Least common denominator of those two fractions is 15

Because 15 cant go any less

3 × 1 = 3 15 × 1 = 15
3 × 2 = 6
3 × 3 = 9
3 × 4 = 12
3 × 5 = 15

Determine the equation of g(x) that results from translating the function f(x)=(x+4)^2 to the right 11 units.

Answers

$f(x)=(x+4)^2\n\nright\ 11\ units\ then\ g(x)=f(x-11)=(x-11+4)^2=(x-7)^2$

17. Find all the real fourth roots of 0.0001.

Answers

3. 0.1778, -0.1778 Are you sure that you don't mean the fourth root of 0.0001?That would be 0.1, -0.1

What value of m will make 4x-7y=5 and 9x+my=3 parallel?

Answers

$l:y=m_1x+b_1\ and\ k:y=m_2x+b_2\n\nl\ ||\ k\iff m_1=m_2\n------------------------\nl:4x-7y=5\to-7y=-4x+5\to y=(4)/(7)x-(5)/(7)\n\nk:9x+my=3\to my=-9x+3\to y=-(9)/(m)x+(3)/(m)\n\nl\ ||\ k\iff-(9)/(m)=(4)/(7)\n\ncross\ multiply:\n\n4m=-9\cdot7\n\n4m=-63\ \ \ \ /:4\n\nm=-15.75\leftarrow answer$

Using the completing-the-square method, find the vertex of the function f(x) = 5x2 + 10x + 8 and indicate whether it is a minimum or a maximum and at what point.a. maximum (1,8)
b. minimum (1,8)
c. maximum (-1,3)
d. minimum (-1,3)

Answers

Answer : d. minimum (-1,3)

$f(x) = 5x^2 + 10x + 8$

The vertex form of quadratic function is

$f(x) = a(x-h)^2 + k$ , where (h,k) is the vertex

To get vertex form we apply completing the square method

To apply completing the square method , there should be only x^2

So we factor out 5 from from first two terms

$f(x) = 5(x^2 + 2x) + 8$

Now we take the number before x (coefficient of x) and divide by 2

$(2)/(2)$ =1

Now square it

$(1)^2 =1$

Add and subtract 1 inside the parenthesis

$f(x) = 5(x^2 + 2x + 1 - 1) + 8$

Now we take out -1 by multiplying 5

$f(x) = 5(x^2 + 2x + 1) -5 + 8$

$f(x) = 5(x^2 + 2x + 1) + 3$

Now we factor x^2 +2x+1 as (x+1)(x+1)

$f(x) = 5(x+1)(x+1) + 3$

$f(x) = 5(x+1)^2 + 3$

h=-1 and k=3

So vertex is (-1,3)

When the value of 'a' is negative , then it is a maximum

When the value of 'a' is positive , then it is a minimum

$f(x) = 5x^2 + 10x + 8$ is in the form of $f(x) = ax^2 + bx + c$

The value of a is 5

5 is positive so it is a minimum

f(x) is minimum at point (-1,3)

The vertex form is a(x-h)²+k, where (h,k) are the coordinates of the vertex.

$f(x)= \n 5x^2+10x+8= \n5(x^2+2x)+8= \n5((x^2+2x+1)-1)+8= \n5((x+1)^2-1)+8= \n5(x+1)^2-5+8= \n5(x+1)^2+3$

The coordinates of the vertex are (-1,3).

The coefficient of x² is positive, so the parabola opens upwards and the vertex is the minimum of the function.

The answer is d.

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