Determine the intercepts of the line. X-intercept:(____,____) Y-intercept:(____,___

erik [133]

Let
x---------------> distance from people living to the city center

we Know that
Zone 1 covers people living within three miles of the city center
Zone 1 ------------> [x < 3 miles]

Zone 2 covers those between three and seven miles from the center
Zone 2 ------------> [ 3 <= x < = 7 miles]

Zone 3 covers those over seven miles from the center
Zone 3 ------------> [ x > 7 miles]

calculate the distance between two points to find the value of x

case A) point (0,0) point (3,4)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(4-0)² +(3-0)²]------> √[16+9]
x=√25-------------> x=5 miles

the answer Part A)
people living in (3,4)
x=5 miles -------------> covers Zone 2 [ 3 < =x <= 7 miles]

case B) point (0,0) point (6,5)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(5-0)² +(6-0)²]------> √[25+36]
x=√61-------------> x=7.81 miles

the answer Part B)
people living in (6,5)
x=7.81 miles -------------> covers Zone 3 [ x > 7 miles]

case C) point (0,0) point (1,2)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(2-0)² +(1-0)²]------> √[4+1]
x=√5-------------> x=2.23 miles

the answer Part C)
people living in (1,2)
x=2.23 miles -------------> covers Zone 1 [ x < 3 miles]

case D) point (0,0) point (0,3)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(3-0)² +(0-0)²]------> √[9]
x=√9-------------> x=3 miles

the answer Part D)
people living in (0,3)
x=3 miles -------------> covers Zone 2 [ 3 < =x <= 7 miles]

case E) point (0,0) point (1,6)
x=√[(y2-y1)² +(x2-x1)²]----------> √[(6-0)² +(1-0)²]------> √[36+1]
x=√37-------------> x=6.08 miles

the answer Part E)
people living in (1,6)
x=6.08 miles -------------> covers Zone 2 [ 3 < = x <= 7 miles]

4 0

2 years ago

Tammi deposited $520 into a bank account that earned simple interest each year. After 5 years, she had earned $156 in interest.

Sveta_85 [38]

Answer:

6%

Step-by-step explanation:

Interest = Principal * rate * time

156 = 520(r)(5)

156 = 2600r

r = 0.06 or 6%

6 0

2 years ago

Read 2 more answers

Using complete sentences, explain the key features of the graph of the tangent function.

Temka [501]

Answer:

We are given the tangent function $f(x)=\tan x$ .

Firstly we know that, $\tan x=\frac{\sin x}{\cos x}$ , where $\sin x$ is the sine function and $\cos x$ is the cosine function.

Now, tangent function will be zero when its numerator is zero.

i.e. $\tan x=0$ when $\sin x=0$ .

i.e. $\tan x=0$ when $x=n \pi$ , where n is the set of integers.

So, tangent function crosses x-axis at $n \pi$ , n is the set of integers.

Further, tangent function will be undefined when its denominator is zero.

i.e. $\tan x=0$ when $\cos x=0$ .

i.e. $\tan x=0$ when $x=(2n-1) \frac{\pi}{2}$ , where n is the set of integers.

Moreover, a zero in the denominator gives vertical asymptotes.

So, tangent function will have vertical asymptotes at $(2n-1) \frac{\pi}{2}$ , n is the set of integers.

Therefore, these key features gives us the graph of a tangent function as shown below.

8 0

2 years ago

Read 2 more answers

Mrs miller sells a hoouse for 179000 if she earns a commission of 6%, how much money does she earn?

Ivenika [448]

$10740

This is because that amount multiplied times .06 is equal to the answer.

8 0

3 years ago

Please help! question attached

Svetradugi [14.3K]

Answer:

36. y=x

37. x=4

38. y=3x-10

39. y=-25x+49

40. $y=-\dfrac{1}{18}x-\dfrac{89}{18}$

41. y=-x+3

Step-by-step explanation:

36. Parallel lines have the same slope. The slope of the line $y=x+42$ is $m=1,$ so the equation of a parallel line is

$y=x+b$

This line passes through the point (2,2), so its coordinates satisfy the equation:

$2=2+b\\ \\b=0$

and the equation of the line is $y=x$

37. The line $x=03$ is vertical ine, so parallel line is also vertical line with equation $x=a.$ Substitute the coordinates of the point (4,3):

$4=a$

hence the equation is $x=4$

38. Parallel lines have the same slope. The slope of the line $y=3x+24$ is $m=3,$ so the equation of a parallel line is

$y=3x+b$

This line passes through the point (2,-4), so its coordinates satisfy the equation:

$-4=3\cdot 2+b\\ \\b=-10$

and the equation of the line is $y=3x-10$

39. Parallel lines have the same slope. The slope of the line $y=-25x+35$ is $m=-25,$ so the equation of a parallel line is

$y=-25x+b$

This line passes through the point (2,-1), so its coordinates satisfy the equation:

$-1=-25\cdot 2+b\\ \\b=49$

and the equation of the line is $y=-25x+49$

40. Perpendicular lines have slopes satisfying $m_1\cdot m_2=-1$ Since the line $y=18x+26$ has the slope $m_1=18,$ perpendicular line has the slope $m_2 =-\dfrac{1}{18}.$

The equation is

$y=-\dfrac{1}{18}x+b$

This line passes through the point (1,-5), so its coordinates satisfy the equation:

$-5=-\dfrac{1}{18}\cdot 1+b\\ \\b=-5+\dfrac{1}{18}=-\dfrac{89}{18}$

and the equation of the line is $y=-\dfrac{1}{18}x-\dfrac{89}{18}$

41. Perpendicular lines have slopes satisfying $m_1\cdot m_2=-1$ Since the line $y=x+2$ has the slope $m_1=1,$ perpendicular line has the slope $m_2 =-1.$