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JulsSmile [24]
2 years ago
12

Line jk passes through points j(-4,-5) and k(-6,3 if the equation of the lines is written in slope-intercept form,y=my+b what is

the value of b?

Mathematics
1 answer:
lidiya [134]2 years ago
6 0
Written in 2-point form, the equation of the line is
  y = (y2-y1)/(x2-x1)·(x-x1) +y1
  y = (3-(-5))/(-6-(-4))·(x-(-4)) + (-5)
  y = 8/-2·(x +4) - 5
  y = -4x -21

The value of b is -21.

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A boat on the ocean is 2 mi from the nearest point on a straight? shoreline; that point is 15 mi from a restaurant on the shore.
Sladkaya [172]

Answer:

a) x  =  0,70 miles

T  =  1/2* (√4 + x²)  +( 15 - x )/3   Objective Function to minimize

b) V(min)  = 2.59 m/hr

Step-by-step explanation:

Let assume the boat is in Point A,  she lands in point B, and R  is the restaurant

Let call  x distance between the point O in  which perpendicular line from the boat get to shoreline, and the point were she land.

We know  distance is

d = v*t       ⇒  t = d/v

She rows at 2 miles/hr  and walk at 3 miles /hr

According to that she takes

c (hypotenuse) of right triangle  AOB/ 2 rowing

and  15 - x /3  walking

Total time is:

T  =  c/2  + ( 15-x )/3          c =√(2)² + x²     ⇒  T = [√(2)² + x²  ] /2  +  ( 15-x )/3  

T  =  1/2* (√4 + x²)  +( 15 - x )/3   (1)

And that is  the Objective function to minimize

a) Taking derivatives on both sides of the equation we get

T´(t)  =  x /( √4 + x²)  - 1/3    ⇒   T´(t)  = 0     x /( √4 + x²)  - 1/3 = 0

3*x - √( √4 + x²) = 0     ⇒  3*x  =  √( √4 + x²)

Squaring both sides

9x²  =  4 + x²     ⇒  8x²  = 4       x² = 1/2      x  =  0,70 miles

If we plug this value in the Objective function we will get the minimum time

1/2* (√4 + x²)  +( 15 - x )/3    ⇒ [√ 4  + 0,5] /2 +  14,3/3 = T (min)

T(min)  =  1.06 + 4.77  = 5.83 hr

Distance L (hypotenuse of right triangle AOR)

L = √(2)²  + (15)²   L  = 15,13 miles

And that distance have to be traveled at least in 5.83 hr rowing

Then  as  v = d/t      V(min)  =  15.13/ 5.83   ⇒    V(min)  = 2.59 m/hr

6 0
2 years ago
A professional writer decides to judge the value of her laptop by the number of times she presses
shusha [124]

Answer:

D.)

15040000 <= k <=19840000

Step-by-step explanation:

V = 1200 -0.00002k

Value V after one year falls in the range of $803.20 and $899.20.

Let's substract these values from 1200.

1200-803.20=396.80

1200-899.20=300.80

So it means that

0.00002k= 396.80

And

0.00002k= 300.80

So

0.00002k= 396.80

K= 396.80/0.00002

K= 19840000

And

0.00002k= 300.80

K = 300.80/0.00002

K= 15040000

So range is between

15040000 <= k <=19840000

7 0
2 years ago
In a recent questionnaire about food, a random sample of 970 adults were asked about whether they prefer eating fruits or vegeta
alukav5142 [94]

Answer:

Z_{0.05}=1.645

Step-by-step explanation:

Given :In a recent questionnaire about food, a random sample of 970 adults were asked about whether they prefer eating fruits or vegetables, and 458 reported that they preferred eating vegetables.

To Find :What value of z should be used to calculate a confidence interval with a 95 % confidence level?

Solution:

Confidence level = 95 % i.e.0.95

So, significance level = 5% i.e. 0.05

So, the value of z corresponding to significance level 0.05 should be used  to calculate a confidence interval with a 95 % confidence level

So, Z_{0.05}=1.645

Hence z should be 1.645 to calculate a confidence interval with a 95 % confidence level.

4 0
1 year ago
One of the solutions to x2 − 2x − 15 = 0 is x = −3. What is the other solution?
Bond [772]

Answer:x=5

Step-by-step explanation: x^2−2x−15=0

(x−5)=0                                                                                                                        x−5=0                                                                                                                           x=5

6 0
1 year ago
The Silver Lake Reservoir in California is being drained to make way for an underwater pipeline. The reservoir holds 400400400 m
MArishka [77]

Divide the total the lake holds by the number of days:

400 million / 25 days = 16 million gallons per day.

3 0
1 year ago
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