Find the equation of the straight line passing through the point (0, 2) which is perpendicular to the line

y = 1/4x + 5

y= (−1/6)x^2+7x−80      multiply both sides by -6

-6y  =    x^2   - 42x  +  480       subtract 480 from both sides

 -6y  - 480   =  x^2  -  42x    take (1/2)  of 42  = 21.....square this  = 441  and add to both sides

 -6y - 480 + 441  =   x^2  - 42x  +  441       simplify the left, factor the right

 -6y - 39   =  (x  - 21)^2      factor the left side as

 -6 (y  +  39/6)   =  ( x - 21)^2       (1)

 Using the form

 4p (y - k)  =  ( x  - h)^2        we  can   write (1)  as

 4 (-3/2)(y - (-39/6) )   =  ( x  - 21)^2

 The vertex  = ( h, k)  =  ( 21, -39/6)   and    p  = -3/2

 And the directrix   is given by 

 y  = k - p  →   y  = -39/6 - (-3/2)  =  -39/6 + 3/2  = -39/6 + 9/6  =

-30/6  = - 5-------> y=-5

the answer Part 1) is

y=-5

Part 2) (y+2)^2= 129X-5 

Using the form

 4p (x - h)  =  ( y  - k)^2        we  can   write (1)  as

 4*(129/4)*(x-5/129)=(y+2)²

 The vertex  = ( h, k)  =  ( 5/129, -2)   and    p  = 129/4

 And the directrix   is given by 

x  = h - p  →   x = 5/129 - (129/4)  =  (20-16641)/516-----> -16621/516

x=-32.21

the answer part 2) is 

Answer:

The answer is 1.

Got it from Apex

Step-by-step explanation:

The word BOOKKEEPER has 10 letters, but with repetitions. There are 30240 distinct permutations. On the circular table, with students of the same major sitting together, there are 1440 different ways to seat the students.

The word BOOKKEEPER has 10 letters, but the letter O appears twice, the letter K appears twice, and the letter E appears three times. To find the number of distinct permutations, we need to divide the total number of permutations by the repetitions. So, we have 10!/(2!2!3!) = 30240 distinct permutations.

In the second question, we need to consider the students with the same major sitting together as a single entity. We can treat the circular table as a linear arrangement by fixing one student in a position and arranging the rest. So, the total number of different ways the students can be seated around the table is (3!2!5!) × 2! = 1440.

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The Average rate of change of f(t) from t = 3 seconds to t = 5 seconds is - [tex]v_{avg} = -80\;ft/s[/tex]

We have a equation -

[tex]f(t) = -16t^{2} +48t+160[/tex]

that calculates the height of the ball from sea level in feet at different times.

We have to find the average rate of change of f(t) from t = 3 seconds to t = 5 seconds.

The rate of change of displacement per unit time is called average velocity. Mathematically -

[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]

We have -                      

[tex]f(t) = -16t^{2} +48t+160[/tex]

For time t = 3 seconds, f(t) is -

[tex]f(3) = -16(3)^{2} + 48(3) + 160\\f(3) = -144 +144 +160\\f(3) = 160\; feets\\[/tex]

For time t = 5 seconds, f(t) is -

[tex]f(5) = -16(5)^{2} + 48(5) + 160\\f(5) = -400+240+160\\f(5) = -400 + 400\\f(5) = 0 feet[/tex]

The formula for average velocity is -

[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]

According to question -

[tex]t_{2} = 5s[/tex]    and     [tex]t_{1} = 3s[/tex]

[tex]d_{2} = f(5) = 0 feet[/tex]     and       [tex]d_{1} = f(3)=160[/tex]

Substituting the values in the formula of average velocity, we get -

[tex]v_{avg} = \frac{0 - 160}{5 - 3} \\v_{avg} = \frac{-160}{2\\} \\v_{avg} = -80\;ft/s[/tex]

Hence, average rate of change of f(t) from t = 3 seconds to t = 5 seconds is [tex]v_{avg} = -80\;ft/s[/tex].

To solve more questions on calculating the average rate of change of height with time, visit the following link -

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Answer:

20

Step-by-step explanation:

Answer:

I just took the test the answer is

Step-by-step explanation:

B. 87,000, and the graph would have a y-intercept at 67,000.

Answer:

Option 4.

Step-by-step explanation:

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side.

(A²-3A+2.25)=-1+2.25

Rewrite as perfect squares

(+/-)(A-1.5)=1.12

first solution

(A-1.5)=1.12--------> A=1.12+1.5-----> A=2.62-----> sin x=2.62

second solution

-(A-1.5)=1.12----> -A+1.5=1.12----> A=1.5-1.12----> A=0.38---> sin x=0.38

the answer is

the equation was factored incorrectly

Its is b. hope this halps

Answer:

answer= 2i

Step-by-step explanation:

To obtain the maximum profit, the company should set the price of each pair of socks to $5. This answer is derived from the vertex of the given quadratic profit function.

The student question asks at which price the sock selling company should sell its product to earn a maximum profit, given the profit function: P(x)=-3(x-5)^2+12. This function is a standard form of a quadratic equation, and in such equation, the maximum value is achieved at the vertex.

In this case, the vertex (h,k) of the quadratic function is (5,12), where 'h' is the value of 'x' that gives the maximum profit 'k'. So the company should set the price at $5 to earn a maximum profit.

This economic model analysis' underlying principle relies on the assumption of maximizing total revenues and minimizing total costs to yield the maximum profit. Hence, recognizing the nature of the profit function is crucial.

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the answer to your question is

 Unit walking rate in miles per hour = 5 2/3 / 2 2/3 = 17/3 / 8/3 = 17/3 x 3/8 = 17/8 = 2 1/8 miles per hour.

Unit walking rate in hours per mile = 1/ 17/8 = 8/17 hours per mile

Answer:

Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles or 5.67 miles in 2 2/3 hours or 2.67 hours.

Rachel’s unit walking rate in miles per hour is = [tex]\frac{5.67}{2.67}[/tex] = 2.125 miles per hour or 2 1/8 miles per hour.

Rachel’s unit walking rate in hours per mile = [tex]\frac{2.67}{5.67}[/tex] = 0.47 hours per mile.