MATHEMATICS HIGH SCHOOL

What is the elapsed time between 2:16 am to 8:10pm

Answers

Answer 1

Answer:

9:44+8:10 = 17.54

Answer : 17 hours and 54 minutes

If you have questions please let me know

I hope that's help !

Answer 2

Answer: The elapsed time between 2:16 am to 8:10pm is 5 hours and 44 minutes.

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angle KLM and angle MLN are complementary. angle LM bisects angle KLM. Find the measures of angle KLM and MLN

Answers

By definition, the measures of two complementary angles adds up to 90 degrees. Therefore, the measure of angle KLN is 90 degrees. Because LM bisects KLN, by definition, LM divides KLN in half. Therefore KLM and MLN each measure 45 degrees. When in doubt, draw a picture.

Final answer:

Using the concepts of complementary angles and bisecting angles, we find that Angle KLM measures 60 degrees and Angle MLN measures 30 degrees.

Explanation:

In this problem, we're dealing with complementary angles and bisecting an angle. Complementary angles are two angles whose measures sum to 90 degrees. When an angle is bisected, it is split into two equal smaller angles.

Firstly, as angle KLM and angle MLN are complementary, the sum of their measures equals 90 degrees, so Angle KLM + Angle MLN = 90 degrees.

Secondly, as angle LM is bisecting angle KLM, this means that angle KLM is split into two equal parts. Let's assume each of those parts is x, that means Angle KLM = 2x.

Given that angle KLM and angle MLN are complementary, we can substitute angle KLM = 2x into the equation, leading us to 2x + Angle MLN = 90 degrees. Since angle MLN is also x because it's a part of bisected angle KLM, we can substitute in Angel MLN = x into this equation, ending up with 2x + x = 90 degrees or 3x = 90 degrees. Solving for x, we find that x = 90 / 3 = 30 degrees.

Therefore, the measure of Angle KLM (2x) is 60 degrees and the measure of Angle MLN (x) is 30 degrees.

Learn more about Angle Measures here:

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Mr Stevens wants to put 17 books on the shelf . He put 8 books on the shelf . how many more books does he need to put on the shelf ?

Answers

8 + x = 17x = 17 - 8x = 99 books left

Mr. Stevens has 9 books left to put on the shelf.

Evaluate |–8| + |b| + a if a = 0 and b = 12.

A. -4
B. 4
C. 12
D. 20

Answers

Answer:

Step-by-step explanation:

abs(-8) = 8

abs(12) = 12

8 + 12 = 20

A is the correct awnser

The quantity demanded per month, x, of a certain make of personal computer (PC) is related to the average unit price, p (in dollars), of PCs by the equationx = f(p) =1009810,000 − p2It is estimated that t mo from now, the average price of a PC will be given byp(t) =4001 +18t+ 200 (0 ≤ t ≤ 60)dollars. Find the rate at which the quantity demanded per month of the PCs will be changing 16 mo from now. (Round your answer to one decimal place.)

Answers

Answer:

The value of dx/dt is $(100p)/(9√((810000-p^2))).(1600)/(√(t)\left(√(t)+8\right)^2)\n$ while the rate of change of quantity demanded per month after 16 months is 18.7.

Step-by-step explanation:

From the given data the equation of quantity demanded for average price is given as is given as

$x=f(p)=(100)/(9)√(810000-p^2)$

The equation of average price p for a given value of t is given as

$p(t)=(400)/(1+(1)/(8)√(t))+200$

Now in order to determine the rate at which the quantity demanded will be changing is given as $(dx)/(dt)$

This is found by using the chain rule as

$(dx)/(dt)=(dx)/(dp).(dp)/(dt)$

Now

$(dx)/(dp)=(d((100)/(9)√(810000-p^2)))/(dp)\n(dx)/(dp)=(100)/(9)(d)/(dp)[(810000-p^2)^(1/2)]\n(dx)/(dp)=(100)/(9)(1)/(2)[(810000-p^2)^(-1/2)](d)/(dp)[(810000-p^2)]\n(dx)/(dp)=(50)/(9)[(810000-p^2)^(-1/2)](-2p)\n(dx)/(dp)=(100p)/(9√((810000-p^2)))$

Now

$\n(dp)/(dt)=(d((400)/(1+(1)/(8)√(t))+200))/(dt)\n(dp)/(dt)=(d)/(dt)\left((400)/(1+(1)/(8)√(t))+200\right)\n(dp)/(dt)=(d)/(dt)\left((400)/(1+(1)/(8)√(t))\right)+0\n(dp)/(dt)=400(d)/(dt)\left((1)/(1+(1)/(8)√(t))\right)\n(dp)/(dt)=400(d)/(du)\left(\left(1+(1)/(8)√(t)\right)^(-1)\right)(d)/(dt)\left(1+(1)/(8)√(t)\right)\n(dp)/(dt)=-(1600)/(√(t)\left(√(t)+8\right)^2)$

So now the value of dx/dt is given as

$(dx)/(dt)=(dx)/(dp).(dp)/(dt)\n(dx)/(dt)=(100p)/(9√((810000-p^2))).(1600)/(√(t)\left(√(t)+8\right)^2)\n$

So the value of dx/dt is $(100p)/(9√((810000-p^2))).(1600)/(√(t)\left(√(t)+8\right)^2)\n$

Now for the time =16 months price is given as

$p(t)=(400)/(1+(1)/(8)√(t))+200\np(16)=(400)/(1+(1)/(8)√(16))+200\np(16)=466.67$

Now the value of x is given as

$(dx)/(dt)=(100p)/(9√((810000-p^2))).(1600)/(√(t)\left(√(t)+8\right)^2)\n\n(dx)/(dt)=(100*466.67)/(9√((810000-466.67^2))).(1600)/(√(16)\left(√(16)+8\right)^2)\n(dx)/(dt)=18.72$

So the rate of change of quantity demanded per month after 16 months is 18.72

Find the slope of the line through the given points.

(1,2), (-3,2)

Answers

the slope can be found by using the equation y2-y1 over x2-x1
2-2 over -3-1
= 0 over -4
your slope is 0

The slope=
$y= (y2-y1)/(x2-x1) (2-2)/(-3-1) (0)/(-4) }$

You are purchasing a new car. In order to determine which car will provide maximum savings, you’ve researched miles per gallon (mpg) ratings of cars. If gas is $3.45 per gallon and you drive an average of 18,000 miles per year, the following rational equation is given: g(x)= 3.45 (18,000/old miles per gallon)-3.45(18,000/new miles per gallon)

In the formula what do you find when you divide 18,000/old miles per gallon?

Answers

Answer:

$(18000)/(x)$ defines the gallons of the gas consumed by the old car in one year.

Step-by-step explanation:

If I purchase a car, I will definitely concentrate on a factor that is gas consumed by the car in a year.

As per statement given in the question if gas is $3.45 per gallon and I drive an average of 18000 miles per year.

If x miles per gallons is the average of the old car and y miles per gallons is the average of of new car.

Then total difference in gallons of the gas consumed by the old and new cars will be represented by the equation.

g(x) = 3.45 $((18000)/(x))$ - 3.45 $((18000)/(y) )$

Here, $(18000)/(x)$ defines total number of gallons of the gas consumed by the old car in one year.

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