MATHEMATICS HIGH SCHOOL

A design engineer is mapping out a new neighborhood with parallel streets. If one street passes through (6, 4) and (5, 2), what is the equation for a parallel street that passes through (−2, 6)?A. y = 1 half x + 5
B. y - 1 half x + 1
C. y = 2x + 10
D. y = 2x − 14

Answers

Answer 1
Answer:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the first street.

(\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{2}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{6}}} \implies \cfrac{ -2 }{ -1 } \implies 2

so we are really looking for the equation of a line whose slope is 2 and it passes through (-2 , 6)

(\stackrel{x_1}{-2}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 2 \n\n\n \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\n \cline{1-1} \n y-y_1=m(x-x_1) \n\n \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{2}(x-\stackrel{x_1}{(-2)}) \implies y -6 = 2 ( x +2) \n\n\n y-6=2x+4\implies {\Large \begin{array}{llll} y=2x+10 \end{array}}

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A runner has a track lap of one minute while at a run, five minutes while at a jog, 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog and 1/10 at a walk what is the total track lap time of the runner. Write the solution as a mixed number or a fraction in lowest terms

Answers

24 seconds running
2 minutes 30 seconds jogging
42 seconds walking
3 minutes 36 seconds in that lap

Final answer:

The total track lap time of the runner is 2 2/5 minutes or 2.4 minutes.

Explanation:

The total track lap time of the runner can be calculated by summing up the individual time spent at each pace (run, jog, walk). Each pace's time is first multiplied by the fraction of the lap completed at that pace.

For the run, the calculation is 2/5 of 1 minute which is 2/5 minute.

For the jog, the calculation is 1/2 of 5 minutes which is 5/2 = 2 1/2 minutes or 2.5 minutes in decimal form.

For the walk, the calculation is 1/10 of 7 minutes which is 7/10 = 0.7 minutes.

Adding these times together gives a total of (2/5) + (5/2) + (7/10) = 12/5 = 2 2/5 minutes or 2.4 minutes in decimal form.

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What should be done so that the expression will have a value of 10?12 - 2 + 22 ÷ 8

Add parentheses around 12 - 2.
Add parentheses around 2 + 2.
Add parentheses around 22 ÷ 8.
Nothing needs to be done.

Answers

Nothing can be changed in order to equate the expression to 10.

What is Equation Modelling?

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is the following expression -

12 - 2 + 22 ÷ 8

[A] : {12 - 2} + 22 ÷ 8

10 + 22 ÷ 8

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[B] : 12 - {2 + 2}2 ÷ 8

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12 - 4 x 2 x 1/8

12 - 4 x 1/4

12 - 1

11  ≠ 10

[C] : 12 - 2 + {22 ÷ 8}

12 - 2 + 2.75

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12.75 ≠ 10

Therefore, nothing can be changed in order to equate the expression to 10.

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A university's freshman class has 5000 students. 80% of those students are majoringin Computer Science. How many students in the freshman class are Computer
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Answers

Answer:

4000 students

Step-by-step explanation:

Number of computer science majors = 80% of 5000

                                                              = 0.8 * 5000

                                                              = 4000

Answer:

4000

Step-by-step explanation:

5000 * .8 is 4000

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Answers

Answer:

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Step-by-step explanation:

As per the statement:

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Selling price of the camera = $45

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Answer:

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Step-by-step explanation:

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