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2 years ago

PLEASE HELP ASAP. I WILL MARK AS BRAINLIEST

Mathematics

1 answer:

hram777 [196]2 years ago

6 0

You must go 45 miles per hour to reach the longest distance.

<h3>Number of hours the car can run</h3>

The given parameters are:

Speed = 60 miles per hour
Time = 5 hours

When the speed increases by 1 mile per hour, the time reduces by 10 minutes.

This means that:

When

Speed = (60 + x) miles per hour

The time is:

Time = 5 hours - 10 minutes * x

Convert minutes to hour

Time = 5 hours - 1/6 * x hour

This gives

Time = 5 - x/6 hour

Hence, the car can run for (5 - x/6) hours

<h3>The distance for 1 tank of gas</h3>

We have:

Speed = (60 + x) miles per hour

Time = (5 - x/6) hours

The distance is calculated using

Distance = Speed * Time

This gives

Distance = (60 + x)(5 - x/6)

Expand

Distance = 300 - 10x + 5x - x^2/6

Evaluate the like terms

Distance = 300 - 5x - x^2/6

Hence, the distance for 1 tank of gas is 300 - 5x - x^2/6 miles

<h3>The longest distance</h3>

We have:

D = 300 - 5x - x^2/6

Differentiate

D' = -5 - x/3

Set to 0

-x/3 = 5

Solve for x

x = -15

Substitute x = -15 in D = 300 - 5x - x^2/6

D = 300 - 5(-15) - (-15)^2/6

Evaluate

D = 337.5

Hence, the longest distance is 337.5 miles

<h3>The speed for the longest distance</h3>

We have:

x = -15

Substitute x = -15 in Time = (5 - x/6) hours

Time = (5 + 15/6) hours

Evaluate

Time = 7.5 hours

The speed is calculated as:

Speed = Distance/Time

This gives

Speed = 337.5/7.5

Evaluate

Speed = 45

Hence, you must go 45 miles per hour to reach the longest distance.

Read more about speed and distance at:

brainly.com/question/4931057

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What is true of the graph of two lines 3y-8=-5x and 6y=-10x+16

Murljashka [212]

Answer:

Both lines are equal (they are the same)

Step-by-step explanation:

Given

$3y - 8 = -5x$

$6y = -10x + 16$

Required

What is true about graph of both lines

<em>Questions like this are better solved when there's option(s) to select from. However, some of the properties of line equation that I'll consider are to check if both lines are either parallel or perpendicular</em>

<em />

To do this,

The first thing to do is to calculate the slope of both lines

$3y - 8 = -5x$

Add 8 to both sides

$3y - 8 + 8 = -5x + 8$

$3y = -5x + 8$

Divide both sided by 3

$\frac{3y}{3} = -\frac{5x}{3} + \frac{8}{3}$

$y = -\frac{5x}{3} + \frac{8}{3}$

The slope of the line is the coefficient of x;

$Slope = -\frac{5}{3}$

Solve for the y intercept; <em>Let x = 0</em>

$y = -\frac{5 * 0}{3} + \frac{8}{3}$

$y = 0 + \frac{8}{3}$

$y = \frac{8}{3}$

Solve for the x intercept; <em>Let y = 0</em>

$0 = -\frac{5x}{3} + \frac{8}{3}$

Subtract $\frac{8}{3}$ from both sides

$0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}$

$- \frac{8}{3} = -\frac{5x}{3}$

Subtract both sides by $-\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = x$

$\frac{3}{5} * \frac{8}{3} = x$

$\frac{8}{5} = x$

$x = \frac{8}{5}$

------------------------------------------------------------------------------------------------------

$6y = -10x + 16$

Divide both sides by 6

$\frac{6y}{6} = -\frac{10x}{6} + \frac{16}{6}$

$y = -\frac{10x}{6} + \frac{16}{6}$

Simplify fractions to lowest term

$y = -\frac{5x}{3} + \frac{8}{3}$

The slope of the line is the coefficient of x;

$Slope = -\frac{5}{3}$

Solve for the y intercept; <em>Let x = 0</em>

$y = -\frac{5 * 0}{3} + \frac{8}{3}$

$y = 0 + \frac{8}{3}$

$y = \frac{8}{3}$

Solve for the x intercept; <em>Let y = 0</em>

$0 = -\frac{5x}{3} + \frac{8}{3}$

Subtract $\frac{8}{3}$ from both sides

$0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}$

$- \frac{8}{3} = -\frac{5x}{3}$

Subtract both sides by $-\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}$

$-\frac{3}{5}*- \frac{8}{3} = x$

$\frac{3}{5} * \frac{8}{3} = x$

$\frac{8}{5} = x$

$x = \frac{8}{5}$

-------------------------------------------------------------------------------------------------------

By comparing the slope, x intercept and y intercept of both lines;

It'll be observed that they have the same slope, x intercept and y intercept

<em>This implies that both lines are equal; in other words, they are the same.</em>

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3 years ago

Please help ill give brain

Rasek [7]

Answer:

23 r1

Step-by-step explanation:

23 R 1

28/653

-56

93 bring down three

=1 which is remainder

28*2=56

28*3=92

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3 years ago

HI can someone do these 5 problems? it will really help me out I'll give out brainliest to the person who answers them. (No link

Softa [21]

Answer:

$73.60

$345

simple interest = amount deposited x time x interest rate

600 + (600 x 0.055 x 5) = $765

600 + (600 x 0.055 x 5) > $2000

$765 $2000

He would not have $2000 in 5 years

Step-by-step explanation:

Total cost of items purchased = $75 + (2 x $8.50) = 92

If there is a 20% discount, he would pay (100 - 20%) 80% of the total cost =

0.8 x $92 = $73.60

commission earned = percentage commission x amount of sales

10% x $3450

= 0.1 x 3450 = 345

Amount he would have in his account = amount deposited + simple interest

simple interest = amount deposited x time x interest rate

600 x 0.055 x 5 = $165

Amount in his account in 5 years = $165 + 600 = $765

He would have less than $2000 in his account. he would have $765

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3 years ago