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2 years ago

A cab company charges $4 per cab ride, plus an additional $3 per mile driven. How long is a cab ride that costs $22?

Mathematics

1 answer:

Doss [256]2 years ago

8 0

Answer:

6 miles

Step-by-step explanation:

Flat fee is $4

Per mile is $3

Equation :

4 + 3m = 22

subtract 4 from both sides

3m = 18

divide each side by 3

m = 6

The ride is 6 miles.

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clothing store sells four shirts for $60.00. The next week, the store runs a special that is buy three shirts for $19.50 each, g

qwelly [4]

Answer:

the 19.50 for each one

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

A rock thrown vertically upward from the surface of the moon at a velocity of 36m/sec reaches a height of s = 36t - 0.8 t^2 met

Verdich [7]

Answer:

a. The rock's velocity is $v(t)=36-1.6t \:{(m/s)}$ and the acceleration is $a(t)=-1.6 \:{(m/s^2)}$

b. It takes 22.5 seconds to reach the highest point.

c. The rock goes up to 405 m.

d. It reach half its maximum height when time is 6.59 s or 38.41 s.

e. The rock is aloft for 45 seconds.

Step-by-step explanation:

Velocity is defined as the rate of change of position or the rate of displacement. $v(t)=\frac{ds}{dt}$
Acceleration is defined as the rate of change of velocity. $a(t)=\frac{dv}{dt}$

The rock's velocity is the derivative of the height function $s(t) = 36t - 0.8 t^2$

$v(t)=\frac{d}{dt}(36t - 0.8 t^2) \\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(36t\right)-\frac{d}{dt}\left(0.8t^2\right)\\\\v(t)=36-1.6t$

The rock's acceleration is the derivative of the velocity function $v(t)=36-1.6t$

$a(t)=\frac{d}{dt}(36-1.6t)\\\\a(t)=-1.6$

b. The rock will reach its highest point when the velocity becomes zero.

$v(t)=36-1.6t=0\\36\cdot \:10-1.6t\cdot \:10=0\cdot \:10\\360-16t=0\\360-16t-360=0-360\\-16t=-360\\t=\frac{45}{2}=22.5$

It takes 22.5 seconds to reach the highest point.

c. The rock reach its highest point when t = 22.5 s

Thus

$s(22.5) = 36(22.5) - 0.8 (22.5)^2\\s(22.5) =405$

So the rock goes up to 405 m.

d. The maximum height is 405 m. So the half of its maximum height = $\frac{405}{2} =202.5 \:m$

To find the time it reach half its maximum height, we need to solve

$36t - 0.8 t^2=202.5\\36t\cdot \:10-0.8t^2\cdot \:10=202.5\cdot \:10\\360t-8t^2=2025\\360t-8t^2-2025=2025-2025\\-8t^2+360t-2025=0$

For a quadratic equation of the form $ax^2+bx+c=0$ the solutions are

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=-8,\:b=360,\:c=-2025:\\\\t=\frac{-360+\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2-\sqrt{2}\right)}{4}\approx 6.59\\\\t=\frac{-360-\sqrt{360^2-4\left(-8\right)\left(-2025\right)}}{2\left(-8\right)}=\frac{45\left(2+\sqrt{2}\right)}{4}\approx 38.41$

It reach half its maximum height when time is 6.59 s or 38.41 s.

e. It is aloft until s(t) = 0 again

$36t - 0.8 t^2=0\\\\\mathrm{Factor\:}36t-0.8t^2\rightarrow -t\left(0.8t-36\right)\\\\\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}\\\\t=0,\:t=45$

The rock is aloft for 45 seconds.

5 0

3 years ago

• A car uses 30 gallons of gasoline for a trip of 800 miles. How many gallons would

nevsk [136]

Quantity of gasoline needed by a car to run 800 miles = 30 gallons

Quantity of gasoline needed by a car to run 1 mile =

= 30 ÷ 800

= 0.0375 gallons

So , to run 1 mile a car would need = 0.0375 gallons of oil

To run 700 miles the quantity of gasoline needed =

= 700 × 0.0375

= 26.25 gallons of gasoline

Therefore , a car will use 26.25 gallons of gasoline on a trip of 700 miles .

7 0

3 years ago

A box measures 3 1/2 ft by 1 1/3 ft by 2/14 ft what is the volume

asambeis [7]

Answer: 2/3^3

Step-by-step explanation:

To find the volume of a box, you use the formula, Lenth*Width*Height=Volume

The Lenth is 3 1/2. The width is 1 1/3 and the height is 2/14

Plug the values in formula

3 1/2*1 1/3*2/14

Covert the mixed numbers into imporper fractions so it is easier to solve

3 1/2=7/2

1 1/3=4/3

7/2*4/3*2/14

Reduce 2/14

2/14=1/7

7/2*4/3*1/7=7*4*1/(2*3*7)=28/42

Reduce 28/42=14/21=2/3

2/3 ft^3

5 0

2 years ago

A rectangular parking lot must have a perimeter of 440 feet and an area of at least 8000 square feet. Describe the possible leng

tangare [24]

Answer:

The possible parking lengths are 45.96 feet and 174.031 feet

Step-by-step explanation:

Let x be the length of rectangular plot and y be the breadth of rectangular plot

A rectangular parking lot must have a perimeter of 440 feet

Perimeter of rectangular plot =2(l+b)=2(x+y)=440

2(x+y)=440

x+y=220

y=220-x

We are also given that an area of at least 8000 square feet.

So, $xy \leq 8000$

So, $x(220-x) \leq 8000$

$220x-x^2 \leq 8000$

So, $220x-x^2 = 8000\\-x^2+220x-8000=0$

General quadratic equation : $ax^2+bx+c=0$

Formula : $x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-220 \pm \sqrt{220^2-4(-1)(-8000)}}{2(-1)}\\x=\frac{-220 + \sqrt{220^2-4(-1)(-8000)}}{2(-1)} , \frac{-220 - \sqrt{220^2-4(-1)(-8000)}}{2(-1)}\\x=45.96,174.031$

So, The possible parking lengths are 45.96 feet and 174.031 feet

3 0

3 years ago

A cab company charges $4 per cab ride, plus an additional $3 per mile driven. How long is a cab ride that costs $22?​

A cab company charges $4 per cab ride, plus an additional $3 per mile driven. How long is a cab ride that costs $22?