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2 years ago

12

A car is traveling at a steady speed. It travels 2 1/3 miles in 3 1/2 minutes. How far will it travel in 24 minutes? How far wil

l it travel in 1 hour?

1 answer:

Vikki [24]2 years ago

5 0

Answer:

a) distance traveled is 16 miles.

b) distance traveled is 40 miles.

Step-by-step explanation:

Speed is a scalar quantity which describe the rate of distance moved with time.

i.e speed = $\frac{distance}{time}$

Given that: distance = 2 1/3 miles = $\frac{7}{3}$ miles, time = 3 1/2 minutes = $\frac{7}{2}$ minutes.

Then;

speed = $\frac{7}{3}$ ÷ $\frac{7}{2}$

= $\frac{7}{3}$ x $\frac{2}{7}$

= $\frac{2}{3}$

The car's steady speed is 0.67 miles per minute.

a) when the time is 24 minutes, the distance covered can be determine by:

distance = speed x time

= $\frac{2}{3}$ x 24

= 16

distance traveled is 16 miles.

b) When the time is 1 hour (60 minutes), the distance traveled can be determined by:

distance = speed x time

= $\frac{2}{3}$ x 60

= 40

distance traveled is 40 miles.

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Describe two ways to write equivalent algebraic expressions

Zolol [24]

Answer:

See below.

Step-by-step explanation:

An example would be:

3x^2 + 6

and

3(x^2 + 2) .

The second way is found by dividing the first one by 3).

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3 years ago

Match each quadratic equation with the best way to solve it.

Blizzard [7]

Answer:

5x^2 + 12x -3 =0 ---------> solve by quadratic formula

x^2 -4x = 8 ----------> solve by completing the square

4x^2 -25 = 0 ----------> solve by square root method

x^2-5x+ 6 = 0 -----------> solve by factoring

Step-by-step explanation:

1. 5x^2 + 12x -3 =0

The best way to solve this equation is quadratic formula as all the terms in the equation have coefficients it will be convenient to solve it through quadratic formula.

2. x^2 -4x = 8

The best way to solve this equation is by completing the square as the factors cannot be made directly.

3. 4x^2 -25 = 0

the best way to solve this equation is to solve by square root method as the 25 and 4 are perfect squares.

4. x^2-5x+ 6 = 0

The best way to solve this equation is to solve by factoring as it can clearly be seen that it is convenient to make factors ..

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2 years ago

Determine any asymptotes (Horizontal, vertical or oblique). Find holes, intercepts and state it's domain.

vesna_86 [32]

Factorize the denominator:

$\dfrac{x^2-4}{x^3+x^2-4x-4}=\dfrac{x^2-4}{x^2(x+1)-4(x+1)}=\dfrac{x^2-4}{(x^2-4)(x+1)}$

If $x\neq\pm2$ , we can cancel the factors of $x^2-4$ , which makes $x=-2$ and $x=2$ removable discontinuities that appear as holes in the plot of $g(x)$ .

We're then left with

$\dfrac1{x+1}$

which is undefined when $x=-1$ , so this is the site of a vertical asymptote.

As $x$ gets arbitrarily large in magnitude, we find

$\displaystyle\lim_{x\to-\infty}g(x)=\lim_{x\to+\infty}g(x)=0$

since the degree of the denominator (3) is greater than the degree of the numerator (2). So $y=0$ is a horizontal asymptote.

Intercepts occur where $g(x)=0$ ( $x$ -intercepts) and the value of $g(x)$ when $x=0$ ( $y$ -intercept). There are no $x$ -intercepts because $\dfrac1{x+1}$ is never 0. On the other hand,

$g(0)=\dfrac{0-4}{0+0-0-4}=1$

so there is one $y$ -intercept at (0, 1).

The domain of $g(x)$ is the set of values that $x$ can take on for which $g(x)$ exists. We've already shown that $x$ can't be -2, 2, or -1, so the domain is the set

$\{x\in\mathbb R\mid x\neq-2,x\neq-1,x\neq2\}$

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2 years ago

Jill sold half of her comic books and then bought sixteen more. She now has 36. With how many did she begin?

Alex777 [14]

Answer:

$\frac{1}{2}x + 16 = 36$

40 comic books

Step-by-step explanation:

Let x be the Jill comic books.

Given:

Jill sold half of her comic books and then bought sixteen more. She now has 36.

$\frac{1}{2}\ (Jill\ books) + 16\ more\ books = 36$

$\frac{1}{2}\ (x) + 16 = 36$

$\frac{1}{2}x + 16 = 36$

Therefore the algebraic equation of the given statement.

$\frac{1}{2}x + 16 = 36$ --------(1)

Now we solve above equation for x.

Subtract by 16 both side of the equation 1.

$\frac{1}{2}x + 16 -16 = 36 -16$

$\frac{1}{2}x = 20$

Multiply by 2 both side of the above equation.

$2\times \frac{1}{2}x =2\times 20$

$x = 40$

Therefore, Jill had 40 comic books.

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2 years ago

Find the volume of a right circular cone that has a height of 11.4 in and a base with a radius of 5.1 in. Round your answer to t

ella [17]

Answer:

Step-by-step explanation:

h=11.4 in

r=5.1 in

v=3.14*r^2*(h/3)

V=3.14*5.1^2*(11.4/3)=3.14*26.01*3.8=310.35

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2 years ago