1/4 + (-3/4)= -4 1/2 + 2= -8+ (-1 1/8) =

Loren drove 200 miles at a certain rate, and his wife, Lois, drove 100 miles at a rate 10 mph slower. If Loren had driven for th

NeX [460]

As long as Loren drove, the law of motion was

$200 = st_1 \implies t_1 = \dfrac{200}{s}$

As long as Loid drove, the law of motion was

$100 = (s-10)t_2 \implies t_2 = \dfrac{100}{s-10}$

So, the total time they took is

$t_1+t_2=\dfrac{200}{s}+\dfrac{100}{s-10}$

Had Loren driven the whole time, the law of motion would have been

$300=st_3 \implies t_3 = \dfrac{300}{s}$

And we know that this time would have been 30 minutes (i.e. 0.5 hours) faster. So, we have

$t_3 = t_1+t_2-0.5$

This translates into

$\dfrac{300}{s}=\dfrac{200}{s}+\dfrac{100}{s-10}-\dfrac{1}{2}$

If we subtract 200/s from both sides, we have

$\dfrac{100}{s}=\dfrac{100}{s-10}-\dfrac{1}{2}$

We can simplify the right hand side by summing the two fractions:

$\dfrac{100}{s-10}-\dfrac{1}{2} = \dfrac{200-(s-10)}{2(s-10)}=\dfrac{210-s}{2(s-10)}$

So, we have to solve

$\dfrac{100}{s}=\dfrac{210-s}{2(s-10)}$

If we cross multiply the denominators, we have

$200(s-10)=s(210-s) \iff 200s-2000=210s-s^2 \iff s^2-10s-2000=0$

Which yields the solutions

$s=-40,\quad s=50$

We accept the positive solution, because the negative would mean to travel backwards, so Loren's rate was 50mph

5 0

3 years ago

Read 2 more answers

Write an algebraic expression for three times a number plus 15

photoshop1234 [79]

Answer:

3x+15

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Type the correct answer in each blank. Use numerals instead of words. If necessary, use / for the fraction bar(s). John hosts an

Law Incorporation [45]

We know that John is hosting an art workshop on the weekends. He has an average of 14 students in each session and charges a fee of $12 per session. . He estimates that for every $2 increases in the fee, the average number of students reduces by 1.

Therefore, we can conclude that his revenue is $14 * 12$ or $168$ bucks.

The session price goes up in a pattern of 2.

For example, from 12 the session price goes to 14, 16, 18 and so on.

As each jumps goes by 2, the amount of students drop by 1.

(i.e from 14 students the number decreases to 13, to 12 and so on.)

As we can see the revenue begins at 168 and continues upward until it reaches 200 dollars and then starts to descend.

This indicates that the U-turn or vertex of the revenue function is approximately 4200, where h represents 4, and k is 200.

To solve we can use Parabola.

⇒ Parabola: any point is at an equivalent separation from:

a settled point (the concentration ), and

a settled straight line (the directrix )

____________________________________________________

$f (x) = a(x - h)^2 + k$ , where (h, k) is the vertex of the parabola.

⇒ $\left \{ {{y=192} \atop {x=2}} \right.$

⇒ $192 = a(2-4)^2+200$

⇒ $-8=a(-2)^2$

⇒ $-8=a*2^2$

⇒ $-8=a*4$

⇒ $-8=4a$

⇒ $-\frac{8}{4} = \alpha$

⇒ $\alpha = -2$

Now lets do the final step: Simplifying

$y-2(x-4)^2+200$ 

$y=-2(x^2-8x+16)+200$

$y=-2x^2+16x-32+200$

$c(x) = -2x^2+16x+168$

3 0

4 years ago

Write an equation of the line below.

pochemuha

Y=mx+b is the equasion of a line.

5 0

4 years ago

The Scale drawing of a field in the shape of a triangle is shown below

nata0808 [166]

I need to see the drawing

7 0

4 years ago