What is the rate and unit rate for 420 miles in 7 hours

What is the y-coordinate of the solution to this system of equations?<br> 5x-8y=1<br> 3x+6y=-21

Vanyuwa [196]

5x-8y=1...(1)
3x+6y=-21...(2)

(1)*3:
15x-24y=3...(3)

(2)*5:
15x+30y=-105...(2)

(3)-(2):
15x-24y-(15x+30y)=3-(-105)
15x-24y-15x-30y=108
-54y=108
y=-2

6 0

3 years ago

You are going to purchase a new iPhone for $479.99 and you have 2 coupons but can only use one. The first coupon is $100 off the

bonufazy [111]

Answer:100 off discount

Step-by-step explanation:

If you use the 20% discount you get only 95 dollars off the price

3 0

3 years ago

1. What angles are<br> congruent to angle 5?

Readme [11.4K]

Answer:

All angles that are either exterior angles, interior angles, alternate angles or corresponding angles are all congruent. The picture above shows two parallel lines with a transversal. The angle 6 is 65°. Is there any other angle that also measures 65° hope this helps you

Step-by-step explanation:

8 0

3 years ago

Every evening, two weather stations issue weather forecast for the next day. The weather forecasts are independent. On average,

EleoNora [17]

Answer:

The probability is 0.6923

Step-by-step explanation:

Let's call R the event that the next day rains, S the event that the next day has sunny weather, R2 the event that the station 2 predicts rain and S1 the event that station 1 predict sunny weather.

The probability that the next day has sunny weather given that station 1 predicts sunny weather for the next day and station 2 predicts rain is calculated as:

P(S/S1∩R2) = P(S∩S1∩R2)/P(S1∩R2)

Where P(S1∩R2) = P(R∩S1∩R2) + P(S∩S1∩R2)

So, the probability P(R∩S1∩R2) that the next day rains, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(R∩S1∩R2) = 0.5 * 0.1 * 0.8 = 0.04

Because 0.5 is the probability that the next day rains, 0.1 is the probability that station 1 predicts sunny weather given that it is going to rain and 0.8 is the probability that station 2 predicts rain given that it is going to rain.

At the same way, the probability P(S∩S1∩R2) that the next day has sunny weather, Station 1 predicts sunny weather and Station 2 predicts Rain is calculate as:

P(S∩S1∩R2) = 0.5 * 0.9 * 0.2 = 0.09

Then, the probability P(S1∩R2) that station 1 predicts sunny weather for the next day, whereas station 2 predicts rain is:

P(S1∩R2) = 0.04 + 0.09 = 0.13

Finally, P(S/S1∩R2) is:

P(S/S1∩R2) = 0.09/0.13 = 0.6923

6 0

3 years ago

1. Try It #1

padilas [110]

Answer:

The slope of the line representing the linear function f(x) is determined as $-\frac{1}{2}$ . The function f(x) is decreasing because the slope is less than zero, i.e., m<0.

Step-by-step explanation:

A linear function f(x) is given with two points, (2,3) and (0,4) lying on the line representing f(x).

It is asked to determine the slope of the line and state if the function is increasing or decreasing. of the value of the slope obtained.

Step 1 of 1

Determine the slope of the line.

The points as given in the question are (2,3) and (0,4). Now, the formula for the slope is given as

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

So, substitute $4 \& 3$ for $y_{2}$ and $y_{1}$ respectively, and $0 \& 2$ for $x_{2}$ and $x_{1}$ respectively in the above formula. Then simplify to get the slope as follows, $m=\frac{4-3}{0-2}$\\ $m=\frac{1}{-2}$\\ $m=-\frac{1}{2}$

The slope of the line is obtained as $-\frac{1}{2}$ . Now, as $-\frac{1}{2} < 0$ , so the function f(x) is decreasing.

7 0

1 year ago