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Maru [420]
3 years ago
8

Which recursive formula can be used to represent the sequence 2,5,8,11,14,..

Mathematics
1 answer:
Natasha_Volkova [10]3 years ago
6 0
The answer is D. a1=2 an=an-1+3
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Two cars simultaneously left Points A and B and headed towards each other, and met after 2 hours and 45 minutes. The distance be
Oksana_A [137]
<h2>Hello!</h2>

The answers are:

FirstCarSpeed=41mph\\SecondCarSpeed=55mph

<h2>Why?</h2>

To calculate the speed of the cars, we need to write two equations, one for each car, in order to create a relation between the two speeds and be able to calculate one in function of the other.

So,

Tet be the first car speed "x" and the second car speed "y", writing the equations we have:

For the first car:

x_{FirstCar}=x_o+v*t

For the second car:

We know that the speed of the second car is the speed of the first car plus 14 mph, so:

x_{SecondCar}=x_o+(v+14mph)*t

Now, from the statement that both cars met after 2 hours and 45 minutes, and the distance between to cover (between A and B) is 264 miles,  so, we can calculate the relative speed between them:

If the cars are moving towards each other the relative speed will be:

RelativeSpeed=FirstCarSpeed-(-SecondCarspeed)\\\\RelativeSpeed=x-(-x-14mph)=2x+14mph

Then, since we know that they covered a combined distance equal to 264 miles in 2 hours + 45 minutes, we have:

2hours+45minutes=120minutes+45minutes=165minutes\\\\\frac{165minutes*1hour}{60minutes}=2.75hours

Writing the equation:

264miles=(2x+14mph)*t\\\\264miles=(2x+14mph)*2.75hours\\\\2x+14mph=\frac{264miles}{2.75hours}\\\\2x=96mph-14mph\\\\x=\frac{82mph}{2}=41mph

So, the speed of the first car is equal to 41 mph.

Now, for the second car we have that:

SecondCarSpeed=FirstCarSpeed+14mph\\\\SecondCarSpeed=41mph+14mph=55mph

We have that the speed of the second car is equal to 55 mph.

Hence, the answers are:

FirstCarSpeed=41mph\\SecondCarSpeed=55mph

Have a nice day!

7 0
3 years ago
Consider the equation: x^2+10x+22=13<br> Need help asap!!!! <br> this is due in a hour!
klio [65]

Answer:

(x + 5)^2 = (5 - 3)^2

Step-by-step explanation:

Given the equation;

x^2 + 10x + 22 = 13

We have;

x^2 + 10x = 13 - 22

x^2 + 10x = -9

Adding half of 10 to both sides and completing the square as usual, we have;

(x + 5)^2 = 5^2 + (-9)

(x + 5)^2 = (5 - 3)^2

7 0
3 years ago
1. Which of the following is the equation of a circle with center (a, −b) and radius r?
choli [55]

Answer:

D

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Find the values of the variables and the measures of the angles
Alekssandra [29.7K]

The angles of the triangle are 39°, 51°, and 90°.

Step-by-step explanation:

Step 1:

The sum of all the angles in any triangle is equal to 180°.

We have two of the three angles in terms of x while the third angle is not given directly. Since it is a right-angled triangle, one of the angles equals 90°.

So the angles of the triangle are 3x, 4x-1, and 90.

Step 2:

Now, we substitute all the angles to a sum of 180 to determine the value of x.

3x + 4x - 1 + 90 = 180.

7x = 91, x = \frac{91}{7} = 13.

So x = 13°. The angles are

3x = 3 (13) = 39, 4x-1 = 4(13) - 1 = 51.

The angles of the triangle are 39°, 51°, and 90°.

7 0
3 years ago
Read 2 more answers
A fair coin is tossed 5 times in a row. The exact probability of the coin landing heads exactly 2 times is?
OLga [1]

|\Omega|=2^5=32\\|A|=10\\\\P(A)=\dfrac{10}{32}=\dfrac{5}{16}

5 0
3 years ago
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