out of fifty students,34 joined the journalism class and 25 joined robotics club.if 16 students joined both clubs,how many stude

Answer:

Rotated 90° clockwise around the origin. (RO 90)

Step-by-step explanation:

Based on the information A(–3, 4) transitions to A'(4, 3), B(4, –5) becomes B'(-5, –4), and C(1, 6) shifts to C'(6, –1). This implies that a point represented as P(x, y) is transformed to P(y, -x) after rotation.

Therefore, if a point P(x, y) is transformed to P(y, -x), this occurs when the shape defined by these three points is rotated 90° clockwise around the origin.

Answer:

Step-by-step explanation:

A polynomial is in its standard form when arranged in descending order based on the variable involved.

Looking at the provided polynomial

• s is presented in descending powers
• r is in ascending order

Thus, the first term of the polynomial should meet these criteria:

• Power of r is less than 2
• Power of s is greater than 4.

The following meets these requirements:

Answer:

Part A:

x+y= 95

x = y+25

Part B: 35 minutes

Part C: No

Step-by-step explanation:

• Part A:

Eric spends a total of 95 minutes daily playing basketball and volleyball combined.

x+y= 95

Where:

x =minutes Eric plays basketball

y = minutes he allocates to volleyball

He dedicates 25 minutes more to basketball compared to volleyball.

x = y+25

Equations are:

x+y= 95

x = y+25

• Part B:

Substituting x=y+25 into the first equation yields:

(y+25) + y =95

Solving for y

y+25+y =95

25+2y=95

2y=95-25

2y=70

y = 70/2

y = 35 minutes

Part C: No

If x = 35

x+y= 95

35+y =95

y= 95-35

y = 60 minutes

Inserting y=60 into the other equation:

x = y+25

35 = 60+25

35 ≠85

Answer:

Step-by-step explanation:

There are 15 antennas in total.

Out of these, 3 are defective.

This means that 12 antennas are functioning: 15-3=12.

To ensure that no two defective antennas are adjacent, we need to have only one defective at a time placed between the functional ones.

So,

We align the 13 functional antennas, then look for the spaces where the defective antennas can fit

__G __ G __ G __ G __ G __G __ G __ G __ G __ G __ G __ G __G __

Each gap represented by an underscore indicates a possible location for a defective antenna, allowing for just one per space.

Consequently, there are 14 potential spots for the defective antennas. With 3 defectives, we are dealing with a combinatorial arrangement.

ⁿCr= n!/(n-r)!r!

The total number of arrangements possible is

14C3=14!/(14-3)!3!

14C3=14×13×12×11!/11!×3×2

14C3=14×13×12/6

That gives us 364 distinct ways to arrange them.