What are the solutions of the equation (2x + 3)2 + 8(2x + 3) + 11 = 0? Use u substitution and the quadratic formula to solve.

Answer:

60.36 steps West from center

85.36 steps North from center

Step-by-step explanation:

Refer to the attached

Musah's starting point and movement are depicted in the image.

• 1. He moves 50 steps towards the North,
• 2. Next, he moves 25 steps towards the West,
• 3. Then he proceeds 50 steps on a bearing of 315°. We now recognize that North is measured at 0°

or 360°, so a bearing of 315° corresponds to North-West 45°.

Note: According to the Pythagorean theorem, a right triangle at 45° with hypotenuse 'a' will have legs equal to a/√2.

What is the distance West of Musah's final position from the center?

25 + 50/√2 ≈ 60.36 steps

What is the distance North of Musah's final position from the center?

• 50 + 50/√2 ≈ 85.36 steps

Let the three consecutive even integers representing the sides of triangle PQR be defined as x, (x + 2), and (x + 4). Given that the perimeter of triangle PQR equals 42 cm.

Answer:

The answer to this question is C: (72,24).

Step-by-step explanation:

According to the information provided:

The price of one cap is $5

The price of one t-shirt is $10

Let x represent the number of caps sold

Let y represent the number of t-shirts sold

The drama club aims to raise at least $500 for their trip.

Hence, we can establish the inequality as follows:

The number of caps sold x (times) price of one cap + number of t-shirts y (times) price of one t-shirt ≥ (greater than or equal to) 500

Inequality: 5x + 10y ≥ 500 (The greater than or equal to symbol indicates the drama club needs at least $500 for the journey.Next, we need to ascertain the number of caps and t-shirts sold.

- We can eliminate

two

of the options which are

the two answers containing negatives

because we understand that multiplying a positive by a negative yields a negative, which is unacceptable. (Thus, Options A and D are not valid.)Now we will substitute x and y into our inequality equation (5x + 10y ≥ 500)B) x = 65 caps, y = 17.5 t-shirts ------> 5(65) + 10(17.5) = 500 results in $500

YOU MAY THINK THIS IS THE ANSWER, BUT! if you look closely at variable y, it indicates they sold 17.5 t-shirts; however, consider how can you sell 17.5 t-shirts?

Thus, this option is also invalid!

C) x = 72 caps, y = 24 t-shirts ------> 5(72) + 10(24)=

$600

which exceeds the required $500 that they needed. Therefore, the correct choice for this question is C, indicating they sold 72 caps and 24 t-shirts, accumulating $600.

Both a and b must be positive whole numbers.

Health inspector visits once a week.
Fire inspector comes every 12 days.

a) health inspector fire inspector.
day 7.                    day 12.   
day 14.                    day 24.
day 21.                    day 36.
day 28.                    day 48.
day 35.                    day 60.

b) 12 x 7 = 84.

Both will coincide on day 84.