AB is a straight line. Find the values of y and z.

What is the solution of 3+(x-2/x-3)<=4

Minchanka [31]

Answer: x < 3

Step-by-step explanation:

Solve the rational inequality by combining expressions and isolating the variable x.

7 0

3 years ago

K(x) = 2x – 4; Find k (x + 4)

Iteru [2.4K]

Answer:

k= −2x−16 /x

Step-by-step explanation:

5 0

2 years ago

What is the length of the unknown leg in the right triangle? 22 32 104 194

Rus_ich [418]

Answer:

Your answer would be B.

Step-by-step explanation:

a^2 + 9^2 = 113^2

Solve exponents.

A^2 + 81 = 113

Subtract 81 from each side.

A^2 = 32.

Square root each side.

A = 32

Hope this helps & good luck!

Feel free to message me if you need more help! :)

7 0

3 years ago

A bird leaves its nest and travels 20 miles per hour downwind for x hours. On the return trip, the bird travels 4 miles per hour

Reil [10]

Answer:

The correct answers are:

A) 60 miles; and B) 3.375 hours.

Explanation:

We will use the equation d = rt for this.

For the first leg of the trip, the bird travels 20 miles per hour for x hours. This gives us the equation

d = 20x

For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour. He also travels 6 miles less than the return distance, for x hours:

d-6 = 16x

To isolate d, we will add 6 to each side:

d-6+6 = 16x+6

d = 16x+6

We will set the two equations equal to one another, since they both equal d:

20x = 16x+6

Subtract 16x from each side:

20x-16x = 16x+6-16x

4x = 6

Divide both sides by 4:

4x/4 = 6/4

x = 1.5

He travels for 1.5 hours both times.

The first time, 1.5 hours at 20 miles per hour is:

d = 1.5(20) = 30 miles

The original trip is 30 miles. This makes the entire trip 30(2) = 60 miles.

On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:

24 = 16x

Divide both sides by 16:

24/16 = 16x/16

1.5 = x

If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:

24/1.5 = 30/x

Cross multiplying,

24*x = 1.5(30)

24x = 45

24x/24 = 45/24

x = 1.875

This gives him a total time of 1.5+1.875 = 3.375 hours

Step-by-step explanation:

7 0

2 years ago

The time needed to complete a final examination in a particular college course is normallydistributed with a mean of 80 minutes

Artist 52 [7]

Answer:

a) 0.023

b) 0.286

c) 10 students will be unable to complete the exam inthe allotted time.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 80 minutes

Standard Deviation, σ = 10 minutes

We are given that the distribution of time to complete an exam is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(completing the exam in one hour or less)

P(x < 60)

$P( x < 60) = P( z < \displaystyle\frac{60 - 80}{10}) = P(z < -2)$

Calculation the value from standard normal z table, we have,

$P(x < 60) =0.023= 2.3\%$

b) P(complete the exam in more than 60 minutes but less than 75 minutes)

$P(60 \leq x \leq 75) = P(\displaystyle\frac{60 - 80}{10} \leq z \leq \displaystyle\frac{75-80}{10}) = P(-2 \leq z \leq -0.5)\\\\= P(z \leq -0.5) - P(z < -2)\\= 0.309- 0.023 = 0.286= 28.6\%$