What are the domain and range of the function f of x equals the quantity of x squared minus 3 x minus 28, all over x plus 4?

In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.

PolarNik [594]

Answer:

JL ≈ 32

Step-by-step explanation:

The triangle JKL has a side of JK = 24 and we are asked to find side JL. The triangle JKL is a right angle triangle.

Let us find side the angle J first from the triangle JKM. Angle JMN is 90°(angle on a straight line).

using the cosine ratio

cos J = adjacent/hypotenuse

cos J = 18/24

cos J = 0.75

J = cos⁻¹ 0.75

J = 41.4096221093

J ≈ 41.41°

Let us find the third angle L of the triangle JKL .Sum of angle in a triangle = 180°. Therefore, 180 - 41.41 - 90 = 48.59

Angle L = 48.59 °.

Using sine ratio

sin 48.59 ° = opposite/hypotenuse

sin 48.59 ° = 24/JL

cross multiply

JL sin 48.59 ° = 24

divide both sides by sin 48.59 °

JL = 24/sin 48.59 °

JL = 24/0.74999563751

JL = 32.0001861339

JL ≈ 32

8 0

3 years ago

While Brendan is vacationing with his family at the cabin, they take a motorboat on the river. The motorboat travels

taurus [48]

Part 1: The speed of the boat traveling downstream is $(18+w)$ miles per hr.

The speed of the boat traveling upstream is $(18-w)$ miles per hr.

Part 2: The speed of the current is 4 miles per hour.

Explanation:

Part (1): The motorboat travels 18 miles per hour in still.

Let w represents the speed of the current.

When the boat travels downstream, the speed of the current will get added to the speed of the boat.

Thus, the expression can be written as $(18+w)$ miles per hr

Hence, the speed of the boat traveling downstream is $(18+w)$ miles per hr.

When the boat travels upstream, the speed of the current will get subtracted to the speed of the boat.

Thus, the expression can be written as $(18-w)$ miles per hr.

Hence, the speed of the boat traveling upstream is $(18-w)$ miles per hr.

Part (2): The boat travels 49 miles upstream in the same time it takes to travel 77 miles downstream.

The distance formula is given by $distance $=$ speed $\times$ time$

Substituting, we have,

$49=(18-w)t\\49=18t-wt$ ---------------(1)

$77=(18+w)t\\77=18t+wt$ ---------------(2)

Solving using elimination method,

$49=18 t-w t\\77=18 t+w t\\-------\\126=36t$

Dividing both sides by 36, we have,

$t=3.5$

Substituting $t=3.5$ in $49=18 t-w t$ , we get,

$49=18(3.5)-w (3.5)\\$

$49=63-3.5w\\$

$-14=-3.5w\\$

$4=w$

Thus, the speed of the current is $w=4$ miles per hour.

5 0

3 years ago

What is the probability that you win $500 in a $1000 raffle

Sidana [21]

If it is a 1000 dollar raffle then you would not win 500 at all

3 0

4 years ago

When flipping a coin three times, what is the probability of landing on tails all two times?

xenn [34]

I believe it is A or B

5 0

3 years ago

Read 2 more answers

Can someone help me with this pls

Oksi-84 [34.3K]

Answer:

x = 1/3 or x = -2/3

Step-by-step explanation:

Let's solve your equation step-by-step.

9x2+3x−2=0

For this equation: a=9, b=3, c=-2

9x2+3x+−2=0

Step 1: Use quadratic formula with a=9, b=3, c=-2.

$x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}$

$x=\frac{-(3)\pm\sqrt{(3)^2-4(9)(-2)} }{2(9)}$

$x=\frac{-3\pm\sqrt{81} }{18}$

x = 1/3 or x = -2/3

4 0

2 years ago

Read 2 more answers