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3 years ago

HELP !! Find the x with the details in this picture^^

Mathematics

1 answer:

zvonat [6]3 years ago

5 0

Answer:

x = 3.9

Step-by-step explanation:

So the whole angle PQS = 111 degrees

it gave you part of it so subtract that off . 111 - 72 = 39 degrees

10 times what equals about 39 degrees.

39/ 10 = 3.9

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12/5 divided by 21/10

Juli2301 [7.4K]

Exact form is 8/7 , as a decimal its 1.142 and mixed number form its 1 1/7

6 0

2 years ago

Two lighthouses are located 75 miles from one another on a north-south line. If a boat is spotted S 40o E from the northern ligh

yuradex [85]

Answer:

The northern lighthouse is approximately $24.4\; \rm mi$ closer to the boat than the southern lighthouse.

Step-by-step explanation:

Refer to the diagram attached. Denote the northern lighthouse as $\rm N$ , the southern lighthouse as $\rm S$ , and the boat as $\rm B$ . These three points would form a triangle.

It is given that two of the angles of this triangle measure $40^{\circ}$ (northern lighthouse, $\angle {\rm N}$ ) and $21^{\circ}$ (southern lighthouse $\angle {\rm S}$ ), respectively. The three angles of any triangle add up to $180^{\circ}$ . Therefore, the third angle of this triangle would measure $180^{\circ} - (40^{\circ} + 21^{\circ}) = 119^{\circ}$ (boat $\angle {\rm B}$ .)

It is also given that the length between the two lighthouses (length of $\rm NS$ ) is $75\; \rm mi$ .

By the law of sine, the length of a side in a given triangle would be proportional to the angle opposite to that side. For example, in the triangle in this question, $\angle {\rm B}$ is opposite to side $\rm NS$ , whereas $\angle {\rm S}$ is opposite to side ${\rm NB}$ . Therefore:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of NB}}{\sin(\angle {\rm S})} \end{aligned}$ .

Substitute in the known measurements:

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of NB}}{\sin(21^{\circ})} \end{aligned}$ .

Rearrange and solve for the length of $\rm NB$ :

$\begin{aligned} & \text{length of NB} \\ =\; & (75\; \rm mi) \times \frac{\sin(21^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 30.73\; \rm mi\end{aligned}$ .

(Round to at least one more decimal places than the values in the choices.)

Likewise, with $\angle {\rm N}$ is opposite to side ${\rm SB}$ , the following would also hold:

$\begin{aligned} \frac{\text{length of NS}}{\sin(\angle {\rm B})} = \frac{\text{length of SB}}{\sin(\angle {\rm N})} \end{aligned}$ .

$\begin{aligned} \frac{75\; \rm mi}{\sin(119^{\circ})} = \frac{\text{length of SB}}{\sin(40^{\circ})} \end{aligned}$ .

$\begin{aligned} & \text{length of SB} \\ =\; & (75\; \rm mi) \times \frac{\sin(40^{\circ})}{\sin(119^{\circ})} \\ \approx\; & 55.12\; \rm mi\end{aligned}$ .

In other words, the distance between the northern lighthouse and the boat is approximately $30.73\; \rm mi$ , whereas the distance between the southern lighthouse and the boat is approximately $55.12\; \rm mi$ . Hence the conclusion.

4 0

2 years ago

An oxygen tank contained 212 12/3 liters of oxygen before 27 1/3 liters were used. If the tank can hold 240 3/8 liters, how much

lukranit [14]

So, initially 240 $\frac{3}{8}$ -212 $\frac{12}{3}$ were empty:

this is :

$240 \frac{3}{8} - 212 \frac{12}{3} = 240 \frac{3}{8} - 212 +4 = 240 \frac{3}{8} - 216= 24 \frac{3}{8}$

12/4 is 4 so that's why i substituted it with 4.

now, later 27 1/3 were used so we add this tho the original empty space

$24 \frac{3}{8}+ 27 \frac{1}{3}$ = $24 \frac{9}{24}+ 27 \frac{8}{24}$ = $51 \frac{17}{24}$

which is the result!

5 0

3 years ago

A color printer prints 8 pages in 5 minutes. How many pages does it print per minute?

fenix001 [56]

Answer:

1.6 OR 8/5

(They are the same thing.)

6 0

3 years ago

Read 2 more answers

You are creating a decorative rope that is at least 20 feet long. You do not have enough 6 inch beads to make the rope, so you w

Inessa05 [86]

You can use at most 24 beads that are 10 inches long to decorate the rope.

Step-by-step explanation:

Given,

Length of rope = 120 feet

1 foot = 12 inches

20 foot = 20*12 = 240 inches

Length of bead = 10 inches

Let,

x represents the number of beads used on rope.

As the rope is 240 inches long, therefore, the total length of beads cannot exceed 240 inches.

Length of each bead*Number of beads ≤ length of rope

$10*x\leq 240\\10x\leq 240$

Dividing both sides by 10

$\frac{10x}{10}\leq \frac{240}{10}\\x\leq 24$

You can use at most 24 beads that are 10 inches long to decorate the rope.

Keywords: inequality, division

Learn more about inequalities at:

#LearnwithBrainly

4 0

3 years ago