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3 years ago

13

Ada has y blue note book and w red notebook .she combined them and was able to see half of the items. how many items did Ada sel

l?

1 answer:

maria [59]3 years ago

5 0

Answer:

She sold 1 item and remains with 1 item

Step-by-step explanation:

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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

3 years ago

Find the measure of 0. Round answer to the nearest tenth. Pleas help

DENIUS [597]

Answer:

$\theta=36.43^{\circ}$

Step-by-step explanation:

Given that,

Base = 42

Perpendicular height = 31

We need to find the value of $\theta$ . It can be calculated using trigonometry as follows :

$\tan\theta=\dfrac{P}{B}\\\\\theta=\tan^{-1}(\dfrac{P}{B})$

Put all the values,

$\theta=\tan^{-1}(\dfrac{31}{42})\\\\\theta=36.43^{\circ}$

So, the value of $\theta=36.43^{\circ}$ .

6 0

3 years ago

What is the volume of the square pyramid with base edges 12 cm and height 12 cm?

aliya0001 [1]

Answer:

V=144

Step-by-step explanation:

To find the volume of a pyramid, use the formula V=B•h, B being the base and h the height. So 12•12=144.

4 0

3 years ago

Read 2 more answers

B) The perimeter of the shape is 25.71 cm

natita [175]

Answer:

$r=4cm$

Step-by-step explanation:

Having the radius to be involved, the shape is a circle.

<u>Circumference formula </u>

$c=2\pi r$

Finding radius, formula will be reversed.

$r=\frac{25.72cm}{2\pi }$

$r=\frac{25.71cm}{2(3.142)}$ $r=\frac{25.71cm}{6.284}$ $r=4.09cm$

4 0

3 years ago

Linda bought a cube jewelry box. The volume of the jewelry box is 64 cubic inches. What is the edge length of Linda’s jewelry bo

yawa3891 [41]

Answer:

The edge length will be equal to 4 inches.

Step-by-step explanation:

The volume of a cube = s * s * s (in which s represent side of the cube)

V = s * s * s

V = s³

64 = s³

64 = 4³

So edge length of the cube will be 4 inches.

7 0

3 years ago