I need help with this ^

Plzzzzzz help! What is the area of figure A?

zloy xaker [14]

Answer:

A=24m^2

Step-by-step explanation:

to find the area of this figure you can approach it multiple ways, the simplest way is to split it into two rectangles

respectively one 6m by 3m and another 3m by 2m

find the areas of each rectangle and add them both to get the total area of the figure

(6m*3m)+(3m*2m)=(18+6)m^2=24m^2

3 0

3 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

Use a system of linear equations with two variables and two equations to solve. A number is 9 more than another number. Twice

Troyanec [42]

9514 1404 393

Answer:

(x, y) = (3, 12)

Step-by-step explanation:

Using the given variable definitions, we can write the equations ...

y = x + 9

2(x +y) = 30

__

Solving the second equation for y, we have ...

y = 15 -x

Substituting this into the first equation gives ...

15 -x = x +9

6 = 2x . . . . . . . . . add x-9

3 = x . . . . . . . . . . divide by 2

y = 3+9 = 12 . . . . substitute into the first equation

The numbers are (x, y) = (3, 12).

4 0

2 years ago

Mr. Huyck needs 8 gallons of punch for the school dance. How many<br> quarts of punch would he need?

koban [17]

32 bc eight times four equals 32

8 0

3 years ago

Read 2 more answers

one leg of a right triangle has length 7. the lengths of the other two sides are whole numbers. the length of the other leg is ?

zalisa [80]

Sets of three integers that could be right triangles are called pythagorean triples. the only pythagorean triple including 7 is 7, 24, and 25. so the length of the other leg is 24 and the length of the hypotenuse is 25. hope this helped!

4 0

3 years ago

Read 2 more answers