What has a slope of 2/3

A cardboard box 6 units high, 4 units wide, and 3 units long can hold 80 pounds of brown rice. A second cardboard box has the sa

iren [92.7K]

I hope this helps but use lingith × with × higth so you would × 6 ×4 ×3

3 0

3 years ago

If a jogger runs a 10-kilometer race in 60 minutes, what is her average speed?

STALIN [3.7K]

Answer:

A

Step-by-step explanation:

Speed = distance/ time

=10km/ 1hr(60mins)

= 10km/ 1hr

=10km/hr

3 0

2 years ago

The graph of a quadratic function has a vertex located at (7,-3) and passes through points (5,5) and (9,5). Which equation best

Serga [27]

Answer:

B) $f(x)=2(x-7)^2-3$ .

Step-by-step explanation:

The vertex form of the equation is given by $f(x)=a(x-h)^2+k$ .

We plug in the vertex to obtain:

$f(x)=a(x-7)^2-3$ .

Since the graph passes through (5,5) and (9,5), they must satisfy its equation.

$5=a(9-7)^2-3$ .

$5+3=4a$ .

$8=4a$

Divide both sides by 4.

$a=2$

Therefore the equation is:

$f(x)=2(x-7)^2-3$ .

4 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

What is a number that names a part of a whole or part of a whole group

Vitek1552 [10]

A number that names a part of a whole or part of a whole group is called a fraction.

4 0

2 years ago