2. The table shows the amount

Mathematics

1 answer:

abruzzese [7]3 years ago

3 0

I think the answer might be B

You might be interested in

A restaurant charges $10 for Seniors 60 years old or older, and under the age of 12. Others will have to pay $15. Write two ineq

mr_godi [17]

Answer: X < 12 and X >= 60

Step-by-step explanation:

Call X the age

6 0

2 years ago

Explain the relationship between angle W and angles X and Y.

Dmitrij [34]

Answer: w is equal to the sum of angles x and y. (W=x+y)

Step-by-step explanation:

The exterior angle of a triangle (in this case w) is equal to the sum of the two remote interior angles of the triangle (in this case angles x and y)

5 0

2 years ago

Question 15 (5 points) Find the angle between u = <7, -2> and v= (-1,2>.

Tema [17]

Answer:

Approximately $2.3127$ radians, which is approximately $132.51^{\circ}$ .

Step-by-step explanation:

Dot product between the two vectors:

$\begin{aligned}& u\cdot v \\ =\; & 7 \times (-1) + (-2) \times 2 \\ =\; & (-11) \end{aligned}$ .

Magnitude of the two vectors:

$\begin{aligned} \| u \| &= \sqrt{{7}^{2} + {(-2)}^{2}} \\ &= \sqrt{53} \end{aligned}$ .

$\begin{aligned} \| v \| &= \sqrt{{(-1)}^{2} + {2}^{2}} \\ &= \sqrt{5} \end{aligned}$ .

Let $\theta$ denote the angle between these two vectors. By the property of dot products:

$\begin{aligned} \cos(\theta) &= \frac{u \cdot v}{\|u\| \, \| v \|} \\ &= \frac{(-11)}{(\sqrt{53})\, (\sqrt{5})} \\ &= \frac{(-11)}{\sqrt{265}}\end{aligned}$ .

Apply the inverse cosine function ${\rm arccos}$ to find the value of this angle:

$\begin{aligned} \theta &= \arccos\left(\frac{u \cdot v}{\| u \| \, \| v \|}\right) \\ &= \arccos\left(\frac{(-11)}{\sqrt{265}}\right) \\ & \approx \text{$2.3127$ radians} \\ &= 2.3127 \times \frac{180^{\circ}}{\pi} \\ &\approx 132.51^{\circ}\end{aligned}$ .