In the figure, <4 is an exterior angle to AUL. Please use complete sentences.

evelyn is going on a hike. she will hike 4 miles in all. so far, she has hiked 1/2 of the total distance. how far has she hiked

lana [24]

Answer:

2 miles

Step-by-step explanation:

1/2 of 4 is 2

Mathematically

1/2 × 4/1

4/2

2

5 0

2 years ago

A rectangle has the following vertices. Find the area of the rectangle. (9, −1), (−1, 7), (−5, 2), (5, −6)

stiks02 [169]

Answer: 82 sq. units .

Step-by-step explanation:

Let A (9, −1), B (−1, 7), C(−5, 2), D(5, −6) are the vertices of rectangle.

Then we plot them on graph ( as provided in attachment)

Length = AB $=\sqrt{(9+1)^2+(-1-7)^2}$ units [By distance formula : $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ ]

$=\sqrt{(10)^2+(-8)^2}=\sqrt{100+64}=\sqrt{164}=2\sqrt{41}$ units

Width = BC = $\sqrt{(-1+5)^2+(7-2)^2}$ units

$=\sqrt{4^2+5^2}\\\\=\sqrt{16+25}\\\\=\sqrt{41}$

Area = length x width

= $2\sqrt{41}\times\sqrt{41}=2\times41= 82\text{ sq. units}$

Hence, the area of the rectangle is 82 sq. units .

7 0

3 years ago

A man standing at point A walks 1 mile south, 3 miles east, 5 miles north, and 7 miles west to reach point B. The length of line

joja [24]

Answer: √32

Step-by-step explanation: so the displacement is north 4 and west 4 and it becomes a right triangle so the hypotenuse is the distance for segment AB

So Drawn out should like straight lines up,down,left,and right. So east is positive while west is negative same for North(+) and South(-)

I recommend sticking with 2 directions first. Starting with north and south right. First you go south 1 mile but then you go north 5miles in math terms

-1+5=4 or down one is one less than 5

Same for east and west. 3+-7 = -4

So we went positive 4 miles up and 4miles to the left

So (-4)^2+4^2= hypotenuse or AB segment in this case

Download pdf

3 0

2 years ago

Show that sin (30°) = 1/2

Natali [406]

Answer:

Geometric proof in explanation.

Step-by-step explanation:

Draw an equilateral triangle.

A equilateral triangle has it's sides all congruent and all it's angles measures 60 degrees.

We are going to draw a line segment to cut the equilateral triangles into two congruent right triangles. I will do this in the attachment with p being positive.

You can see we will get 30-60-90 triangles.

We don't need to find the adjacent measurement to the angle whose measurement is 30 degrees since sine is opposite over hypotenuse.

$\sin(30^\circ)=\frac{\frac{p}{2}}{p}=\frac{p}{2} \cdot \frac{1}{p}=\frac{1}{2}$