Identify the equations as parallel lines, perpendicular lines, or neither.

This figure is made up of a quadrilateral and a semicircle.

Arturiano [62]

Answer:

The correct option is B. The area of the figure is 40.4 units².

Step-by-step explanation:

The line AB divides the figure in two parts one is a rectangle and another is semicircle.

The distance formula is

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The length of AB is

$AB=\sqrt{(2+3)^2+(4-2)^2}=\sqrt{25+4}=\sqrt{29}$

The length of AD is

$AD=\sqrt{(-1+3)^2+(-3-2)^2}=\sqrt{4+25}=\sqrt{29}$

Since AB=AD, therefore ABCD is a square. The area of the of square is

$A_1=a\times a=\sqrt{29}\times \sqrt{29} =29$

The area of square is 29 units².

The area of a semicircle is

$A_2=\frac{\pi}{2}r^2$

Since AB is the diameter of the semicircle, therefore the radius of the semicircle is

$r=\frac{d}{2}=\frac{\sqrt{29}}{2}$

The area of the semicircle is

$A_2=\frac{3.14}{2}(\frac{\sqrt{29}}{2})^2=40.3825$

The area of the figure is

$A=A_1+A_2=29+11.2825=40.3825\approx 40.4$

Therefore the area of the figure is 40.4 units². Option B is correct.

5 0

3 years ago

Sylvia is making a pot of stew that needs 3 quarts of beef broth. How many cups of beef broth does she need? Please explain how

Sergeeva-Olga [200]

12 cups because there are 2 cups in a pint and 2 pints in a quart

6 0

3 years ago

Read 2 more answers

2) Find the slope of the line

algol13

Assuming each line goes up by 1. we basically need to find a number that goes by rise/run. to get to the next point we need to go up 1, then to the left by 3. notice the slope is negative so we need to add a negative integer.

answer:

-1/3 (C)

hope this helps! :D

4 0

3 years ago

Read 2 more answers

A basketball gymnasium is 25 meters high, 80 meters wide and 200 meters long. We want to connect two strings, one from each of t

Rudiy27

Answer:

a) the centre is at (12.5 m, 40 m , 100 m ) with respect to our position

b) the length of the strings S will be 216.85 m

c) the angle that is formed by the strings is 1.23 rad

Step-by-step explanation:

assuming that we stand on one of the corners on the floor , so our coordinates are (0,0,0) , then the coordinates of the center of the gymnasium are found through

x center = (25 + 0)/2 = 12.5 m

y center = (80+ 0)/2 = 40 m

z center = (200+ 0)/2 = 100 m

then the centre is at (12.5 m, 40 m , 100 m ) with respect to our position

b) the length of the strings S will be the modulus of the vector that points from our position to the diagonally opposite corners

|S| = √(25²+80²+200²) = 216.85 m

c) the angle can be found through the dot product of the vectors that represent the strings S₁ and S₂

S₁ =(25,80,10)

S₂ =(-25,80,100)

then

S₁*S₂ = 25*(-25) +80*80 + 100*100 = 15775

but also

S₁*S₂ = |S₁||S₂| cos θ = |S|² * cos θ

S₁*S₂ = |S|² * cos θ

cos θ= S₁*S₂/|S|²

θ= cos ⁻¹ ( S₁*S₂/|S|² ) = cos ⁻¹ [15775/(25²+80²+200²)] = 1.23 rad

7 0

3 years ago

Help

Evgen [1.6K]

Answer:

8.6

Step-by-step explanation:

The square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6

5 0

3 years ago