Answer:
(d) 944 mm³
Step-by-step explanation:
The volume of a prism is given by the formula ...
V = Bh
where B is the area of the base, and h is the distance between bases.
__
<h3>base area</h3>
Here, the base of the prism is a rectangle with a semicircle on top. The circle has a diameter of 9 mm, so a radius of 4.5 mm. The area of the semicircle is ...
A = 1/2πr² = 1/2π(4.5 mm)² ≈ 31.809 mm²
The area of the rectangle is the product of its length and width.
A = LW = (9 mm)(6 mm) = 54 mm²
So, the total base area is ...
31.809 mm² +54 mm² = 85.809 mm²
<h3>prism volume</h3>
The prism volume is this area multiplied by the length of the figure:
V = Bh = (85.809 mm²)(11 mm) ≈ 944 mm³
The volume of the figure is about 944 mm³.
Answer:
y=2x+1
Step-by-step explanation:
Since we are given a point and a slope, we can use the point slope formula
m is the slope. In this case, m is 2.
y1 is the y coordinate of the point given. y1 is 3.
x1 is the x coordinate of the point given. x1 is 1
y-3=2(x-1)
Now, we need to get the equation into point slope form: y=mx+b
To do this, we need to get y by itself
First, distribute the 2 on the right
y-3=2*x+ 2*-1
y-3=2x-2
Add 3 to both sides
y-3+3=2x-2+3
y=2x+1
The equation is in y=mx+b form, so our final equation is:
y=2x+1
Answer:
1) 5/9
2) 4/7
3) 3/8
Step-by-step explanation:
1) 5/9
2) 4/7
3)3/8
Answer:
2/3
Step-by-step explanation:
We can find the slope by using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 12-18)/(20 -11)
= -6/-9
= 2/3
Answer:
∠ 5 = 40°
Step-by-step explanation:
∠ 1 and ∠ 2 are adjacent angles and supplementary, thus
∠ 2 = 180° - ∠ 1 = 180° - 140° = 40°
∠ 5 and ∠ 2 are alternate angles and congruent , thus
∠ 5 = 40°
