Answer: 3
Step-by-step explanation
9 divided by 2 =4.5
3 divided by 2 = 1.5
so then we do 4.5 divided by 1.5=3 so the answer is 3
We require a picture of said spinner to see which sides say a and which say b
Answer:
101.9 sq ft
Step-by-step explanation:
The figure is missing: find it in attachment.
Here we want to find the lateral surface area of the figure, which is the sum of the areas of all faces.
We have in total 5 faces:
- 1 of them is rectangle with sizes (8.5 ft x 3.3 ft), so its area is
- 1 of them is a rectangle with sizes (3.3 ft x 5.1 ft), so its area is
- 1 of them is a rectangle with sizes (6.8 ft x 3.3 ft), so its area is
- Finally, we have 2 triangular faces (top and bottom), so their area is
where
b = 5.1 ft is the base
h = 6.8 ft is the height (because the triangle is a right triangle)
So the area of the triangle is
So the total lateral surface area of the figure is:
Step-by-step explanation:
the area of a triangle
baseline × height / 2
in our case
baseline × height / 2 = 60 in²
height = 6×baseline - 16
baseline × (6×baseline - 16) / 2 = 60
baseline × (3×baseline - 8) = 60
3×baseline² - 8×baseline = 60
baseline = x
3x² - 8x - 60 = 0
general solution to a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 3
b = -8
c = -60
x = (8 ± sqrt(64 - 4×3×-60))/(2×3) =
= (8 ± sqrt(64 + 720))/6 = (8 ± sqrt(784))/6 =
= (8 ± 28)/6
x1 = (8 + 28)/6 = 36/6 = 6
x2 = (8 - 28)/6 = -20/6 = -10/3
x2 as a negative number is not a valid solution for a length in a geometric shape.
so, x = 6 in is our solution for the baseline.
height = 6x - 16 = 6×6 - 16 = 36 - 16 = 20 in
base = 6 in
Problem 1 Answer: x = 2/3y+8
Show Work:
Step 1: Add 2y to both sides.
3x−2y+2y=24+2y
3x=2y+24
Step 2: Divide both sides by 3.
3x/3 = 2y+24/3
x = 2/3y+8
Problem 2 Answer: x=−2y+48
Show Work:
Add -2y to both sides.
x+2y+−2y=48+−2y
x=−2y+48
