Answer:
The answer is 36 x⁴ y⁴
Step-by-step explanation:
Answer:
(0, -5)
Step-by-step explanation:
When you move down you subtract the amount from the y-axis.
Answer:
B
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - 5 and (a, b) = (2, - 7), thus
y - (- 7) = - 5(x - 2) , that is
y + 7 = - 5(x - 2) → B
Answer:
The area is 64ft ^2.
Step-by-step explanation:
I believe this is an isosceles triangle and if so our base will be 16ft and our height will be 8ft, knowing this we can solve for the area.
Use the form A=bh/2
Now plug it in...
A=16x8/2
A=128/2
A=64ft ^2
Hope this helps :)
Answer: Prism B is 6 inches taller than Prism A.
Step-by-step explanation:
To find the height difference between Prism B and Prism A, we need to compare their dimensions and surface areas.
1. Start by calculating the surface areas of Prism A and Prism B. The surface area of a rectangular prism is given by the formula \(2lw + 2lh + 2wh\), where \(l\) is the length, \(w\) is the width, and \(h\) is the height.
For Prism A:
Surface area of Prism A = \(2(6 \times 2) + 2(6 \times h) + 2(2 \times h)\)
= \(12 + 12h + 4h\)
= \(12 + 16h\)
For Prism B:
Surface area of Prism B = \(2(4 \times 3) + 2(4 \times h) + 2(3 \times h)\)
= \(24 + 8h + 6h\)
= \(24 + 14h\)
2. Since the two prisms have the same surface area, we can set their surface area equations equal to each other and solve for \(h\):
\(12 + 16h = 24 + 14h\)
3. Simplify the equation:
\(16h - 14h = 24 - 12\)
\(2h = 12\)
4. Solve for \(h\) by dividing both sides of the equation by 2:
\(h = \frac{12}{2}\)
\(h = 6\)
Therefore, Prism B is 6 inches taller than Prism A.
To find the difference in height between Prism A and Prism B, we compare their base areas and calculate their respective heights based on the same surface area.
Prism A has a length of 6 inches and a width of 2 inches, while Prism B has a length of 4 inches and a width of 3 inches. To compare their heights, we need to find their base areas first.
The base area of Prism A is 6 x 2 = 12 square inches, and the base area of Prism B is 4 x 3 = 12 square inches as well. Since they have the same surface area, their heights must be different.
To find the difference in height, we divide the surface area by the base area to get the height. For Prism A, 12 / 12 = 1 inch. For Prism B, 12 / 12 = 1 inch as well. Therefore, Prism B is 1 inch taller than Prism A.
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The quantity of pure water is 64 gallons which are to be evaporated.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The total amount of salt must be equal before and after evaporation.
Multiply the percent of salt in the solution before evaporation by the total gallons of solution
= 12% x 160 gallons convert 12% to decimal form (12% ÷ 100)
= 0.12 * 60
Subtract the number of gallons of pure water that should be evaporated from the total number of gallons of the solution and multiply by the percent of salt in the solution after evaporation
= 20% * (160 - x)convert 20% to decimal form (20% ÷ 100)
= 0.20(160 - x)
Set the before & after evaporation equations equal to one another to solve for x.
0.12 x 160 = 0.20(160 - x)
19.2 = (0.20 * 160) + (0.20 * -x)
19.2 = 32 - 0.20x
-12.8 = -0.20x
64 gallons = x
Therefore, the quantity of pure water is 64 gallons which are to be evaporated.
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