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katen-ka-za [31]
3 years ago
14

Explain why 6^3x7^3=42^3 is correct.

Mathematics
2 answers:
trapecia [35]3 years ago
5 0
Because 6 x 6 x 6 is 216 and 7 x 7 x 7 is 343 if you multiply those two umbers together you will get the same answer as 42 x 42 x 42 which is 74,088
Orlov [11]3 years ago
4 0

Answer:

{6}^{3} \times {7}^{3}  =  {(6 \times 7)}^{3}  =  {42}^{3}

Step-by-step explanation:

When two or more quantities have the same exponents, their bases can be multiplied together.

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Jane made a door frame for the house but does not have a tool to measure the angles. How can she check that the corner is 90 deg
Ainat [17]

The door frame is a rectangle. The diagonals of a rectangle are congruent. She can measure the two diagonals and make sure they are congruent.

3 0
3 years ago
Read 2 more answers
Question 18(Multiple Choice Worth 1 points)
Y_Kistochka [10]

Answer:

B

Step-by-step explanation:

2^2 x 2^3 = 2^5

2^5/2^4 = 2^1

4 0
3 years ago
Help I don’t get it
julia-pushkina [17]
The area is 45 inches
3 0
3 years ago
Find the approximate radius of a sphere with a surface area of 400 square inches.
Simora [160]
The equation for surface area of a sphere is SA=4*pi*r^2
We can plug in what we know to solve for r
400=4*pi*r^2
100=pi*r^2 (divide out the 4)
100/pi=r^2 (divide out the pi)
√(100/pi)=r (square root of both sides)
r=5.6 rounded to the nearest tenth
7 0
3 years ago
A rectangular cow pasture is enclosed on three sides by a fence and the fourth side is part of the side of a barn that is $400$
Rudiy27

Let us list out the given information:

Cost per foot = $5

Total fencing cost = $1200

Let L be the length of the barn that will maximize the area of the pasture and W be the width of the rectangular cow pasture.

From the given information, we need to do the fencing for three sides covering 1 L and 2 W's because other L will be the fourth side is part of the side of a barn. We need to write the equation based on the cost information.

If cost/foot is $5, then cost of length ' L ' will be 5L dollars and cost of '2W' width equals 10W dollars. Total cost is $1200. We can set up second equation as

5L + 10W = 1200. This can be simplified by dividing throughout the equation by 5 to get L+ 2W= 240. Solving for L we get L = 240 - 2W

Area of a rectangle is given by A = L ×W.

Substituting 240 - 2W for L we get the area function as..

A=(240 - 2W)×W= 240W-2W²

A = -2W²+240W.

When we have a function of the form f(x) = ax^2 + bx + c, then maximum value of the function can be obtained for x = -b/2a. Using that idea we can find the maximum area.

Here in the area function a = -2 and b = 240

For W = -b/2a = -240/2(-2) = -240/-4 = 60 feet, we get maximum area.

The question is asking us to find Length. We can substitute W = 60 in the equation L = 240 - 2W to find the Length.

L = 240 - 2(60) = 240 - 120 = 120 feet.

Conclusion: The length of the side parallel to the barn that will maximize the area of the pasture is 120 feet.

Note: Here the information 400 feet in the sentence "the fourth side is part of the side of a barn that is 400 feet long" given to distract us, we might not require that information to find the Length.

3 0
3 years ago
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