<u>Answer:</u>
B.The area of the base of the pyramid is 24cm^2.
C.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.
E.The volume of this pyramid is 72cm3.
<u>Step-by-step explanation:</u>
Area of base of the pyramid = l × w = 4 × 6 = 24 cm^2
Volume of rectangular pyramid = (l × w × h)/3 = (4 × 6 × 9)/3 = 72 cm^3
Volume of rectangular prism = w × h × l = 9 × 4 × 6 = 216 cm^3
So according to these calculations, the correct answer options are:
B.The area of the base of the pyramid is 24cm^2.
C.A rectangular prism with the dimensions of 9 cm by 4 cm by 6 cm will have 3 times volume of this pyramid.
E.The volume of this pyramid is 72cm3.
Answers: perpendicular bisector; image
- The reflection of a point P across a line m is the point P' if line m is the <u> perpendicular bisector </u> of segment PP'
- Point P' is called the <u> image </u> of point P.
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Explanation:
If we were to reflect point P over line m to land on P', then we've gone from pre-image to image.
Let's say that Q is the point on segment PP' and it's also on line m. We consider Q the midpoint of segment PP' which means PQ and P'Q are the same length. This indicates P and P' are the same distance away from the mirror line, and that point Q bisects segment PP'. Also, line m is perpendicular to segment PP'. So that's where the "perpendicular bisector" comes from.
By substitution, the solution of the system of equations, 4x + 2y = 7 and y = 5x, is (1/2 , 5/2).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
4x + 2y = 7 (equation 1)
y = 5x (equation 2)
Since the second equation is already expressed in y in terms of x, substitute the second equation to the first equation.
4x + 2y = 7 (equation 1)
4x + 2(5x) = 7
4x + 10x = 7
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solving for x.
4x + 10x = 7
14x = 7
x = 1/2
Substitute the value of x in the second equation and solve for y.
y = 5x
y = 5(1/2)
y = 5/2
Hence, the solution of the given system of equations is (1/2 , 5/2).
To learn more about solving systems of equations: brainly.com/question/25869125
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Answer: 28 hours
Step-by-step explanation:
Hi, the cost for the trampoline park without a membership is equal to the price of the jump tickets per hour (12) multiplied by the number of hours (h).
Cost without membership= 12h
With the membership the price of each jump ticket has a 15% discount ( so, 100-15 =85% of the total price ). To calculate the cost for this case we have to add the cost of the membership 50, and multiply the cost of each jump ticket (12) by 0.85 (percentage in decimal form)
Cost with membership = 50 +12 (0.85) h
If both cost are equal:
50 +12 (0.85) h = 12 h
Solving for h
50+10.2h =12h
50= 12h-10.2h
50= 1.8h
50/1.8= h
27.78 =h
h =28 (rounded)
