Answer:
79
Step-by-step explanation:
Let's start by writing out what we know:
A = 647 in base-n
A = 513 in base-(n+2)
To find A in base-10, we need to use the place value system and the definition of each base. Let's first convert A to base-10 using the given information.
In base-n, A is equal to:
A = 6n^2 + 4n + 7
In base-(n+2), A is equal to:
A = 5(n+2)^2 + 1(n+2) + 3
A = 5(n^2 + 4n + 4) + (n + 2) + 3
A = 5n^2 + 21n + 20
Now we have two expressions for A, so we can set them equal to each other and solve for n:
6n^2 + 4n + 7 = 5n^2 + 21n + 20
Simplifying and rearranging, we get:
n^2 + 8n + 13 = 0
Using the quadratic formula, we can solve for n:
n = (-8 ± sqrt(8^2 - 4(1)(13))) / (2(1))
n = (-8 ± 2) / 2
n = -3 or n = -5
Since n is a positive integer, we can disregard the negative solution and conclude that n = 3.
Now that we know n, we can substitute it back into the expression for A in base-n and solve for A in base-10:
A = 6n^2 + 4n + 7
A = 6(3^2) + 4(3) + 7
A = 79
Therefore, the number A written in base-10 is 79.
Hope this helps!
Find the square
(8m + 7)^2
Answer:
(8m + 7)^2 = 64m^2 + 112m + 49
(8m)^2 = 64m^2
2(8m)(7) = 112m
7^2 = 49
figure B is a scaled copy of Figure A. What is the skill factor from Figure A to Figure B?
Answer:
1/4 = 0.25
Step-by-step explanation:
Scale Factor from Figure A to Figure B = Figure B dimensions ÷ Figure A dimensions
Take any one side of Figure B and compare it with the corresponding side of Figure A and the ratio will give the scale factor. Since the figures are similar, the ratios of the other corresponding sides will be the same
Take horizontal top side of A which has a length of 4
The corresponding side of B has a length of 1
Therefore scale factor = 1/4 = 0.25
The other ratios are the same:
1.1/4.4 = 1.5/6 = 1/4 = 0.25
Adjacent angles. View the photo ccd
Answer: ∠DEA
Step-by-step explanation:
Starting Angle: ∠FBG
Adjacent (SAME) Angle: ∠DEA
The top and bottom margins of a poster are 6 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 380 square centimeters, find the dimensions of the poster with the smallest area.
Width =
Height =
Let's denote the width of the printed material on the poster as "x" cm and the height as "y" cm.
According to the given information, the top and bottom margins are each 6 cm, and the side margins are each 8 cm. This means that the actual width of the entire poster, including the margins, is "x + 2(8)" cm, and the actual height, including the margins, is "y + 2(6)" cm.
Given that the area of the printed material on the poster is fixed at 380 square centimeters, we can set up the following equation:
Actual Area of Poster = Area of Printed Material on Poster
(x + 2(8))(y + 2(6)) = 380
(x + 16)(y + 12) = 380
To find the dimensions of the poster with the smallest area, we need to minimize the product (x + 16)(y + 12).
Since the given area of the printed material on the poster is fixed at 380 square centimeters, the actual area of the entire poster, including the margins, will be minimized when (x + 16)(y + 12) is minimized.
To minimize the product (x + 16)(y + 12), we need to minimize both x + 16 and y + 12, as they are both positive quantities.
Since x and y represent the width and height of the printed material on the poster, respectively, the smallest possible values for x + 16 and y + 12 would be 0, which means x = -16 and y = -12. However, since width and height cannot be negative, we need to find the next best option.
The smallest possible values for x + 16 and y + 12 that are greater than or equal to 0 would be when x = 0 and y = 0. This means that the width of the printed material on the poster should be 0 cm and the height should be 0 cm, which would make the dimensions of the poster with the smallest area:
Width = 0 cm
Height = 0 cm
However, please note that this would mean there is no printed material on the poster, as the width and height are both 0. If you want to have a non-zero width and height for the printed material on the poster, you would need to adjust the given area of the printed material on the poster accordingly.
ASAP Dr. Rollins is both an anthropologist and archeologist. While excavating some ruins in South America, he discovered a scale drawing of a replica of a Mayan pyramid.
-The scale for the drawing to the replica was 1 inch : 2 feet.
- The scale for the replica to the actual pyramid was 1 foot : 14 feet.
If the height of the pyramid on the drawing was 3 1/2 inches, what was the height of the actual pyramid?
A. 98 feet
B. 49 feet
C. 91 feet
D. 196 feet
The height of the actual pyramid is 98 feet.
How to determine the height of the actual pyramid?
To determine the height of the actual pyramid, we need to use both scales and convert the measurements.
First, let's convert the height of the drawing to the height of the replica,
1 inch : 2 feet (scale for drawing to replica)
[tex]3 \frac{1}{2} \: inches[/tex] = 7 feet (height of the replica)
Next, let's convert the height of the replica to the height of the actual pyramid:
1 foot : 14 feet (scale for replica to actual)
7 feet = 7 x 14 = 98 feet (height of the actual pyramid)
Therefore, the height of the actual pyramid is 98 feet, so the answer is A) 98 feet.
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4) Construct the truth tables for the following
(a) pV r
The truth tables for the logic expression is
p q p v q
F F F
F T T
T F T
T T T
Constructing the truth tables for the logic expressionFrom the question, we have the following parameters that can be used in our computation:
p v r
The expression is pronounced p or r
The rule of the truth table is
The expression is true if any of p or q is trueThe expression is false if both p and q are falseUsing the above as a guide, we have the following truth tables
p q p v q
F F F
F T T
T F T
T T T
The above represents the truth tables for the logic expression
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6 The Montreal Biosphere is a geodesic dome that surrounds an environmental
museum in Montreal, Canada. The dome has a volume of 6,132,812.5 cubic feet.
The structure is 75% of a full sphere. What is the length of its diameter?
The geodesic dome has a diameter of 249.958 feet.
How to determine the diameter of the Montreal Biosphere
In this problem we must determine the diameter of a geodesic dome located in Montreal, Canada, (D), in feet. The volume of the geodesic dome (V), in cubic feet, is well described by this formula:
V = (3 / 4) · (π / 6) · D³
If we know that V = 6,132,812.5 ft³, then the diameter of the geodesic dome is:
6,132,812.5 = (3 / 4) · (π / 6) · D³
D³ = 15,617,078.79 ft³
D = 249.958 ft
The diameter of the geodesic dome is equal to 249.958 feet.
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