5 (-15) =
Answer:
20 i think:))))))))))))
Answer:
8 = 2^3
Step-by-step explanation:
8 = 4*2
4 is not a prime number so we break 4 into 2*2 and replace it
8 = 2*2*2
All of these are prime
We see there are three 2's multiplied together, that means 2 is the base and 3 is the exponent
8 = 2^3
2^3 is index form
Answer:
x = 12y
Step-by-step explanation:
The statement is valid because the measure of the vertices located in the center of the pentagon is the quotient of 360 and 5, and the sum of two base angles in the given isosceles triangle is 108.
==========================================================
Explanation:
Check out the diagram below. I have added x and y such that
x = base angle
y = vertex angle (located adjacent to center of polygon)
The pentagon is sliced up like a cake into 5 equal portions. Each vertex angle is y = 360/5 = 72 degrees.
The two base angles x must add with the vertex angle y to get 180
(angle1)+(angle2)+(angle3) = 180
x+x+y = 180
2x+y = 180
2x+72 = 180
2x = 180-72
2x = 108
This is true for any one of the five triangles. Notice that for angle LMN, we can divide it into LMQ and QMN where Q is the center of the polygon. Both of these angles are x. Since we've shown 2x = 108, we can see that LMN must also be 108 as well.
Choice A is close, but we wouldn't use the exterior angle theorem. Choice B is the better answer.
To determine the length of the car park as depicted in the blueprint (scale drawing), we first need to find the scale factor used by John. Since he used a scale factor of 1 inch : 15 feet, we can multiply the actual length of the car park by this ratio to get the length of the car park on the blueprint.
So, if the actual car park is 12 ft long, the length of the car park on the blueprint would be:
12 ft * 1/15 ft/inch = 8 inches
Therefore, the length of the car park as depicted in the blueprint is 8 inches.
Answer:
Step-by-step explanation:
To find the values of a and b, we can use the given information and apply the properties of rectangles and parallel lines.
First, let's calculate the area of the rectangle PQRS. We are given that the area is 84 cm², and since PQRS is a rectangle, its area is equal to the product of its length and width. Therefore, we can set up the equation:
Length × Width = 84
Next, we know that XY is parallel to PS. This means that the length of XY is equal to the length of PS. Since the length of PS is a + b cm, we can write:
Length of XY = a + b
Now, we are given that the area of PXYS is 21 cm². Using the same logic, the area of PXYS is equal to the product of its length and width, so we can set up another equation:
Length of XY × Width of XY = 21
Since the width of XY is 9 cm (given as RY), we can substitute the values into the equation:
(a + b) × 9 = 21
Simplifying this equation, we get:
9a + 9b = 21
Now, we have two equations:
1) Length × Width = 84
2) 9a + 9b = 21
To solve these equations simultaneously, we need to rearrange equation 1) to solve for either length or width. Let's solve for length:
Length = 84 / Width
Substituting in the value of width from equation 2), we get:
Length = 84 / (9a + 9b)
Now, we can substitute this expression for length into equation 2):
(84 / (9a + 9b)) × (9) + 9b = 21
Simplifying this equation, we get:
84 + 9b = 21(9a + 9b)
Expanding, we get:
84 + 9b = 189a + 189b
Combining like terms, we get:
-180b = 189a - 84
Dividing by -180, we get:
b = (189a - 84) / -180
We have found the expression for b in terms of a.
To find the value of a, we can substitute this expression for b into equation 2):
9a + 9((189a - 84) / -180) = 21
Simplifying this equation will give us the value of a.
Please note that without specific numerical values or additional constraints, it is not possible to determine the exact values of a and b. However, by solving the equations as shown above, we can express the values of a and b in terms of each other.