Option B is correct after applying the property of integer exponent and simplification.
<h3>What is an integer exponent?</h3>
In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
We have:
Thus, option B is correct after applying the property of integer exponent and simplification.
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20 x 2=40
10 x 4=40
8 x 5= 40
so 2 bags of balloons
4 bags of horns
5 packages of candy
Answer:
third angle = (-6x + 161)°
Step-by-step explanation:
180° = (x)° + (5x + 19)° + third angle →
180° = (6x + 19)° + third angle →
180° – (6x + 19)° = (6x + 19)° + third angle – (6x + 19)° →
180° – (6x + 19)° = third angle →
180° + -(6x + 19)° = third angle →
180° + (-6x)° + (-19)° = third angle
180° – 6x° – 19° = third angle
(180° – 19°) – 6x° = third angle
161° – 6x° = third angle
third angle = 161 – 6x°
third angle = -6x° + 161°
third angle = (-6x + 161)°
Answer:
1. I am not sure about the first one. I tried everything and nothing I got from any of my work is looking right.
2. AB = 5
3. 8
The dimensions of the garden that will require the least amount of fencing are 450 m and 900 m and the perimeter of the area is 1800 m.
<h3>What is the area of the rectangle?</h3>
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
Let's suppose x and y are the sides of the rectangular garden and y is the parallel to the river.
Then according to the problem:
2x + y = P ..(1)
P is the perimeter of the rectangle.
xy = 405000 (area of the rectangle)
Plug the value of y in the equation (1) from the above equation.
P(x) = 2x + 405000/x
P'(x) = x—405000/x² = 0
x = 450 m
P''(x) > 0 hence at x = 450 the value of P(x) is minimum.
y = 405000/450
y = 900 m
P(min) = 1800 m
Thus, the dimensions of the garden that will require the least amount of fencing are 450 m and 900 m and the perimeter of the area is 1800 m.
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