Answer:
Minimum umber of degrees that an equilateral triangle can be rotated before it carries onto itself = 120°
Step-by-step explanation:
Refer the figure given below.
We need to find angle ADC to get the same equilateral triangle after rotation.
∠ADC = 180 - ( ∠DAC + ∠DCA) = 180 - ∠DAC - ∠DCA
∠DAC = ∠DCA = 0.5 x 60 = 30°
Substituting
∠ADC = 180 - 30- 30 = 180 - 60 = 120°
Minimum umber of degrees that an equilateral triangle can be rotated before it carries onto itself = 120°
Answer:
Step-by-step explanation:
In order to solve for b, we must isolate the variable. We can start by subtracting 5 from both sides.
Simplify.
Add b to both sides.
Simplify.
Multiply everything by 3 to remove the fractions.
Simplify.
2b + 3b = 45
Simplify.
5b = 45
Divide 5 from both sides.
5b ÷ 5 = 45 ÷ 5
Simplify.
b = 9
For more information on solving variables, check out the following answers!
Answer:
Step-by-step explanation:
Build a Polynomial Knowing its Roots
If we know a polynomial has roots x1, x2, ..., xn, then it can be expressed as:
Where a is the leading coefficient.
Note the roots appear with their signs changed in the polynomial.
If the polynomial has a leading coefficient of 1 and roots 2i and 3i with multiplicity 1, then:
The image of the right rectangular prism is missing, so i have attached it.
Answer:
volume of the right rectangular prism = 625 in³
Step-by-step explanation:
The rectangular prism is made of equal-sized cubes. Thus, let's first find the volume of 1 cube.
Formula for volume of one cube is;
V = a³
where
a is the length of one side of the cube
We are told that this length is 2½ inches
Thus;
a = 2½ = 5/2 inches
>> V = (5/2)³
>> V = 125/8 in³
Now, in the rectangular prism attached, if we count the number of cubes we have, it is equal to 40 cubes
Therefore, the volume of the prism is;
Volume of one cube × 40
>> volume of the prism = (125/8) × 40
volume of the prism = 625 in³
