From the picture, we see that there are two congruent sides. Therefore, following the Isosceles Triangle Theorem, if two sides in a triangle are congruent, then the angles opposite those sides are congruent. So, we know that the angles opposite of the congruent sides have an angle measure of x°. We are given the measure of the angle at the top vertex of 100°. Following the Triangle Sum Theorem, the three interior angles in a triangle must sum up to 180°. Therefore, we can create an Algebraic equation to solve for the two base angles that measure x°.
x+100+x=180
x=the base angle measures since they are congruent.
100+x+x=180
Community Property of Addition
100+2x=180.
Added x+x as like terms to = 2x.
100-100+2x=180-100
Subtraction of 100 from both sides to cancel it out and move it.
2x=80
Subtraction operation
2x/2=80/2
Divided by 2 to cancel it out on both sides and move it.
x=40°.
Therefore, the two base angles (angles opposite of the two congruent sides) are 40°.
2(40)+100=80+100=180.
So x=40
Answer:
14.20669 years
Roughly 14 years and 2.5 months.
Step-by-step explanation:
Assuming this is compound interest.
The formula is 
Final Amount
Principal Amount
Interest Rate
# of times interest is compounded per year
Time in years
We are looking for the times in years to double the money so
Lets solve for 
.
Step 1.
Plug in our numbers into the compound interest formula.
Step 2.
Simplify the equation.
Evaluate 
Evaluate 
Step 3.
Divide both sides of the equation by 
Evaluate 
Step 4.
Take the natural log of both sides of the equation and rewrite the right side of the eqaution using properties of exponents/logarithms.
Step 5.
Divide both sides of the equation by 
Step 6.
Evaluate
Roughly 14 years and 2.5 months.
Answer:
Geometric sequence
Step-by-step explanation:
A=s^2, where s is a side length, and we are told A=150ft^2 so:
s^2=150
s=√150
s≈12.25 ft
So you would need a piece of carpet 13ft by 13ft
The answer is 270 because 250 + 8% = 270
