You are doing weekly math homework 6th weekend 19
For this case we have the following transformation:
Assume k> 0
To graph f (x) + k, move the graph k units up.
Applying the transformation we have:
y = x ^ 2 + 5/2
Answer:
The equation of the new parabola is:
y = x ^ 2 + 5/2
Answer: 10 inches.
Step-by-step explanation:
We have to solve a system of equations.
The formula to calculate a triangle area is A = (b.h)/2
where b is the base and h is the height. This will be our first equation.
Since the height is 4 inches greater than the base, the second equation will be: h = b+4
We replace h and the value of the area (70 square inches) in the first equation, and we solve it by using the cuadratic equation formula:
70 = (b . (b+4)) / 2
70 . 2 = b² + 4b
140 = b² +4b
0 = b² + 4b - 140
The roots of this polynomial are -14 and 10. Since a distance can't be negative, the length of the base is 10 inches.
Answer:
√17
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a ratio of two integers. Or in other words, an irrational number can't be expressed as a fraction. You really cant divide one integer by another integer to get √17, so that makes it an irrational number.
So you have some initial amount x and we want to know how long it will take with compound interest to triple our original amount x (so 3x). The equation sets up like 3x(the amount we want)= x(original amount) times 1.062(the interest increase)^t So 3x=x(1.062)^t where t is the amount of years. When you divide both sides by x it cancels out and you end up with 3=1.062^t. Take the natural log of both sides. Ln(3) = Ln(1.062^t) and the t being an exponent can come in front of the the natural log. Ln(3) = t(Ln(1.062)) Divide both sides by (Ln(1.062)),. Ln(3)/Ln(1.062)=t. And you should just plug that into a calculator to find t.
