Answer:
r = -8sin(theta)
Step-by-step explanation:
used desmos
Rewrite g(x) as x-1
------
4
and then substitute this result for x in f(x) = x^2 - 3x + 3:
f(g(x)) = (x-1)^2 / 4^2 - 3(x-1)/4 + 3.
At this point we can substitute the value 5 for x:
f(g(5)) = (5-1)^2 / 4^2 - 3(5-1)/4 + 3
= 16/16 - 3(4/4) + 3 = 1 - 3 + 3 = 1
Therefore, f(g(5)) = 1.
Answer:
YES
NO
NO
Step-by-step explanation:
The given polynomial is: 
(x - a) is a factor of a polynomial iff x = a is a solution to the polynomial.
To check if (x - 5) is a factor of the polynomial f(x), we substitute x = 5 and check if it satisfies the equation.
∴ f(5) = 5³ + 4(5)² - 25(5) - 100
= 125 + 100 - 125 - 100
= 225 - 225
= 0
We see, x = 5 satisfies f(x). So, (x - 5) is a factor to the polynomial.
Now, to check (x + 2) is a factor.
i.e., to check x = - 2 satisfies f(x) or not.
f(-2) = (-2)³ + 4(-2)² - 25(-2) - 100
= -8 + 16 + 50 - 100
= -108 + 66
≠ 0
Therefore, (x + 2) is not a factor of f(x).
To check (x - 4) is a factor.
∴ f(4) = 4³ + 4(4)² - 25(4) - 100
= 64 + 64 - 100 - 100
= 128 - 200
≠ 0
Therefore, (x - 4) is not a factor of f(x).
A boat travels 45 miles east then 60 miles north, how far is it from where it started. Draw this. The hypotenuse of the right triangle is the square root (45^2)+(60^2)=square root of 2025=3600=square root of 5625, or 75 miles.
Okay. So to find the unit rate,divide pounds of flour by the number of cups. Turn the mixed numbers into improper fractions, which are 11/2 and 25/16. To divide fractions, keep the fraction the same, change the division symbol into multiplication, and flip the second fraction over. Then, multiply straight across. 11/2 * 16/25 is 176/50 or 3 13/25 in simplest form. To find out if there are more or less than 35 cups of flour in a 10-pound bag, you can round the number to the nearest whole number and multiply it by 10. For the exact unit rate, there are 3 13/25 cups of flour per 1 pound bag. Now, multiply that number by 10. Going back to improper fractions, 176/50 * 10/1 is 1,760/50 or 35 1/5 in simplest form. There are more than 35 cups of flour in a 10-pound bag of flour.
