Answer:
x^2 + -2 sqrt(7) x + 7
Step-by-step explanation:
Expand the following:
(x - sqrt(7))^2
(x - sqrt(7)) (x - sqrt(7)) = (x) (x) + (x) (-sqrt(7)) + (-sqrt(7)) (x) + (-sqrt(7)) (-sqrt(7)):
x x - sqrt(7) x - sqrt(7) x - (-sqrt(7) sqrt(7))
(-1)^2 = 1:
x x - sqrt(7) x - sqrt(7) x + (sqrt(7))^2
x x = x^2:
x^2 - sqrt(7) x - sqrt(7) x + sqrt(7)^2
Cancel exponents. (sqrt(7))^2 = 7:
x^2 - sqrt(7) x - sqrt(7) x + 7
Combining like terms, sqrt(7) x (-1) + sqrt(7) x (-1) = -2 sqrt(7) x:
Answer: x^2 + -2 sqrt(7) x + 7
Answer:
C = (g + 5)
Step-by-step explanation:
Given the cost of a customers smartphone bill,
C=10g+50
We are required to factor the polynomial.
First, determine the G.C.D of both terms
The GCD of 10g and 50 is 10
Next, we divide each of the term by 10 and balance it by multiplying the expression by 10.
C = 10g + 50
= 10 (10g / 10 + 50/10)
The cost polynomial factored is C=10(g+5).
The population Pa of insect A after t years is given by the equation
Pa = 1.3(1-0.038)^t
while the population Pb of insect B after t years is
Pb = 2.1(1-0.046)^t
We equate the above expressions to find the number of years t it will take the two populations to be equal:
Pa = Pb
1.3(1-0.038)^t = 2.1(1-0.046)^t
1.3(0.962)^t = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.
We can now solve for t:
(0.962)^t / (0.954)^t = 2.1/1.3
(0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
t = log (2.1/1.3) / log (0.962/0.954)
t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.
1) start with (x-h)^2 + (y-k)^2 = r^2. Insert the given info: center at (-1,8) and radius 5:
(x+1)^2 + (y-8)^2 = 5^2 (answer)
To convert a mixed number to its lowest form, one needs to change the mixed number into an improper fraction and then reduce this improper fraction to the lowest possible fraction. To do these conversions, one needs to perform a few calculations. One also has to understand the definitions of "mixed number," "improper fraction" and "proper fraction."
A proper fraction is a fraction that has a lower number in the numerator and a higher number in denominator, such as the fraction three-fourths. An improper fraction is the inverse of this, which entails the higher number in numerator and lower number in the denominator, like 5/3. A mixed number is a whole number with a fraction, such as 1 3/4.
To convert the mixed number 1 3/4, one has to multiply the denominator 4 by the whole number 1 that gives 4, add this 4 to the 3 in the numerator to get 7 and place 7 over the denominator to find the improper fraction 7/4. In this case, this is the lowest form for this mixed number. However, if the mixed number is 6 4/6, then this converts to the improper fraction 40/6. One can divide the numerator and denominator of 40/6 by 2 to find that 20/3 is the lowest form for the mixed number 6 4/6.To convert a mixed number to its lowest form, one needs to change the mixed number into an improper fraction and then reduce this improper fraction to the lowest possible fraction. To do these conversions, one needs to perform a few calculations. One also has to understand the definitions of "mixed number," "improper fraction" and "proper fraction."
