y= x + 2 and y = x^2 - 4
Substitute mx + b for y
x^2 - 4 = x + 2
Solve for x
x^2 - 4 = x + 2
x^2 - x - 6 = 0
(x - 3)(x + 2) = 0
x - 3 = 0; x = 3
x + 2 = 0; x = -2
Substitute the first x value into the linear equation and solve for y
y = 3 + 2
y = 5
One solution is (3, 5)
Substitute the second x value into the linear equation and solve for y
y = -2 + 2
y = 0
Another solution is (-2 , 0)
Answer:
200$
Step-by-step explanation:
10 TIMES 20 IS 200
Positive value of x for the given function 2h(x) = log₂(x² +2) is equal to √62.
As given in the question,
Function h is given by : 2h(x) = log₂(x² +2)
Using the definition of logarithm function
aˣ = y
⇒x= logₐy
For h(x) =3, Apply definition of logarithm function we get,
2× 3 = log₂(x² +2)
⇒6= log₂(x² +2)
⇒2⁶ = x² +2
⇒x² = 64-2
⇒x²= 62
⇒x = √62
Therefore, positive value of x for the given function 2h(x) = log₂(x² +2) is equal to √62.
Learn more about function here
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Answer:
Each side of triangle A changed by a factor of 1/2.
The unknown side length in triangle B has a measure of 7.5.
Step-by-step explanation:
He made each side 1/2 as long so it changed by a factor of 1/2. 1/2 times 15 is 7.5.
In economics, there are two types of interest: simple interest and compounded interest. In commercial banks, the compounded interest is used. The equation for compounding interest is
F = P(1+i)^n
where
F is the future worth
P is the present worth
i is the interest rate
n is the time
You should not that the units for i and n must be consistent. If you use n in years, the i must be in percent per year compounded yearly. But since the given interest is given quarterly, we have to convert this first from nominal interest rate, r, to effective interest rate, i,eff:
i,eff = (1 + r/m)^m - 1, where m is the number of quarters in 1 year. That would be 4. Substituting the values
i,eff = (1 + 0.036/4)⁴ - 1 = 0.0365
We use this to the first equation where n=30 years
F = $5,140.17(1 + 0.0365)³⁰
F = $15,068.04
Thus, after 30 years, the money would be worth $15,068.04. The interest earned is equal to:
Interest earned = $15,068.04 - $5,140.17
Interest Earned = $9,927.87
