Answer:

Step-by-step explanation:
To write the expression as a single logarithm, or condense it, use the properties of logarithms.
1) The power property of logarithms states that
. In other words, the exponent within a logarithm can be brought out in front so it's multiplied by the logarithm. This means that the number in front of the logarithm can also be brought inside the logarithm as an exponent.
So, in this case, we can move the 3 and the 4 inside the logarithms as exponents. Apply this property as seen below:

2) The product property of logarithms states that
. In other words, the logarithm of a product is equal to the sum of the logarithms of its factors. So, in this case, write the expression as a single logarithm by taking the log (keep the same base) of the product of
and
. Apply the property as seen below and find the final answer.

So, the answer is
.
We can tell if this is a factor of the polynomial shown by using the remainder theorem.
First, we need to set x + 1 equal to 0.
x + 1 = 0
Now, we solve for x.
x = -1
Now, we can plug this value into the polynomial, and if the solution is 0, it means there is a remainder of 0, which means they divide perfectly.
(-1)^3 - 10(-1)^2 + 27(-1) - 12 = -50
x + 1 is not a factor of the provided polynomial.
Answer:
The error Tara made is she rewrote incorrectly 3 3/8 as 17/8 and 4 1/9 as 13/9,
the corrected number can be rewrote as 3 3/8 as 27/8 and 4 1/9 as 37/9.
Step-by-step explanation:
To find the Product of:

The Number can be rewrote as,

Tara made error here she rewrote the number incorrectly 3 3/8 as 17/8 amd 4 1/9 as 13/9.
Now multiplying the fraction we get

Because she rewrote incorrectly which led her answer to multiplication of fraction, the product too was incorrect which she wrote as 221/72.
Answer:
so conditional statement is If x then y.
The converse of conditional statement could be true but does not always have to be
if conditional statement is true both ways, it's an if and only if statement
Probably the easiest way to do this is to use synthetic division. We already know one of the zeros of the quadratic so we can use that number to find the other zero. If the point is (4, 0), then when y = 0, x = 4. Thus, 4 is a zero. Put 4 outside the "box" and put the coefficients from the quadratic inside, like this: 4 (1 -1 -12). Draw a line and bring down the first one under it. Multiply that 1 by the 4 to get 4. Put that 4 up under the -1 and add to get 3. Multiply 3 by 4 to get 12. Put that 12 up under the -12 and add to get 0. The numbers left under the line are the coefficients for the next polynomial, called the depressed polynomial, and this polyomial is one degree less than the one we started with. Those coefficients are 1 and 3. Therefore, the polynomial is x + 3 = 0. That means that the other zero, or x-intercept, is x = -3.