The correct answer is: No, the remainder is -114
Further explanation:
In order to check whether the given term is a factor of given polynomial or not we will put
x+2=0
x=-2
Given

As the remainder is -114, the term x+2 is not a factor of given polynomial
The correct answer is: No, the remainder is -114
Keywords: Polynomials, expressions
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Answer: $7800 was invested at 9%
$5900 was invested at 3%
Step-by-step explanation:
Let x represent the amount invested in the fund that paid a dividend of 9%.
Let y represent the amount invested in the fund that paid a dividend of 3%.
Last year, the first fund paid a dividend of 9% and the second a dividend of 3%, and you received a total of $879. This means that
0.09x + 0.03y = 879- - - - - - - - - 1
This year, the first fund paid a 10% dividend and the second only 1%, and you received a total of $839. It means that
0.1x + 0.01y = 839 - - - - - - - - - -2
Multiplying equation 1 by 0.1 and equation 2 by 0.09, it becomes
0.009x + 0.003y = 87.9
0.009x + 0.0009y = 75.51
Subtracting, it becomes
0.0021y = 12.39
y = 12.39/0.0021
y = 5900
Substituting y = 5900 into equation 1, it becomes
0.09x + 0.03 × 5900 = 879
0.09x + 177 = 879
0.09x = 879 - 177
0.09x = 702
x = 702/0.09
x = 7800
Answer:
A
Step-by-step explanation: Scale Factor is defined as a ratio between the actual figure to that of the other figure.
And as it is clearly given in the question that 2 cm of length corresponds to 100 meters so the ratio comes out to be 1:50.
So the scale factor of the actual farm to the photo is A that is 1 to 50.
Answer:
k is 2/3 and y is -1/3 when x is -0.5.
Step-by-step explanation:
The direct variation relationship is y = kx, where k is the const. of var.
Subbing 3 for x and 2 for y, 2 = 3k, or k = 2/3.
Now, if x = -0.5, y = (2/3)(-1/2) = -1/3
k is 2/3 and y is -1/3 when x is -0.5.
For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:
g(f(x)) = x = f(g(x))
<u>The restriction is:</u>
x ≠ 4
<u>The inverse is:</u>

Here our function is:

We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.
(x - 4)^2 = 0
x - 4 = 0
x = 4
So the only value of x that we need to remove from the domain is x = 4.
To find the inverse we try with the general form:

Evaluating this in our function we get:

Remember that the thing above must be equal to x, so we get:

From the two above equations we find:
b = 11
a = 4
Thus the inverse equation is:

If you want to learn more, you can read:
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