Answer:
Step-by-step explanation:
1 has been divided into three equal parts. Each of these parts is 1/3. Let's calculate how many times 1/3 is in 3.
The equation of the perpendicular line to the given line is: y = -5/4x - 30.
<h3>What is the Equation of Perpendicular Lines?</h3>
The slope values of two perpendicular lines are negative reciprocal of each other.
Given that the line is perpendicular to y = 4/5x+23, the slope of y = 4/5x+23 is 4/5. Negative reciprocal of 4/5 is -5/4.
Therefore, the line that is perpendicular to it would have a slope (m) of -5/4.
Plug in m = -5/4 and (x, y) = (-40, 20) into y = mx + b to find b:
20 = -5/4(-40) + b
20 = 50 + b
20 - 50 = b
b = -30
Substitute m = -5/4 and b = -30 into y = mx + b:
y = -5/4x - 30
The equation of the perpendicular line is: y = -5/4x - 30.
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Answer:
Explanation:
Here, we want to use the factor theorem to check if the given linear expression is a factor of the binomial
Now, according to the factor theorem, a factor of a polynomial would leave no remainder when divided by it
Mathematically, it means when we substitute the factor value into the polynomial, it is expected that the remainder is zero is the substituted is a factor of the polynomial
We set x-2 to zero:
Now, we substitute 2 into the polynomial as follows:
There is a remainder of -28 and thus, the linear factor is not a factor of the binomial
In an arithmetic series, the value of the nth term is calculated using the equation,
an = ao + (n - 1)(d)
where an and ao are the nth and the 1st term, respectively. d is the common difference, and n is the number of terms.
In the given, an = 48, a0 = 93, d = -5 and n is unknown. Substituting the known values,
48 = 93 + (n - 1)(-5)
The value of n from the equation is 10. Thus, the answer is the last choice.
Answer:
x = 50
Step-by-step explanation:
101 + (x + 29) = 180
130 + x = 180
x = 180 - 130
x = 50
