Is (-3,2)(−3,2)left parenthesis, minus, 3, comma, 2, right parenthesis a solution of -4x -10y < -9−4x−10y<−9minus, 4, x, m
r-ruslan [8.4K]
Answer:
The answer to your question is The point (-3, 2) is not a solution
Step-by-step explanation:
Inequality
- 4x - 10y < - 9
-point (-3, 2)
Process
1.- To solve this problem, just substitute the point in the inequality and simplify
a) Substitution
-4(-3) - 10(2) < - 9
b) Simplification
12 - 20 < - 9
c) Result
- 8 < - 9
This is false, -8 > -9
Elsa's answer is incorrect since there is a solution of the given equation. In the given logarithmic problem, we need to simplify the problem by transposing log2(3x+5) in the opposite side. The equation will now be log2x-log2(3x+5)=4. Using properties of logarithm, we further simplify the problem into a new form log (2x/6x+10)=4. Then transform the equation into base form 10^4=(2x/6x+10) and proceed in solving for x value which is equal to 1.667.
The second one is correct so its 2
Using derivatives, it is found that regarding the tangent line to the function, we have that:
- The equation of the line is y = 962x - 5119.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The slope of the line tangent to a function f(x) at x = x' is given by f'(x'). In this problem, the function is given by:
f(x) = 5x³ + 2x + 1.
The derivative is given by:
f'(x) = 15x² + 2.
Hence the slope at x = 8 is:
m = f'(8) = 15(8)² + 2 = 962.
The line goes through the point (8,f(8)), hence:
f(8) = 5(8)³ + 2(8) + 1 = 2577.
Hence:
y = 962x + b
2577 = 962(8) + b
b = -5119.
Hence the equation is:
y = 962x - 5119.
More can be learned about tangent lines at brainly.com/question/8174665
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