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Subtract 3x from both sides:
-7 = 2x + 1
Subtract 1 from both sides:
-8 = 2x
Divide both sides by 2:
x = -4
HJP
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slope = (y2 - y1) / (x2 - x1)
In this case, the two points are (3, 4) and (-2, 5), so we can substitute into the formula:
slope = (5 - 4) / (-2 - 3)
slope = 1 / (-5)
slope = -1/5
Therefore, the slope of the line passing through the points (3, 4) and (-2, 5) is -1/5.
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Method 1: Factoring
We can rewrite the equation as (x - 2)(x - 4) = 0 by finding two numbers that add up to -6 and multiply to give 8. These numbers are -2 and -4. Therefore, the solutions are x = 2 and x = 4.
Method 2: Quadratic Formula
The quadratic formula is:
x = (-b ± sqrt(b² - 4ac)) / 2a
In this case, a = 1, b = -6, and c = 8. Substituting these values into the formula, we get:
x = (-(-6) ± sqrt((-6)² - 4(1)(8))) / 2(1)
x = (6 ± sqrt(36 - 32)) / 2
x = (6 ± sqrt(4)) / 2
x = (6 ± 2) / 2
Simplifying, we get:
x = 4 or x = 2
Therefore, the solutions are x = 2 and x = 4.
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4x - 5 ≥ 0
4x ≥ 5
x ≥ 5/4
Therefore, the domain of f(x) = √(4x - 5) is all real numbers greater than or equal to 5/4, or in interval notation:
[5/4, ∞)
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log₂(x) + log₂(x + 4) = 3
log₂(x(x + 4)) = 3
Rewriting in exponential form, we get:
2³ = x(x + 4)
8 = x² + 4x
Rearranging the terms, we get:
x² + 4x - 8 = 0
We can solve for x using the quadratic formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
In this case, a = 1, b = 4, and c = -8. Substituting these values into the formula, we get:
x = (-4 ± sqrt(4² - 4(1)(-8))) / 2(1)
Simplifying, we get:
x = (-4 ± sqrt(72)) / 2
x = (-4 ± 2sqrt(18)) / 2
x = -2 ± sqrt(18)
Therefore, the solutions are:
x = -2 + sqrt(18) ≈ 0.15
x = -2 - sqrt(18) ≈ -4.15
Note that we need to reject the negative solution x = -2 - sqrt(18) because the argument of the logarithm must be positive. Therefore, the only solution is:
x = -2 + sqrt(18) ≈ 0.15
HJP
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x + 2y = 10
3x - y = 7
Bot
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x + 2y = 10
3x - y = 7
We can use the elimination method, which involves multiplying one or both equations by a constant so that one of the variables is cancelled out when the equations are added.
In this case, we can multiply the second equation by 2 so that the y term is cancelled out when added to the first equation:
x + 2y = 10
6x - 2y = 14
Adding the two equations, we get:
7x = 24
Dividing both sides by 7, we get:
x = 24/7
Substituting this value into the first equation, we get:
(24/7) + 2y = 10
Subtracting 24/7 from both sides, we get:
2y = 26/7 - 24/7
Simplifying, we get:
2y = 2/7
Dividing both sides by 2, we get:
y = 1/7
Therefore, the solution to the system of equations is:
x = 24/7
y = 1/7
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∫(x² + 3x + 5) dx
We can apply the power rule of integration, which states that:
∫xⁿ dx = (x^(n+1))/(n+1) + C, where C is the constant of integration.
Using this rule, we can integrate each term separately:
∫(x² + 3x + 5) dx = ∫x² dx + ∫3x dx + ∫5 dx
= (x^(2+1))/(2+1) + 3(x^(1+1))/(1+1) + 5x + C
= (x³)/3 + (3x²)/2 + 5x + C
Therefore, the solution is:
∫(x² + 3x + 5) dx = (x³)/3 + (3x²)/2 + 5x + C
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1. Stay calm. It’s important not to respond to the person in an angry or aggressive way, as this may escalate the situation and make things worse.
2. Do not engage with this person. As they keep attacking and making false accusations, it's unlikely that you'll be able to have a productive conversation with them. Responding to them may also give them a sense of power and validation which only encourages them to continue.
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