In physical science, we often use the formula S = d/t to calculate speed.
Suppose your given the speed of a car, S, and time traveled, t, and need to calculate the distance the car traveled.
Which of the following equations would solve for the distance, d?
A: S - t = d
B: S = dt
C: d = St
D: d = s/t
The correct equation to solve for the distance, d, would be:
C: d = St
-6x + 9 = 4x + 14
To solve the equation -6x + 9 = 4x + 14, we want to isolate the variable x on one side of the equation.
Let's start by getting rid of the constants on both sides. We can do this by subtracting 9 from both sides:
-6x + 9 - 9 = 4x + 14 - 9
Simplifying, we have:
-6x = 4x + 5
Next, let's move all the terms with x to one side by subtracting 4x from both sides:
-6x - 4x = 4x + 5 - 4x
Simplifying, we have:
-10x = 5
Finally, to solve for x, we divide both sides by -10:
-10x / -10 = 5 / -10
Simplifying, we have:
x = -5/10
Simplifying the fraction, we have:
x = -1/2
Therefore, the solution to the equation -6x + 9 = 4x + 14 is x = -1/2.
Does the equation 8x + 10 = 8x + 10 have one solution, infinite solutions, or no solutions?
The equation 8x + 10 = 8x + 10 is an identity equation. It means that the equation is true for all values of x.
In this case, since the terms on both sides of the equation are exactly the same, no matter what value we substitute for x, the equation will always be true.
Therefore, the equation 8x + 10 = 8x + 10 has infinite solutions.
how many solutions does 3x + 5 = 3x - 6 have?
The equation 3x + 5 = 3x - 6 simplifies to -11 = -6.
In this case, we end up with a contradiction because the left side of the equation, -11, is not equal to the right side, -6.
Therefore, the equation 3x + 5 = 3x - 6 has no solution.
how many solutions does 6x + 8 ≥ 2x - 4 have?
To determine the number of solutions for the inequality 6x + 8 ≥ 2x - 4, we need to simplify and solve it.
Let's start by subtracting 2x from both sides of the inequality:
6x - 2x + 8 ≥ 2x - 2x - 4
Simplifying, we have:
4x + 8 ≥ -4
Next, let's subtract 8 from both sides:
4x + 8 - 8 ≥ -4 - 8
Simplifying, we have:
4x ≥ -12
Finally, to solve for x, we divide both sides of the inequality by 4:
(4x) / 4 ≥ -12 / 4
Simplifying, we have:
x ≥ -3
Therefore, the inequality 6x + 8 ≥ 2x - 4 has infinitely many solutions. All values of x greater than or equal to -3 satisfy the inequality.
To calculate the distance traveled by a car given the speed and time traveled, you need to use the formula S = d/t. This formula represents speed as the ratio of distance traveled (d) to the time taken (t).
To solve for the distance (d), you need to isolate it on one side of the equation. Let's go through each given equation one by one to determine which one solves for distance.
A: S - t = d
This equation does not solve for distance (d) because it represents the difference between the speed (S) and time (t), not their ratio.
B: S = dt
This equation solves for distance (d). By rearranging the equation, you can isolate d as follows:
S = dt
Divide both sides by t: S/t = d
C: d = St
This equation also solves for distance (d). It is the same as the previous option, but the variables are swapped. Rearranging the equation gives:
d = St
D: d = s/t
This equation is similar to the correct one, but uses a lowercase 's' instead of uppercase 'S' as the speed variable. Since the formula given in the question uses an uppercase 'S', this equation is not solving for distance (d) correctly.
Therefore, the correct equation to solve for the distance (d) is option B: S = dt.