Given A = bh solve for b. A) b = Ah B) b = \frac{h}{A} C) b = \frac{A}{h} D) h = \frac{A}{b} 6) What is the slope between the points (3, 5) and (-2, -4)?
The Correct Answer and Explanation is:
Problem 1: Solve for bbb
The equation given is:A=bhA = bhA=bh
To solve for bbb, divide both sides of the equation by hhh:b=Ahb = \frac{A}{h}b=hA
Thus, the correct answer is C) b=Ahb = \frac{A}{h}b=hA.
Explanation:
This equation is a simple rearrangement. Since AAA is the area of a rectangle, bbb is the base, and hhh is the height, solving for the base is straightforward by isolating bbb on one side. Dividing both sides of the equation by hhh leaves us with the formula b=Ahb = \frac{A}{h}b=hA, which is consistent with the relationship between the area, base, and height of a rectangle.
Problem 2: Find the slope between the points (3,5)(3, 5)(3,5) and (−2,−4)(-2, -4)(−2,−4)
The formula for the slope between two points (x1,y1)(x_1, y_1)(x1,y1) and (x2,y2)(x_2, y_2)(x2,y2) is:slope=y2−y1x2−x1\text{slope} = \frac{y_2 – y_1}{x_2 – x_1}slope=x2−x1y2−y1
Here, the coordinates of the two points are (3,5)(3, 5)(3,5) and (−2,−4)(-2, -4)(−2,−4). Using the formula, we get:slope=−4−5−2−3\text{slope} = \frac{-4 – 5}{-2 – 3}slope=−2−3−4−5
Simplifying the numerator and the denominator:slope=−9−5=95\text{slope} = \frac{-9}{-5} = \frac{9}{5}slope=−5−9=59
Thus, the slope between the points (3,5)(3, 5)(3,5) and (−2,−4)(-2, -4)(−2,−4) is 95\frac{9}{5}59.
Explanation:
The slope formula measures how much the yyy-coordinate changes for a unit change in the xxx-coordinate between two points. This is calculated by subtracting the yyy-coordinates (vertical change) and dividing by the difference in xxx-coordinates (horizontal change). The negative signs cancel each other out, resulting in a positive slope of 95\frac{9}{5}59.
