You need to use a ratio of height (H) to shadow length (L) to solve the first problem. It's basically a use of similar triangles, with two perpendicular sides, and with the shadow making the same angle with the vertical.
6 ft = 72 ins, so that rH/L = 72/16 = 9/2 for the player.
So the bleachers are 9/2 x 6 ft = 27 ft.
For the second problem, 9 ft = 108 in, so that the ratio of the actual linear dimensions to the plan's linear dimensions are 9ft/(1/2in) = 2 x 108 = 216.
So the stage will have dimensions 216 times larger than 1.75" by 3".
That would be 31ft 6ins x 54ft.
Live long and prosper.
Answer:
B. a pair of alternate exterior angles with measures of 130° and 50°
Step-by-step explanation:
Alternate exterior angles formed when two parallel lines are cut across by the same transversal line, are said to be congruent.
Therefore, a pair of alternate exterior angles cannot have different angle measures of 130° and 50°. Rather, both alternate exterior angles should be of equal measure of degree.
All other scenarios are possible result except option B: "a pair of alternate exterior angles with measures of 130° and 50°".
Yes this is a correct statement.
Answer:
The product of the slopes of lines is -1.
i.e. m₁ × m₂ = -1
Thus, the lines are perpendicular.
Step-by-step explanation:
The slope-intercept form of the line equation
where
Given the lines
y = 2/3 x -3 --- Line 1
y = -3/2x +2 --- Line 2
<u>The slope of line 1</u>
y = 2/3 x -3 --- Line 1
By comparing with the slope-intercept form of the line equation
The slope of line 1 is: m₁ = 2/3
<u>The slope of line 2</u>
y = -3/2x +2 --- Line 2
By comparing with the slope-intercept y = mx+b form of the line equation
The slope of line 2 is: m₂ = -3/2
We know that when two lines are perpendicular, the product of their slopes is -1.
Let us check the product of two slopes m₁ and m₂
m₁ × m₂ = (2/3)(-3/2
)
m₁ × m₂ = -1
Thus, the product of the slopes of lines is -1.
i.e. m₁ × m₂ = -1
Thus, the lines are perpendicular.
Answer: To simplify this problem you combine the like terms in the equation (numbers with the same variables.)
Demo: 12r + -4r = 8r
