<span>Is the following definition of perpendicular reversible? If
yes, write it as a true biconditional.</span>
Two lines that intersect at right angles are perpendicular.
<span>A. The statement is not reversible. </span>
<span>B. Yes; if two lines intersect at right
angles, then they are perpendicular.
</span>
<span>C. Yes; if two lines are perpendicular, then they intersect at
right angles. </span>
<span>D. Yes; two lines
intersect at right angles if (and only if) they are perpendicular.</span>
Your Answer would be (D)
<span>Yes; two lines
intersect at right angles if (and only if) they are perpendicular.
</span><span>REF: 2-3 Biconditionals and Definitions</span>
Answer: b, d
Step-by-step explanation:
Corresponding angles are formed when two parallel straight lines are cut by a transversal
In the figure, are alternate angle
Answer:
x = 3 pizzas
Step-by-step explanation:
- Not sure what the question is asking, but I am assuming that the question is asking how many pizzas needs to be ordered for the restaurant ordered to equal each other.
- Set up equation:
- Simplify the equation:
Answer:
The solution is (-17,80.5) and (1,8.5)
Step-by-step explanation:
Equation 1 :
Equation 2:
Substitute the value of y from equation 2 in equation 1
Equation 1 :
After substitution :
Substitute the value of x = -17
y = -4x+12.5
y = -4(-17)+12.5
y=80.5
Substitute the value of x = 1
y = -4(1)+12.5
y=8.5
Hence the solution is (-17,80.5) and (1,8.5)
Answer:
(a) y = -3/5 x + 13/5
(b) y = 5/3 x + 1/3
Step-by-step explanation:
(a) The slope of the tangent line is dy/dx. Use implicit differentiation:
x² + y² + 4x + 6y − 21 = 0
2x + 2y dy/dx + 4 + 6 dy/x = 0
2x + 4 + (2y + 6) dy/dx = 0
x + 2 + (y + 3) dy/dx = 0
(y + 3) dy/dx = -(x + 2)
dy/dx = -(x + 2) / (y + 3)
At the point (1, 2), the slope is:
dy/dx = -(1 + 2) / (2 + 3)
dy/dx = -3/5
Using point-slope form of a line:
y − 2 = -3/5 (x − 1)
Simplifying to slope-intercept form:
y − 2 = -3/5 x + 3/5
y = -3/5 x + 13/5
(b) The normal line is perpendicular to the tangent line, so its slope is 5/3. It also passes through the point (1, 2), so point-slope form of the line is:
y − 2 = 5/3 (x − 1)
Simplifying to slope-intercept form:
y − 2 = 5/3 x − 5/3
y = 5/3 x + 1/3