Answer:
The last option is correct
Step-by-step explanation:
A translation of 2 units down takes S to the point (1, -1). Then a counterclockwise rotation about the origin takes S to the point (-1, -1) where we have S' .
Answer:
The probability that a randomly selected carton has a puncture or a smashed corner is 0.143
Step-by-step explanation:
we know that P(A∪B) = P(A) + P(B) - P(A∩B).
since given that P(A) = Probability of getting puncture = 0.08
P(B) = probability of getting smashed corner = 0.07
P(A∩B) = probability of getting both puncture and smashed corner = 0.007
P(A∪B) = probability of getting any of them
so P(A∪B) = 0.08 + 0.07 -0.007 = O.143
This is vague. Any dimensions that make a triangle can make more than one, just draw another right next to it. What's really being asked is which dimensions can make more than one non-congruent triangle.
<span>A. Three angles measuring 75°,45°, and 60°.
That's three angles, and 75+45+60 = 180, so it's a legit triangle. The angles don't determine the sides, so we have whole family of similar triangles with these dimensions. TRUE
<span>B. 3 sides measuring 7, 10, 12?
</span>Three sides determine the triangles size and shape uniquely; FALSE
<em>C. Three angles measuring 40</em></span><span><em>°</em></span><em>, 50°</em><span><em>, and 60°? </em>
40+50+60=150, no such triangle exists. FALSE
<em>D. 3 sides measuring 3,4,and 5</em>
Again, three sides uniquely determine a triangle's size and shape; FALSE
</span>
Answer:
y = - 
x + 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x - 3 ← is in slope- intercept form
with slope m = 3
Given a line with slope m then the slope of a line perpendicular to it is
= - 
= - , hence
y = - x + c ← is the partial equation of the perpendicular line
To find c substitute (3, 1) into the partial equation
1 = - 1 + c ⇒ c = 1 + 1 = 2
y = - x + 2 ← equation of perpendicular line
