<h2>
Answer: y = ⁵/₂ x - 13 OR y + 8 =
⁵/₂ x - 5 </h2>
<h3>
Step-by-step explanation:</h3>
<u>Find the slope of the perpendicular line</u>
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are <em>negative-reciprocal</em>s of each other.
⇒ if the slope of this line = - ²/₅
then the slope of the perpendicular line (m) = ⁵/₂
<u>Determine the equation</u>
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-8) = ⁵/₂ (x - 2)
∴ y + 8 = ⁵/₂ (x - 2)
We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:
since y + 8 = ⁵/₂ (x - 2)
y = ⁵/₂ x - 13
Answer:
a)
b)
c)
d)
Step-by-step explanation:
We will use the following trigonometric identities
.
Recall that given a right triangle, the sin(theta) is defined by opposite side/hypotenuse. Since we know that the angle is in quadrant 2, we know that x should be a negative number. We will use pythagoras theorem to find out the value of x. We have that
which implies that . Recall that cos(theta) is defined by adjacent side/hypotenuse. So, we know that the hypotenuse is 7, then
b)Recall that , then using the identity from above, we have that
c) Recall that . Then,
d) Recall that and . Then
Hello!
So a tangent line is perpendicular to the radius, which means it creates a 90 degree angle with the radius of the circle. The sum of the interior angles of any triangle is 180 degrees. To determine if line BC is a tangent line, we have to determine if angle ABC is 90 degrees. Well we know the degrees of the other two angles of the triangle, so let's set up an equation:
180 = 48 + 47 + x
180 = 95 + x
85 = x
Since angle ABC must be 85 degrees (not 90), line BC is not a tangent line.
Answer:
<span>BC←→ is not a tangent line because m∠ABC ≠ 90°.</span>
Answer: 4/25
=========================================
Explanation:
Let's define two events A and B
A = event of selecting red on the first draw
B = event of selecting red on the second draw
P(A) is the notation that means "probability of event A occurring"
P(A) = 2/5 because there are 2 red marbles out of 5 total (2 red + 3 black = 5)
Similarly, P(B) = 2/5 as well because A and B deal with the same color red, and because Abby put the first marble back
Multiply the probabilities
P(A and B) = P(A)*P(B) ... see note below
P(A and B) = (2/5)*(2/5)
P(A and B) = (2*2)/(5*5)
P(A and B) = 4/25 which is the answer
Note: the equation used is only valid if events A and B are independent, which they are in this case. The fact we put the marble back means the chances of picking red are the same as before.
9514 1404 393
Answer:
p -12
Step-by-step explanation:
p take-away 12 is ...
p - 12