Answer:
Look for the y-intercept where the graph crosses the y-axis. Look for the x-intercept where the graph crosses the x-axis. Look for the zeros of the linear function where the y-value is zero.
Step-by-step explanation:
Answer:
<em>The angle between their paths when they started is 93°.</em>
Step-by-step explanation:
<u>The Law of Cosines</u>
It relates the length of the sides of a triangle with one of its internal angles.
Let a,b, and c be the length of the sides of a given triangle, and x the included angle between sides a and b, then the following relation applies:

When the two ships travel in different directions from the same point in the plane, they form an angle we called x in the image below.
Tyler's ship sails a=35 miles and Noah's ship sails for b=42 miles. At some time they are c=56 miles apart.
Since we know the values of all three side lengths, we solve the equation for x:

Substituting values:

Calculating:

Computing the inverse cosine:


The angle between their paths when they started is 93°.
Answer:
(5, 3 ) and (-
, - 10 )
Step-by-step explanation:
Given the 2 equations
2x - y = 7 → (1)
xy = 15 → (2)
Rearrange (1) expressing y in terms of x , that is
y = 2x - 7 → (3)
Substitute y = 2x - 7 into (2)
x(2x - 7) = 15
2x² - 7x = 15 ( subtract 15 from both sides )
2x² - 7x - 15 = 0 ← in standard form
(x - 5)(2x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - 
Substitute these values into (3) for corresponding values of y
x = 5 : y = 2(5) - 7 = 10 - 7 = 3 ⇒ (5, 3 )
x = -
: y = 2(-
) - 7 = - 3 - 7 = - 10 ⇒ (-
, - 10 )
Given:
Consider the below figure attached with this question.
m(arc(SW)) = (12x-5)°, m(arc(TV))= (2x+7)°,and measure of angle TUV = (6x-19)°.
To find:
The m(arc SW).
Solution:
Intersecting secant theorem: If two secants intersect outside the circle, then the angle on the intersection is half of the difference of the larger subtended arc and smaller subtended arc.
Using Intersecting secant theorem, we get




Multiply both sides by 2.




Divide both sides by 2.

Now, the measure of arc SW is:




Therefore, the measure of arc SW is 151 degrees.